Gear Technical - Gears and Gearbox Manufacturer

T: +44 1246 455500 [email protected] www.ondrives.comUpdated July 2021 subject to change for use as a guide only.

Gear TechnicalGear Technical

Description Symbol Unit EquationNormal Module mnTransverse Module mt = mnNormal Pressure Angle αn degrees = 20°Transverse Pressure Angle αt degrees = αnNumber of Teeth zProfile Shift Coefficient x = zero for Ondrives standard gearsAddendum ha mm = 1.00 · mn (for Ondrives standard gears)Dedendum hf mm = 1.25 · mn (for Ondrives standard gears)Tooth Depth h mm = 2.25 · mn (for Ondrives standard gears)Gear Ratio u = z2 / z1Centre Distance a mm = (d1 +d2) / 2Pitch Circle Diameter d mm = z · mn Tip Diameter da mm = d + (2mn · x) + (2 · mn)Root Diameter dr mm = da – (2 · h)Normal Pitch pn mm = π · mnNormal Tooth Thickness in Pitch Circle sn mm = (pn / 2) + 2mn · x · tan αnWhen working with a pair of gears the subscript 1 and 2 denotes input (drive) and output (driven) gear.Tip diameter is the theoretical diameter of the gear without tooth thickness tolerance applied.For sn when x = zero, this is the theoretical tooth thickness. Actual tooth thickness will be less. The subscript e is for upper allowance values and i for lower allowance values.

da1 dr1

sn

pn

a

d1

Spur Gears

Updated July 2021 subject to change for use as a guide only.

T: +44 1246 455500 [email protected] www.ondrives.com

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TorqueStated value for metal spur gears is maximum torque (T2) based on two identical gears with the same number of teeth running at standard centres. Value is minimum from surface stress or bending stress.Other factors including duty cycle and temperature will affect maximum allowable torque and service life. Wear is dependant on lubrication. We recommend that each user compute their own values based on actual operating conditions and test in application.

Gear QualityStandard metal gears are supplied to quality Grade 7 DIN 3961 based on Pitch total deviation Fp, Pitch deviation fp, Radial runout Fr and Pitch error fu. Skive hobbed gears are supplied to quality Grade 6 DIN 3961. GG25 Cast Iron, PEEK GF30® and Delrin (POM) are supplied to quality Grade 8 DIN 3961.Ondrives can manufacture gears to higher grades on request. Ondrives can offer testing certification for a gear’s individual parameters using the latest CMM machine with gear measuring software.Double and single flank testing is available on request. Please contact our technical department for details.Comparisons of Grade StandardsExample 3 mod, 50 teeth, 30mm face width spur gear.

Working characteristicsof driving machineUniformLight ShocksModerate ShocksHeavy Shocks

Uniform1.001.101.251.50

Light Shocks1.251.351.501.75

Moderate Shocks1.501.601.752.00

Heavy Shocks1.751.852.002.25+

Working characteristics of driven machine

MaterialsInput SpeedBending Stress Factor SbSurface Stress Factor Sc

817M40

32,000 3,000

805M20

50,00011,000

303 Stainless

20,000 1,800

316 Stainless

15,800 1,400

GG25 Cast Iron

7,6001,350

100 rpm Uniform, 12 hours running per day

Stated value for plastic spur gears is maximum torque (T2) based on two identical gears with the same number of teeth running at standard centres. Value is minimum from surface stress, bending stress or bulk/surface temperature using method from BS 6168:1987.The torque capacity of plastic gears is highly dependant on operating condition. All values are reference only. We recommend that each user test in application under specific operation conditions of application.

* Reference Only ** Approximate value based on initial light greasing.Maximum torque for titanium gears is approximately 30% of 817M40 steel gears.Due to lack of stress factors we are unable to offer specific values. Testing in application is required.Torque for anti-backlash spur gears is limited by the spring rating. Please contact our Technical department for details.When selecting gears application factors should be applied to required torque. T2 > Trequired x Ka Application factor Ka

MaterialsInput Speed / No. of Load CyclesLimiting Bending StressLimiting Surface StressInitial TemperatureMax. Bulk or Surface TemperatureCoefficient of Friction

Delrin POM (White)100 rpm / 108

22.0 N/mm2

22.0 N/mm2

20°C60°C

0.18 (Dry)

PEEK GF30® (Light Brown)100 rpm / 108

30 N/mm2*

80 N/mm2*

20°C80°C

0.25**

Spur Gears

Pitch total deviation Fp µm 32 44 50 51Pitch deviation fp µm 8 12 13 13Radial runout Fr µm 22 31 40 41Pitch error fu µm 10 15 - -Double flank composite transmission error Fi" µm 26 36 61 61Double flank tooth-to-tooth transmission error fi" µm 11 15 21 20

StandardGrade

DIN 39616

DIN 39617

ISO 13287

AGMA10



da1 dr1

st

pt

aβ

d1

Parallel Helical Gears

Description Symbol Unit EquationNormal Module mnTransverse Module mt = mn / cos βAxial Module mx = mn / sin βNormal Pressure Angle αn degrees = 20°Transverse Pressure Angle αt degrees = tan-1 (tan αn / cos β)Helix Angle β degrees = 15°Lead Angle λ degrees = 90 - βNumber of Teeth zProfile Shift Coefficient x = zero for Ondrives standard gearsAddendum ha mm = 1.00 · mn (for Ondrives standard gears)Dedendum hf mm = 1.25 · mn (for Ondrives standard gears)Tooth Depth h mm = 2.25 · mn (for Ondrives standard gears)Gear Ratio u = z2 / z1Centre Distance a mm = (d1 +d2) / 2Pitch Circle Diameter d mm = z · mt = (z · mn) / cos βTip Diameter da mm = d + (2mn · x) + (2 · mn)Root Diameter dr mm = da – (2 · h)Normal Pitch pn mm = π · mnTransverse Pitch pt mm = π · mt = (π · mn) / cos βAxial Pitch px mm = π · mx = (π · mn) / sin βNormal Tooth Thickness in Pitch Circle sn mm = (pn / 2) + 2mn · x · tan αnTransverse Tooth Thickness in Pitch Circle st mm = (pt / 2) + 2mn · x · tan αt = Sn / cos βWhen working with a pair of gears the subscript 1 and 2 denotes input (drive) and output (driven) gear.Tip diameter is the theoretical diameter of the gear without tooth thickness tolerance applied.For sn & st when x = zero, this is the theoretical tooth thickness. Actual tooth thickness will be less. The subscript e is for upper allowance values and i for lower allowance values.For two helical gears to run together one must be left hand and the other right hand helix.



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TorqueStated value for metal spur gears is maximum torque (T2) based on two identical gears with the same number of teeth running at standard centres. Value is minimum from surface stress or bending stress.Other factors including duty cycle and temperature will affect maximum allowable torque and service life. Wear is dependant on lubrication. We recommend that each user compute their own values based on actual operating conditions and test in application.

Gear QualityStandard gears are supplied to quality grade 7e25 DIN 3961 based on the following parameters

Radial Runout Fr =

Pitch Deviation fp =

Total Pitch Deviation Fp =

Pitch Error fu =

Ondrives manufacture gears to higher quality grades on request. Ondrives can offer testing certification of a gears individual parameters using the latest CMM machine with gear measuring software. Double and single flank testing is available on request. Please contact our technical department for details.

Comparisons of Grade StandardsExample 3 mod, 50 teeth, 30mm face width 15° helix parallel helical gear.


Uniform1.001.101.251.50

Light Shocks1.251.351.501.75


Heavy Shocks1.751.852.002.25+



817M40

32,000 3,000

805M20

50,00011,000

303 Stainless

20,000 1,800

316 Stainless

15,800 1,400


When selecting gears application factors should be applied to required torque. T2 > Trequired x Ka Application factor Ka

Pitch total deviation Fp µm 47 50 55Pitch deviation fp µm 12 13 12Radial runout Fr µm 31 40 44Pitch error fu µm 15 - -Double flank composite transmission error Fi" µm 36 61 65Double flank tooth-to-tooth transmission error fi" µm 15 21 20

StandardGrade

DIN 39617

ISO7

AGMA10




β

λ

da1

px

st

pt

a

d1

Crossed Axis Helical Gears

Description Symbol Unit EquationNormal Module mnTransverse Module mt = mn / cos βAxial Module mx = mn / sin βNormal Pressure Angle αn degrees = 20°Transverse Pressure Angle αt degrees = tan-1 (tan αn / cos β)Helix Angle β degrees = 45°Lead Angle λ degrees = 90 - βNumber of Teeth zProfile Shift Coefficient x = zero for Ondrives standard gearsAddendum ha mm = 1.00 · mn (for Ondrives standard gears)Dedendum hf mm = 1.25 · mn (for Ondrives standard gears)Tooth Depth h mm = 2.25 · mn (for Ondrives standard gears)Gear Ratio u = z2 / z1Centre Distance a mm = (d1 +d2) / 2Pitch Circle Diameter d mm = z · mt = (z · mn) / cos βTip Diameter da mm = d + (2mn · x) + (2 · mn)Root Diameter dr mm = da – (2 · h)Normal Pitch pn mm = π · mnTransverse Pitch pt mm = π · mt = (π · mn) / cos βAxial Pitch px mm = π · mx = (π · mn) / sin βNormal Tooth Thickness in Pitch Circle sn mm = (pn / 2) + 2mn · x · tan αnTransverse Tooth Thickness in Pitch Circle st mm = (pt / 2) + 2mn · x · tan αtWhen working with a pair of gears the subscript 1 and 2 denotes input (drive) and output (driven) gear.Tip diameter is the theoretical diameter of the gear without tooth thickness tolerance applied.For sn & st when x = zero, this is the theoretical tooth thickness. Actual tooth thickness will be less. The subscript e is for upper allowance values and i for lower allowance values.For two crossed axis helical gears to run together both must be right hand or left hand helix.



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Direction of Rotation

Right Hand Helix Left Hand Helix


TorqueStated value is maximum torque (T2) based on two identical gears with the same number of teeth running at standard centres. Crossed axis helical gears transmit load by point contact. The limiting condition is typically surface stress. Other factors including duty cycle and temperature will affect maximum allowable torque and service life. Wear is dependant on lubrication.We recommend that each user compute their own values based on actual operating conditions and test in application.


Uniform1.001.101.251.50

Light Shocks1.251.351.501.75


Heavy Shocks1.751.852.002.25+


When selecting gears application factors should be applied to required torque. T2 > Trequired x Ka Application factor Ka

817M40

32,000 3,000

805M20 (SAE 8620) Case Hardened

50,00011,000

100 rpm uniform speed

Mineral OilBetween 60mm2/s and 130mm2/s at 60°C


LubricationLubrication Viscosity




d2 dr2 da2 de2

a

X N

λ

N Xd1

Worms & Wheels

Description Symbol Unit EquationAxial Module mxNormal Module mn = mx · cos λ Normal Pressure Angle αn degrees = 20°Transverse Pressure Angle αt degrees = tan-1 (tan αn / cos λ)Lead Angle λ degrees = tan-1 ((mx · z1) / d1)Helix Angle β degrees = 90 - λNumber of Starts on Worm z1Number of Teeth on Wheel z2Profile Shift Coefficient x = zero for Ondrives standard wormsAddendum ha mm = 1.00 · mx (for Ondrives standard worms)Dedendum hf mm = 1.25 · mx (for Ondrives standard worms)Tooth Depth h mm = 2.25 · mx (for Ondrives standard worms)Gear Ratio u = z2 / z1Centre Distance a mm = (d1 +d2) / 2Reference Diameter of Worm d1 mm = (mx · z1) / tan λReference Diameter of Wheel d2 mm = mx · z2Tip Diameter of Worm da1 mm = d1 + (2 · mx)Root Diameter of Worm dr1 mm = da1 – (2 · h)Tip Diameter of Wheel da2 mm = d2 + (2 · mx)Root Diameter of Wheel dr2 mm = da2 – (2 · h)Outside Diameter of Wheel de2 mm = da2 + mxNormal Pitch pn mm = π · mnAxial Pitch px mm = π · mxNormal Tooth Thickness in Pitch Circle sn mm = sx · cos λTransverse Tooth Thickness in Pitch Circle sx mm = (px / 2)QualitySteel and Stainless Steel worm = Quality 6, DIN 3974. Bronze wormwheel = Quality 7, DIN 3974. PEEK and Delrin worms = Quality 7, DIN 3974. PEEK and Delrin wormwheel = Quality 8, DIN 3974.When working with a gear set, the subscript 1 denotes a worm and 2 a wormwheel. Tip diameter is the theoretical diameter of the gear without tooth thickness tolerance applied.For sn & sx when x = zero, this is the theoretical tooth thickness. Actual tooth thickness will be less. The subscript e is for upper allowance values and i for lower allowance values.



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pn

dr1 d1 da1

sn px sx

hahf

Worms & Wheels Worms & Wheels

TorqueStated value is maximum torque based on lowest figure from surface durability, tooth root strength or wear.Values for bronze and cast iron wheel are for matching with steel 817M40 worm.Value is output torque (T2) at wheel.Tooth root failure of teeth on wheel before teeth of worm is assumed.Other factors including worm shaft deflection, duty cycle and temperature will affect maximum allowable torque and service life. Wear is dependant on lubrication.We recommend that each user compute their own values based on actual operating conditions and test in application.

Delrin POM 50%*60°C

PEEK GF30®55 - 65%*

80°CMaximum torque as % of CA104 Aluminium Bronze WheelMaximum Wheel Temperature


Uniform1.001.101.251.50

Light Shocks1.251.351.501.75


Heavy Shocks1.751.852.002.25+


* Approximate value based on plastic wheel running with steel worm to allow initial selection. Testing in application will be required.Torque for anti backlash wormwheel gears is limited by the spring rating. Please contact our Technical department for details.When selecting gears application factors should be applied to required torque. T2 > Trequired x Ka Application factor Ka



Coefficient of friction µ (Mineral Oil)Velocity

Range(m/s)

0.0-0.91.0-1.92.0-2.93.0-3.94.0-4.95.0-5.96.0-6.97.0-7.98.0-8.99.0-9.9

10.0-10.911.0-11.912.0-12.913.0-13.914.0-14.915.0-15.916.0-16.917.0-17.918.0-18.919.0-19.920.0-20.921.0-21.922.0-22.923.0-23.924.0-24.925.0-25.926.0-26.927.0-27.928.0-28.929.0-29.9

30.0

00.15000.04380.03290.02760.02420.02190.02020.01870.01760.01690.01610.01550.01490.01460.01430.01410.01390.01370.01350.01340.01320.01310.01300.01290.01280.01270.01260.01250.01240.01230.0123

0.10.08030.04230.03220.02720.02390.02170.02000.01860.01750.01680.01600.01540.01490.01460.01430.01410.01380.01360.01340.01330.01310.01300.01290.01290.01280.01270.01260.01250.01240.0123

-

0.20.06940.04100.03160.02680.02360.02150.01990.01850.01740.01660.01590.01540.01490.01460.01430.01410.01380.01360.01340.01330.01310.01300.01290.01280.01270.01260.01250.01240.01240.0123

-

0.30.06230.03960.03090.02650.02340.02140.01970.01840.01730.01660.01590.01530.01480.01450.01420.01400.01380.01360.01340.01330.01310.01300.01290.01280.01270.01260.01250.01240.01240.0123

-

0.40.05830.03820.03040.02610.02320.02120.01960.01830.01730.01640.01590.01530.01480.01450.01420.01400.01380.01360.01340.01330.01310.01300.01290.01280.01270.01260.01250.01240.01240.0123

-

0.50.05430.03690.02970.02570.02290.02100.01940.01820.01720.01640.01580.01520.01470.01440.01420.01390.01380.01360.01340.01330.01310.01300.01290.01280.01270.01260.01250.01240.01240.0123

-

0.60.05210.03590.02930.02540.02260.02090.01930.01810.01720.01640.01570.01510.01470.01440.01420.01390.01370.01350.01340.01320.01310.01300.01290.01280.01270.01260.01250.01240.01240.0123

-

0.70.05000.03520.02890.02510.02240.02070.01920.01790.01700.01630.01560.01510.01470.01440.01420.01390.01370.01350.01340.01320.01310.01300.01290.01280.01270.01260.01250.01240.01240.0123

-

0.80.04800.03440.02860.02480.02230.02050.01900.01780.01690.01620.01560.01500.01460.01440.01410.01390.01370.01350.01340.01320.01310.01300.01290.01280.01270.01260.01250.01240.01230.0123

-

0.90.04590.03360.02800.02450.02210.02030.01890.01770.01690.01620.01560.01500.01460.01440.01410.01390.01370.01350.01340.01320.01310.01300.01290.01280.01270.01260.01250.01240.01230.0123

-

µ for Velocities 0-30m/s

Example: if Vg = 1.2 then µ = 0.0410

Worms & Wheels

EfficiencyThe following allows an approximate value for the efficiency of the gears to be found allowing required input torque and gearforces to be calculated. Efficiency is dependant on lubrication and the figures below do not include bearing, seal and other losses.

η = tan λ / tan (λ+ pz)pz = arctan (µ)vg = (d1 · n1) / (19098 . cos λ)T1 = (T2 / u) * η

T1 = Input Torque (Nm)T2 = Output Torque (Nm)u = Ratioη = Efficiencyλ = Lead Angle (degrees)µ = Coefficient of Frictionpz = Angle of Frictionvg = Sliding Velocity (m/s)n1 = rpm of Wormd1 = Reference Diameter of Worm (mm)



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Ftm1 = 2000* (T1 / d1) = - Fxm2Ftm2 = 2000* (T2 / d2) = - Fxm1Frm1 = Ftm1* [tan 20 / (sin λ + pz) ] = - Frm2

pz = arctan (µ)Ftm = Tangential force (N)Fxm = Axial force (N)Frm = Radial force (N)When working with a gear set, the subscript 1 denotes a worm and 2 a wormwheel.

Ondrives worm and wheel gears are supplied right hand lead as standard.The arrows show the direction of rotation.

Ftm1 = -Fxm2

Worms & Wheels Worms & Wheels

Gear Forces and Direction of Rotation

Frm1 = -Frm2

Ftm2 = -Fxm1



da

F

hahf

δ1

δ2

d

X

Re

Bevel Gears

Description Symbol Unit EquationNormal Module mn Pressure Angle α degrees = 20°Shaft Angle Σ degrees = (90° for Ondrives standard gears)Number of Teeth z1, z2Gear Ratio u = z2 / z1Pitch Diameter of Worm d1, d2 mm = z · mnPitch Cone Angle δ1 degrees = δ1 = tan-1 (sin Σ / (u + cos Σ))Pitch Cone Angle δ2 degrees = δ2 = Σ - δ1Cone Distance Re mm = d2 / 2 sin δ2Addendum ha mm = 1.00 · mn (for Ondrives standard gears)Dedendum hf mm 0.6 to 1.0mn = 1.25 · mn (standard gears) 1.5 to 2.0mn = 1.22 · mn (standard gears) 4.0mn = 1.20 · mn (standard gears)Outside Diameter da mm = d + 2 ha · cos δPitch Apex to Crown X mm = Re cos δ - ha sin δQuality Grade 7 DIN 3965

TorqueStated value is maximum torque (T2) based on two identical gears with the same number of teeth running at standard centres. Value is minimum from surface stress or bending stress.Other factors including duty cycle and temperature will affect maximum allowable torque and service life.Wear is dependant on lubrication.We recommend that each user compute their own values based on actual operating conditions and test in application.


817M40

32,000 3,000

805M20

50,00011,000

303 Stainless

20,000 1,800

316 Stainless

15,800 1,400




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Bevel Gears Materials

Material Equivalents

Ondrives can manufacture gears in a range of additional materials including bronzes, engineering plastics, special steels and stainless steels.Gears can be heat treated by a range of methods to improve performance.Please contact our Technical sales team who will be happy to discuss your specific requirements.

Material805M20

817M40T080M40

722M24T303S21316S1617-4PHCA104

PB2Brass CZ121PEEK GF30Delrin POM

Cast Iron GG25Titanium Ti-6AL-4V

Case Hardened

Nitride HardenedCold DrawnCold DrawnCondition A

Sand Cast

Continuous CastGrade 5

Density(Kg/m3)

7,8507,8507,8507,8508,0008,0007,7807,5808,6008,4701,4901,4107,2004,420

Elongationafter

Fracture11%

5 - 13%7 - 17%

13%35 - 45%

40%10%15%5%

20%2.7%30%

-10 - 18%

TensileStrength(N/mm2)

980850 - 100510 - 600850 -1000480 - 510

5151103 750

360 - 500410156 67

145 - 195895 -1000

0.2% ProofStress

(N/mm2)785680340650

180 - 200205100430

170 - 280200

---

828 - 910

B.S. 970 817M40T805M20303S21316S16080M40655M13722M24

PB2CA104

Brass CZ121

B.S. 1452Cast Iron 250

Titanium Ti-6AL-4V

En24T3625858J8

3640B

ISOCu89Sn11

GZ-CuAL10NiCuZn39Pb3

EnEN-GJL-250

B.S.2TA11

DIN40NiCrMo8-4 / 34CrNiMo620NiCrMo2-2 / 20NiCrMo2

X10CrNiS189X5CrNiMo17133

C4014NiCr14

32CrMo12

DINCuSn12

CuAL10Ni-

DINDIN 1691 GG25

UNSR56400

Werkstoff1.6562, 1.6582

1.65231.43051.44361.05111.57521.7361

Werkstoff3.7165

SAE/AISI4340, 4337

8620303316

10403415, 3310, 9314

-

SAE/AISISAE 64

ASTM B150 UNC C63200UNC C38500

AMS4911/4928



Delrin POM (White)DIN EN ISO 1043-1: POM C | polyacetal comopolymer.

Very good dimensional stabilitycompared to Nylon & Hostaform.Minimal absorption of moisture.

Good sliding properties.High wear resistance.

High surface hardness.High mechanical strength and stiffness

compared to Nylon & Hostaform.Can be in contact with food (FDA).

Delrin gears can be run dry or greased/oiledto improve wear.

PEEK GF30® (Light Brown)DIN EN ISO 1043-1: PEEK | polyetheretherketone.

Excellent dimensional stability.Outstanding high mechanical strength and hardness

over a broad temperature range.Shows only a slight distortion under the impact of

mechanical load and high temperature.Good electrical insulating properties.

Extremely high flame resistance.Self-extinguishing.

Very low smoke emission in a case of a fire.Can be run dry for slow speed hand operation.

Gears should be greased/oiled for all other operating conditions.

General PropertiesDensityAbsorption of MoistureMechanical propertiesYield Stress/ Tensile StrengthElongation at BreakTensile Modulus of ElasticityBall Indentation HardnessShore - HardnessCoefficient of Friction against hardened and ground steel (dry)Thermal PropertiesMelting TemperatureThermal Properties Coefficient of Linear Thermal ExpansionService Temperature, long term (min.)Service Temperature, long term (max.)Service Temperature, short termHeat Deflection TemperatureElectrical Properties Dielectric Constant Dielectric Dissipation FactorSpecific Volume ResistivitySurface ResistivityComparative Tracking Index (test solution A)Dielectric Strength

kg/m3

N/mm2

N/mm2

N/mm2

Skala D

°CW / (m · K)

10-6 K-1

°C°C°C°C

Ω · cmΩ

kV/mm

Delrin POM 14100.20%

6730.0%2800 150 81

0.10-0.30

1650.31110 -50100140110

3.800.00210131013 600 40

PEEK GF30®14900.14%

1562.7%9700 230 88

0.38-0.46

3430.43 30 -20250310315

3.200.00110141013 175 20

Materials



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The backlash figures given for spur, helical and crossed axis helical gears is the theoretical backlash for two identical gears at standard centre distance to the ISO 286 centre distance tolerance.It is given as circumferential backlash in mm measured on pitch circle diameter. An upper and lower value is quoted.Theoretical backlash is the difference between tooth thickness without and with tolerance applied.Backlash is calculated according to DIN 3967Ondrives can manufacture gears to a wide range of tolerances to suit customer application.Please contact our Technical Sales team who will be happy to discuss your specific requirements.Tooth Thickness Tolerances

Asn = Tooth thickness allowance which is the difference between measured gear tooth thickness and theoretical value measured in the normal section.

When working with a pair of gears the subscript 1 and 2 denotes input (drive) and output (driven) gear. For worm and wheel, 1 relates to the worm and 2 to the wormwheel. The subscript e is for upper allowance and i for lower allowance.Tsn = Tooth thickness tolerance measured in the normal section. (mm)Asne = Sn – SneAsni = Asne – Tsn = Sn – Sni

Circumferential Backlash jtThis is the length of arc on the pitch circle diameter through which each can be rotated whilst the other is held stationary.It is measured in the transverse section.

Units = mm & degrees

Normal Backlash jnThis is the shortest distance between the flanks of the gears when the opposite flanks are in contact.It is measured in the transverse section.For spur, helical, crossed axis helical gear Units = mm & degrees

Change in Circumferential due to Centre Distance Tolerance ∆ja Units = mm & degrees

Deviation from Centre Distance

As (mm)0.0010.0100.0150.0200.0250.0300.0350.0400.0450.050

Change inBacklash∆ja (mm)

0.0010.0070.0110.0150.0180.0220.0250.0290.0330.036


As (mm)0.0010.0100.0150.0200.0250.0300.0350.0400.0450.050


0.0010.0080.0110.0150.0190.0230.0260.0300.0340.038


As (mm)0.0010.0100.0150.0200.0250.0300.0350.0400.0450.050


0.0010.0100.0150.0210.0260.0310.0360.0410.0460.051

Spur Gear Parallel Helical Gear Crossed Axis Helical Gear

Materials Backlash

Gear TypeSpur

Spur (Skive hobbed)Pinion

Parallel HelicalCrossed Axis Helical

Worm & WormwheelGear Type

Bevel

Module 0.5 to 0.87e/8e DIN 58405

6e DIN 584057e DIN 584057e DIN 584057e DIN 58405

7e/8e DIN 58405Module 0.6 to 4.07f24 DIN 3965/3967

Module 1.0 to 3.0e25 DIN 3967e25 DIN 3967e25 DIN 3967e25 DIN 3967e25 DIN 3967e25 DIN 3967

Centre Distance Tol.Js7Js7

-Js7Js8Js8



*Asne is converted from base tangent length allowance (Aw) according to Aw = Asn * cos 20°

e25 DIN 3967

7e DIN 58405

Angular Backlash jθ Units = mm & degrees

d2 = Reference diameter (mm)As = Centre distance tolerance (i.e. a = 30mm Js7, As = ±0.0105mm)αn = Normal pressure angle (αn = 20°)β = Helix angle (β = zero for spur gears) Replace helix angle β with lead angle λ for worm and wheel.1° = 60 arc minutes

360 x π x d2

Backlash

Reference Diameterd (mm)

Over Upto

Upper ToothThickness Allowance

Asne

ToothThickness Tolerance

Tsn - 10 10 50 50 125 125 280

-0.022mm-0.030mm-0.040mm-0.056mm

0.020mm0.030mm0.040mm0.050mm

Reference Diameterd (mm)

NormalModule

msn

Upper ToothThickness Allowance

Asne

ToothThickness Tolerance

Tsn

from 3 to 6

>6 to 12

>12 to 25

>25 to 50

>50 to 100

>100 to 200

>200 to 400

>0.16 to 0.25>0.25 to 0.6>0.6 to 1.6

>0.16 to 0.25>0.25 to 0.6>0.6 to 1.6

>0.16 to 0.25>0.25 to 0.6>0.6 to 1.6>1.6 to 3

>0.16 to 0.25>0.25 to 0.6>0.6 to 1.6>1.6 to 3

>0.16 to 0.25>0.25 to 0.6>0.6 to 1.6>1.6 to 3

>0.6 to 1.6>1.6 to 3

>0.6 to 1.6>1.6 to 3

0.0280.0300.0350.0300.0350.0400.0350.0400.0450.0500.0400.0450.0500.0550.0450.0500.0550.0630.0630.0700.0700.080

0.0110.0120.0140.0120.0140.0160.0140.0160.0180.0200.0160.0180.0200.0220.0180.0200.0220.0240.0240.0290.0290.032



Gear

Tech

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Example for Calculating Backlash for Two Non-Identical GearsInput Gear PSG0.5-20 7eOutput Gear PSG0.5-40 7e1. Calculate the reference diameter d for each gear PSG0.5-20 d1 = z * mn = 10.00mm PSG0.5-40 d2 = 20.00mm2. Find Asne and Tsn from the tables overleaf PSG0.5-20 Asne = -0.035mm Tsn = -0.014mm PSG0.5-40 Asne = -0.040mm Tsn = -0.016mm3. Calculate Asni for each gear PSG0.5-20 Asni = Asne - Tsn = -0.035-0.014 = -0.021mm PSG0.5-40 Asni = Asne - Tsn = -0.040-0.016 = -0.024mm4. Calculate the centre distance of the two gears and the centre distance tolerance centre distance = (10 + 20) / 2 = 15mm Js7 = ±0.009mm5. Calculate the change in backlash due to centre distance

6. Calculate the maximum backlash Remove the minus sign on Asn

7. Calculate the minimum backlash Remove the minus sign on Asn

8. Convert to angular backlash

1° = 60 arc minutes

28.208 to 13.072 arc minutes

0

0

Backlash Backlash

360 x π x d2



OverInc.

F6

F7

G6

G7

H6

H7

H8

H9

H10

H11

J6

J7

J8

JS6

JS7

JS8

K6

M6

M7

36

18102210124

16480

120

180

300

480

7505

–36

–610–84

–46

–69

–92

–6–1–90

–12

610

22132813145

20590

150

220

360

580

9005

–48

–712

–104.5

–4.57.5

–7.511

–112

–7–3

–120

–15

1018

27163416176

246

110

180

270

430

700

11006

–510–815

–125.5

–5.59

–913.5

–13.52

–9–4

–150

–18

1830

33204120207

287

130

210

330

520

840

13008

–512–920

–136.5

–6.510.5

–10.516.5

–16.52

–11–4

–170

–21

3040

4050

5065

6580

80100

100120

120140

140160

6843834339145414250

400

630

1000

1600

2500

18–726

–1441

–2212.5

–12.520

–2031.5

–31.54

–21–8

–330

–40

160180

180200

200225

7950965044156115290

460

720

1150

1850

2900

22–730

–1647

–2514.5

–14.523

–2336

–365

–24–8

–370

–46

225250

41255025259

349

160

250

390

620

1000

1600

10–614

–1124

–158

–812.5

–12.519.5

–19.53

–13–4

–200

–25

4930603029104010190

300

460

740

1200

1900

13–618

–1228

–189.5

–9.515

–1523

–234

–15–5

–240

–30

5836713634124712220

350

540

870

1400

2200

16–622

–1334

–2011

–1117.5

–17.527

–274

–18–6

–280

–35

Hole Sizes (mm)

Micrometres (10-3m)

Limits and Fits



Gear

Tech

nica

lGe

ar Te

chni

cal

OverInc.

f6

f7

g5

g6

g7

h6

h7

h8

h9

h10

h11

j6

j7

js5

js6

js7

k6

m6

m7

36

–10–18–10–22–4–9–4

–12–4

–160

–80

–120

–180

–300

–480

–756

–28

–42.5

–2.54

–46

–691

124

164

610

–13–22–13–28–5

–11–5

–14–5

–200

–90

–150

–220

–360

–580

–907

–210–53

–34.5

–4.57.5

–7.5101

156

216

1018

–16–27–16–34–6

–14–6

–17–6

–240

–110

–180

–270

–430

–700

–1108

–312–64

–45.5

–5.59

–9121

187

257

1830

–20–33–20–41–7

–16–7

–20–7

–280

–130

–210

–330

–520

–840

–1309

–413–84.5

–4.56.5

–6.510.5

–10.5152

218

298

3040

4050

5065

6580

80100

100120

120140

140160

–43–68–43–83–14–32–14–39–14–54

0–25

0–40

0–63

0–100

0–160

0–250

14–1122

–189

–912.5

–12.520

–20283

40155515

160180

180200

200225

–50–79–50–96–15–35–15–44–15–61

0–29

0–46

0–72

0–115

0–185

0–290

16–1325

–2110

–1014.5

–14.523

–23334

46176317

225250

–25–41–25–50–9

–20–9

–25–9

–340

–160

–250

–390

–620

–1000

–16011–515

–105.5

–5.58

–812.5

–12.5182

259

349

–30–49–30–60–10–23–10–29–10–40

0–19

0–30

0–46

0–74

0–120

0–190

12–718

–126.5

–6.59.5

–9.515

–15212

30114111

–36–58–36–71–12–27–12–34–12–47

0–22

0–35

0–54

0–87

0–140

0–220

13–920

–157.5

–7.511

–1117.5

–17.5253

35134813

Hole Sizes (mm)

Micrometres (10-3m)

Limits and Fits Limits and Fits



Keyways to DIN 6885 Js9 sliding fit. D10 free fit and P9 tight fit available on request.Woodruff keyways available on request.Standard bore tolerance H7 ISO 286. Other tolerances available.Special bore shapes available including square and hexagon.

t1

t2

b r

r

h

Modifications

Bore Size dOver

- 6 810121722303844

Bore Size dIncluding

6 81012172230384450

Keyway Sizeb x h

- 2 x 2 3 x 3 4 x 4 5 x 5 6 x 6 8 x 710 x 812 x 814 x 9

PinHole 1.5 2.0 3.0 4.0 5.0 6.0 8.010.010.010.0

TappedHole

M3 x 0.5 M3 x 0.5 M3 x 0.5 M4 x 0.7 M5 x 0.8 M6 x 1.0 M8 x 1.25 M10 x 1.5 M10 x 1.5 M12 x 1.75

Shaft t1 Bore t1Width Depth

Keyb x h2 x 23 x 34 x 45 x 56 x 68 x 7

10 x 812 x 8

Shaft bN9

-0.004/-0.029-0.004/-0.029+0.000/-0.030+0.000/-0.030+0.000/-0.030+0.000/-0.036+0.000/-0.036+0.000/-0.043

Bore bJs9

+0.012/-0.012+0.012/-0.012+0.015/-0.015+0.015/-0.015+0.015/-0.015+0.018/-0.018+0.018/-0.018+0.021/-0.021

Nominal1.21.82.53.03.54.05.05.0

Tolerance+0.10/–0.00+0.10/–0.00+0.10/–0.00+0.10/–0.00+0.10/–0.00+0.20/–0.00+0.20/–0.00+0.20/–0.00

Nominal1.01.41.82.32.83.33.33.3

Tolerance+0.10/–0.00+0.10/–0.00+0.10/–0.00+0.10/–0.00+0.10/–0.00+0.20/–0.00+0.20/–0.00+0.20/–0.00

Radiusr

Max – Min0.16 – 0.080.16 – 0.080.16 – 0.080.25 – 0.160.25 – 0.160.25 – 0.160.40 – 0.250.40 – 0.25

Gear Technical - Gears and Gearbox Manufacturer

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