Single Axis Actuator[Technical Data]մSelection of Single Axis Actuators 1
Single Axis Actuator

Select the nominal SX actuatorfrom the travel and the rating
list below.

Determine the ball screw
lead so that the operation
speed will be within themaximum speed shown in(Table 4). At this stage, theselection is temporary.

Examine the load applied to the rail andput it in formulas (1) and (2) on page
A-058.Obtain the equivalent load Fe
for each process and put it in formula(3) on page A-058 Obtail the averageload Fm and calculate the lifetime.

Examine the load applied
to the ball screw and thesupport bearing. Put it informula (3) on page A-058,
obtain the average load Fm
and calculate the lifetime.

Ӗ Rated load (Table 1)

RailZ

Ball screwBearing(ﬁxed side)

Item
Dynamic load rating Ca (N)Static load rating Coa (N)Radial clearances
Advanced
Dynamic load rating Ca (N)Advanced
Static load rating Coa (N)Thread shaft diameter (mm)Lead (mm)Core diameter
Ball center diameter
Dynamic load rating Ca (N)Axial load
Static load rating Coa (N)SX2001
SX20053277
6199−3~0482822642
1026
66
155.3
4.918
6.15
6.3730461

Ӗ Moment equivalent coefﬁcient at rail (Table 2)
Type
SX20_ _
SX26_ _
SX30_ _
SX45_ _

Block
1 piece
Close contact between 2 pcs.
1 piece
Close contact between 2 pcs.
1 piece
Close contact between 2 pcs.
1 piece
Close contact between 2 pcs.

Kp
0.228
0.144
0.17
0.114
0.137
0.09170.11150.0840

Ky
0.228
0.144
0.17
0.114
0.137
0.09170.11150.0840Ӗ Allowable Static Load / Allowable Static Moment (Table 4)
AllowableNo. of Static Load (kg)blocksHorizontal
B16199
SX20_ _B212398
B16199
SX20_ _C
B212398
B111871
SX26_ _B223742
B111871
SX26_ _C
B223742
B117218
SX3005
B234436
B117218
SX3005C
B234436
B117218
SX3010
B234436
B1
17218
SX3010C
B234436
B132441
SX4510
B264882
B132441
SX4520
B264882
Type

Allowable StaticMoment (Nm)
MaMb
Mc
272793353
353
186
272793353
353
186
7070225902
902
450
7070225
902
902
450
126
126
3871515
1515
774
126
126
387
1515
1515
774
126
126
387
1515
1515
774
126
126
387
1515
1515
774
291
291
972
3945
3945
1944
291
291
972
3945
3945
1944

Ӗ Allowable Static Load / Allowable Static Moment (Short Block) (Table 5)Type
SX3005
SX3010SX4510SX4520

A057

Allowable
No. of Static Load (kg)blocksHorizontal
S19271
S218542
S19271
S2
18542
S1
17175
S234350
S117175
S234350

Allowable StaticMoment (Nm)
Ma
Mb
Mc
6363
208
579
579
417
63
63
208
579
579
417
145
145
515
1444
1444
1029
145
145
5151444
1444
1029

SX2602
SX26056522
11871−4~01712
1600
2251
2097
882
56.4
6.46
8.3
8.3
1637
1205

SX3005
SX3010
9732
6305
17218
9271
−4~01831
1129
2389
1386
1010510
8.2
10.3
10.3
2702
2197

SX4510SX4520
18450
11826
32441
17175
−6~04167
2499
5945
3381
15151020
11.7
15.5
15.75
4335
4106

Ӗ Rail geometrical moment of inertia (Table 3)Kr
0.0667
0.06670.05270.05270.04450.04450.03340.0334TypeSX (mm4 )Ly (mm4)

SX2001
SX2606SX30_ _SX45_ _

3.2×103
1.0×104
2.5×104
8.8×104

5.2×104
1.4×105
3.1×105
10.4×105

Ӗ Maximum travel speed (Table 6)
Type
SX20_ _SX26_ _Lead

L (mm)

01
05
02
05

−−−−
150
200
300
400
500
600
150
200
300
400
500
600
340
390
440
490
540
590
340
390
440
490
540
590

06

SX30_ _1010

SX45_ _20

Maximum travel
speed (mm/s)
Advanced
190
690
290
520
410
410
410
410
370
250
830
830
830
830
740
500
550
550
550
550
550
550
1110
1110
1110
1110
1110
1110

Mass
Center of(kg/100mm) Gravity h (mm)0.224.40.37
6.1
0.6
7.8
1.10
11.0

Ӗ Load coefﬁcient fw (Table 7)
Vibration/
impactSpeedfwSubtle

Super-low speedV≤ 0.25m/s
Low speed
0.25m/s<V≤ 1m/s
Medium speed
1m/s <V≤ 2m/s
High speed
2m/s<V

1~1.2

Small
MediumLarge

1.2~1.5
1.5~2
2~3.5

Y axisX axishX

Mb

Ma = Pitching
Mb = Yawing
Mc = Rolling

MaMc

Single Axis Actuator

Life Span
For the SX actuator, calculate the life span of the rail, ball screw and support bearing.
The actuator life span is determined to be the smallest value from among these results.

ℓ1(mm)t1(s)ℓ2(mm)t2(s)ℓ3(mm)t3(s)V(mm/s)Load mass: W kgStroke: Ls mm
Acceleration: a mm/s2
Maximum speed : v mm/s
Gravity: g=9.81m/s2
acceleration: Horizontal
Speed diagram : (Fig. 1)
Operating conditions : (Fig. 2)

Examination

Ls (mm)=ℓ1+ℓ2+ℓ3
T(s)=t1+t2+t3
Speed diagram (Fig. 1)
WWZ

Selection

Status of load applied (Fig. 2)

Select the temporary model number based on the load mass W (kg) and the maximum speed V (mm/s). Then prepare a speed diagram based on theacceleration, maximum speed and travel. The conditions that can develop this speed diagram will serve as the basis for the selection calculation.

Calculation

Lifetime Calculation Example

Examine the status of the load applied (Fig. 2) to the rail of the SX actuator. Put each load in the formula below (formula (1) for
single nut block speciﬁcations and formula (2) for double nut block speciﬁcations), and obtain the equivalent load Fe.

Equivalent Load

Rail Life Span

In the case of single block

Obtain the rail life span for the SX actuator from formula (4).

Fe=YHFH+YVFV+YpKpMa+YyKyMb+YrKrMc −(1)L=La×

In the case of double block
Fe=YHFH/2+YVFV/2+YRKRMa+YPKPMb+YYKYMc(Cfw·Fm3) −(4)L: Rail lifetime (km) La: Travel distance (km) fw: Load coefﬁcient
C: Basic dynamic load rating (N)−(2)

Fe : Equivalent Load
FH : Horizontal load acting on blocks
FV : Vertical load applied to the block
Ma : Pitching direction moment applied to the block
Mb : Yawing direction moment applied to the block
Mc : Rolling direction moment applied to the block
Kp : Equivalent coefﬁcient for pitching direction moment
Ky : Equivalent coefﬁcient for yawing direction moment
Kr : Equivalent coefﬁcient for rolling direction moment

When the travel length and the number of reciprocal motions per minute areconstant, the number of life span hours can be calculated from formula (5).

L×10 62·ℓs·n1×60

Lh=−(5)

Lh: Life span hours (h) ℓs: Travel (mm) n1: Reciprocal motions per minuteLife span of ball screw and support areas
Obtain the average load from the load applied in the axial direction. Calculate life span forboth ball screws and bearings from formula (6). Obtain the average load from formula (3).

YH,YV,Yp,YY,YR:1.0 or 0.5

Lr=When the actuator is used under moment loads, calculate the load by multiplying
the guide moment equivalent coefficient in Table 2. In formulas (1) and (2), inorder to obtain the equivalent load Fe, the maximum value among FH, Fv, KpMa,
KyMb and KrMc is determined to be 1.0, and the remaining items are set at 0.5.

(Cafw·Fm3) · ℓ×10

6−(6)Lr: Life span of ball screw (km) ℓ: Ball screw lead (mm)fw: Load coefﬁcient Ca: Basic dynamic load rating of screw and support (N)Average LoadAs Ma and Mb for the SX actuator vary with acceleration and deceleration,
obtain the average load Fm from formula (3).
3

Fm=1
(Fe13 · L1+Fe23 ·L2+Fe3 3 ·L3+ ··· +Fen3 ·Ln) −(3)LS

Fm: Average load for ﬂuctuating loads (N) L: Total travel distance (km)A058

Single Axis Actuator[Technical Data] Selection of Single Axis Actuators 2
Single Axis Actuator

Rated lifetime calculation example
1 Model number for examination
Operating conditions : SX26
Rail: C (Basic dynamic load rating)=6522N

Ball screw: Ca (Basic dynamic load rating)=1712N Coa (Basic static load rating)=2251N

Co (Basic static load rating)=11871N

Support bearings : Ca (Basic dynamic load rating)=1637N Poa (Basic static load rating)=1205NXℓ1(mm)t1(s): 10kgLoad mass

Maximum speed : 250mm/s

Zℓ2(mm)t2(s)ℓ3(mm)t3(s)V(mm/s)Acceleration: 833mm/s2Stroke: 200mm

Gravity: g=9.81m/s2

Ls(mm)=ℓ1+ℓ2+ℓ3
T(s)=t1+t2+t3

Position: Horizontal

Speed diagram (Fig. 1)

Speed diagram: (Fig. 1)
W

Operating Conditions : (Fig. 2)W

2 Examination

Status of load applied (Fig. 2)

Temporary selection
Use a travel distance of 200 mm with an acceleration of 833 mm/s2 and a maximum speed of 250 mm/s. Based on these conditions, assume that the SX26 series isused. (The selection software can be used on the Misumi website after customer registration has been completed.)

3 Calculation
3−1

Examination of rail

3−2 Examination of ball screw

Multiply the moment equivalent coefﬁcient in the table with the load according
to the condition in which one nut block is used.

Obtain the axial loads for the parts and the average load from the speed
diagram.

Load for nut block

Lifetime of ball screw

1) At constant speed

Axial load1) At constant speed

Fe1=Yv Fv=Yv·W·g=1·10·9.81=98.1(N)2) At acceleration

2) At acceleration

Fe2=YvFv+Yp Kp Ma=0.5·98.1+1·0.17·70·0=60.95(N)3) At deceleration

Static safety coefﬁcientCoCo
fs==Femax
W·g=11871
98.1= 121.1

Rated life span
Axial average load31(Fe13 ·L1 +Fe2 3·L2+Fe3 3·L3+ ··· +Fen 3 ·Ln)= 87.72(N)
Ls

Rated life span
L=A059C

Fe2=Fe1+W·a × 10−3 =0.981+10·0.833 =9.311(N)3) At deceleration

Fe3=Yv Fv+Yp Kp Ma=0.5·98.1+1·0.17×70·0=60.95(N)Fm=

Fe1=μ·W·g=0.01 × 10 × 9.81=0.981(N)3( fw·Fm ) ×50=11.89×10

6

fw: Load coefﬁcient 1.2
La: Travel distance

Fe3=Fe1−W·a×10−3 =7.352(N)Statica safety coefﬁcient
Coa
Coa=fs=Femax
Fe2=2251= 241.76
9.311

P1=

Rated life span
Axial avera ge load

n·π 2 ·E·I
ℓa×0.5=5562.02(N)

23

Fm=

P1 : Buckling loadℓa : Distance between mounting points 250(mm)E : Young's modules 2.06×105 (N/mm 2 )n : Coefﬁcient according to mounting method
0.5: Safety factor
I : Minimum geometrical moment of inertia of screw shaft

1(Fe 13 ·L 1+Fe 2 3 ·L 2+Fe 3 3 ·L 3+ ···+Fen3·Ln)=6.096(N)
Ls

Rated life span
L=Cafw·Fm(3−3Axial load

Allowable tension/compression load

Fe1=0.981(N)Fe2=9.311(N)Fe3=7.352(N)·π·d1 24=4818.06

Poa
Fe2=129.42

Equivalent load
Axial average load
32π·ℓb 26Z

Poa=Femaxfs=

Critical speed

N1=

6

Static safety coefﬁcient

P2 : Allowable tension/compression load (N): Allowable tension/compression stress 147(N/mm2 )d1 : Root diameter of screw shaft 6.46(mm)60· 2) ·ℓ×10 =25.64×10 (km)Examination of support bearingd1 : Root diameter of screw shaft 6.46(mm)P2=3fw : Load coefﬁcient 1.2ℓ : Ball screw lead 2 (mm)π·d14
= 85.49(mm4 )64

I=Single Axis Actuator

Buckling load

·E×10 3 ·I·A

Fm=
−1×0.8=12485(min )1(Fe1 3·L1 +Fe2 3·L2 +Fe3 3·L3 + ··· +Fen 3·Ln) =6.096(N)LS

Rated lifetime3

N1 : Critical speedℓb : Distance between mounting points
E : Young's modules 2.06×10 5 (N/mm 2 ): Coefﬁcient according to mounting method (Fixed-Support 3.927): Density (7.85×10−6 kg/mm 3 )0.8: Safety factor

L=Ca( fw·Fm) ·ℓ×10 =22.41×10 (km)66

fw : Load coefﬁcient 1.2ℓ : Ball screw lead 2 (mm)

DN value
DN=62250(≤70000)
D : Ball center to center diameter (8.3mm)
N : Maximum number of operating revolutions (min−1 )SX2602
Static safety factor
Buckling load (N)Allowable tension/compression load (N)Critical speed (min-1)
DN value
Rated lifetime (km)Maximum axial load (N)Maximum number of operating revolutions

Rail
121.1
−−−−11.89×106−−

Ball screw
241.765562.024818.06
12485
62250
22.31×106
9.311
7500

Support bearing
129.42−−−−19.505×106−−

A060