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Gear Backlash Types & Calculations

This document discusses different types of backlash that must be considered when designing gear systems. It defines real backlash as the clearance allowance that must be manufactured into gears due to machining tolerances and working conditions. There are two main ways to incorporate backlash into spur and helical gears: decreasing tooth thickness or increasing center distance. Proper backlash depends on factors like lubrication needs, thermal expansion, and machining errors. The backlash amount should be just enough for requirements without excessive machining costs.

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890 views2 pages

Gear Backlash Types & Calculations

This document discusses different types of backlash that must be considered when designing gear systems. It defines real backlash as the clearance allowance that must be manufactured into gears due to machining tolerances and working conditions. There are two main ways to incorporate backlash into spur and helical gears: decreasing tooth thickness or increasing center distance. Proper backlash depends on factors like lubrication needs, thermal expansion, and machining errors. The backlash amount should be just enough for requirements without excessive machining costs.

Uploaded by

shaheen_ratnani
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Backlash of gears Page 1 of 2

Backlash of gears

Backlash types (defined for each gear in a gear set)

Real gears must be manufactured with a specific backlash allowance. Designate the allowance by considering the machining and working
conditions.

In spur and helical gearing, there are two alternate ways to obtain the appropriate amount of backlash. First, decrease tooth thickness by
sinking the hob deeper into the blank than the theoretical standard depth is. Second, increase the center distance than theoretically
computed.

When designing a backlash, consider following factors:

 Lubricant space required.

 Differential expansion between the gear components and the housing.

 Errors in machining. Run-out of both gears, errors in profile, pitch, tooth thickness, helix angle and center distance. The smaller the
amount of backlash, the more accurate the machining of the gears is.

 Working conditions such as frequent reversing or overrunning load.

The amount of backlash must not be excessive for the requirements of the job. Ensure it is sufficient so that machining costs are not higher
than necessary.

It is customary to make half of the allowance for backlash on the tooth thickness of each gear of a pair, although there are exceptions. For
example, on pinions having low numbers of teeth, it provides all the allowance on the driven gear. It avoids weakening the pinion teeth.

 Circular backlash jt [mm/in]

 Normal backlash jn [mm/in]

 Center backlash jr [mm/in]

 Angular backlash jΘ [deg]

The Relation between Circular The Relation between Circular The Relation between
Direction jt and Normal Direction jt and Center Circular Direction jt and
Type of Gear Meshes Direction jn Direction jr Angular Backlash jΘ

Spur Gear jn = jt cos α

Helical Gear jnn = jtt cos αn cos β

mk:@MSITStore:file:///C:\Program%20Files\Autodesk\Inventor%202011\Help\admengh... 10/28/2010
Backlash of gears Page 2 of 2

Backlash of Helical Gear Mesh

The helical gear has two kinds of backlash when referring to the tooth space. There is a cross section in the normal direction of the tooth
surface “n”, and a cross section in the transverse direction perpendicular to the axis “t”.

jnn Backlash in the direction normal to the tooth surface

jnt Backlash in the circular direction in the cross section normal to the tooth

jtn Backlash in the direction normal to the tooth surface in the cross section perpendicular to the axis

jtt Backlash in the circular direction perpendicular to the axis

In the plane normal to the tooth: jnn = jnt cos αn

On the pitch surface: jnt = jtt cos β

In the plane perpendicular to the axis

jtn = jtt cos αt

where:

α Pressure angle
αn Pressure angle in normal direction, α = αn
αt Pressure angle in transverse direction
β Helix angle
d Pitch diameter

mk:@MSITStore:file:///C:\Program%20Files\Autodesk\Inventor%202011\Help\admengh... 10/28/2010

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