1.7 Backlash
Summary of the backlash is “play” or “clearance” between one pair of gear.

Normal backlash

Circumferential backlash
Fig. 17 Backlash
Great care is taken to produce the gear with zero deviation. However we are unable to completely eliminate deviation from manufacturing and surface heat treatment. A gear always has innate deviations of Tooth profile, Pitch,Runout, Tooth thickness and Helix by manufacturing process.
The Gearbox has innate deviation from manufacturing process. For example, shorter Centre distance compared withdesigned dimension, insufficient parallelism of axis or inaccurate right angle.
When starts the operation for gearbox, generation of heat from the load causes the gearbox to deform. Continuous operation increases the temperature of gearbox and thermal expansion of each part. As a result, swelling of theteeth causes oscillation, noise, sand burning and damages the tooth or bearing.		
Proper backlash from the “Play in the gears” are necessary to absorb the deviations of noise and oscillation in orderto have smooth rotation.
When assembling the gears, please provide the proper backlash between flanks.
Methods that provide the proper backlash to the gears are as follows;
1) Method to shift centre distance away. (Locating distance for Bevel gear)
This method does not provide the modification to the Tooth thickness, as it does not decrease Tooth thickness. Thismethod simply shifts Centre distance away to obtain proper backlash to flanks.
2) Method of deeper cut during gear cutting process.
This method provides a deeper cut to reduce Tooth thickness when manufacturing the gear. Proper backlash is obtained if the gears are assembled with designated Centre distance.

23

Backlash for KG-STOCK GEARSKG STOCK GEARS has been using method 2) from previous page. This method gives a proper backlash when assembled with designated centre distance of gearbox without adjustments.
Refer to the below references 11 to 13 for amount of backlash when assembling a pair of KG STOCK GEARS with designated centre distance.
Table 11. 	Amount of backlash for KG Spur gear (engagement of one pair with same material)
Module (m)Materials Amount of backlash (mm)Range below m=0.9 is 0.02 - 0.06
Range from m=0.9
to m=3.0

D, SU, BS

0.06 × m - 0.12 × m

Range from m=3to m=5Range below m=0.9

Backlash (mm)
SCM, S, SU, BSD

0.02-0.08

0.03-0.10

S0.04 × m - 0.10 × m

Range from m=0.9 to m=2.00.05-0.12

0.05-0.16

0.04 × m - 0.08 × m

Range from m=2 to m=40.06-0.15-S0.06 × m - 0.12 × m

Range from m=4 to m=60.08-0.20-

Range from m=6 to m=70.10-0.22-Table 12.	Amount of backlash of Worm gear pairrange from m 1.0 and above ( one pair ofengagement)
Amount of backlash (mm)Range below m=0.8 is 0.06 - 0.15
Below 500.08 - 0.20

Range from 50 to 150

0.15 - 0.30

Range from 150 to 300

0.30 - 0.50

Range below m=0.8, is 0.06 - 0.15(mm)24Module (m)SCM

D: Polyacetal, SU: Stainless steel, S: Carbon steel, BS: Brass
SCM: Chromium molybdenum steel (Ground spur gear)

Centre distance

Table 13. 	Backlash of Bevel gear (one pair of gear engagement)

SU: Stainless steel, S: Carbon steel, SCM: Chromium molybdenumsteel, D: Polyacetal

Measurement of the backlash(1) Spur and Helical gears
There are a number of methods to measure the backlash for Spur and Helical gears.
Introduced are two (2) methods of measurement asfollows;a) Circumferential backlash jt
Assemble one pair of gear with designated centre
distance, fix one side of gear, put an indicator (Dialgauge) to Pitch circle of Mating gear and turn gear tothe left and right to measure the amount of backlash.
For Helical gear, measure backlash on the Pitch circumference at right angle section to axis.
In JIS, this is called the Circumferential backlash. Circumferential backlash for Spur and Helical gears isstipulated in JIS B 1703.
b) Backlash jn in perpendicular direction to flank.
Method of placinging indicatior perpendicularly toflank then follow same procedure in a).
In addition, another method is by putting a soft metal, eg. lead, between Flanks to measure the flattened
metal thickness by a micrometer. This method ofmeasurement may show different results comparedwith the method of simply using indicator to Flank
because it is under the influence of play from bearing or other part’s tolerance deviation. This method iscalled Normal backlash in JIS.
For Spur gear with Pressure angle α , it has the following relationship between jt and jn .
jn = j t cosα

jt = jn / cosα

When α is 20°, cosine 20° = 0.93969, jt and jn have
similar value.

Fixed

Fig. 18 Measurement of Circumferential backlash

Fixed

Normal tooth
proﬁleFig. 19 Measurement of Normal backlash

For Helical gear, an indicator is placed perpendicularly to the helixes of tooth for measurement. When
Normal pressure angle is α n and a helix angle is β ,therelationship between jt and jn are as follows.
jn = jt cos α n cosβ

j t = jn / cos α n cosβ

To measure backlash for Crossed helical gear pair
(Screw gear) with indicator, fix either Pinion or Gear.
When using either Pinion or Gear with Non-paralleland Non-intersecting axis, the reading on the indicator depends on which is chosen to be fixed. UsuallyPinion is fixed and indicator is placed to flank of gear.

25

(2) Bevel gearTo Measure the backlash for Bevel gear pair, there are
two (2) types of measurements. Circumferential backlash jt and normal backlash jn, which is the same for
Spur and Helical gears.
Fix the pinion and put an indicator to outer gear tomeasure.
Normal pressure angle α n and centre (mean) gear

Lever type Dial Gauge

Action of measuring pointertooth of helix angle β m of Spiral bevel gear have thefollowing relationship between jt and jn.
jn = jt cos α n cos β m

j t = jn / cos α n cos β m(The above calculation formula is for Spiral bevel gear.
For Straight bevel gear, it is cosine β m =1)

Fig. 20 Measurement method of backlash for theBevel gear (Circumference direction)Circumferential backlash for Bevel gear pair is stipulated in JIS B 1705.
In addition to this, there is another method to assemble the Bevel gear with a designated Locatingdistance. Fix a gear and move the Pinion in axis direction. Measure the amount of movement with an indicator.
Bevel gear has the following relationship between
Circumferential backlash jt and Locating direction jx.
jx = j t / 2 tan α n sin δ 1
jx = j tt / 2 tan d t sin δ 1Straight bevel gear
Spiral bevel gear

Herebyjtt :	Circumferential backlash at Transverse planejtt=jt/cosine α t
α t: Transverse pressure angle Įt = tan −1 (tan Į n /cosβ )For example, Straight bevel gear with Pressure angle
20° and gear ratio 1:1. Assuming that Circumferential
backlash jt is 1.0mm therefore backlash of Locating
direction is 1.94mm. Which means it can measureminute backlash to about twice the accuracy.

26

FixedFig. 21 Move the pinion in axis direction to measure
the backlash.

(3) Backlash of Worm gear pair
Generally the Worm gear is fixed and indicator isplaced to flank of Worm wheel for backlash measurement. This is the same method for both Spur and Helical gears pair.
Shown in Table 22, value for KG-Worm gear pair withassembled designated centre distance. Due to undefined backlash for Worm gear in JIS currently.
When using worm gear pair for accurate locatingand positioning, it is necessary to keep backlash to aminimum. Providing large backlash for power transmission is recommend due to expansion caused bygeneration of heat. Even though the backlash may belarger, performance of worm gear pair will almost bethe same.
Racing angle of Worm gear caused by backlash become a crucial problem occasionally.
Below is the explanation of the calculation formula
for racing angle of Worm gear instead of backlash ofWorm wheel.
Place an indicator to flank of Worm Wheel as show inFig. 22 to measure circumferential backlash.

Fig. 22 Method of measurement for Worm gear pair
(Circumference direction)

For example,
Module is 2.0,
Gear ratio 1：30,
Reference diameter of Worm gear is 31.0 mm,
Lead angle of Worm gear is 3°42’’ ,Lead of Worm gear is 6.2963,
Measurement amount of Circumferential backlash is0.2 mm.
Calculation formula is as follows.
(Lead) : (360°) = (Measured circumferential backlash): (Racing angle of Worm gear) therefore,Racing angle of Worm gear =360° × Circumferential backlash= 360° × 0.2 / 6.2963
Lead= 11°27'
Worm gear provides the racing of 11°27’ .
(Lead of Worm gear : It is the distance of a point on
the flank as it moves forward in axis direction when
the Worm gear turns one revolution.)27