1.6 Features of common gears
Chapter 1.2 covered briefly on types of gear. The main gear features are explained here.

Helical gear

Helical gear has characteristics of transferability oflarger load, less vibration and lower noise comparedwith Spur gear.
However, thrust load (axial direction) occurs due tohelix angle. It is therefore necessary to design thrustbearings. (Refer to chapter 2 for thrust load)
When using parallel axis, engage with right and left
hand of Helical gears at the same angle.
Using Screw gear for Non-parallel and Non-intersecting axis is called Crossed helical gear.
Roll up a piece of right-angled triangle paper as seenin Fig. 8. The straight lines of slope of the right-angled
triangle become a thread curve (helix). Helical gear
adopts this curved line as Tooth trace curve.
This right angled triangle unrolls to draw layers of Helical gear to become Fig. 9.

Fig. 8 Helix

Pitch diameter

alm

Helix
angle B

Viewing the gear
vertical line of centre tobe parallel to axis
direction, Tooth tracerise up to right
direction is Helical gearwith right hand.

Circumference length of Pitch circle �dHelixangle BrNoTransversepitch PthtcpiPn

In view of gear verticalline of centre parallel toaxial (vertical) direction,
Tooth trace rise up toleft direction is Helicalgear with left hand.

Circumference length of Pitch circle �dFig. 9 Helical gear (right and left hands)

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There are types of Normal and Axial for Helical gear.
Standard tooth profile for Normal type of Helicalgear is a section of the Tooth profile perpendicular to
Tooth trace of Helical rack which is obtained by set-ting the Reference pitch radius to infinity.
Standard tooth profile for Axis type of Helical gear isperpendicular to gear axis.
Fig. 10 shows both of the Reference sections.

mn=πPnAnRCDos2c2aAxis

DAnb

Normal section

BPnPx

DPx

AtAt

Axis section

Pt=πmsFig. 10 Types of Normal and Axial
Regarding to manufacturing method, the same hob
cutter and grinding wheel can be used to fabricate
any helix angle gear. As long as the Normal type ofHelical gear has same Normal module mn (called module of hob cutter) and same Normal pressure angle
an (called pressure angle of hob). Even if helix angle βwas changed
Therefore, stock of hob cutters (tools) and manufacturing cost can be saved making Normal type of Helical gear economic and widely used generally.
However, calculating Centre distance for Normal typeof Helical gear, it is necessary to adjust the helix angle
to obtain an integer number for Centre distance dueto the cosine β in the denominator.
Regarding the manufacturing method, the hob cutter (tool) and grinding wheel must be changed tofabricate Axial type of Helical gear if helical angle β ischanged. Therefore mass production for this type ofgear is very limited.
Since calculation for Helical gear is the same as Spurgear, integer number for centre distance is easily obtained.
Note (1) Adopted old gear terms.

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At the above Fig. 10, under perpendicular section to
Tooth trace, the Pitch diameter becomes oval. Half oflength of oval with major and minor axis is used for
calculation below.
aD2cosEb

D
2

Formula for the radius of curvature R of oval at theC-point is as follows,
Ra2b

D2cos 2 E

Therefore assuming this is a Spur gear with Radius of(1)pitch circle R, it is commonly called Virtual spur gearfor Helical gear.
(1)
The relation between Virtual number of teeth ofSpur gear zv and actual number of teeth z of Helicalgear is as follows.
zX
(1)

z
cos3 EThe Virtual number of teeth of Spur gear becomes
the standard for strength calculation of Helical gear,
calculation of profile shifted gear and selection of hob
cutter.

Where helix direction of both gears are the same, theformula for shaft angle Σ is ,(Reference)
The Crossed helical gear (Screw gear) is simply a typeof Helical gear. The Parallel helical gear has the samehelix angle with opposite helix hand. Where as the
Crossed helical gear (Screw gear) is engaged with
Non-parallel and Non-intersecting axis with any optional helix angle.
Method of correct engagement, Normal module mnand Normal pressure angle α n must be the same.
When two non-profile shifted gears are engaged, each
Reference cylinder helix angle are indicated as β 1 andβ 2,¦E1  E 2

Where helix direction of both gears are different, formula for shaft angle Σ is,¦E 1  E 2 or¦E 2  E1

Therefore these become the relation of Shaving cutter and Machined gear.
In Theory, Crossed helical gear (Screw gear) has spot
contact and can only take small loads.

Pinion(Right hand)3

B2(Left hand)

B1

B1

B2
3Gear(Right hand)Fig. 11 Engagement of Crossed helical gear (Screw gear)

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Bevel gear

The relationship between Virtual number of teeth of
Spur gear zv and Actual number of teeth z of Bevelgear is as follow.

D2

This is Bevel gear, that is formed by making gear
teeth to the Reference surface of a coned friction
wheel. Usage of this conical gear is to transfer power
to Crossed or Angular axis of gear. This Reference surface is called Pitch cone of Bevel gear.
Classification by shape of tooth trace that straight
Tooth trace to axis direction is called Straight bevel
gear. Spiral Tooth trace to axis direction is called Spiral bevel gear.
In Fig. 12, Spur gear with Radius of pitch circle Rv1
and Rv2 of Back cone is thought to be Tooth profile ofBevel gear.
This Spur gear is an incomplete circle. The incomplete
circle Spur gear after being completed is called a Vir(1)tual spur gear , which is equivalent to a Bevel gear.

zXzcosG(δ : Pitch angle)

The Virtual number of teeth of Spur gear is standard
for strength calculation of Bevel gear and selection ofhob cutter.
This is Crown gear where Pitch surface of Bevel gearis changed into a flat surface and perpendicular to axial direction. Using high gear ratio and using creative
motion of Bevel gear for examination from imaginary
Tooth profile of Crown gear.
Bevel gear with shaft angle of 90° and gear ratio 1:1 iscommonly called Miter gear.

Gear 2

Rv2

D1

Pinion 1Rv1

(1)

Fig. 12 Virtual spur gear for Bevel gear

Note(1) Adopted old gear terms

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(1) Straight bevel gear
Straight bevel gear has a straight Tooth trace. Standard straight bevel gear and Gleason system straightbevel gear are common types.
A Standard Straight bevel gear is equivalent to a Standard spur gear due to Virtual spur gear. Undercut occurs in small Number of teeth.
However, Gleason system for Straight bevel gear provides fewer problems of Undercut in small Number ofteeth of Pinion because Gleason system for Straightbevel gear is designed to become profile shifted gear
between Pinion and Gear. Refer to the below Table 7
for comparison table of the features between Standard system and Gleason system.
Table 7. 	Comparison table for the features between
Gleason system and Standard system
Gleason system

Standard system

There are fewer
problems in Pinion
due to positive
Rack shift (Gearis negative Rackshift)

It is designed without rack shift andUndercut occurs
easily.

Balance ofstrength for
Pinion and Gear

Maintains excellent balance by
Rack shiftUnbalanced
without Rack shift

Bottomclearance

There is no Tip
interference at Toe
due to Parallel bottom clearance.

Occur Tip interference at Toe easily
due to not Parallelbottom clearance

Cause ofUndercut(2) Spiral bevel gear
Fig. 13, angle between Tooth trace and Pitch conesurface element in Bevel gear with curved Tooth trace
is called Spiral angle.
Mean spiral angle β m is spiral angle at centre of Facewidth. Unless otherwise specified, this Mean spiralangle is commonly called spiral angle.
For Gleason system of Spiral bevel gear, Standardspiral angle is 35° with arc of Tooth trace. Gleason system cutter performs to produce Crowning at Tooth
trace automatically.
In general, Shaft angle is 90° and matches with left
and right hand gears.
Refer to Fig. 14 for Right and Left hand of Spiral gear.
To prevent thrust force to axis direction, due tocurved tooth, thrust bearing is necessary. (Refer to thethrust force in Chapter 2)Shown in Table 9. Comparison table for minimum
Number of teeth to prevent Undercut for Gleason
Spiral bevel gear.

Spiral angle(for Spiralbevel gear)

Fig. 13 Spiral angle at centre of Facewidth.

∗ Miter gear is designed without Rack shift.
Coniflex® gear has Tooth trace with Crowning toStraight bevel gear as named by Gleason company.
Due to above features and Crowning, Gleason
Straight bevel gear provides much lesser single contacts and assembly problems as compared to othermethods.
Table 8 classifies the minimum Number of teeth toprevent Undercut for Gleason Straight bevel gear.
Table 8.	Classifies the minimum Number of teeth to prevent Undercut for Gleason Straight bevel gear.
α=20°

α=14.5°

Number of
Number of
Number of
Number ofteeth of Pinion teeth of Gear teeth of Pinion teeth of Gearz1z2z1z2

1330

2457

14202540

15172635

1616273128

29292919

Left hand

Right handFig. 14 Spiral bevel gear with Left and Right hand.

Table 9.	Comparison table shows the minimum Number of teeth to prevent
Undercut for Gleason Straight spiral bevel gear.
α=20°

α=16°

α=14.5°

Number of
Number of
Number of
Number of
Number of
Number ofteeth of Pinion teeth of Gear teeth of Pinion teeth of Gear teeth of Pinion teeth of Gear

20z1z2z1z2z1z2

1226

1659

1970

1322174520601420183621421519193122401618202923361717212724332226253223252630242427292828

(Reference)
These are types of Crown gear (similar relation between Rack and Spur gear) with curved line Tooth trace. Spiralbevel gears have following types shown in Fig. 15.

(B) Involute curved line(A) Curtate trochoidcurve

Base circle(E) Straight line(C) Arc circle(Gleason system)(D) Arc circle(Zerol Bevel gear)∗Gleason system of large size Spiral bevel gear is close to rectilinear tooth but there is aslight spiral Tooth trace by modified rolling.

Fig. 15 Types of Spiral bevel gear (curved line of Tooth trace for Crown gear)21

Worm gear pairThis is a Worm gear pair used as one pair of Threaded worm gear engaged with Worm wheel. It is commonly used inhigh speed reducing ratio.
Due to the low efficiency character, it is an important point to use proper lubricant oil to prevent heat generation.
To prevent thrust force to axis direction due to curve tooth, thrust bearing is necessary. (Refer to thrust force in Chapter 2)
Helix angle of Tooth for Worm gear is called Lead angle. Helix angle for Worm Wheel is called Helix angle same for
Helical gear.
Generally Worm gear and Worm wheel match with Non-parallel and Non-intersecting axis. Shaft angle is 90°. For example, right lead angle of Worm gear matches with right helix angle of Worm wheel.
Worm gear with 2 or more number of threads are commonly called Multi-threaded worm gear.
Use suitable lead angle from Worm gear to fabricate the Helix angle for Multi thread Worm wheel.
Regarding the engagement for KG-Worm gear and KG-Worm wheel, refer to Table 10.
Table 10.	The Engagement of KG-Worm and KG-Worm wheel (Assembled Gear pair should have same module.)

Symbol for Direction ofthread and Number ofthread.

Worm gear

Worm wheel

R1(Right hand /Single thread)
R2(Right hand/Double thread)
L1(Left hand/Single thread)
L2(Left hand/Double thread)

R1(Right hand, fabricate helix angle by single thread of Worm gear)
R2(Right hand, fabricate helix angle by double thread of Worm gear)
L1(Left hand, fabricate helix angle by single thread of Worm gear)
L2(Left hand, fabricate helix angle by double thread of Worm gear)

There are the types of Normal and Axis worm gear pair, same as Helical gear. Normal type of Worm gear pair hascome into wide use generally because it is economical.
When calculating Centre distance for Normal type of Worm gear pair, fraction appears due to tanγ . In case of small
lead angles, adjust Worm wheel by method of Negative Rack Shift to designated centre distance.

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