Supporting industries across the world through precision technology
Achieving “the precision infinitely close to zero error” to fulfill customers’
requirements for high accuracy and high productivity in every field of industry
is the basic and primary focus of product manufacturing at KURODA.

“Always challenging what is new, and creating new value”● Ball screw related manufacturing locations● Precision machining technology

KURODA, based on its strong commitment
to precision and its craftsman’s DNA that
dictates it “make the things it needs using its
own faculties”, has developed a large numberof underlying technologies originating from its
legacy as a gauge manufacturer ranging frommeasurement techniques to machine tools
such as proprietary surface grinding machines
and in-house-developed thread grinding
machines. KURODA’s products manufactured
from these underlying technologies havebecome essential in a wide range of fields,such as machines, cars, medical care, andsemiconductors.

Kazusa Akademia Plant (Chiba)· Precision Ball Screws· Support Units

Asahi Plant (Chiba)· Rolled Ball Screws· Ballscrew Actuators

Futtsu Plant (Chiba)· Ball Screw-Related Components

JENAER GEWINDETECHNIK GmbH (Germany)· Precision Ball Screws● More than 90 years of history
Since its foundation in 1925, KURODA has
continuously supported many industries withreliable technologies related to “precision”.
The relationships, trust, mutual technologies,
and know-how KURODA has accumulated
over these 90 years of history make it a highly
credible company.

● Overseas locations● Global network

In recent years, KURODA has accelerated
its global expansion to support industrial
advancement all over the world throughprecision technology.
As part of this effort, KURODA has entered into
partnerships including the acquisition of the
JENATEC group and will continue to expand
its overseas sales organization to make the
KURODA brand and KURODA-JENATEC
brand better known in the world.

United States
South Korea
China
Malaysia
Germany

KURODA JENA TEC INC.
KURODA PRECISION INDUSTRIES KOREA LTD.
KURODA PRECISION INDUSTRIES PINGHU CO., LTD.
KURODA JENA TEC PRECISION INDUSTRIES PINGHU CO., LTD.
KURODA PRECISION INDUSTRIES(M) SDN.BHD.
JENAER GEWINDETECHNIK GmbH

Introduction-3

KURODA aspires to the principle of “CHALLENGE & CREATE”, making
linear motion systems based on expertise in gauge manufacturing.

KURODA supports high precision applications using materials
and equipment that can achieve JIS lead accuracy grade C0.

KURODA’s Ball Screws

Materials and Heat Treatment

KURODA’s Ball Screws are an outgrowth of a legacy ingauge manufacturing.
In order to obtain characteristically advantageous features
such as high efficiency in motion control, KURODA’s ballscrews are utilized as an essential element in the control
mechanism of a wide variety of automatic machines
including machining tools, precision positioning tables,
industrial robots, and semiconductor fabrication devices.

KURODA makes it a rule to purchase dedicated ball screw
materials based on detailed specifications intended for ourcompany and internally control the heat treatment processes
such as carburizing, quenching and induction hardening, of
which records are carefully kept to assure traceability.

High Quality Standards

Grinding

In recent years, the technical development of various machines forhigher accuracy and higher speed has been increasingly accelerated
and the users’ needs are much more diversified than ever. On thestrength of our traditional precision machining technology and our
unceasing research into ideal ball screws, we are supplying highquality ball screws that are manufactured from carefully selectedmaterials especially in terms of quality with our advanced grinding
technologies and under our extremely tight quality control using themost modern test and measuring equipment.

KURODA uses high precision thread grinders dedicatedfor ball screws developed and manufactured uniquely
by KURODA based on its screw gauge manufacturingknow-how. These are carefully maintained at KURODA toenable ball screw manufacturing with JIS C0 grade highaccuracy. These machines realize the world’s highest
level of machining precision due to the combination of avast machining database built up over a half-century with
KURODA’s highly proficient technicians.

Introduction-4

The ball screw shafts, nuts, and recirculation parts that weremachined to a high accuracy are meticulously assembled
and finished through excellent work by experienced workers.
The axial clearance and preloading are strictly administered
to realize a smooth operability and high positioning accuracy
that satisfies the requirements of a variety of machines andequipment.

Inspection

Thread Grinding

Shipment

Functional Test

Assembly

Dimensional Inspection

Grinding

Additional Machining

Non-destructive Test

Heat Treatment

Programming

DesignLathe, Milling Machine

Assembly

Responding to rapid diversification of needs, KURODA
has been pursuing more research and development on ballscrews by looking ahead to the advancement of precisionengineering technology for the next generation. We areconducting intensive studies into the basics of ideal ballscrews jointly with academic laboratories to accumulate andanalyze comprehensive test data on the accuracy, hardness,
service life, and other vital factors of ball screws, and haveestablished various evaluation systems.
Cylindrical Grinding

Machining Center

Forming

Research and Development

In order to assure stable measurement at JIS C0 grade leadaccuracy, we have established a structure including our
proprietary lead measuring machine installed in a strictly
controlled thermostatic chamber as well as measuringmachines classified by applications so as to satisfy any
needs for various applications and measurement accuracies
c overing all processes from development to mass
production.
Introduction-5

BALL SCREWS AND

LINEAR MOTION PRODUCTS

KURODA products can support
your linear motion systems.
To fulfill a variety of needs and requirements of our customers,
we provide a wide selection of products including ball screws,

KURODA will recommend the optimal linear motion system which satisfies
your needs.

linear motion products, and related tools and equipment.
Standard Precision Ball Screws

Ballscrew Actuators■ Ball screws with C3 accuracy
grade
GP series (ø8 - ø20 mm)
DP series (ø6 - ø14 mm)

A ballscrew actuator is a product in which ball screws andlinear motion guides are integrated in one unit.
Please refer to KURODA’s ballscrew actuator catalog.
■ Actuators with repeated positioning accuracy of ±1 μm(P grade) and ±3 μm (H grade)
SG series (Mounting height: 20-55 mm)■ Ball screws with C5 accuracy
grade
GG series (ø8 - ø32 mm)
FG series (ø10 - ø25 mm)
HG series (ø8 - ø20 mm)■ Ball screws with C7 accuracy
grade
GE series (ø8 - ø32 mm)
FE series (ø10 - ø25 mm)
GW series (ø8 - ø25 mm, withrolled screw shaft)
RW series (ø8 mm, resin nut)
■ Ball screws with C10 accuracy grade
GY series (ø8 - ø40 mm, with rolled screw shaft)

Custom Precision Ball Screws■ Ball screws with C0-C10
accuracy grades
GR series (ø5 - ø125 mm)
DR series (ø6 - ø50 mm)■ Ball screws with C3-C7
accuracy grades
FR series (ø10 - ø40 mm)

Introduction-6

Related Products■ Actuators with repeated positioning accuracy of ±3 μm(H grade), ± 5μm (U grade) and ±10 μm (W grade)
SE series (Mounting height: 15-45 mm)■ Support units
Square type BUK series(Bearing inner diameter: ø6 - ø25 mm)
Square type BUKE series(Bearing inner diameter: ø6 - ø12 mm)
Round type BUM series(Bearing inner diameter: ø6 - ø25 mm)
Round type BUT series(Bearing inner diameter: ø20 - ø40 mm)■ Low particle generating grease
KURODA C-Grease (Clean grease)
KURODA S-Grease (Clean and oscillation-proof grease)■ Lubricating unit for ball screws
LUBSEAL (Applicable shaft diameter: ø10 - ø25 mm)■ Slide screws with resin nuts
PW series (Accuracy grade C7, ø10, ø12 mm)
PY series (Accuracy grade C10, ø10, ø12 mm)

Couplings and Other Related Products■ Couplings
Miki Pulley Co., Ltd.
http://www.mikipulley.co.jp/JP/
Sakai Manufacturing Co., Ltd.
http://www.sakai-mfg.com/
ISEL Co., Ltd.
http://isel.jp/■ Full-cover type actuators
SC series (Mounting height: 23-45 mm)(Repeated positioning accuracy: ±3 μm (H grade), ±5 μm(U grade) and ±10 μm (W grade))

Introduction-7

Ball Screws Product Range
Features andkeywords· High rotational speed· Low noise· Compact· Long service life

Features andkeywords· Compact· Fine-pitch positioning

Features and keywords· High speed conveyance· Large lead

Introduction-8

SeriesF series

FG series
FE series

Single nut

FR series

Single nut
Double nut

SeriesNut combination

DP series
D series

DR series

SeriesH series

Nut combination

HG series

Single nut
Single nut
Integral nut

Nut combination
Single nut

Accuracy
grade
C5
C7
C3 to C7
C3 to C5

Accuracy
grade
C3
C0 to C7
C0 to C5

Shaft diameterScrew shaft type

Product line

ø10 to ø25

Unfinished shaft
endsStandard
product

Free design

Customproduct

ø10 to ø40
ø32 to ø40

Shaft diameter Screw shaft type
ø6 to ø14
ø6 to ø50
ø16 to ø50

Accuracy
Shaft diameter
grade
C5

Ball Screws Product Range

ø8 to ø20

Screw shaft type

Series· Wide variety of shaft diameters· Wide variety of lead sizes· For positioning· For transfer

G series

Nut combination

GP series
GG series
GE series

Single nut

GR series

Single nut
Integral nut
Double nut

Product line

One end finished Standard productFree design

Features and keywords

Custom productProduct line

Unfinished shaft ends Standard productFeatures and keywords· For transfer· Wide variety of nut types(round and square types)

Features and keywords· For transfer· For lighter load applications

SeriesRolledG series

GW series
GY series

SeriesR series

RW series

Nut combination

Single nut

Nut combination
Single nut

Accuracy
Shaft diameterScrew shaft type Product line
grade
C3
ø8 to ø20
One end finishedStandard
C5
ø8 to ø32
Unfinished shaft ends product
C7
C0 to C7
ø5 to ø125
Custom
C0 to C5
ø20 to ø63Free design
product
C0 to C5
ø8 to ø125

Accuracy
Shaft diameter
grade
C7

ø8 to ø25

C10

ø8 to ø40

Accuracy
Shaft
grade
diameter
C7

ø8

Screw shaft type

Product line

Unfinished shaft ends

Standardrolledproduct

Screw shaft type

Product line

Unfinished shaft
endsStandard rolled
product

Introduction-9

Products Related to Ball Screws
Support units
Features andkeywords· Compact body
· Fit for any mounting
configurations· Built-in locking
function

SeriesBearingcombination

Bearing type

Accuracy grade of bearing

Square type BUK series Combined angular ballP5 grade (P0 grade for
DF (face-to-face)bearing
deep groove ball bearing)
Round type BUM series
High-thrust angular ballRound type BUT series
DF (face-to-face)
P4 gradebearing
Square type BUKE series Radial ball bearing--P0 grade

Bearing innerdiameterø6 to ø25

Data including product information, technical information, catalogs,
and CAD data of linear motion products such as ball screws andballscrew actuators can also be viewed from the KURODA website.

www. kuroda-precision.co.jp

ø20 to ø40
ø6 to ø12

BUT (Round type)

BUK (Square type)
BUKE (Square type)
BUM (Round type)Low particle generating grease
OperatingThickener
temperature range

Features and keywords

Series· For clean environment· Excellent lubricating performance· Excellent torque performance· High rust prevention performance

KURODAC-Grease-30 to +150°C

Urea

KURODAS-Grease-20 to +150°C

Urea

Model number
C1-080G-J (Supplied in a 80 g bellows-shaped container)
C1-400G-J (Supplied in a 400 g bellows-shaped container)
S1-080G-J (Supplied in a 80 g bellows-shaped container)
S1-400G-J (Supplied in a 400 g bellows-shaped container)

Slide screws with resin nuts
Features and keywords· Precise resin nut· Excellent mechanical property· Chemical-proof performance· Compact· Low price

SeriesNutcombination

PW series
Slide screw

Accuracy
grade

Screw shaft
type

Product line

ø10, ø12

Unfinishedshaft ends

Standard
product

C7
Single nut

PY series

Shaft
diameter

C10

2D CAD data ᴾ
2D CAD data (DXF format) can be
downloaded free of charge from the
KURODA website.

3D CAD data ᴾ
3D CAD data can be downloaded free ofcharge from the PARTcommunity CAD
data downloading service.

Catalogs
The catalogs of ball screws, ball screw linear motion products, ballscrew actuatorsand other products can be downloaded from the KURODA website.
For pamphlets, please contact your nearest sales location.
Introduction-10

Introduction-11

Overview ofball screws

Overview ofball screws

Proper usage for safety

Be sure to read the following instructions before use.
For general instructions, refer to the text of this catalog.

KURODA Ball Screws Catalog
Proper usage for safety― ――――――――――――――――― A- 2 to 4
Features of KURODA ball screws― ―――――――――――― A- 5
Construction, materials and heat treatment―――――――― A- 6
Types―of―nuts―and―flanges――――――――――――――――― A- 7
Custom products― ―――――――――――――――――――― A- 8 to 9
Ordering instructions (How to interpret ball screw model numbers) A-10 to 13

The following safety precautions recommend the correct usage of our products to prevent an
injury and damage.
These precautions are classified into 3 categories: “DANGER”, “WARNING” and “CAUTION”
according to the degree of possible injury or damage and the degree of impendence of suchinjury or damage.
Be sure to follow all these precautions, as they contain important matters regarding safety.

DANGER
Indicates an impending hazardous
situation that may arise due toimproper handling or operationand could result in a serious injury
or death.

WARNING
Indicates a potentially hazardous
situation that may arise due toimproper handling or operationand could result in a serious injury
or death.

CAUTION
Indicates a potentially hazardous
situation that may arise due toimproper handling or operationand could result in an injury orproperty damage only.

Be sure to obey “Industrial Safety and Health Act” and other safety rules and regulations inaddition to these precautions.
There are some situations that may lead to a serious result according to circumstances, even if it
is mentioned in the category of “CAUTION”. Be sure to follow these precautions, as they contain
important matters.

WARNING●― Select a ball screw properly.

As operating conditions for products mentioned in this catalog are diverse, the applicability of ballscrew to the intended system should be determined by the total system designer or the person who
determined specifications for such system after conducting analysis and testing as necessary.
The person who determined the applicability of the system shall be responsible for assuring theintended system’s performance and safety. When configuring a system, the system designer should
thoroughly examine all specifications for such a system by referring to the latest product catalog anddata, and also take into consideration the possibility of equipment-related issues.

●― ―The ball screw should be handled by persons who have sufficient knowledge
and experience.
· Thoroughly read this catalog and operation manual before use.
· Never disassemble the ball screw. Dust may enter inside, degrading the accuracy of the ball screw
and may lead to an accident. When the ball screw has been disassembled from necessity, return it to
KURODA for repair and reassembling. (Fees will be incured.)· When mounting a ball screw to a machine and dismounting it from the machine, check that a means offall prevention has been put in place and that the moving part of the machine has been fixed beforehand.

● The products listed here are primarily for industrial use. When using the ballscrew in the following conditions or environments, take the proper safetymeasures and consult KURODA beforehand.
· Conditions and environments other than specified and outdoor use.
· Applications to nuclear power equipment, railroads aircraft, vehicles, medical equipment, equipment
contacting food and drink, and the like.
· Applications which require extreme safety and will also greatly affect persons and property.

● During operation, make sure to keep your hands away from screws and ends
of ball screw shafts, which are rotating parts, to prevent your hands frombeing caught.
● Pay adequate attention not to allow the products to be used for military
purpose including for arms and weapons.
A-1

A-2

Ball screw/General instructions (2)Be sure to read the following instructions before use.
Also refer to “Proper usage for safety”.

Be sure to read the following instructions before use.
Also refer to “Proper usage for safety”.

Caution for design

WARNING●― Rotational speed
Referring to the section describing permissible
rotational speed in this catalog, use a ball screw ator lower than the listed permissible rotational speed.
Using the product at or above the permissible
rotational speed could cause damage of its
recirculation components and result in inoperable
conditions. When using a vertical shaft, the damage
may lead to dangerous accidents such as fallingballs or parts.

CAUTION●― Dust―preventive―cover
If it is likely that dust or other contaminant may enter
inside the ball screw, be sure to attach a dust
preventive cover, such as bellows or lead screw
cover (steel bellows). Attaching a wiper at both ends
of a nut will be more effective for dust prevention.
The dust or contaminant caught in the ball screw
could cause various defects including malfunction,
abnormal noise, excessive vibration, accelerated
wear-out, and early chipping.

Dust preventive
deviceLead screw cover

Felt wiper

Caution for mounting and use

WARNING●― Do―not―overrun―the―product.
If a nut of the ball screw is overrun and receives animpact at a stroke end, a resulting impression createdon a screw groove could cause malfunction. If an endof the screw groove has a portion with no flute, suchoverturn could damage ball recirculation components,
which may result in inoperable conditions.
If a ball screw nut has been allowed to overrun,
please contact KURODA to have it repaired at charge.
●― Pay―adequate―attention―to―the―accuracy―grade.
A moment load caused by misalignment of a ballscrew, bearing, guide, nut, and housing and improper
angularity may result in malfunction, abnormal noise,
excessive vibration, shorter product service life aswell as breakage of screw shafts due to rotating
bending fatigue. Be careful with such defects because
they may lead to a serious accident.
●― ―Be― careful― with― falling― off― of― components― due― to―their own weight.
Since a ball screw has a low friction factor, its shaft or
nut could potentially fall off due to its own weight. Be
careful not to have your hand or fingers be caught
under the fallen component.

Bellows

Wiper●― Mounting―of―the―ball―screw
When mounting of the ball screw to a machine, thesystem design should allow its screw shaft to be
mounted without taking off the nut. Removing andattaching the nut may cause some balls to drop
outside of their recirculation path, which may result indamage of recirculation components. If such removalof a nut is inevitable, consult KURODA beforehand.

Resin wiper, lip seal,
brush wiper●― Take―care―not―to―injure―yourself.
The shafts and nut corners may have sharp edges forstructural reasons, and there may be a risk of injuries
such as cuts.
In order to prevent injuries, take adequate care whenhandling products and wear protective equipment
such as gloves during work.

CAUTION●― Imbalanced―load
In your system design, ensure that a radial or
moment load is not directly loaded to the ball screw.
Otherwise, it may result in shorter product service
life due to concentrated load to a certain portion ofballs in the screw.

A-3●― Do―not―remove―the―nut.
When balls have dropped out of the nut or the nut has
been removed from a shaft, do not attempt toreassemble them yourself. Return them to KURODA
for repair. (Fees will be incured.)
KURODA’s standard precision ball screws haveunfinished shaft ends. The unfinished products areprovided with a sleeve for separating the nut.

●― Be―careful―of―any―dust―or―contaminants.
While a machine is assembled, put a cover to preventthe screw shaft from catching any dust or contaminants.
Such contamination could cause malfunction of themachine.
●― ―W hen― a― component― such― as― bearing,― gear,― or―pulley is attached to a screw shaft, handle themwith care so that there is no damage from impact.
Such impact could cause the screw shaft to bend.
If an impact is accidentally applied to the shaft,check it first to see if it is not bent by checking thecoupling of the screw shaft with a dial gauge, before
assembling the additional components.
●― U― se―the―product―within―the―operating―temperature―limit.
Ball screws are designed to have a normal operating
temperature limit of 60°C or below. Using them in anenvironment exceeding the temperature limit may
result in a damaged lubrication or sealing components.
If you need to use the screw in a special environment,
consult with KURODA beforehand.

Lubricants

CAUTION●― Type―of―lubricant
Unless specified, Alvania Grease S2 or Maltemp PS
No.2 is contained in the nut as lubricant. Since rustpreventive oil applied to the screw shaft also serves
as lubricant, the ball screw can be used without
additional application.
Do not replace the initially applied lubricant with any
product not listed below. Do not remove the rustpreventive oil, either.
GreaseApplication

Product name

Manufacturer
SHOWA SHELL SEKIYUGeneralK.K.
purposeMultemp PS No. 2 Grease KYODO YUSHI CO., LTD.
KURODA PRECISION
KURODA C-Grease
INDUSTSRIES LTD.
For dust
prevention KURODA S-Grease
KURODA PRECISION(Support for oscillation
INDUSTSRIES LTD.
resistance)
Alvania Grease S2Lubricating oil
Application
Generalpurpose

Product name
Daphne Mechanic Oil
Mobil Vactra Oil

Manufacturer
IDEMITSU KOSAN CO.,LTD.
EXXON MOBILCORPORATION

Note) All product names of greases and oils are registered trademarks of theirrespective companies.

Overview ofball screws

Overview ofball screws

Ball screw/General instructions (1)Storage

CAUTION●― Storage―method
Store the ball screws in an indoor place where
temperature difference is as small as possible,
avoiding high and low temperatures and high humidity.
It should be stored in a horizontal state in the
packaging originally sent by KURODA. In order toprevent unnecessary contamination by dust or
rusting of the ball screws, do not open the outer
packaging or any of the internal packaging unlessnecessary.

Checkup and caution

CAUTION●― ―Checking the lubricant status and application of grease
For the sake of usability and dust prevention,
lubricant for ball screws is, in general, contained onlyin the nut. When specified or required for overseas
export, lubricant may be applied to the screw shaft.
Depending on the screw size and screw shaft length,
the amount of grease in the nut may not be sufficient.
After running the nut back and forth the length of the
shaft, check to see if the rolling side of the screw
groove has enough grease on it. If the amount is notenough, apply additional grease to the screw shaft.
●― Checkup―and―reapplication―of―lubricant
Check the lubricant 2 to 3 months after the ball screw
is used for the first time. If it is extremely dirty, it isrecommend that you wipe off old grease and apply
new grease. Then, check and supply the lubricant once
every year as a general rule. However, as the service
life of lubricants varies according to operating conditions
and environment, adjust the intervals properly.
When reapplying additional lubricant, use the samebrand of lubricant as was initially included.
For a ball screw model provided with a nut which does
not have a grease filler hole, supply a sufficient amountof grease directly to the screw shaft and screw groove,
carefully applying it over the components until thegrease goes into the nut. For a model provided with anut having a filler hole, supply a necessary amount ofgrease from the filler hole or a feeder (grease nipple,
etc).
After applying additional grease, run the work for a fullstroke to ensure the proper coverage of the grease on
all components. Wipe off excess grease attached on
the end of the screw shaft.
For more details on the size of the filler hole, refer todimensions of each ball screws size.

A-4

ball screws provide highaccuracy as well as excellent reliability, as aresult of our grinding, assembly, and inspection
operations implemented in our plants under astrict temperature control, which is built on ourgauge production expertise accumulated overmany years.

High transmission
efficiency

Excellent durability

ball screws maintain excellent
durability achieved by carefully selectedmaterials, proper heat treatment, and machining
with advanced product technologies.

Small axial clearance

Sinceball screws adopt agothic-arch groove profile, its axial clearance
can be finely adjusted and rotated with minimal
force. In addition, by applying preload to thescrew, the axial clearance could be adjusted to
0 to achieve advanced rigidity.

Ball screws have outstanding transmission
efficiency of over 90%, incomparably higher
than slide screws. Their required torque is justless than a third of what slide screws require.
Therefore, it is easier to transfer linear motion
into rotary motion.
100
90
Efficiency η (%)

80
70
60
50
40
30
20

μ=0.003
μ=0.005
μ=0.008
μ=0.010Ball screw
Rotary → Linear
μ=0.1
μ=0.2
μ=0.3
Slide screw(Trapezoidal
screw thread)10

μ: Coefficient of friction
0 1 2 3 4 5 6 7 8 9 10
Lead angle (degree)
μ=0.003100
μ=0.005
μ=0.00890
μ=0.010Ball screw
80
70
60
50
40
30
20
10

Linear → Rotary
μ=0.1
Slide screw(Trapezoidal
screw thread)μ: Coefficient of friction

0 1 2 3 4 5 6 7 8 9 10
Lead angle (degree)

Figure―1:―Mechanical―efficiency―of―ball―screws
A-5

Construction

Ball screws are configured to have steel balls enclosed between ascrew shaft and a nut, wherein steel balls rotate while they recirculate
in the device.
ball screws are designed to adopt one of the following
four standard recirculation systems.

Tube Method
Pick-up Tube■―Tube―Method

This is a standard recirculation system for ball screws, using a curved
tube as a recirculation part. In this system, steel balls are guided into
the tube, make 1.5, 2.5, or 3.5 turns along the screw groove to returnto the starting point, forming a circuit.
To enhance the load capacity of the screw, the number of circuits canbe increased.

End Cap Method

End Cap■―End―Cap―Method

This recirculation system has end caps attached to both ends of thenut, which are capable of scooping up the steel balls and forwarding
them back to the starting point. A through hole is provided in the bodyof the nut to allow the steel balls to pass through. This system isadopted by ball screws with large leads (e.g. screw lead with twice or
three times as large as the screw shaft diameter).

Deflector Method
Deflector (metal)■―Deflector―Method
Figure 2: Ball screw groove profile

Fine feeding

Due to rolling contacts made by balls, the ballscrews can accurately provide fine feeding,even with extremely small starting friction at
low speed, without exhibiting the stick slip
tendency of slide screws.

High-speed operation

With high transmission efficiency and a low
rate of self heat generation, KURODA ballscrews can provide a high speed rotation.

Easy maintenanceDue to rolling contacts made by balls, no special
maintenance other than regular supply of grease
is required under normal operating conditions.

Wide variation

In order to fulfill a diverse range of customer
requirements there are a wide variety of seriesball screws
and models of
made available. Products include miniatureball screws, super large lead ball screws,
high rotational speed ball screws, standard
precision ball screws and more.

This system is compact and has the most optimal rotational balanceamong the recirculation systems listed in this catalog. Steel balls
rolling between a screw shaft and a nut are guided by a deflector
inserted in the nut to make one recirculation per lead, forming acircuit.

End Deflector Method
End Deflector■―End―Deflector―Method

This system has end deflectors incorporated into both ends of thenut, which are capable of scooping up steel balls and forwarding
them back to the starting point. A through hole is provided in the
body of the nut to allow the steel balls to pass through. The system is
Figure 3: Recirculation
designed for a smooth flow of the steel balls. This structure realized
systemhigher rotational speed and low-noise operation in a compact nut
body.
Table―1:―Materials―and―heat―treatment● Ground ball screws

Materials―and―heat―treatment

Material
Heat treatment Hardness
The hardness of the screw groove surface is asteel Carburizing and 58 to 62
critical factor for the service life of a ball screw.
Nut Chromium-molybdenum
SCM420quenching
HRC
The rigidity of the shaft must satisfy the requireChromium-molybdenum steel Carburizing and 58 to 62
ments of a shaft for transmission of loads. In
SCM415quenchingHRC
SCM420order to fulfill such needs, KURODA ball screws Screw
shaft
Chromium-molybdenum
steel
Induction58
to 62
are generally manufactured to maintain the
AISI4150HV
quenching
HRC
minimum standard hardness of 58 HRC with thematerials listed in Table 1. The screws also go ● Rolled ball screws
through a surface hardening process to enhanceMaterial Heat treatment
Hardness
their hardness to attain 58 to 62 HRC. AdditionS45C
Induction
Screw shaft
56 to 62HRC
ally, for some products which required heat reS55C
quenchingsistance and/or corrosion resistance, stainless
Nut
SCM420
Steel balls
58 to 62HRC
steel may be used to achieve hardness of 56 to
60 HRC or
Steel ball
SUJ2
Quenchingabove
59 HRC through a surface hardening process.

A-6

Overview ofball screws

Excellent reliability andhigh accuracy

Efficiency η (%)

Overview ofball screws

ball screws

Single Nut

In order to fulfill the diversified needs of our customer in various industries such as mounting/placement machines, semiconductor fabrication equipment, liquid crystal (LC) manufacturingmachines, clean robots, SEM equipment, small machine tools, medical instruments, automotive
provides, upon your request, various customized
production facilities, etc.,
ball screws with special specifications. Our custom products include super precision ballscrews (C0 grade or above), high rotational speed ball screws, stainless ball screws for
special environments, low maintenance ball screws, and ball screws compliant with various
environmental requirements.

■―Nut―combination―types
This is the simplest configuration. It is usually usedwith a small axial clearance. In order to improve thepositioning accuracy, axial clearance can be eliminatedand a preload can be applied by loading oversizedballs. The single nut type with a preload is suitable formachines requiring small to medium loads and light tonormal preloading, including semiconductor fabrication
devices, assembling robots, precision instruments,and small NC machine tools, which require very highpositioning accuracy.

■―――Super―precision―ball―screws―(capable―of―fine―pitch―forwarding―by―a―scale―of―0.1―μm/pulse)

When a machine requires fine feeding with high accuracy, torque variation contributes toaccuracy degradation. With a laser scanner, SEM instrument, and test/analysis equipment,
torque variation causes fluctuations in the transfer speed of the machine. Under such conditions,a highly accurate continuous operation may
not be achieved. However, building upon
Dynamic preload torqueprecision processing expertise acquired
5
1N·cm
through years of gauge production business,has successfully developed in380mm
5house screw grinders to control the profile ofthe screw groove, circularity, and cylindricality
Shaft diameter: 15
Lead: 5in a highly accurate manner. With the reduced
Rotational speed for measurement: 50 min-1
torque variation achieved by this precise
Lubricant: Turbine oil #2
control, we have realized ball screws capable(ISO VG68)
of fine feeding by to a degree of 0.1 μm/pulse.

Integral Nut

This type of nut has a screw portion separated into aload side and preload side via a pitch shift. The nut isoffset according to the desired amount of preload. It
provides the features of having a load side and preloadside of a double nut integrated in one component.
The integration into one body enables the nut to be
shorter while maintaining stable rigidity and excellent
operational performance.
The integral nut is suitable for all types of machines
and equipment requiring medium to higher loads andnormal to higher preloading.

Double Nut

Two separate nuts, one designated as the load side andthe other as the preload side are joined. They are rotatedin opposite directions and fixed in tension by a pin inserted
between them. A double nut is available in wider variety
of sizes than integral nuts, and is suitable for applications
with medium to higher preloading and with medium tohigher loads, such as machines or equipment requiring
highly precise positioning as well as high rigidity.

■―――Super―precision―ball―screw―(entire―deflection―of―a―screw―shaft―is―1/4―to―1/3―of―C0―grade―screw)■―Flange―types

The type of a flange is represented by a symbol provided for each nominal size as shown below.
Type symbol

A

B

C

As long as the deflection of the screw shaft is within the permissible range and the shaft is kept
straight though a typical mounting arrangement where rigid linear bearings are set at both endsof the ball screw, there is usually limited influence on operational accuracy. However, in suchcases that a simplified guiding system has been put in place for weight or size considerations,bending of the ball screw may adversely impact operational accuracy, resulting in pitchingprovides customized ball screws
or yawing errors. To prevent such issues,
manufactured through our unique processing method, with which the deflection of the screw
shaft center is mitigated to 1/4 to 1/3 of permissible deflection for C0 grade screws. For more.
information, please contact■―High―rotational―speed―ball―screw
Flange typeType symbol

Square flange
D

Rectangle flangeE

Round flange
H

KURODA provides special ball screws capable of fulfilling our customers’ needs for rotational
speed with a DmN of over 70,000. These ball screws are suitable for use in machine tools,
robots, and other applications requiring high rotational speed. The F series is the standard
product line designed for high rotational speed and low noise. Custom products in the G series
can also be designed to meet the DmN requirements of high speed applications.
.
For more information, please contact

Flange type
Single side cut, round flange Square (without spot facing) Double side cut, round flange

A-7

A-8

Overview ofball screws

Custom products

N·cm

Overview ofball screws

Types

●―All-stainless―steel―ball―screw
Stainless steel ball screws which can be usedin vacuum atmospheric conditions, clean room
conditions, or an environment with special
requirements such as chemical resistance,
are also available. The stainless steel screws
demonstrate minimal outgassing and excellent
corrosion resistance.
For more information, please contact

Materials of all-stainless steel screws· Screw shaft, nut, and balls Martensitic stainless steel
Austenitic stainless steel,· Recirculation components precipitation hardening
stainless steel, etc.
· Small screws and parts
Austenitic stainless steel.

●―Customized―surface―treatment
If you intend to use a ball screw in an environment where corrosion resistance is necessary,
we can accommodate your needs by applying an additional anticorrosive black coating forrust-proofing. The black coating has a thickness of 1-2 μm. Some of the coating may bepartially removed from areas subjected to consistent ball contact during the initial period after
commencement of operation, but rust prevention will be maintained thereafter. If you need moreadvanced corrosion resistance, further additional fluorine coating on top of the anticorrosive
black coating can be applied. Other types of surface treatment will also be provided uponrequest.
.
For more information, please contact■―Ball―screws―with―lubricating―unit

LUBSEAL is a lubricating unit attached to the ball screw nut which supplies a proper amountof grease to the screw groove. Recommended for use in semiconductor fabrication equipment,
liquid crystal manufacturing machines, testing instruments, food processing machines, medical
instruments, machine tools, and automobile manufacturing equipment. By adding LUBSEAL tocompatible ball screws, the maintainance interval between grease applications can be greatly
increased.

■―Various―types―of―grease

KURODA also provides a wide range of grease which fulfills your requirements, including
clean room compliance, anti-fretting corrosion, extreme pressure, low temperature, and wide.
temperature range. For more information, please contact■―――Examples― of―other―custom― ball―screws― with― special― dimensions―and rating requirements
also provides custom ballscrews with dimensions or specifications
which are not listed as standard products inthe catalog.
Various ball screws which require special
profiles and dimensions to accommodateright-handed and left-handed screws, leads inimperial/US units (i.e. inches), hollow screw
shafts, square nuts and others are available.
Ball screws which are configured with ascrew shaft having a gear, spline, serrationor the like, or are capable of withstanding
heavy loads can also be made upon request.
For more information, please contact.

A-9●―Example―of―custom―nut―dimensions
Screw shaft

Ball screw nut
Component or housing attachment

Ordering instructions (How to interpret ball screw model numbers)
ModelnumberSeries
FE
(1)

Shaft
Number Nut
Lead
Diameterof Circuits Type
15
10
P
S
(2)
(3)
(4)
(5)

Ball Re- Wiper Thread
Overall
Flange circulation
Shaft Thread
Accuracy Axial
Screw Shaft
Type System Material Direction
Grade Clearance
Length End Type Length
−
H
P
N
R
− 1500X
1440 −
C5
F
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)

(1) Ball Screw Series
SeriesStandard series
Order-made series
Remarks* Order-made Ball Screws are indicated with □R, □M,
F Series FE/C7 grade, FG/C5 grade
FR, FM, FZ/C3-C7 gradesand □Z which designate the following:□R: Order-made Ball Screws with established
D Series DP/C3 grade
DR, DM, DZ/C0-C7 grades
KURODA specifications and design. Details arein this catalog.
GE/C7 grade, GG/C5 grade, GP/C3 grade
GR, GM, GZ/C0-C10 grades □M: listed
Customized Order-made Ball Screws with
G Series
established KURODA specifications andGY/C10 grade (rolled screw), GW/C7 grade (rolled screw) GT/C7 or C10 grade (rolled screw)
design, but with a customized flange.
□Z: Customized Order-made Ball Screws with
H Series HG/C5 grade−
specifications and design other than the above.
R Series RW/C7 grade−
GT indicates customized rolled ball screws.
(3) Ball Screw Lead
(2) Screw Shaft Diameter (unit: mm)
Indicated by a two-digit number or a number-alphabet combination.
Indicated by a two-digit number or a number-alphabet combination.
· To show a lead with a 1-digit number, 0 needs to be added in· To show a screw shaft diameter with a 1-digit number, 0 needs
front to make it a two-digit code.
to be added in front of the diameter to make it a two-digit code.
(Example) Lead of 1 mm → 01
(Example) Screw shaft diameter 5 mm → 05
· Leads whose actual value is not a whole number (i.e. including· Screw shaft diameters with 3-digits are indicated as follows:
an increment of 0.5 mm) are represented with the letter F as
100 mm → A0, 125 mm → C5
indicated below. 1.5 mm → 1F, 2.5 mm → 2F
(4) Number of Circuits of the Ball Screw Nut
Symbol Number of circuits
Applicable recirculation system
Symbol Number of circuits
Applicable recirculation systemA
1.5 turns, 1 circuit
H
1 turn, 2 circuits
B
1.5 turns, 2 circuits
J
1 turn, 3 circuits
C
1.5 turns, 3 circuits
K
1 turn, 4 circuits
Deflector method
D
2.5 turns, 1 circuitL
1 turn, 5 circuits
Tube method
E
2.5 turns, 2 circuits
M
1 turn, 6 circuits
F
2.5 turns, 3 circuits
P
See specifications. End deflector method
G
3.5 turns, 1 circuitQ
See specifications. End cap method
R
3.5 turns, 2 circuits
Not listed above (including ballZ
Other
screw shafts sold separately)(5) Nut Type(6) Flange Type
SymbolNut type
SymbolFlange typeS
Single nut
A, B, C,T
Integral nut
Refer to page A-7.
D, E, HD
Double nut (pin type)N
No flange (e.g. square nut)
E
Double nut (spacer type)
Other: shapes and dimensions not listed in the catalog
F
Flange double nut (spacer type)Z(including ball screw shafts sold separately)Z
Other (including ball screw shafts sold separately)(7) Ball Recirculation System (nut body shape)(8) Wiper Material(9) Thread Direction
SymbolBall recirculation system
SymbolWiper material
SymbolDescription
A
Round type (tube method)P
Plastic wiper
R
Right-hand threadT
Protruded tube type (tube method)L
Lip sealL
Left-hand thread
U
Inlaid tube type (tube method)F
Felt wiper
Other (including ball screwZ
shafts sold separately)K
Square type (tube method)
B
Brush wiper(10) Overall Screw Shaft Length (indicatedD
Deflector methodN
No wiperby a 4-digit number)G
Guide plate method
S
LUBSEALTM· The shaft length is indicated in theE
End cap method
Other (including ball screw
Z
metric system (unit: mm), roundedshafts sold separately)P
End deflector method
down to the nearest whole number.
(11) Shaft End Configuration(14) Axial Clearance
SymbolDescription
Product line
SymbolAxial clearanceA
Both ends unfinished Standard product lineS
0 mm (preloaded)B
One end finishedStandard product line
F
0.005 mm or lessX
Both ends finishedStandard product line, order-made product line
H
0.010 mm or lessD
Both ends unfinished For ordering GY series screw shafts without
M
0.030 mm or lessball screw nuts
Y
Both ends finishedL
0.200 mm or less(12) Thread Length (indicated by a 4-digit number)
Axial clearance for rolled ball screws (Refer· The length is indicated in the metric system (unit: mm), rounded down toYto the specifications of the GY/GW series.)
the nearest whole number.
Z
Other(13) Accuracy Grade· The accuracy grade is indicated by C0, C1, C2, C3, C4, C5, and C7.
Because accuracy grade C10 is 3-digits long, “CA” is used instead.

A-10

Overview ofball screws

Overview ofball screws■―Ball―screw―compliant―with―special―environmental―requirements

■―Ordering―instructions―for―rolled―ball―screws

Unfinished―shaft―ends

Unfinished―shaft―ends■―GE,―GG,―FE,―or―FG―series―ball―screws■―GY―series―ball―screws● For screws without additional end machining<Example>
GE/FE- Overall screw shaft length A
GG/FG- Overall screw shaft length A
Model Number● With additional machining
Enter the overall screw shaft length followed by X (the symbol for finished shaft ends), thread
length, accuracy grade, and axial clearance.
GE/FE- Overall screw shaft length X Thread length - C 7M
GG/FG
- Overall screw shaft length X Thread length - C 5F■―HG―series―ball―screws● For screws without additional end machining<Example>
HG- Overall screw shaft length A
Model Number● With additional machining
Enter the overall screw shaft length followed by X (the symbol for finished shaft ends), thread
length, accuracy grade, and axial clearance.
<Example>
HG- Overall screw shaft length X Thread length - C 5 FH

One―shaft―end―finished■―GP/DP―series―ball―screws● For screws without additional end machining<Example>GP- Overall screw shaft length B - C 3 SFDP
- Overall screw shaft length B - C 3 SF
Model Number● With additional machining
Enter the overall screw shaft length followed by X (the symbol for finished shaft ends), thread
length, accuracy grade, and axial clearance.
GP- Overall screw shaft length X Thread length - C 3 SFDP
- Overall screw shaft length X Thread length - C 3 SF

A-11

Overview ofball screws

Overview ofball screws■―Ordering―instructions―for―standard―precision―ball―screws[For ball screws with both a shaft and nut]
● For screws without additional end machining<Example>
GY- Overall screw shaft length A
Model Number● With additional machining
Enter the overall screw shaft length followed by X (the symbol for finished shaft ends), thread
length, accuracy grade, and axial clearance.
GY- Overall screw shaft length X Thread length - CAY[Nut only]
Fill in the information up to “Thread Direction”. There is no need to fill in the overall screw shaft
length etc. because there is no shaft.
<Example>
GY[Shaft only]● For screws without additional end machining
Enter D as a symbol for the shaft end type.
<Example>
GY
ZZ - ZZZZ - Overall screw shaft length D● With additional machining
Enter the overall screw shaft length followed by Y (the symbol for GY Series shafts soldseparately with finished shaft ends), thread length, accuracy grade, and axial clearance.
<Example>
GY
ZZ - ZZZZ - Overall screw shaft length Y Thread length - C AY
Note) GY Series screw shafts with the same diameter and lead size are compatible regardlessof nut type.

Unfinished―shaft―ends■―GW―series―ball―screws[For ball screws with both a shaft and nut]
● For screws without additional end machining<Example>
GW- Overall screw shaft length A
Model Number● With additional machining
Enter the overall screw shaft length followed by X (the symbol for finished shaft ends), thread
length, accuracy grade, and axial clearance.
GW- Overall screw shaft length X Thread length - C7Y

A-12

Overview ofball screws■―Ordering―instructions―for―order-made―ball―screws■―――For― order-made― ball― screws―with―nut―specifications―and―design― listed―in―
this catalog
Simply enter the overall screw shaft length, X (the symbol for finished shaft ends), thread
length, accuracy grade, and axial clearance after the listed Model Number information.
<Example>
GR/DR/FR- Overall screw shaft length X Thread length - Accuracy grade Axial clearance
Model Number■―――For―order-made―ball―screws―with―a―custom―flange,―but―otherwise―listed―nut―
specifications―and―design
Enter GM/DM/FM followed by shaft diameter, lead, number of circuits, and nut type. Select theapplicable the flange type (either N for no flange or Z for flange types other than those listed).
Enter the ball recirculation system, wiper material, thread direction, and finally overall screw
shaft length, X (the symbol for finished shaft ends), thread length, accuracy grade, and axial
clearance.
<Example>
GM/DM/FM-Z- Overall screw shaft length X Thread length - Accuracy grade Axial clearance
Model Number■―――For― customized― order-made― ball― screws― with― specifications― and― design―other than the above
Enter GZ/DZ/FZ followed by shaft diameter, lead, number of circuits, and nut type. Enter Z
for flange type. Enter the ball recirculation system, wiper material, thread direction, and finallyoverall screw shaft length, X (the symbol for finished shaft ends), thread length, accuracy
grade, and axial clearance.
<Example>
GZ/DZ/FZ-Z- Overall screw shaft length X Thread length - Accuracy grade Axial clearance
Model Number■―Ordering―instructions―for―customized―rolled―ball―screws■―――For―rolled―ball―screws―with―specifications―and―design―other―than―the―those―listed in this catalog

Standard precision ball screws
Page

Features and specifications of standard precisionball screws―――――――――――――――――――――― B-

2

Ordering instructions, size reference chart ――――― B-

3

6 mm shaft diameter ――――――――――――――――― B-

4 to

8 mm shaft diameter ――――――――――――――――― B-

6 to 175

10 mm shaft diameter ―――――――――――――――― B- 18 to 29
12 mm shaft diameter ―――――――――――――――― B- 30 to 53
14 mm shaft diameter ―――――――――――――――― B- 54 to 55
15 mm shaft diameter ―――――――――――――――― B- 56 to 85
16 mm shaft diameter ―――――――――――――――― B- 86 to 89
20 mm shaft diameter ―――――――――――――――― B- 90 to 113
25 mm shaft diameter ―――――――――――――――― B-114 to 127
32 mm shaft diameter ―――――――――――――――― B-128 to 131

Enter GT followed by shaft diameter, lead, number of circuits, and nut type. Enter Z for flange
type. Enter the ball recirculation system, wiper material, thread direction, and finally overall
screw shaft length, X (the symbol for finished shaft ends), thread length, accuracy grade, andaxial clearance.
<Example>GT-Z- Overall screw shaft length X Thread length - Accuracy grade Axial clearance
Model Number

A-13

B-1

Technical dataof ball screws

Technical data of ball screws
Page

Lead accuracy――――――――――――――――――――――― F- 2 to 3
Mounting accuracy and tolerance――――――――――――― F- 4 to 7
Preload torque――――――――――――――――――――――― F- 8
Screw shaft design― ――――――――――――――――――― F- 9 to 12
Service life calculation――――――――――――――――――― F-13 to 14
Ball screw design suitability―――――――――――――――― F-15 to 20
Torque――――――――――――――――――――――――――― F-21 to 22
Guide for ball screw selection――――――――――――――― F-23 to 29
Ball screw ordering information―――――――――――――― F-30 to 31

F-1

■―Cumulative―mean―lead―error―and―permissible―variation―values●―Accuracy―grades―C0-C5
Table―2――Cumulative―mean―lead―error―(±Ec) and permissible variation values (ec)Lead accuracy

Accuracy grade
Effective
threadlength (mm)The lead accuracy of ball screws is defined by the following characteristics in accordance with
the JIS Standard. The permissible values are shown in Tables 2 and 3.
Effective thread length
Cumulative nominal lead＋0

Cumulative
actual lead−

Cumulative
specified lead
Cumulative
mean lead

C
M
Ec

One
revolution
2π rad

ec
e2π

e300
300

■―Terms―and―definitions
Specified―leadIn most cases, the lead is the same as thenominal lead, but there are instances in which
the nominal designation is adjusted when theapplication so requires.
(Example: Nominal lead 10 mm → Specified
lead 9.9995 mm)
Cumulative―specified―lead―target―value―“C”
In cases in which expansion and contractionof the screw due to temperature change
or influence from the external load can be
anticipated, a target value of cumulative leaddetermined by testing or technical experienceshould be established in advance. For
presetting procedures, see the cumulative
specified lead setting procedures on page
F-20.
Cumulative actual lead
Cumulative lead obtained by either continuous
measurement of an actual ball screw or bymeasurement of a section including the axial
center of the screw shaft.
Cumulative―mean―lead―“M”
A straight line representing the trend of
F-2

cumulative actual lead. It is obtained by theleast-squares method or an approximation
similar to this method using the curve
representing the cumulative actual leadcorresponding to the effective travel of a nut or
the effective thread length of the screw shaft.
Cumulative―mean―lead―error―“Ec”
A value obtained by subtracting the cumulative
specified lead target value (C) from thecumulative mean lead (M).
Variation
The maximum difference of the cumulative
actual lead contained between two lines
drawn parallel to the cumulative mean lead. It
is prescribed by ec, e300, e2π.
ec : Variation for the effective travel of the nut
or the effective thread length of the screw
shaft.
e300 : Variation for a length of 300 mm arbitrarily
taken within the effective thread length of
the screw shaft.
e2π : Variation for one revolution (2 π rad) madewithin the effective thread length of thescrew shaft.

Over
−
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000

Or less
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6000

C0

C1

C2

C3

±EC

eC

±EC

eC

±EC

eC

±EC

eC

±EC

eC

±EC

eC

4
5
6
6
7
8
9
11

3.5
3.5
4
4
5
6
6
7

6
7
8
9
10
11
13
15
18
22
26
32

5
5
5
6
7
8
9
10
11
13
15
18

9
10
11
12
14
16
18
21
26
31
37
43

6
7
7
9
10
11
12
13
15
18
21
24

12
13
15
16
18
21
24
29
35
41
50
62
76

8
10
10
12
13
15
16
18
21
24
29
35
41

15
17
19
20
24
28
32
38
46
54
66
80
97

11
13
13
16
17
19
21
24
28
32
38
46
54

23
25
27
30
35
40
46
54
65
77
93
115
140
170

18
20
20
23
25
27
30
35
40
46
54
65
77
93

Table 3 Permissible variation values
Accuracy grade
Item
Permissible value(Unit: μm)
C5

C4

e300
3.5

C0

e2π
3

e300
5

C1

e2π
4

e300
6

C2

e2π
5

e300
8

C3

e2π
6

e300
11

C4

e2π
7

(Unit: mm)
C5
e300
e2π
18
8

●―Accuracy―grades―C7―and―C10

Table 4 Permissible values forcumulative lead error (Unit: μm)
The cumulative lead error of C7 and C10 grade ball screws
Accuracy grade
C7
C10
is prescribed by the permissible value for the lead error of a
Cumulative lead error 0.05/300 0.21/300
specified lead which had a length of 300 mm arbitrarily taken
within the effective thread length of Table 5 Accuracy grade and axial clearance
Accuracy grade
Nutthe screw shaft, in accordance with Symbol Axial clearance(mm)
combination C0 C1 C2 C3 C4 C5 C7 C10
JIS Standard.
S
0
Double nut ○ ○ ○ ○ ○ ○
−
−

■――A
― ccuracy grade and axial
clearance

S0○ ○ ○ ○ ○ ○−−F
0.005 or less−
○ ○ ○ ○ ○−−H
0.010 or less Single nut −
−
−
−
○ ○ ○
−
M
0.030 or less
−
−
−
−
○ ○ ○
−
Possible combinations of accuracy
L
0.200 or less
−
−
−
−
−
−
○ ○
grade and axial clearance are shown * Integral Nuts have the same possible combinations of axial clearance and lead accuracy grade as Double Nuts.
* The above table is for ground ball screws only. For rolled ball screws in GY/GW series, refer to the pages
in Table 5.
describing rolled ball screws.
* For any combinations not listed above, consult KURODA.

■―Accuracy―grade―and―manufacturable―screw―shaft―length

When the slenderness ratio (shaft length against shaft diameter) is large, it is sometimes difficult
to manufacture a ball screw with the desired accuracy. The following table shows the maximum
length of screw shafts of each accuracy grade that can be reliably manufactured. When ballscrews exceeding the manufacturable range are required, consult KURODA.
Table 6 Accuracy grade and manufacturable screw shaft length(Unit: mm)Screw shaft diameter
Accuracy
grade
5
6
8
10
12 15 · 16 20
25
28
32
36
40
45
50
55
63 70·80·100·125C090 160 240 340 420 500 800 1100 1200 1600 1800 2000 2000 2000 2000 2000−
C1
120 180 280 400 500 600 900 1300 1500 1800 2000 2200 2300 2800 3000 3000
3000
C2
120 180 280 400 500 600 1100 1600 1800 2200 2500 2800 3000 3600 4000 4500
4500
C3
140 210 340 480 600 700 1400 1800 2000 2500 2800 3200 3600 4000 5000 5000
5000
C4
140 210 340 480 600 800 1400 1800 2000 2500 2800 3200 3600 4000 5000 5000
5000
C5140 210 340 655 900 1500 2000 2000 2200 2800 3100 3600 4100 4500 5000 5000
5000
C7
−
−
340 655 900 1500 2000 2300 2600 3200 3600 4600 5000 5000 5000 5000
5000
C10
−
−
−
−
− 1500 2000 2300 2600 3600 4000 4600 5000 5000 5000 5000
5000
(Note) When the lead is larger than the nominal screw shaft diameter, C0 and C1 accuracy grades are not manufacturable.

F-3

Technical dataof ball screws

Technical dataof ball screws

Technical data of ball screws

■―Accuracy―of―each―part―of―the―screw―shaft

Tables 7 and 8 show the tolerance of the radial runout of the thread groove and mounting
portions when measured against the axial line of the supported shaft end (7) and theperpendicularity of the outer face of the supported shaft end (8).

Table 11 A

A

Tables 12-17 G or E-F

Table 7 A

Table 7 A

G
E
Table 7 E-FAFFigure 5 Mounting accuracy of the ball screw (Illustration)
Table 7 Radial runout of the thread groove and mounting portions when measured
against the axial line of the supported shaft end(Unit: μm)
Nominal screw shaft diameter (mm)Runout tolerance (maximum)Over
Or less
C0
C1
C2
C3
C4
C5
−
8
3
5
7
8
9
10
8
12
4
5
7
8
9
11
12
20
4
6
8
9
10
12
20
32
5
7
9
10
11
13
32
50
6
8
10
12
13
15
50
80
7
9
11
13
15
17
80
125
−
10
12
15
17
20
(Note) As the measurement of nominal screw shaft diameter takes into account the influence of the screw shaft axial runout,
it is necessary to correct the measurements. Calculate the correction value by using the total runouts (tolerance) of
the screw shaft axial runout shown in Tables 12 to 17 corresponding to the ratio of the overall screw shaft length tothe distance between the supporting point and the measuring point (L1 and L2) and add it to the tolerance shown in
the above table.

Table 8 Perpendicularity of the outer face of the supported shaft end when measured
against the axial line of the supported shaft end(Unit: μm)

F-4

Perpendicularity tolerance (maximum)
C1
C2
C3
C4
6
7
8
9
6
7
8
9
7
8
8
10
8
9
10
11
9
10
12
13
10
11
13
15
11
12
14
16
12
13
15
17

C5
10
10
11
13
15
17
18
20

Table 10 Radial runout of the outer diameter of the nut body (when cylindrical) whenmeasured against the axial center of the screw shaft(Unit: μm)

Table 8 E-F

C0
2
2
2
2
2
3
−

C0
5
5
6
7
7
8
−
−

Table 10 A

Table 8 E-F

Nominal screw shaft diameter (mm)Over
Or less
−
8
8
12
12
20
20
32
32
50
50
80
80
125

Table―9――――Perpendicularity―of―the―flange―mounting―surface―and―the―outer―diameter―of―the―nut body when measured against the axial center of the screw shaft(Unit: μm)
Outer diameter of the nut (mm)Over
Or less
−
20
20
32
32
50
50
80
80
125
125
160
160
200
200
250

Table 9 G

Table 8 E-F

Tables 9, 10 and 11 show the perpendicularity of the flange mounting surface and the outer
diameter of the nut body (9), the radial runout of the outer diameter of the nut body (10), and theparallelism tolerance of the outer diameter of the nut body (11) when measured against the axial
center of the screw shaft.

Perpendicularity tolerance (axial runout) (maximum)
C1
C2
C3
C4
3
3
4
4
3
3
4
4
3
3
4
4
3
3
4
4
3
3
4
5
4
4
5
6
4
5
6
7

Outer diameter of the nut (mm)Over
Or less
−
20
20
32
32
50
50
80
80
125
125
160
160
200
200
250

C0
5
6
7
8
9
10
−
−

C1
6
7
8
10
12
13
16
18

Runout tolerance (maximum)
C2
C3
7
9
8
10
10
12
12
15
16
20
17
22
20
25
23
28

C4
10
11
13
17
23
26
29
33

C5
12
12
15
19
27
30
34
38

Table 11 Parallelism tolerance of the outer diameter of the nut body (when planar) whenmeasured against the axial center of the screw shaft(Unit: μm)
Basic mounting length (mm)Over
Or less
−
50
50
100
100
200

C0
5
7
−

C1
6
8
10

Parallelism tolerance (maximum)
C2
C3
7
8
9
10
11
13

C4
9
11
15

C5
10
13
17

C5
5
5
5
5
5
7
8

F-5

Technical dataof ball screws

Technical dataof ball screws■―Accuracy―of―the―nut―mounting―portion

Mounting accuracy and toleranceTable 15 Total runout of the axial center of the screw shaft [C3]Tables 12 to 17 show the permissible values for total runout of the axial center of the screw shaft.
Table 12 Total runout of the axial center of the screw shaft [C0]Overall screw
shaft length

Over
−
125
200
315
400
500
630
800
1000
1250
1600

Nominal screw
shaft diameter

Or less
125
200
315
400
500
630
800
1000
1250
1600
2000

Over
Or less

−
8

8
12

12
20

0.015
0.025
0.035

0.015
0.020
0.025
0.035
0.045
0.050

0.015
0.020
0.020
0.025
0.035
0.040
0.050
0.065
0.085
0.110

20
32

0.015
0.020
0.020
0.025
0.030
0.035
0.045
0.055
0.070
0.095

32
50

0.015
0.020
0.020
0.025
0.030
0.040
0.050
0.065

50
80

0.015
0.020
0.025
0.030
0.040
0.045

Table 13 Total runout of the axial center of the screw shaft [C1]
Overall screw
shaft length

Over
−
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150

Nominal screw
shaft diameter

Or less
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000

Over
Or less

−
8

8
12

12
20

0.020
0.030
0.040
0.045

0.020
0.025
0.030
0.040
0.050
0.060

0.015
0.020
0.025
0.030
0.040
0.045
0.060
0.075
0.095
0.130

20
32

0.020
0.020
0.025
0.030
0.035
0.040
0.055
0.065
0.085
0.120

32
50

0.020
0.025
0.025
0.030
0.040
0.045
0.060
0.080
0.100
0.130

50
80

Overall screw
shaft length

Over
−
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000

F-6

Or less
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000

Over
Or less

−
8

8
12

12
20

0.025
0.035
0.045
0.050

0.020
0.030
0.035
0.045
0.055
0.065

0.020
0.020
0.025
0.035
0.045
0.050
0.065
0.080
0.105
0.140

20
32

0.025
0.025
0.030
0.035
0.040
0.045
0.060
0.070
0.095
0.130

32
50

0.025
0.025
0.030
0.035
0.045
0.050
0.065
0.090
0.110
0.140

(Unit: mm)
80
125

0.020
0.025
0.030
0.035
0.045
0.055
0.070
0.090
0.120

0.030
0.035
0.040
0.050
0.060
0.080

50
80

(Unit: mm)
80
125Table 14 Total runout of the axial center of the screw shaft [C2]Nominal screw
shaft diameter(Unit: mm)
80
125

0.025
0.030
0.035
0.040
0.050
0.065
0.080
0.100
0.130

0.030
0.035
0.045
0.055
0.065
0.090
0.110

Overall screw
shaft length

Over
−
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000

Nominal screw
shaft diameter

Or less
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000

Over
Or less

−
8

8
12

12
20

0.025
0.035
0.050
0.060

0.025
0.035
0.040
0.050
0.065
0.080

0.020
0.025
0.030
0.040
0.050
0.055
0.070
0.095
0.120
0.160

20
32
0.020
0.030
0.035
0.040
0.045
0.055
0.065
0.085
0.110
0.140

32
50

0.025
0.030
0.035
0.040
0.050
0.060
0.075
0.095
0.120
0.160
0.220

50
80

(Unit: mm)
80
125

0.030
0.035
0.040
0.045
0.055
0.070
0.085
0.110
0.150
0.200

0.030
0.035
0.040
0.050
0.060
0.075
0.100
0.130

50
80

(Unit: mm)
80
125

0.035
0.040
0.050
0.055
0.060
0.080
0.100
0.130
0.170
0.220

0.035
0.040
0.045
0.060
0.070
0.090
0.120
0.150

50
80

(Unit: mm)
80
125

0.040
0.045
0.050
0.060
0.070
0.085
0.110
0.140
0.180
0.240
0.320

0.045
0.050
0.055
0.065
0.080
0.095
0.120
0.160
0.210

Table 16 Total runout of the axial center of the screw shaft [C4]Overall screw
shaft length

Over
−
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000

Nominal screw
shaft diameter

Or less
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000

Over
Or less

−
8

8
12

12
20

0.030
0.040
0.055
0.070

0.030
0.040
0.050
0.060
0.075
0.090

0.030
0.035
0.040
0.050
0.055
0.070
0.080
0.100
0.130
0.170

20
32
0.030
0.035
0.040
0.050
0.055
0.065
0.070
0.090
0.120
0.150

32
50

0.035
0.040
0.050
0.055
0.060
0.070
0.080
0.110
0.130
0.180
0.240

Table 17 Total runout of the axial center of the screw shaft [C5]Overall screw
shaft length

Over
−
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000

Nominal screw
shaft diameter

Or less
125
200
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300

Over
Or less

−
8

8
12

12
20

0.035
0.050
0.065
0.075

0.035
0.040
0.055
0.065
0.080
0.090

0.035
0.040
0.045
0.055
0.060
0.075
0.090
0.120
0.150
0.190

20
32
0.035
0.040
0.045
0.050
0.060
0.070
0.085
0.100
0.130
0.170

32
50

0.035
0.045
0.050
0.055
0.065
0.075
0.095
0.120
0.150
0.200
0.260

F-7

Technical dataof ball screws

Technical dataof ball screws■―Total―runout―of―the―axial―center―of―the―screw―shaft

Backward(-)

Actual torque(maximum)Mean
actual torque

Effective thread length

Fixed

(+)

Actual torquePositive actual torque variation
Torque variation
Starting torque■―Terms―and―definitions

PreloadA way to reduce the backlash or to increase
the rigidity of ball screws. This is achieved byloading oversized steel balls or by inducing
tension between a pair of nuts which areforced in opposite axial directions.
Preload torque
The torque required to continuously rotate thescrew shaft or nut of a preloaded ball screw
when no external load is applied.
Standard torque
The target preload torque value.
Torque variation value
The deviation in preload torque from thetarget preload torque. The value is described
as a plus (+) or minus (-) value to thestandard torque.
Torque variation ratio
A ratio of torque variation to the standard
torque.

Actual torque
Preload torque measurement of an actual ballscrew.
Mean actual torqueAn arithmetic mean of the maximum andminimum values of the actual torquemeasured by running the nut back and forth
over the effective thread length.
Actual torque variation
A maximum variation of actual torquemeasured by running the nut back and forth
over the effective thread length. The value isdescribed as a plus (+) or minus (-) value tothe mean actual torque.
Actual torque variation ratio
A ratio of actual torque variation to mean
actual torque.

■―Measuring―conditions

Rotational speed for measurement: 100 min
Viscosity of lubricant: ISO VG100

Application example● Typical mounting
method● Medium to high speed
range● Medium accuracy tohigh accuracy

Figure 6
Characteristics of
preload torqueDistance between loading points(Buckling load: both ends fixed)

Fixed

Distance between supports(Critical speed: both ends fixed)
Fixed

Fixed

● Medium speed● High accuracy

Distance between loading points(Buckling load: both ends fixed)

Fixed

Distance between supports(Critical speed: one end fixed and the other end free)
Fixed
Free

● Low speed● Short shaft length● Medium accuracy-1

Distance between loading points(Buckling load: both ends fixed)■―Permissible―ratio―of―torque―variation

Table 18 Permissible ratio of torque variation

Effective thread length (mm)Reference
4000 or lesstorqueSlenderness ratio: 40 or less
Slenderness ratio: 60 or less(N·cm)
Accuracy grade
Accuracy grade
Over Or less
C0
C1
C2
C3
C4
C5
C0
C1
C2
C3
C4
C5
20
40 ±35% ±40% ±45% ±45% ±50% ±55% ±40% ±45% ±50% ±55% ±60% ±65%4060 ±25
±30
±35
±35
±40
±45
±33
±38
±45
±45
±50
±50
60
100 ±20
±25
±30
±30
±35
±35
±25
±30
±35
±35
±40
±40
100
250 ±15
±20
±25
±25
±30
±30
±20
±25
±30
±30
±35
±35
250
630 ±10
±15
±20
±20
±25
±25
±15
±20
±25
±25
±30
±30
630
1000
−
−
±15
±15
±20
±20
−
−
±20
±20
±25
±25
(Note) Slenderness ratio is the value obtained by dividing the thread length (mm) of the screw shaft by the nominal screw shaft diameter (mm).

F-8

Mounting method
Distance between supports(Critical speed: one end fixed and the other end supported)
Supported
Fixed

Supported

Distance between supports(Critical speed: one end fixed and the other end supported)
Supported
Fixed● Low to medium
speed range● Low accuracy tomedium accuracy

Distance between loading points(Buckling load: one end fixed and the other end supported)

F-9

Technical dataof ball screws

There are four basic methods of mounting a screw shaft as shown below. Since the method ofscrew shaft support has a direct relationship to permissible axial load and permissible rotational
speed at critical speed, sufficient consideration should be given, especially when the conditionsof use require high accuracy or demanding performance.

Effective thread length

Reference
torque0(-)

Reference
torqueFrictional
torque■―Mounting―and―supporting―methods―for―the―screw―shaft(+)

Mean actual
torqueForward

Screw shaft design

Starting torque
Negative actual torque variation
Actual torque
Torque variation
Actual torque(minimum)Technical dataof ball screws

Preload torque

106
2

3

1.5

8

1.5
2

106

6
5

1.5

8

4
3

6
5

106

6
5
4

4

6
5
4

3

1.5

3

2

105

2

3

1.5

8

2

105

6
5

1.5

8

4

105

6
5

3

8

4

2

6
5
4

3

1.5
24000N

2

104

3

1.5

8

105
8

1.5
104
8
6
5
4
3
2

8

1.5
103
8
6
5
4
3

●―――Permissible― axial― load― against― buckling―
load: P●―――B uckling― load― calculated― by― Euler's―
Formula: Pk

P = αPk (N) ……………………………… (1)Where,
Pk : Buckling load (N)α : Safety factor (α = 0.5)
It may be necessary to set the safety
factor at a larger value according to thedegree of safety required.

nπ EI
Pk =
(N) ………………………… (2)2ℓGenerally, the buckling load of a long column
can be calculated by Euler's Formula.
However, when the slenderness ratio/k (k:Second cross section) is 90 or less, use the
Rankine Forumla or the Tetmajer Formula.

Screw shaft diameter (mm)
ø80
ø63
ø50

2

2

104

6
5

1.5

8

4

104

6
5

3

8

4

2

6
5

3

1.5

ø40
ø32
ø25
ø20
ø15

ø10

4
103 2
2
10
1.5 2
3 4 5 6 7 8 9 103 1.5 2
3
Fixed-Fixed
Supported-Supported
Distance between loading points (mm)Fixed-Supported
Fixed-Free
Screw shaft supporting method

Figure 7 Diagram of permissible axial load
F-10

4

5 6 7

Example:― Selection― of― the―shaft diameter
How to determine anappropriate shaft diameter
when the screw shaft is
supported with the “FixedSupported” method and acompression load of 24000N(maximum axial load) is applied
to a distance of 2000 mm
between loading points:
1. Find out the intersecting
point where the permissible
axial compression loadon the scale of “FixedSupported” is 24000N andthe distance between loading
points is 2000 mm as shownby a thick line in Figure 7.
2. T h e n , s e l e c t a s h a f t
diameter of 40 mm or more,
represented by one of the
diagonal lines located above
the intersecting point.

2

Where,
Pk : Load at which buckling starts (N)ℓ : Distance between loading points (mm)52
E : Young’s modulus (2.06 X 10 N/mm )I : Minimum secondary moment of the4screw shaft root cross section (mm )
I=

π 4
d
64

d : Screw shaft root diameter (mm)Refer to dimension tables.
n : Coefficient to be determined by the
supporting method of the ball screw
Supported-Supported n = 1
Fixed-Supported n = 2
Fixed-Fixed n = 4
Fixed-Free n = 0.25■―Permissible―rotational―speed

The permissible rotational speed of ballscrews is expressed by a DmN value whichindicates the upper limit of the operating
speed of recirculating balls in the nut and thecritical speed of the rotary shaft.
The optimum shaft diameters for various
rotational speeds are shown in Figure 8.
(1) The diagonal line indicates the rotational
speed determined by the critical speed.
Please refer to the scale that corresponds tothe correct method of screw shaft support.
(2) The lines parallel to to the line representing
the distance between supports indicate
the limit of the permissible rotational speed
obtained from the DmN value. Pleaserefer to the scale that corresponds to the“Supported-Supported” method of screw
shaft support.
(3) Th e l i n e s p e rp e n d i cu l a r to th e l i n e
representing the distance between
supports indicate the screw shaft lengths
that can be manufactured by standard
processes as KURODA. (See Table 6 on
page F-3.)●―DmN―value◦ GR, DR, GE/GG, GP, DP, and HG series
DmN ≤ 70000 ………………………… (3)◦ GY and GW series
DmN ≤ 50000 ………………………… (3)◦ FR and FE/FG series
DmN ≤ 135000
Where,
Dm: Screw shaft diameter (mm) + A (mm)-1
N : Maximum rotational speed (min )N (max) ≤ 5000
Ball diameter
0.80001.00001.20001.58752.00002.38122.7780

A
0.24
0.30
0.30
0.30
0.40
0.60
0.60

Ball diameter
3.17503.96884.76256.35007.14387.93759.5250

A
0.80
0.80
1.00
1.80
2.00
2.00
2.40

Note) Consult KURODA if the number of
revolutions on your application exceeds
the DmN value above or N (max) 5000.
F-11

Technical dataof ball screws

A diagram of permissible axial load forselecting the minimum shaft diameter for theaxial load is shown below.
(1) The diagonal line indicates the permissible
axial load determined by the buckling of
the screw shaft. Please refer to the scalethat corresponds to the correct method ofscrew shaft support.
(2) The lines parallel to the line representing
the distance between supports indicate
the permissible tensile/compression load.
Please refer to the Supported-Supported
scale.
(3) Th e l i n e s p e rp en d icu la r to th e lin e
representing the distance between
supports indicate the screw shaft lengths
that can be manufactured by standard
processes as KURODA. (See Table 6 on
page F-3.)

Permissible axial load (N)Technical dataof ball screws■―Permissible―axial―loadNc = fa

60λ
2
2 πℓ

EI × 10−1(min )
γA

Resonance phenomenon arising from therotational speed of a ball screw and thecharacteristic frequency of the screw shaft
is caused by the unbalance of deflection by
the empty weight of the shaft at the distance“ℓ” between supports of the rotation systemand the critical speed corresponding to
the characteristic frequency increases theamplitude of the vibration.
When the ball screw is used, the nut
serves as a mobile bearing, and therefore,
the distance “ℓ” between supports always
changes and the shaft deflection changes
as well. Since the critical speed shown
in Formula (4) is inconstant, consider thepermissible rotational speed to assure safety.

3……… (4)

Where,ℓ : Distance between supports (mm)fa : Safety factor (0.8)
52
E : Young’s modulus (2.06 X 10 N/mm )I : Minimum secondary moment of the4screw shaft root cross section (mm )
π 4
d
I=
64
d : Screw shaft root diameter (mm)Refer to dimension tables.
-63
γ : Specific gravity (7.8 X 10 kg/mm )A : Sectional area of the screw shaft root2
diameter (mm )
π 2
d
A=
4

E x a m p l e ― 1 : ― D e t e r m i n i n g ― t h e―permissible rotational speed
How to determine permissible
rotational speed when the screw
shaft is supported with the “FixedSupported” method, the screw shaft
diameter is 20 mm and the distance
between supports is 1500 mm:
1. The vertical dotted line in Figure 8
shows that the distance between
supports is 1500 mm. Find the pointof intersection with the diagonalline representing the critical speedof a screw shaft with a diameter of
20 mm.
2. The scale for the “SupportedSupported” method of screw shaft
support indicates that, in this case,the permissible rotational speed is-11076 min .

λ : Coefficient to be determined by themethod of ball screw support
Supported-Supported λ = πFixed-Supported
λ = 3.927
Fixed-Fixed
λ = 4.730
Fixed-Free
λ = 1.875
3

ø10

2

5

1.5

4

103
8

5

6
5
4

4

3

2

2
1.5
102
8
6
5
4
3

3

1.5
103
8
6
5
4
3
2
1.5

2
1.5

102
8

10
8

6
5

5
4

3

3

2

2
1.5

Screw shaft diameter (mm)

ø15
ø20
ø25
ø32
ø40
ø50

1.5

ø63

103

ø80

8

ø100

103

1070 6
8 min-1 5

6
5
4
3
2
1.5
102

4
3
2
1.5
10

2

8

8

6
5

6

4

5

3

4

2
3
102 1.5 2
Fixed-Fixed
Supported-Supported
Fixed-Free
Fixed-Supported
Screw shaft supporting method

34

5 6 7 8 9103

1.5

2

3

4

5

Distance between supports (mm)Figure 8 Diagram of the permissible rotational speed
F-12

Example― 2:― How― to― determine― an―appropriate shaft diameter
How to determine an appropriate
shaft diameter that can meet amaximum rotational speed “1000-1min ” when the screw shaft is
supported with the “Fixed-Fixed”
method and the distance between
supports is 2000 mm:
1. The thick vertical line in Figure 8
shows that the distance between
supports is 2000 mm. Find thepoint of intersection with thehorizontal line representing thepermissible rotational speed “1000-1min ”on scale for the “Fixed-Fixed”
method of screw shaft support.
2. Shaft diameters represented by thelines above the intersecting point
have a permissible rotational speed-1of “1000 min ” or more. In thiscase, a shaft diameter of 25 mm isfound to be sufficient.

Service life calculation■―Service―life―of―ball―screws

The service life of a ball screw is defined asa total number of revolutions with which thescrew can perform proper operation withoutcausing operation-affecting wear (flaking) to
the thread groove and/or balls. The flaking
is caused by metal fatigue due to constantstress. The service life of a ball screw isdetermined by the basic dynamic load rating.

■―Service―life

The service life of a ball screw is calculatedby the following formula:

( )

6

Lh =

( 60L10N ) P f (N)
h

m

6

1
3

The basic static load rating (C0) represents
an axial load at at certain amount of staticload in which the sum of the permanent
deformities of the steel balls and the thread
groove surface equal to 0.01 percent of thesteel ball diameter.
In most cases, the permanent deformities will
not cause operational issues. However, whenhigh accuracy or very smooth operation are
required, it is recommended that a ball screw
having a C0 value notably larger than thestatic load be selected. For basic static load
ratings, refer to the dimension tables listed inthis calatog.

3

10C(hours) …………… (5)60Nm Pmfw

Where,
Lh : Service life (hours)
C : Basic dynamic load rating (N)Refer to dimension tables.
Pm: Average axial load (N)-1
Nm: Average rotational speed (mm )fw : Load factor (coefficient by operating
condition)
Smooth operation without concussive
impactfw = 1.0 to 1.2
Normal operation
fw = 1.2 to 1.5
Operation associated with concussive
impact or vibration
fw = 1.5 to 2.0
The basic dynamic load rating that satisfies
the intended service life is obtained from thefollowing formula:
C=●―Basic―static―load―rating:―C0m W

If a ball screw is selected using overly
conservative service life values, the size andcost of the resulting ball screw may increase
unnecessarily. Some case examples ofstandard life requirements are given below forreference.
Machine tools
20000 hours
Industrial machinery
10000 hours
Automated control equipment 15000 hours
Measuring instruments
15000 hours●―Basic―dynamic―load―rating:―CThe basic dynamic load rating (C) is an axial
load in which when a certain number ofball screws are run for 1 million revolutions(106 revolutions) and 90% of that group ofball screws does not experience operationaffecting wear (flaking). For basic dynamic
load ratings, refer to the dimension tables
listed in this calatog.

●―――Average―axial―load―“Pm”―and―average―
rotational―speed―“Nm”
To select a suitable ball screw, determine
the following values. It may be difficult toaccurately predict these operating conditions,but it is advisable to gather accurate
values because the service life is inversely
proportional to the load value multiplied by apower of three. Accurate values will result in agreater selection of suitable ball screws.

(t1 + t2 + t3 = 100%)
Axial load

Rotational speed Operating time ratio

P1N (maximum)N1 min−1

P2N (normal)

N2 min−1t2 %

P3N (minimum)N3 min

−1

t3 %

t1 %

F-13

Technical dataof ball screws

2

Permissible rotational speed (mm-1)

Technical dataof ball screws●―Critical―speed:―Nc

(

3

3

3

)

P1 N1t1 + P2 N2t2 + P3 N3t3 13(N) …(6)N1t1 + N2t2 + N3t3
N1t1 + N2t2 + N3t3
-1(min )……………(7)Nm =t1 + t2 + t3
Pm =When the difference between the maximum
axial load (P1) and the minimum axial load(P 3) is small, or when the load exhibits
linear change, an approximate value can becalculated from the following formula:Pm ≈■―Hardness―and―service―life

2P1 + P3
(N)………………………(8)3load rating (C’) and the basic static load
rating (C0’) are calculated with the following
formulas, assuming that the respective
hardness factors are (f H) and (f H’).

When special materials for corrosion
resistance, etc. are used, the thread groove
cannot be hardened to HRC58-62. In suchcases, the basic dynamic load rating andthe basic static load rating decrease inproportion to the decreased hardness. Whenthe hardness value is low, the basic dynamic

C′ = fHC (N) ……………………… (10)C0′ = fH′C0 (N) ……………………… (11)Table―19――Hardness―factors
Hardness HRC 58 or above
1.0
fH
fH′
1.0

56
0.88
0.83

54
0.72
0.61

■―Temperature―and―service―life

52
0.58
0.45

When an operating a ball screw made ofstandard material (See Table 1 on pageA-6) at a constant temperature of 100°C or
above or when operating it at a extremely
high temperature for a short period of time,
the composition of the material changes;
thus, the basic dynamic load rating andthe basic static load rating decrease ast h e t e m p e r a t u r e i n c r e a s e s . H o w eve r,t e m p e r a t u r e s o f u p t o 10 0 ° C w i l l n o t

50
0.47
0.32

F-14

100 or below
1.0
1.0

125
0.95
0.93

150
0.90
0.85

30
0.16
0.07

20
0.10
0.03

10
0.07
0.02

adversely affect operation. When the ballscrew operates at a temperature at 100°C
or above, the basic dynamic load rating(C’’) and the basic static load rating (C 0 ’’)
are calculated by the following formulas,
assuming that the respective temperaturefactors are (f t) and (f t’).
C″ = ftC (N) ……………………… (12)C0″ = ft′C0 (N) ……………………… (13)Table 20 Temperature factors
Temperature (°C)
ft
ft′

40
0.27
0.14

175
0.85
0.78

200
0.75
0.65

Ball screw design suitability
In order to work out an optimum design for machines, it is necessary to examine the rigidity of
the feed screw system, the positioning accuracy and the driving torque in due consideration of
the required function, performance and cost.

■ Rigidity of the feed screw system

To improve the positioning accuracy andresponsiveness of precision machines andequipment when they are controlled, it isnecessary to take into consideration therigidity of each component of the feed screw
system. The rigidity (K) of the feed screw
system is calculated by the following formula:P(N/µm) ……………………… (14)δWhere,
P : Axial load applied to the feed screw
system (N)δ : Axial elastic deformation of the feedscrew system (μm)
The relationship between the rigidity of thefeed screw system and that of each component
is as follows:
1
1
1
1
1
=
+
+
+
………… (15)
K
Kℓ
Kn
Kb
Kh
K=

Where,
Kℓ : Rigidity of the screw shaft to tension andcompression
Kn : Rigidity of the nut
Kb : Rigidity of the support bearing
Kh : Rigidity of the nut mounting portion andthe bearing mounting portion●―――Tension―and―compression―strength―of―the―screw shaft: Kℓ
Kℓ =P(N/µm) ……………………… (16)δℓWhere,
P : Axial load (N)δℓ : Amount of expansion or contraction of
the screw shaft (μm)
When an external axial load is applied to thescrew shaft, the axial expansion and contraction
is calculated by the following formulas. The
axial expansion and contraction come out
directly as the backlash of the ball screw.

1. When the supporting method is “Fixed-Free”
Fixed

Free

ℓ

δℓ =

4Pℓ
3
(17)
2 ×10 (µm) …………………
Eπd

Where,
P : Axial load (N)52
E : Young’s modulus (2.06 X 10 N/mm )d : Screw shaft root diameter (mm)ℓ : Distance between loading points (mm)2. When the supporting method is “Fixed-Fixed”
Fixed

Fixed

ℓ

ℓ′
L

δℓ =

4Pℓℓ′
3
……………… (18)
2 ×10 (µm)
Eπd L

Where,
P : Axial load (N)52
E : Young’s modulus (2.06 X 10 N/mm )d : Screw shaft root diameter (mm)ℓ, ℓʹ: Distance between loading points (mm)
L : Distance between supports (mm)The maximum value is obtained fromL
Formula (18) when ℓ = ℓʹ =
.
2
PL
3
δℓ =
2 ×10
Eπd

(

)

Therefore, the maximum expansion andcontraction of the screw shaft supportedwith the both ends fixed becomes 1/4 ofthose using the “Fixed-Free” method ofscrew shaft support.

F-15

Technical dataof ball screws

Technical dataof ball screws

In the case of machine tools, the maximum
load (P 1) is a “load applied at the time ofheaviest cutting”. The normal load (P2) is a“load applied during general cutting”. The
minimum load (P3) is a “load applied at thetime of rapid feeding of the cutting tool before
starting cutting and at the time of quick
return after completion of cutting”. Once theabove-mentioned values are determined,
the average axial load (Pm) and the averagerotational speed (Nm) can be obtained fromthe following formulas:

2.6
sin α

( QD ×10 ) K (µm) …… (19)
2

1
−2 3

b

Q=

P
Z sin αP : Axial load (N)Z : Number of steel balls
Theoretical rigidity (K NS) obtained from theamount of elastic deformation when an axial
load equivalent to 30% of the basic dynamic
load rating (C) is shown in the dimension
table for each of the product series.
Rigidity (K nS) corresponding to an arbitrary
axial load (P) is calculated by the following
formula:
KnS = KNS( ) (N/µm) …………… (20)
P
0.3C

1
3

Where,
C : Basic dynamic load rating (N)P : Axial load (N)(δ nS) in Formula (19) is calculated by thefollowing formula using the rigidity (KNS) of thesingle nut and the basic dynamic load rating (C).
(0.3C) PδnS =(µm) ……………… (21)
KNS
1
3

2
3

Where,
KNS: Theoretical rigidity of the single nut (N/μm)
Refer to the content for each series.
C : Basic dynamic load rating (N)P : Axial load (N)F-16

Knw = KNW

( )

PL 13
(N/µm) …………… (22)1
15 C

Where,PL : Preload (N)C : Basic dynamic load rating (N)δnw1

Double nut preload effect
Nut B Fixed pin Nut A
PL

PL

Px
P0

P0′

PL

Deformation δ
δnw0
δnw0
Nut B
Nut A

Figure 10 Preload diagram

Proper ball screw preload

T h e a x i a l e l a st i c d ef o r m at i o n (δ n w 0 ) i s
proportional to a value obtained by raisingt he a x ial l oad (P) to t wo - t hirds p ower
according to the Hertz’s law of point contact.
Therefore, deformation caused by preloadingis:δnw0 = C·PL
Deformation caused by an external loadwhen the preload applied to one nut iscompletely released is:2δnw0 = C·Px
From the above two equations,
PX 23 2δnw0
=
=2
PL
δnw0
Therefore, the released preload is:
2
3

2
3

PL0

P0+PL0P0

Figure 9 Double nut preload effect
In Figures 9 and 10, Nuts A and B undergo
an elastic deformation of (δ nw0) by preload(PL) respectively. When external load (P0) is
applied to Nut A, the elastic deformation of
Nuts A and B is:δnwA = δnw0 + δnw1
δnwB = δnw0 - δnw1

Classification―of―preload
Light
preload( )Normalpreload1
20 C or1
1
20 to 15C

less

MediumpreloadHeavy
preload

C

more

1
1
15 to 101
10 C or

C: Basic dynamic load rating (N)Elastic― displacement― curve― of― the―preloaded nut

Fi g ure 11 sh ow s e last i c di sp lac e m e nt
curves of a single nut (non-preloaded) anda preloaded nut. Where an axial load (PX),
which is three times as large as the preload(P L), is applied, the elastic displacementof the preloaded nut is just one half of theelastic displacement of the single nut (nonpreloaded).
tnu ed)
gle loadni
S preParallel
n(no

2δnw0

δnw0

a

PL

ut
dn
c

ade

lo
Pre

b
Px ≈ 3PL
Axial load P

Figure―11――Elastic―deformation―curve―of―the―nut

PX = 2.8PL ≈ 3PL …………………… (23)
Where,
Px: Released preload (N)(External axial load when preload applied
to one nut returns to zero)
PL: Preload (N)F-17

Technical dataof ball screws

As shown in equation (23), the preload
ef fect is about 3 times as much as thepreload amount. Generally, therefore, thepreload amount is set at 1/3 of the maximum
axial load. On the other hand, taking into
consideration the life and efficiency, thepreload amount is usually set at 1/20 to 1/10of the basic dynamic load rating.

Preload

PL0

Backlash―and―preload

The backlash of a ball screw is the sum of theaxial clearance and the elastic deformation
caused by the axial load at the contact pointof the steel balls with the thread groove. The
axial elastic deformation can be reduced to agreat extent by setting a proper preload andthus, the rigidity can be increased.

n
tio
ma B
for utDe of N

Where,
α : Contact angle of steel balls with thethread groove (45°)
Db: Steel ball diameter (mm)K : Accuracy and structure coefficient(1.4-1.6)
Q : Load per steel ball (N)The load applied to Nuts A and B is:
PA = PL + P0 - P0′ = P0 + PL0
PB = PL - P0′ = PL0
Therefore, an amount of (P0’) of the externalload (P 0) is offset because the deformationof Nut B decreases. As a result, the elastic
deformation of Nut A is reduced. This effectwill continue until (δ nwB) is zeroed, namely
until the elastic deformation caused by theexternal load becomes (δnw0) and the preload
applied to Nut B is completely released.

Elastic deformation δnwδns =The dimension table for each product series
gives theoretical rigidity (KNW) obtained fromthe amount of elastic deformation that will
occur when a preload of 1/15 of the basic
dynamic load rating (C) is applied to the nut
and an axial load of about 3 times or less ofthe preload is applied. These values are ofpractical use, because they were calculatedon the basis of the results of the rigidity test
including the nut rigidity test. Rigidity (K nw)
corresponding to an arbitrary preload can beobtained from the following formula:Defof orm
Nu atit A onWhen a ball screw receives an axial load,
the steel balls and the thread groove will be
deformed. The relationship between the axial
load (P) and the axial elastic deformation (δns)
is calculated by the following formula:

Rigidity of the preloaded nut: Knw

Axial load P →Technical dataof ball screws●―Rigidity―of―the―nut:―Kn
Rigidit y of the single nut (nonpreloaded): Kns

Preloading is to be applied, in general, to
two nuts in tension (tension preloading) or incompression (compression preloading) usingbolts.
K U R O D A’ s b a l l s c r e w s u s e t e n s i o npreloading unless otherwise specified.

● Preloaded with spacer
In this method, preload is adjusted by the
thickness of a spacer inser ted between
the two nuts. Both tension preloading andcompression preloading are available.

Figure 16 Preloaded with spacer (I)Screw shaft

Figure 12 Tension preloading
Direction of compression Direction of compression
Spacer
Nut B
Nut A

Screw shaft

Figure 13 Compression preloading● Preloaded with pin (standard method of
KURODA)This is the simplest and most ef fective
tension preloading method. The required
preload is attained and kept by inserting a pin
between the two nuts.

Figure 17 Preloaded with spacer (II)Integral nut preloading method

In this method, a slightly offset lead at thecenter of a nut generates preload in the nut.
Direction of tension

Direction of tensionℓ + ΔℓScrew shaftℓFigure 18 Integral nut preloading method

Single nut preloading method

In this method, a nut is preloaded by putting
oversized steel balls between the thread
groove of the screw shaft and that of the nut.
Nut

Figure 14 Preloaded with pin (I)Screw shaft

Figure 19 Single nut preloading method

Figure 15 Preloaded with pin (II)F-18

The rigidity of a bearing to which preload(PL) is applied is calculated with the following
formulas:● Rigidity of the ball bearing
Kb =Direction of tension Direction of tension
Fixed pin
Nut B
Nut A

Screw shaft
Direction of tension Direction of tension
SpacerNut B
Nut A●―Rigidity―of―the―support―bearing:―Kb

2.83PL
(N/µm) ………………… (24)δbWhere,PL : Preload (N)δb : Axial elastic deformation to preload (μm)
Axial elastic deformation of the angular ballbearing is:22Q 13(µm) ……………… (25)δb =sin α Db
P
Q=
Z sin α
Axial elastic deformation of the thrust ballbearing is:2Q 13(µm) ………………… (26)δb = 2.4
Db
P
Q=
Z
Where,
δb : Axial elastic deformation (μm)α : Contact angle
Db: Steel ball diameter (mm)Q : Load per steel ball (N)Z : Number of steel balls
P : Axial load (N)

( )

( )

● Rigidity of the roller bearing
Kb =2.16PL
(N/µm)
δb……………… (27)

Where,PL : Preload (N)δb : Axial elastic deformation to preload (μm)
Axial elastic deformation of the tapered
roller bearing is:
0.9
0.6 Q
· 0.8 (µm) ……………… (28)δb =sin α ℓP
Q=
Z sin αWhere,
δb : Axial elastic deformation (μm)α : Contact angle
Q : Load per roller (N)Z : Number of rollers
P : Axial load (N)ℓ : Effective contact length of the roller (mm)●―――Rigidity―of― the― nut― mounting― portion―and the bearing mounting portion: Kh
In designing these portions, pay due regard
to the thickness and the distance from themounting surface to the ball screw shaft
center, so that the rigidity of the nut bracket
and the bearing box may be improved. Whenthe distortion due to tension of the set bolt
is not negligible, use the mounting method
shown in Figure 17 on page F-18.

●―Torsional―rigidity―of―the―screw―shaft

The screw shaft is twisted around the axial
line by the torsional moment (driving torque),resulting in rotational strain. The torsional
deformation can be calculated as the axial
deformation of the ball screw by the following
formulas:L…………………………… (29)
2π
32T
θ=
…………………………… (30)4πd G
Where,
δT : Axial deformation caused by torsion (cm)ℓ : Distance between working points (cm)
θ : Angle of torsion (rad/cm)
L : Lead of the ball screw (cm)
T : Torsional moment (N·cm)
d : Root diameter of the screw shaft (cm)52
G : Modulus of rigidity (83 X 10 N/cm )δT = ℓθIf the angle of torsion for the driving shaft isexcessively large, defections on the partsof the driving mechanism may be caused
and result in torsional vibration of the shaft
system. For ordinary driving shafts, the angleof torsion due to the maximum operating
torsional moment should be set within 4.36 X-5
10 (rad/cm).

ℓFigure 20

F-19

Technical dataof ball screws

Technical dataof ball screws

Double nut preloading methods

This paragraph deals with how to select the accuracy grade, how to determine the cumulative
specified lead, and how to take effective measures against thermal strain, which will exert agreat influence upon the positioning accuracy.

●―――Selection― guide― for― the― accuracy―
grade classified according to thetype of the machine
Select the accuracy grade of the ball screw
suited for the required positioning accuracy
from Tables 2 and 3 on page F-3. KURODA
recommends that you select the accuracy
grade in accordance with the following table.

Table―21―――E― xamples― of― the― accuracy― grade―of the ball screw recommendable
according to the type of the machine
Accuracy
grade
X, Y C1 to C3
Machining centers
Milling machines
Z C2 to C5
X C1 to C3
LathesZ C3 to C5
X C0 to C2
NC machine
Grinding machines
Z C1 to C3
tools
X, Y C1 to C3
Electric dischargemachines
Z C2 to C5
Punching machines
C3 to C5
Wood working machines
C5 to C7
(NC routers)
Cartesian coordinates typeC1 to C5
(assembly)
Industrial
Vertical revolute typerobots
C2 to C5
(assembly)
SCARA type (assembly)
C3 to C5
Exposure system
C0 to C1
Drawing system
Etching equipment
C3 to C7
Semiconductor Ion implanting equipment
manufacturing Wire bonders
C1 to C2equipment
Die bonders
Wafer probers
C0 to C2
Electrical parts charging
C2 to C7
apparatus, Insert machines
Electronic color separating
C0 to C2
apparatus
Printing
equipment
Electronic composing
C1 to C3
machines
Color graphic printers
C1 to C3Business
XY plotters
equipment
C1 to C3
Auto drawing machines
Type of the machine

F-20●―――Determining―the―cumulative―specified―lead
In most cases, the lead is the same as
the nominal lead, but there are instancesin which the nominal designation isadjusted to account for expansion due totemperature increase during operation or
the expansion or contraction of the screw
shaft due to the external load. In such cases,
inform KURODA of the target value of the
cumulative lead. The typical target values of
the cumulative lead classified according to
the type of the machine are shown in Table
22 below. To correct the expansion, a tensile
load may sometimes be applied to the screw
shaft when mounting.

Table 22 Target values of the cumulative
lead classified according to themachine type
(Unit: mm)
Machine type
NC lathes
Machining centers

Axis
X
Z
X, Y

Target value of the
cumulative lead(per meter)-0.02 to -0.05-0.02 to -0.03-0.03 to -0.04●―――Measures―to―be―taken―for―thermal―
displacement
As the ball screw is constructed so that its
rolling motion involves a slight sliding motion,
it inevitably suffers a thermal strain due torising temperature. The temperature increaseis closely related to operating conditions. The
expansion of the thermal displacement canbe calculated by the following formula:Δℓ = ρtℓ (mm) ………………………… (31)Where,
Δℓ : Axial thermal displacement (mm)
ρ : Coefficient of thermal expansion-6-1(11.7 X 10 °C )t : Temperature increase of the screw shaft(°C)ℓ : Effective thread length (mm)Driving torque
Frictional characteristics of the ball screw
and selection of the drive motor■―Friction―and―efficiency

The efficiency “η” of a ball screw obtainedby the analysis of a mechanical model of thescrew can be calculated as follows, assumingthat the coefficient of friction = μ and thescrew lead angle = β.
● When converting the rotational force into
the axial force (normal operation):
1 - μ tan β…………………… (32)
1 + μ / tan β● When converting the axial force into therotational force (reverse operation):η=

1 - μ / tan β…………………… (33)η′ =1 + μ tan β■―Load―torque

The load torque (constant-speed driving
torque) required for designing a driving unit
(motor, etc.) can be calculated as follows.

●―Normal―operation

When converting the rotational force into theaxial force
PL(N·cm) …………………… (34)2πηWhere,
T : Load torque (N·cm)
P : Axial external load (N)L : Lead of the ball screw (cm)
η : Efficiency of the ball screw (0.9)
T=●―Friction―torque―caused―by―preload

A torque produced by preloading. As theexternal load increases, the preload applied
to the preloaded nut is gradually released
and consequently, the friction torque caused
by preload is also reduced.
Without load:
PL L(N·cm) …………………… (36)2π1−
K = 0.05 (tanβ) 2

TP = K

Where,PL : Preload (N)L : Lead of the ball screw (cm)
K : Coefficient of internal friction
β : Lead angle-1β ≈ tan( πDL )

D : Screw shaft diameter (cm)■―Selection―of―the―drive―motor

S e l e c t a dr i ve m oto r w hi c h m e et s t hefollowing conditions.
1. The motor should be able to sufficiently
bear the load torque applied to its output
shaft.
2. The motor should be able to start andstop at the required pulse speed when the
moment of inertia is applied to its output
shaft.
3. The required acceleration constant anddeceleration constant can be obtained
when the moment of inertia is applied tothe output shaft of the motor.
Table

F

●―Reverse―operation

When converting the axial force into therotational force
2πT(N) ………………………… (35)η′L
Where,
P : Axial external load (N)T : Load torque (N·cm)
L : Lead of the ball screw (cm)
η’ : Efficiency of the ball screw (0.9)
P=

Ball screw J3

WWorkpiece
Gear J2
Z2
Pinion J1
Z1

Motor

Figure 21

F-21

Technical dataof ball screws

Technical dataof ball screws■―Notes―for―positioning―accuracyA torque required for driving at a constant
speed against an external load
T1 =PL
(3P −P) Z
+T
( 2πη
)Z
3P
L

1

P

L

2

(N·cm) … (37)
Where, P ≤ 3PL
T1 : Driving torque at a constant speed(N·cm)
P : Axial external load (N)P = F + µMg
F : Anti-thrust repulsive force by cutting force(N)
M : Weight of the table and work (kg)μ : Coefficient of friction of the sliding surface
2
g : Acceleration of gravity (9.8 m/s )L : Lead of the ball screw (cm)
η : Mechanical efficiency of the motor
including the ball screw and the gear
TP: Friction torque caused by preload (N·cm)
Refer to Formula (36).
P : Preload (N)Z1 : Number of teeth of the pinion
Z2 : Number of teeth of the gear●―――Acceleration―torque―applied―to―the―output shaft of a motor
A torque required for accelerative driving
against an external load•

T2 = JMω = JM ×

2πN
-2
× 10
60t
(N·cm) … (38)

( ZZ ) (J + J + J + J )2

JM = J1 + J4 +

1

2

2

3

5

6

2

(kg·cm ) … (39)

Where,
T2 : Driving torque at the time of acceleration(N·m)•ω : Angular acceleration of the motor shaft
2(rad/s )N : Rotational speed of the motor shaft-1(min )
t : Acceleration time (s)JM : Moment of inertia applied to the motor
2(kg·cm )F-22

2

J1 : Moment of inertia of the pinion (kg·cm )2
J2 : Moment of inertia of the gear (kg·cm )J3 : Moment of inertia of the ball screw
2(kg·cm )J4 : Moment of inertia of the motor rotor
2(kg·cm )J5 : Moment of inertia of the moving object
2(kg·cm )2
J6 : Moment of inertia of the coupling (kg·cm )M : Mass of the table and work (kg)
L : Lead of the ball screw (cm)Moment of inertia of the cylinders such as
the ball screw and the gear
(Calculation of J1-J4 and J6)
J=

Guide for ball screw selection
When a ball screw is selected, a number of factors are examined from various points of view on
the basis of the above-mentioned basic subjects by a process of trial and error. Therefore, theprocedure cannot be categorically determined. An example of general procedures and main
subjects for examination regarding each item and reference pages are mentioned below:
Selection
procedures● Work and table mass ● Maximum feed rate ● Velocity diagram ● External load
Operatingconditions( )2

J5 = ML
2(kg·cm ) ……………… (41)2π●―――Total―torque―applied―to―the―output―
shaft of a motor
The total torque can be calculated by adding
the value of Formula (38) to that of Formula(37).
TM = T1 + T2 (N·cm) ………………… (42)
Where,
TM: Total torque applied to the output shaft ofthe motor (N·cm)
T1 : Driving torque at a constant speed(N·cm)
T2 : Driving torque at the time of acceleration(N·cm)
After provisionally selecting a motor, checkthe motor for the following three items. The
motor you select should satisfactorily meetthe respective values.
(1) Effective torque value(2) Acceleration constant(3) Over-load characteristics and tolerance tooverheat of the motor at the time of repetitive
starting and stopping● Maximum stroke ● Mounting condition (horizontal and vertical)● Duty (operation) cycle ● Operation coefficient ● Mounting and supporting method● Expected life ● Positioning accuracy ● Environmental conditions ● Lubrication

πγ 4
2D ℓ (kg·cm ) ……………… (40)32

Where,
D : Outside diameter of the cylinder (cm)ℓ : Length of the cylinder (cm)γ : Specific gravity of the material-33
γ = 7.8 X 10 (kg/cm )Subjects to be
examined(Selection of the lead)● Maximum feed rate ● Maximum rotational speed of the motor ● Positioning resolution
Lead● List of nominal screw shaft diameters and leads (B-3, C-3, D-3)
● Torque (F-21)(Designing and life calculation of the nut)

Number of
circuits● Average axial load and average rotational speed (F-13)● Service life estimation (F-13)● Permissible rotational speed (DmN value) (F-11)● Dimensions

Screw shaft● Screw shaft supporting method (F-9)● Permissible buckling load (F-10)● Permissible rotational speed (critical speed) (F-12)● Accuracy grade and manufacturable shaft length (F-3)(Designing of the screw shaft)(Design for accuracy)
Accuracy grade
and rigidity● Lead accuracy and axial clearance (F-3)● Countermeasures against thermal change (F-20)● Rigidity of feed screw system (F-15)

Lubrication anddust prevention● Lubrication and operating cautions (A-3, A-4)

Selection ofball screws

For the model number of ball screws, see A-10.

(Others)

F-23

Technical dataof ball screws

Technical dataof ball screws●―――C onstant― torque― applied― to― the―output shaft of a motorcalculated in the same manner as in the caseof lead 6 is:Pm = 2600 (N)-1
Nm = 419 (min )C = 26720 (N)Accordingly, a nut in suitable size with thesmallest diameter can be selected from page
C-41 as follows:●―Machine―tool<Specifications>● Mass of the work and the tableM = 1300 (kg)● Maximum stroke
Smax = 800 (mm)● Rapid traverse speed
Vmax = 12000 (mm/min)● Friction factor of the linear guide
μ = 0.02● Load condition
Classification
Rapid traverse speed
Light/medium cutting
Heavy cutting

Axial load
(N)
300
5000
9000

Feed speed Operating(mm/min) time rate (%)
12000
25
600
55
120
20

Work

According to the maximum rotational speedof the motor and the rapid traverse speedof the motor, the lead can be selected asfollows:
Vmax
L≥= 6 (mm)Nmax

2.―Nut―design

Examination of the necessary basic dynamic
load rating and the permissible rotational
speed (DmN value)<In the case of lead 6>
Load conditions
Classification
Rapid traverse speed
Light/medium cutting
Heavy cutting

Axial load
(N)
300
5000
9000

OperatingRotational-1
speed (min ) time rate (%)
2000
25
100
55
20
20

Calculating the axial average load (Pm) andthe average rotational speed (N m) from theload conditions (Formulas (6) and (7) on
page F-14) results in the following formulas:
Pm = 2600 (N)-1
Nm = 559 (min )To calculate the necessary basic dynamic
load rating (C), transformation formula (5)
F-24

Table

(Rigidity of the screw shaft) ℓ3
ℓ3/2
Fixed

● Positioning accuracy±0.04/800 (mm)● Expected service life
25000 (hours)-1● Drive motor
Nmax = 2000 (min )● Shaft-end supporting method
Fixed-Fixed

1. Lead (L)Cutting force

ℓ3/2
Fixed

Fixed

Distance between loading points(Buckling load: Fixed-Fixed) ℓ1
Distance between supports(Critical speed: Fixed-Fixed) ℓ2

shown on page F-13 is used assuming thatthe life (L h) is 25000 hours and operation
coefficient (f w) is 1.2, as shown below.
C=( 60L10N ) P f = 29420 (N)
n

m

6

1
3

m w

A nut in suitable size with the smallest
diameter can be selected from page C-43 as
follows:
Outside diameter 36, lead 6, and 2.5 turns with 3 circuits
Then, when the DmN value (Formula (3) on
page F-11) is sought to find the permissible
rotational speed, DmN = 36.8 X 2000 =
73600 is found as against the permissible
DmN ≤ 70000, showing that it exceeds thepermissible value. Consequently, this size is
not suitable. Therefore, increase the lead to 8,
make the maximum rotational speed lower,
and take another examination.
<In the case of lead 8>
Load conditions
Classification
Rapid traverse speed
Light/medium cutting
Heavy cutting

Axial load
(N)
300
5000
9000

OperatingRotational-1
speed (min ) time rate (%)
1500
25
75
55
15
20

The necessary basic dynamic load rating (C)Outside diameter 32, lead 8, and 2.5 turns with 2 circuits
T hen, D m N value is found to be D m N= 3 3 X 15 0 0 = 4 9 5 0 0, sh ow ing t hat it
satisfies the permissible value. Proceedwith the following examination based on
this size.

3. Screw shaft design

Examining the overall screw shaft length (ℓ),
permissible axial load (P0), and critical speed(Nc)
Assuming that: ℓ = Maximum stroke + nut
length + allowance + size of both shaft ends
= 800 + 145 + 80 + 175 = 1200
To o b t a i n t h e p e r m i s s i b l e a x i a l l o a d ,examine the buckling load assuming that the
distance between loading points ℓ 1 = 930.
The following formula can be obtained by
Formulas (1) and (2) on pages F-10 and F-11:
P0 = 141400 (N)This can fully satisfy the operating conditions.
The critical speed is calculated from Formula-1(4) on page F-12 as follows: Nc = 6490 (min )Where, the distance between load working
points ℓ 2 = 940.
This can fully satisfy the operating conditions.

Rigidity of the nut (Knw)
Rigidity to an arbitrar y preload amountassuming that 1/3 of the
maximum axial load is preload (PL) can beobtained using Formula (22) on page F-16.
PL 13
Knw = KNW 1
15 C
1
3000
3
= 590 1
= 660 (N/µm)
15 × 32300
As a result of the above-mentioned examination,
the nut model number GR3208ED-DALR isselected from page C-41.

(

( )

)

5. Accuracy

Select C5 (ec = ±0.025) from the positioning
accuracy ±0.04/800 and the permissible
va l u e s f o r va r i at i o n (e c ) o n p a g e F- 3 ,assuming that the directivity of cumulative
mean lead can be corrected on the control
side.

6. Result of ball screw selection

The model number of the selected ball screw is
GR3208ED-DALR-1200X0985-C5S on pageC-41.

4. Ball screw rigidity

Rigidity of the screw shaft (Kℓ)
Calculate at the position ℓ3/2 where the axial
deflection is maximized, assuming that the
distance between bearing end faces ℓ 3 =1005.
T h e f o l l o w i n g f o r m u l a i s o b t a i n e d by
Formulas (16) and (18) on page F-15.
2
Eπd
-3
Kℓ =
× 10 = 50 (N/µm)ℓ3
52
E : Young’s modulus (2.06 X 10 N/mm )d : Screw shaft root diameter (mm)F-25Technical dataof ball screws

Technical dataof ball screws■―Example―of―ball―screw―selection

●―X-axis―of―Cartesian―robot―(horizontal―position)<Specifications>● Mass of the work and the tableM = 50 (kg)● Maximum stroke
Smax = 720 (mm)● Rapid traverse speed
Vmax = 1000 (mm/s)● Acceleration/deceleration constantt = 0.15 (S)● Positioning accuracy±0.1/720 (mm)● Repeat accuracy±0.01 (mm)● Expected life
Lh = 30000 (hours)● Friction factor of the linear guide
μ = 0.02-1● Drive motor
Nmax = 3000 (min )● Duty cycle model diagram
V
mm/s

240 mm (stroke)

Table

Coupling

Drive
motor

Distance between supports(Critical speed: Fixed-Supported) ℓ2

Distance between loading points(Buckling load: Fixed-Fixed) ℓ1

1000 mm/s

0.15 0.09 0.15 0.51
0.15 0.57 0.15 0.53
0.9
0.9 X 3 = 2.7
1.4
4.1 (1 cycle)

1. Lead (L)According to the maximum rotational speed
and the rapid traverse speed of the motor,
the lead can be selected as follows:
Vmax × 60
L≥= 20 (mm)Nmax

2.―Nut―design

Examination of the necessary basic dynamic
load rating and the permissible rotational
speed (DmN value)
Calculation of the axial load in each patternof operations:(a) At the time of acceleration
Vmax
-3
2
Acceleration (α) =× 10 = 6.67 (m/s )t
Axial load (Pa) = (Mα + μMg) = 343 (N)2(g: Gravitational acceleration 9.8 m/s )(b) At the time of a constant speed
Axial load (Pb) = μMg = 10 (N)(c) At the time of deceleration
Axial load (Pc) = (Mα - μMg) = 324 (N)
F-26

(

Work

720 mms

Operating time (s) during one cycle of eachpattern
Operation pattern
Operating time

Transformation formula (5) shown on page
F-13 is used assuming that the operation
coefficient f w = 1.2, as shown below.
60Lh0Nm 13
× Pm × fw = 3700 (N)C=
610
A ball screw in suitable size can be selectedfrom standard ball screw GE and GG series(page B-78, B-79) as follows:
Outside diameter 15, lead 20, and 1.5 turns with 1 circuit
When looking for a DmN value (Formula (3)on page F-11) as the permissible rotational
speed, DmN = 15.8 X 3000 = 47400 is foundas against the permissible DmN ≤ 70000,
showing that it satisfies the permissible
value. Proceed with the following examination
based on this size.

(a)
0.6

(b)
0.84

(c)
0.6

Total operating time
2.04

Load conditions at the time of lead 20
Operation pattern
(a)
(b)
(c)
Axial load
343N
10N
324N
−1
−1
−1
Rotational speed 1500 min 3000 min 1500 min
Operating time ratio
29.4%
41.2%
29.4%

Calculating the axial average load (Pm) andthe average rotational speed (N m) from theload conditions (Formulas (6) and (7) on
page F-14) results in the following formulas:
Pm = 249 (N)-1
Nm = 2118 (min )Calculation of the necessary basic dynamic
load rating (C)T h e n e t o p e r a t i o n l i f e ( L h 0 ) exc l u d i n g
downtime based on the expected life iscalculated as follows:
2.04
Lh0 = 30000= 14927 (hours)
4.1

( )

)

on the repeated positioning accuracy ±0.01.

5. Result of ball screw and support
unit selection
Provided that additional machining of standard
ball screw GG series with unfinished shaft ends
is performed, the following model number isselected from page B-78 and B-79:
GG1520AS-BALR-1100A
The model number of the suitable support
unit selected from page E-16 and E-17 is
BUK-12 .

3. Screw shaft design

Examining the overall screw shaft length (ℓ),
critical speed (Nc), and buckling load (Pk)ℓ = Maximum stroke + nut length +allowance + size of both shaft ends = 720 +
62 + 60 + 78 = 920 (mm)To o b t a i n t h e p e r m i s s i b l e a x i a l l o a d ,examine the buckling load assuming that the
distance between loading points ℓ 1 = 820.
The following formula can be obtained by
Formulas (1) and (2) on pages F-10 and F-11:
Pk = 7220 (N)This fully satisfies the operating condition.
Assuming that the distance bet ween
supports ℓ 2 = 790, the critical speed can beobtained by Formula (4) (Fixed-Supported)on page F-12 as follows:-1
Nc = 3024 (min )This satisfies the operating condition.

4. Accuracy

Examination of the accuracy grade and theaxial clearance
The accuracy grade that can satisfy the
positioning accuracy of ±0.1/ 750 mm isdetermined, from the permissible valueof the lead accuracy (page F-3), to be C5(cumulative mean lead error ±Ec = 0.035 andvariation ec = 0.025).
Axial clearance is set to 0.005 or less based
F-27

Technical dataof ball screws

Technical dataof ball screws■―Example―of―ball―screw―selection

V
mm/minTable

1300 (stroke)

0.5

4.7

(Downward)
0.5 5 0.5 4.7
21.4 (1 cycle)

0.5

5

1. Lead (L)According to the maximum rotational speed
and the rapid traverse speed of the motor,
the lead can be selected as follows:
Vmax
L≥
= 10
Nmax

2.―Nut―design

Examination of the necessary basic dynamic
load rating and the permissible rotational
speed (DmN value)
Calculation of the axial load in each patternof operations:(a) At the time of upward acceleration anddownward deceleration
Vmax
-3
2
Acceleration (α) =× 10 = 0.5 (m/s )t·60
Axial load (Pa) = (Mα + Mg) = 1030 (N)2(g: Gravitational acceleration 9.8 m/s )(b) At the time of a constant speed
Axial load (Pb) = Mg = 980 (N)(c) At the time of upward deceleration anddownward acceleration
Axial load (Pc) = (Mg - Mα) = 930 (N)()

3. Screw shaft design

15000 mm/min(Upward)

F-28

Work

shown on page F-13 is used assuming thatthe operation coefficient f w = 1.5, as shown
below.
60Lh0Nm 13
C=× Pm·fw = 14057 (N)610
A suitable nut size can be selected from rolledball screw GY series (page D-72 and D-73)
based on the repeat accuracy 0.5 as follows:
Outside diameter 25, lead 10, and 2.5 turns with 2 circuits
When looking for a DmN value (Formula (3)on page F-11) as the permissible rotational
speed, DmN = 26.8 X 1500 = 40200 is foundas against the permissible D mN ≤ 50000,
showing that it satisfies the permissible
value. Proceed with the following examination
based on this size.

Technical dataof ball screws<Specifications>● Mass of the work and the tableM = 100 (kg)● Maximum stroke
Smax = 1300 (mm)● Rapid traverse speed
Vmax = 15000 (mm/min)● Acceleration/deceleration constantt = 0.5 (S)● Repeat accuracy
0.5 (mm)● Expected life
Lh = 20000 (hours)● Friction factor of the linear guide
μ = 0.02-1● Drive motor
Nmax = 1500 (min )● Duty cycle model diagram

Distance between supports(Critical speed: Fixed-Supported) ℓ2●―Elevator―(vertical―position)

Distance between loading points(Buckling load: Fixed-Fixed) ℓ1

Technical dataof ball screws■―Example―of―ball―screw―selectionsOperating time (s) during one cycle of eachpattern (s)Operation pattern
Operating time

(a)
1

(b)
9.4

(c)
1

Total operating time
11.4

Load conditions at the time of lead 10
Operation pattern
Axial load
Rotational speed
Operating time ratio

(a)
(b)
(c)
1030N
980N
930N
−1
−1
−1
750 min1500 min
750 min
8.8 %82.4 %
8.8 %Calculating the axial average load (Pm) andthe average rotational speed (N m) from theload conditions (Formulas (6) and (7) on
page F-14) results in the following formulas:
Pm = 980 (N)-1
Nm = 1368 (min )Calculation of the necessary basic dynamic
load rating (C)T h e n e t o p e r a t i o n l i f e ( L h 0 ) exc l u d i n g
downtime based on the expected life iscalculated as follows:
11.4
Lh0 = Lh
= 10654 (hours)
21.4
As the operation accompanied by vibration
is anticipated, transformation formula (5)( )Examination of the overall screw shaft length(ℓ) and permissible axial load (Pk)ℓ = Maximum stroke + nut length + safety
stroke + size of both shaft ends
To obtain permissible axial load, examine
the buckling load, assuming that distance
bet ween load working points ℓ 1 = 1440.
The following formula can be obtained by
Formulas (1) and (2) (Fixed-Fixed) on pages
F-10 and F-11:
Pk = 16290 (N)This satisfies the operating condition.
Assuming that distance between supports δ2= 1420, the following formula can be obtainedby Formula (4) (Fixed-Supported) on page
F-12:
-1
Nc = 1520 (min )This satisfies the operating condition.

4. Result of Ball Screw Selection

Provided that additional machining of rolledball screw GY series is per formed, thefollowing model number is selected frompage D-72 and D-73:
GY2510ES-HULR-2000A

F-29

Date
Company name
Department

Ballscrew specification data sheet (Sample)

Contact personnel

Conditions of use

Mass (weight) of table
Maximum table speed
mm/secShaft rotation
Nut rotation
GreaseOil
Moving conditions
Lubrication
Mount method
Horizontal
VerticalOthers (Description:)
Mount/Support method Fixed-support
Fixed-fixed
Fixed-free
Support-support
No
Yes (strokemm)
Oscillation°C)
Clean room
VacuumOthers ()
Environmental conditions Temp. (Expected life
Ex.: 8 hours/day, 240 days/year, 5 years

Ballscrew specifications
Screw shaft diameter
Lead
Nut type

Thread direction
Nuber of circuits

Single nut

Operating conditions

Axial clearance
Accuracy grade
Double nut
Integral nut

Case A(when axial load and table speed can be classified into several patterns, such as
when using a pressing device)

Table speed2

Acceleration timesec

OthersType of slide guide
Name of motor
Quantity of screw shafts used
Change control

Rolling (model number:)

Downtime

sec

Deceleration timesec
SlidingEx.: One per head, Four per tableNo

Thread direction
Nuber of circuits

Single nut

Axial clearance
Accuracy grade
Double nut
Integral nut

Case A

Yes

Memo (Please draw a configuration diagram, etc.)(when only the speed changes, such as for transfer application, and when largely
impacted by inertial force)

Table speed
250

300

5

Acceleration time
0.3
sec

6

OthersType of slide guide
Name of motor
Quantity of screw shafts used
Change control

Rolling (model number:)
One per X-axis

No

300 mm

F-30

Request for
KURODA

Downtime10

sec

Deceleration time
0.3
sec
SlidingEx.: One per head, Four per table

Yes

Total
50 kg

Guide

Request for
KURODAmm

4

Memo (Please draw a configuration diagram, etc.) Stroke

Request for calculation of ball screw life

mm/secStroke3Support

Request for selection of ball screws
Contact personnel:

Thread length
Overall length

Case B(when axial load and table speed can be classified into several patterns, such as
when using a pressing device)1

4
6

Ballscrew specifications

2
mm

5

Mass (weight) of table
Maximum table speed
mm/sec
50kg
250
Shaft rotation
Nut rotation
GreaseOil
Moving conditions
Lubrication
Mount method
Horizontal
VerticalOthers (Description:)
Mount/Support method Fixed-support
Fixed-fixed
Fixed-free
Support-support
No
Yes (strokemm)
Oscillation°C)
Clean room
VacuumOthers ()
Environmental conditions Temp. ( 25
Expected life
20000 hours (including downtime) Ex.: 8 hours/day, 240 days/year, 5 years

No. of patterns Axial load Table speed Usage time

mm/secStroke3

TEL / FAX

Operating conditions

Case B1XYZ Industries, Co., Ltd.

Conditions of use

Screw shaft diameter
Lead
Nut type

Thread length
Overall length(when only the speed changes, such as for transfer application, and when largely
impacted by inertial force)

No. of patterns Axial load Table speed Usage time

Contact personnel

Date
Company name
Department

TEL / FAX

Technical dataof ball screws

Technical dataof ball screws

Ballscrew specification data sheet

Request for selection of ball screws
Contact personnel:

Ceiling
SupportBall screw Servo motor(Lead 5)

Floor
Request for calculation of ball screw life

F-31

Reference data

Reference data
Page

Table of standard tolerance grades and limit deviations
for holes――――――――――――――――――――――――

Appendix-2

Table of standard tolerance grades and limit deviations
for shafts― ――――――――――――――――――――――

Appendix-3

Dimensions of C-shaped snap rings――――――――――

Appendix-4

Dimensions of parallel keys and key grooves―――――

Appendix-5

Hardness conversion chart― ―――――――――――――

Appendix-6

Dimensions of the counterbore and internal thread forthe hexagon-headed bolt― ――――――――――――――

Appendix-7

Appendix-1

Appendix-2
Appendix-3

Tolerance grades for holes

Reference data

10
6
14
10
18
14
24
18
30
24
40
30
50
40
65
50
80
65
100
80
120
100
140
120
160
140
180
160
200
180
225
200
250
225
250

6
3
10
6
14
10
18
14
24
18
30
24
40
30
50
40
65
50
80
65
100
80
120
100
140
120
160
140
180
160
200
180
225
200
225

++ 98
78
++ 40
30

++ 78
60
++ 30
20

++ 75
92
++ 32
40

75
+ 61
+ 32
25

++ 61
50
++ 25
20

++ 50
39
++ 20
14

++ 73
92
89 ++112++ 40
50 ++ 40
50

++ 59
73
++ 32
40

59
+ 47
+ 32
25

++ 47
38
++ 25
20

++ 38
28
++ 20
14

75 ++106
89 ++ 134112++ 90
50 ++ 60
50 ++ 60
50
++ 60

++ 61
75
++ 40
50

++ 50
61
++ 32
40

50
+ 40
+ 32
25

++ 40
32
++ 25
20

++ 32
24
++ 20
14

+ 58
68
+ 36
+ 43
+ 68
+ 43
+ 79
+ 50
+ 79
+ 50

+ 208 + 245 + 305 + 125 + 148 + 185+ 145 + 145 + 145 + 85 + 85 + 85
+ 242 + 285 + 355 + 146 + 172 + 215+ 170 + 170 + 170 + 100 + 100 + 100+ 242 + 285 + 355 + 146 + 172 + 215+ 170 + 170 + 170 + 100 + 100 + 100

++ 49
58
++ 30
36

41
++ 49
25
++ 30

++ 33
41
++ 20
25

++ 27
33
++ 16
20

27
+ 22
+ 16
13

++ 22
18
++ 13
10

++ 18
12
++106

+ 174 + 207 + 260 + 107 + 126 + 159
208 + 120
245 + 120305 ++125+ 120
72 ++148
72 ++185
72+ 145 + 145 + 145 + 85 + 85 + 85++ 14690 ++ 106174 ++ 174
207 ++ 220
260 ++107
126 ++ 134
159++ 100120 ++ 100
120 ++ 100
120 ++ 60
72 ++ 60
72 ++ 6072

119 ++ 174
142 ++ 220
180++ 14680 ++10080 ++10080++100

98 ++ 142
117 ++ 149
++119
180
++ 65
80 ++ 65
80 ++ 65
80++ 77
93 ++ 12098 ++117149++ 50
65 ++ 50
65 ++ 50
65

93 ++120
+ 76
98
+ 50
40 + 50
40

++ 76
60
++ 40
30

++ 62
48
++ 40
30
77
+ 62
+ 50
40

++ 60
45
++ 30
20

++ 48
34
++ 30
20

++ 76
90
++ 30
36

64
++ 76
25
++ 30

++ 53
64
++ 20
25

++ 43
53
++ 16
20

43
+ 35
+ 16
13

++ 35
28
++ 13
10

++ 28
20
++106

+ 96 + 122+ 50 + 50+ 83 + 106+ 43 + 46+ 96 + 122+ 50 + 50+ 71 + 90
83 ++106+ 36
36+ 43 + 46

++ 60
71
++ 30
36

50
++ 60
25
++ 30

++ 41
50
++ 20
25

++ 34
41
++ 16
20

34
+ 28
+ 16
13

++ 28
22
++ 13
10

++ 22
16
++106

+ 44
+ 15

+ 39
+ 14
+ 44
+ 15

+ 34
39
+ 12
+ 14

++ 29
34
++ 10
12

25
++ 29
++109

++ 20
25
++ 79

++ 17
20
++ 67

17
+ 14
+ 65

++ 14
12
++ 54

++128
++ 42

+ 22
+ 250
0

++ 19
22
00

16
++ 19
00

++ 13
16
00

11
++ 13
00

++119
0

++ 98
00

++ 86
00

+ 35
+ 400
0

++ 30
35
00

25
++ 30
00

++ 21
25
00

++ 18
21
00

18
+ 15
0

++ 15
12
00

++ 12
10
00
±± 43

±± 65

++ 70
84 ± 5.5±900 ± 6.5 ± 10.570
+ 58
5.5 ± 7.5
±9
± 4.5
0

++ 58
48 ± 4.5 ± 7.5
±4
±6
00

++ 48
40
00

++ 74
87 ++ 120140 ± 9.5 ± 150000 ± 11 ± 17.5

62 ++ 120100++ 74
± 8 ± ±12.5
± 9.5
15
00
00

++ 52
84
62 ++100± 6.5
12.5± 8 ±± 10.5
00
00

++ 43
52
00

43
+ 36
0

++ 36
30
00

++ 30
25
00

+ 61
+ 115 + 185+ 29 0 + 46 0 + 72 0
± 14.5
+ 15
0
0

± 23

± 23

± 20

+ 54 + 87 + 140± 11 ± 17.5
+ 630 + 1000 + 1600
± 12.5 ± 20
0
0
0

++ 46
54
00

39
++ 46
00

++ 33
39
00

++ 27
33
00

27
+ 22
0

++ 22
18
00

++ 18
14
00

+ 54 + 25 + 40 + 63 + 100 + 160± 12.5
+ 14
0
0
0
0
0
+ 61
+ 115 + 185± 14.5+ 29 0 + 46 0 + 72 0
+ 15
0
0

+ 47
54
+ 12
+ 14

++ 40
47
++ 10
12

34
++ 40
++109

++ 28
34
++ 79

++ 24
28
++ 67

24
+ 20
+ 65

++ 20
16
++ 54

++ 16
12
++ 42

140
160
180
200
225
250

120
140
160
180
200
225

50

40

120

40

30

100

30

24

100

24

18

80

18

14

65

14

10

80

10

6

50

6

3

65

3

Or less-

Over

Range of standard
dimensions (mm)

- 30
- 60
- 40
- 76

- 30
- 48
- 40
- 62

- 40
- 92

- 32
- 75

- 25
- 61

- 20
- 50

- 14
- 39

e9

- 50 - 50- 89 - 112

- 40
- 73

- 32
- 59

- 25
- 47

- 20
- 38

- 14
- 28

e8

- 60 - 60 - 60
- 90 - 106 - 134

- 50
- 75

- 40
- 61

- 32
- 50

- 25
- 40

- 20
- 32

- 14
- 24

e7

- 170 - 170 - 100 - 100 - 100- 242 - 285 - 146 - 172 - 215- 145 - 145 - 85 - 85 - 85
- 208 - 245 - 125 - 148 - 185- 120 - 120 - 72 - 72 - 72
- 174 - 207 - 107 - 126 - 159- 100 - 100- 146 - 174- 80 - 80- 119 - 142- 65 - 65- 98 - 117

- 50
- 93

- 20
- 45

- 20
- 34

- 50
- 77

d9

d8

- 50
- 79

- 43
- 68

- 36
- 58

- 30
- 49

- 25
- 41

- 20
- 33

- 16
- 27

- 13
- 22

- 10
- 18

-6
- 12

f6

- 36
- 90

- 30
- 76

- 25
- 64

- 20
- 53

- 16
- 43

- 13
- 35

- 10
- 28

-6
- 20

f8

- 50 - 50- 96 - 122- 43 - 43- 83 - 106

- 36
- 71

- 30
- 60

- 25
- 50

- 20
- 41

- 16
- 34

- 13
- 28

- 10
- 22

-6
- 16

f7

- 15
- 35

- 14
- 32

- 12
- 27

- 10
- 23

-9
- 20

-7
- 16

-6
- 14

-5
- 11

-4
-9

-2
-6

g5

- 15
- 44

- 14
- 39

- 12
- 34

- 10
- 29

-9
- 25

-7
- 20

-6
- 17

-5
- 14

-4
- 12

-2
-8

g6

0
- 20

0
- 18

0
- 15

0
- 13

0
- 11

0
-9

0
-8

0
-6

0
-5

0
-4

h5

0
- 29

0
- 25

0
- 22

0
- 19

0
- 16

0
- 13

0
- 11

0
-9

0
-8

0
-6

h6

0
- 46

0
- 40

0
- 35

0
- 30

0
- 25

0
- 21

0
- 18

0
- 15

0
- 12

0
- 10

h7

±2

js5

±6

±5

js7

± 4 ± 5.5±9

± 3 ± 4.5 ± 7.5

±4

±3

js6

0
0
- 72 - 115± 10 ± 14.5

± 23

± 20

± 11 ± 17.5

± 9 ± 12.5

0
± 7.5
- 87

± 15

± 8 ± 12.5
0
± 6.5 ± 9.5
- 74

0
± 5.5
- 62

0
± 4.5 ± 6.5 ± 10.5
- 52

0
- 43

0
- 36

0
± 2.5
- 30

0
- 25

h9

0
0
- 63 - 100

0
- 54

0
- 46

0
- 39

0
- 33

0
- 27

0
- 22

0
- 18

0
- 14

h8

Tolerance grades for shafts

-- 12
-- 98

-8
- 37

-8
- 33
-8
- 37

-6
- -288
- 33

-- 56
-- 24
28

-- 54
20
-- 24

-- 44
-- 17
20

-- 44
15
-- 17

- 34
- 15
12

-- 31
- -129

+ 24
+4

+ 21
+3

+ 18
+3

+ 15
+2

+ 13
+2

+ 11
+2

+9
+1

+7
+1

+6
+1

+4
0

k5

+ 13
- 33

+ 12
- 28
+ 13
- 33

+4
- 21
+5
- 24
+5
- 24

+ 10
+- 25
12
- 28

++109
-- 21
25

++ 97
18
-- 21

++ 67
-- 15
18

++ 66
12
-- 15

+ 56
- 12
10

++ 53
- -109+ 30- -109

+4
-+184
- 21

++ 44
-- 15
18

++ 43
13
-- 15

++ 23
11
-- 13

++ 22
- -119

+2
- 97

++ 22
-- 76

+ 20
-- 66

Table 2: Standard tolerance grades and limit deviations for shafts JIS B 0401-2:1998 (ISO 286-2:1988)

6
3

3-

+ 33
+4

+ 28
+3

+ 25
+3

+ 21
+2

+ 18
+2

+ 15
+2

+ 12
+1

+ 10
+1

+9
+1

+6
0

k6

0
- 46

0
- 40
0
- 46

0
- 350
- 40

00
-- 30
35

00
25
-- 30

00
-- 21
25

00
18
-- 21

0
- 18
15

00
-- 15
12

- 02
-- 12
12

+ 37
+ 17

+ 33
+ 15

+ 28
+ 13

+ 24
+ 11

+ 20
+9

+ 17
+8

+ 15
+7

+ 12
+6

+9
+4

+6
+2

m5

- 14
- 60

- 12
- 52
- 14
- 60

- 10
12
- 45
- 52

- -109
-- 39
45

-- 98
33
-- 39

-- 78
-- 28
33

-- 75
23
-- 28

- 45
- 23
19

-- 44
-- 19
16

-- 44
-- 16
14

- 41
- 70

- 36
- 61
- 41
- 70

- 30
36
- 52
- 61

-- 26
30
-- 45
52

21
-- 26
37
-- 45

-- 18
21
-- 31
37

15
-- 18
26
-- 31

15
- 12
- 26
21

- -129
-- 21
17

-- 96
-- 17
12

- 33
- 79

- 28
- 68
- 33
- 79

- 24
28
- 59
- 68

-- 21
24
-- 51
59

17
-- 21
42
-- 51

-- 14
17
-- 35
42

11
-- 14
29
-- 35

- -119
- 29
24

-- 98
-- 24
20

-- 86
-- 20
16

n6

+ 60
+ 31

+ 52
+ 27

+ 45
+ 23

+ 39
+ 20

+ 33
+ 17

+ 28
+ 15

+ 23
+ 12

+ 19
+ 10

+ 16
+8

+ 10
+4

p6

+ 79
+ 50

+ 68
+ 43

+ 59
+ 37

+ 51
+ 32

+ 42
+ 26

+ 35
+ 22

+ 29
+ 18

+ 24
+ 15

+ 20
+ 12

+ 12
+6

Reference data

+ 46
+ 17

+ 40
+ 15

+ 35
+ 13

+ 30
+ 11

+ 25
+9

+ 21
+8

+ 18
+7

+ 15
+6

+ 12
+4

+8
+2

m6

Unit: μm = 0.001 mm

- 22
- 51

- 20
- 45
- 22
- 51

- 16
20
- 38
- 45

-- 14
16
-- 33
38

12
-- 14
28
-- 33

11
-- 12
-- 24
28

- -119
20
-- 24

- 79
- 20
16

-- 75
-- 16
13

-- 54
-- 13
10

Unit: μm = 0.001 mm
Over Or less D8 D9 D10 E7 E8 E9 F6 F7 F8 G6 G7 H6 H7 H8 H9 H10 JS6 JS7 K6 K7 M6 M7 N6 N7 P6 P7Range of standard+ 34 + 45 + 60 + 24 + 28 + 39 + 12 + 16 + 20 + 8 + 12Tolerance+ 6 +grades
10 + 14for +holes
25 + 40
0
0
-2
-2
-4
-4
-6
-6
dimensions (mm)
3
±3
±5
+
20
+
20
+
20
+
14
+
14
+
14
+
6
+
6
+
6
+
2
+
2
0
- 10 M6- 8 M7- 12 N6- 10 N7- 14 P6- 12 P7- 16
Over Or less D8 D9 D10 E7 E8 E9 F6 F7 F8 G6 G7 H6 H70 H80 H90 H100 JS6 JS7 K6- 6 K7Table 1: Standard tolerance grades and limit deviations for holes JIS B 0401-2:1998 (ISO 286-2:1988)

Range of standard
dimensions (mm)

Key

1.5

1.7

11

19
22
23

12
14
15

11.5
13.4
14.3

12
14
15

11.1
12.9
13.8

16

14.7

2.2

3.6

24

16

15.2

17
18
19

15.7
16.5
17.5

2.2
2.6
2.7

3.7
3.8
3.8

25
26
27

17
18
19

16.2
17.0
18.0

24

18.5
20.5
22.2

2.7
2.7
3.1

3.9
4.1
4.2

28
31
33

20
22
24

19.0
21.0
22.9

3.1

4.3

34

25

23.9

3.1

4.4

35

26

24.9

3.1
3.5

4.6
4.8

38
40

28
30

26.6
28.6

3.5
4.0
4.0

5.0
5.4
5.4

43
46
47

32
35
36

30.3
33.0
34.0

4.5

5.6

50

38

36.0

4.5
4.5
4.8

5.8
6.2
6.3

53
55
58

40
42
45

38.0
39.5
42.5

4.8
5.0

6.5
6.7

62
64

48
50

45.5
47.0

5.0
5.0

7.0
7.0

70
71

55
56

52.0
53.0

5.5
6.4
6.4

7.2
7.4
7.8

75
81
86

60
65
70

57.0
62.0
67.0

7.0

7.9

92

75

72.0

7.4
8.0

8.2
8.4

97
103

80
85

76.5
81.5

8.0

8.7

108

90

86.5

8.6
9.0
9.5
9.5
10.3

9.1
9.5
9.8
10.0
10.9

114
119
125
131
143

95
100
105
110
120

91.5
96.5
101.0
106.0
116.0

20
22
25

23.2
26

28

24.2
25.9

30

27.9

32
35
36

29.6
32.2
33.2

38

35.2

42

37.0
38.5
41.5

40
45
48
50
55
56

75

70.5

80
85

74.5
79.5

90

84.5

95
100

89.5
94.5
98.0
103.0
113.0

105

1.2
± 0.06± 0.20(2)

1.6± 0.251.8± 0.40

50.8
51.8
55.8
60.8
65.5

± 0.05± 0.18± 0.07

44.5
45.8

60
65
70

110
120

1

2

± 0.452.5± 0.083± 0.09± 0.55
4

2

2.5

3

1.15

2×2
3×3

0
- 0.111.5
1.35
0- 0.21

(2)

1.75

0
- 0.25+ 0.14
0

1.95
2

2.2
0
- 0.302.7

0- 0.353.2

0- 0.544.2

2.5

3+ 0.180(Note 1) The nominal sizes in column “1” are preferable to the sizes in column “2”. The latter may be used when needed.
(Note 2) The thickness (t) = 1.6 mm. Thickness of 1.5 mm is permissible until determined otherwise. In this case the value “m” is 1.65 mm.
(Remarks) 1. The minimum width of the annular part of the snap ring must not be smaller than the board thickness (t).
2. The corresponding shaft dimensions above are shown as recommended dimensions for reference purposes only.

Appendix-4

420
3 - 0.025

4×4

4

5×5
6×6

5
6

(7 × 7)78×7

8

10 × 812 × 810
12

14 × 9(15 × 10)16 × 10

14
15
16

0
- 0.0300- 0.036

t2
t1

25
2
3

0
- 0.0254
5
6
7

0- 0.030Cℓ0.16 to 0.25

6 to 20
6 to 3623

h90.25 to 0.40

0
- 0.03078
8

8 to 454

10 to 56
14 to 705
6

16 to 80

718 to 908

22 to 110
28 to 140101236 to 160
40 to 180
45 to 180

14
15
16

b1

b2
r1 and r2- 0.004± 0.0125- 0.0290.08 to 0.16
0
± 0.0150- 0.030
0.16 to 0.25
0
± 0.0180- 0.036

1.2
1.8

1.0
1.4

2.5

1.8

3.0
3.5

2.3
2.8

+ 0.1
0

6 to 88 to 1010 to 1212 to 17
17 to 22

4.0

3.0

20 to 25

4.0

3.3

22 to 30

5.0
5.0

3.3
3.3

30 to 38
38 to 44

5.5
5.0
6.0

44 to 50
50 to 55
50 to 58

18 × 1118

1150 to 200

18

7.0

3.8
5.0
+ 0.2
4.3
0
4.4

20 × 1222 × 14(24 × 16)

20
22
24

12
14
16

56 to 220
63 to 250
70 to 280

20
22
24

7.5
9.0
8.0

4.9
5.4
8.0

65 to 75
75 to 85
80 to 90

25 × 1428 × 1632 × 1825
28
32

70 to 280
80 to 320
90 to 360

25
28
32

9.0
10.0
11.0

5.4
6.4
7.4

85 to 95
95 to 110
110 to 130(35 × 22)35

22100 to 400

35

36 × 20(38 × 24)
40 × 2236
38
040 - 0.062

20
24
22

(42 × 26)42

26

45 × 25
50 × 28

45
50

25
28

56 × 32

56

32

63 × 32
70 × 3680 × 4063
070 - 0.074
80

32
36
40

90 × 4590
0100 × 50 100 - 0.087

45
50

0
- 0.0430- 0.052910
100- 0.090(1)

Ref.
Corresponding
shaft
diameter d

3.2
3.4
3.5

18

Nominalkey sizeb×hStandard groove

Tolerance oft1 and t2

1.8
2.0
2.1

1.2

10

h

Standard
dimensions of t2

3.1

17

Standard Tolerance Standard Tolerance Minimum
dimensions
dimensions0
9.6- 0.0910.5bStandard
dimensions of t1

1.8

d1

n

Tolerance
(Js9)

3.0

d3

m

Dimensions of key groove

Tolerance
(N9)

1.6

d2

Unit: mm
Dimensions of key
Standard dimensionsof b1 and b2± 0.15

10.2

S2 = tolerance of h × 1/2

Toleranced0Standard Tolerance Standard Tolerance Approximate Approximate Minimum
dimensions
dimensions
9.3

11

a

d

b1

6.3

“d5” represents the maximum circumferential
diameter when the ring is snapped onto the shaft.
Unit: mmCorresponding shaft (for reference purpose only)bb2Standard
dimensions

10

f

ℓ 1.6
6.3

Tolerance (h9)

2

d1

r2

1.6

h

n

Snap ring(1)

Nominal size
1

c

S2

Position the holes at the neb of the snap ring (diameter d0)
so that they protrude out of the snap ring groove and are
visible above the external diameter of the shaft end.

Cross section of key groove

b

d5
t
a

d0

S1

d 2 d125

d4
d3

Key groove

S1 = tolerance of b × 1/2

b

h

m

Reference data

Table 4: Dimensions of parallel keys and key grooves JIS B 1301:1996

Standard
dimensions

Reference data

Table 3: C-Shaped Snap Rings JIS B 2804:2001

14
16
18

0.40 to 0.60

0- 0.1100.60 to 0.80

h11

0
- 0.130

1.00 to 1.20-

0.25 to 0.40
0
± 0.0215- 0.0430± 0.0260- 0.052
0.40 to 0.60

58 to 65

11.0

11.0

125 to 140

36
12.0
38
12.0
0
± 0.0310
40 - 0.062
0.70 to 1.00 13.0

8.4
12.0
9.4

130 to 150
140 to 160
150 to 170
160 to 180

-

42

13.0

13.0

-

45
50

15.0
17.0
20.0

10.4
170 to 200
+ 0.3
11.4
200 to 230
012.4
230 to 260-

56

1.60 to 2.00-

63
1.20 to 1.60 20.00
± 0.0370
70 - 0.074
22.0
80
25.0

12.4
14.4
15.4

260 to 290
290 to 330
330 to 380

2.50 to 3.00-

90
2.00 to 2.50 28.00
± 0.0435
100 - 0.087
31.0

17.4
19.5

380 to 440
440 to 500

0- 0.160(Note 1) “ℓ” must be selected from the following values: 6, 8, 10, 12, 14, 16, 18, 20, 22, 25, 28, 32, 36, 40, 45, 50, 56, 63, 70, 80, 90, 100, 110,
125, 140, 160, 180, 200, 220, 250, 280, 320, 360, or 400.
The dimensional tolerance values for “ℓ” are generally h12 in accordance with JIS B 0401 (Dimensional tolerances and fit).
(Note 2) The corresponding shaft diameters should be determined in consideration of proper torque for key strength. The the above list indicatesstandard diameters for general use and is intended for reference purposes only.
(Remark) It is recommended that you avoid using the nominal sizes with parentheses whenever possible.
(Reference) When you need a key with a tolerance smaller than the key tolerance specified above, the tolerance for the key width (b) should be
h7. In this case, a tolerance for height (h) should be h7 for nominal sizes of 7X7 or smaller and h11 for the sizes of 8X7 or larger.

Appendix-5

RockwellC-scalehardness(150 kgf)
68
67
66
65
64
63
62
61
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
(18)
(16)
(14)
(12)
(10)
( 8)
( 6)
( 4)
( 2)
( 0)

Appendix-6

Vickers
hardness
940
900
865
832
800
772
746
720
697
674
653
633
613
595
577
560
544
528
513
498
484
471
458
446
434
423
412
402
392
382
372
363
354
345
336
327
318
310
302
294
286
279
272
266
260
254
248
243
238
230
222
213
204
196
188
180
173
166
160

Table 6: Dimensions of the counterbore and internal thread for the hexagon-headed bolt

Brinell hardness

Rockwell hardness

Standard balls

Tungstencarbide balls

A-scale60 kgf load
Bralepenetrator

B-scale100 kgf load
Ball diameter:
1/16 inch

Shore
hardness

500
487
475
464
451
442
432
421
409
400
390
381
371
362
353
344
336
327
319
311
301
294
286
279
271
264
258
253
247
243
237
231
226
219
212
203
194
187
179
171
165
158
152

739
722
705
688
670
654
634
615
595
577
560
543
525
512
496
481
469
455
443
432
421
409
400
390
381
371
362
353
344
336
327
319
311
301
294
286
279
271
264
258
253
247
243
237
231
226
219
212
203
194
187
179
171
165
158
152

85.6
85.0
84.5
83.9
83.4
82.8
82.3
81.8
81.2
80.7
80.1
79.6
79.0
78.5
78.0
77.4
76.8
76.3
75.9
75.2
74.7
74.1
73.6
73.1
72.5
72.0
71.5
70.9
70.4
69.9
69.4
68.9
68.4
67.9
67.4
66.8
66.3
65.8
65.3
64.7
64.3
63.8
63.3
62.8
62.4
62.0
61.5
61.0
60.5
-

(109.0)(108.5)(108.0)(107.5)(107.0)(106.0)(105.5)(104.5)(104.0)(103.0)(102.5)(101.5)(101.0)
100.0
99.0
98.5
97.8
96.7
95.5
93.9
92.3
90.7
89.5
87.1
85.5
83.5
81.7

97
95
92
91
88
87
85
83
81
80
78
76
75
74
72
71
69
68
67
66
64
63
62
60
58
57
56
55
54
52
51
50
49
48
47
46
44
43
42
41
41
40
38
38
37
36
35
35
34
33
32
31
29
28
27
26
25
24
24

D’
D
H

H”

d1
d’
d

Unit: mmNominal size (d) M3
M4
M5
M6
M8 M10 M12 (M14) M16 (M18) M20 (M22) M24 (M27) M30
Thread pitch (P) 0.5
0.7
0.8
1
1.25 1.5 1.75
2
2
2.5
2.5
2.5
3
3
3.5
3
4
5
6
8
10
12
14
16
18
20
22
24
27
30
d1
d’
3.4
4.5
5.5
6.6
9
11
14
16
18
20
22
24
26
30
33
D
5.5
7
8.5
10
13
16
18
21
24
27
30
33
36
40
45
D’
6.5
8
9.5
11
14 17.5 20
23
26
29
32
35
39
43
48
H
3
4
5
6
8
10
12
14
16
18
20
22
24
27
30
H”
3.3
4.4
5.4
6.5
8.6 10.8 13 15.2 17.5 19.5 21.5 23.5 25.5 29
32(Remark) The bolt hole diameters (d’) listed above are in accordance with bolt hole grade 2 in JIS B 1001 (Diameterof clearance holes and counterbores for bolts and screws).

Appendix-7

Reference data

Reference data

Table 5: Hardness Conversion Chart