Spur Gears Description Symbol Unit Equation Normal Module m n Transverse Module m t = m n Normal Pressure Angle α n degrees = 2 Transverse Pressure Angle α t degrees = α n Number of Teeth z Profile Shift Coefficient x = zero for Ondrives standard gears Addendum h a mm = 1. m n (for Ondrives standard gears) Dedendum h f mm = 1.25 m n (for Ondrives standard gears) Tooth Depth h mm = 2.25 m n (for Ondrives standard gears) Gear Ratio u = z 2 / z 1 Centre Distance a mm = (d 1 +d 2 ) / 2 Pitch Circle Diameter d mm = z m n Tip Diameter d a mm = d + (2m n x) + (2 m n ) Root Diameter d r mm = d a (2 h) Normal Pitch p n mm = π m n Normal Tooth Thickness in Pitch Circle s n mm = (p n / 2) + 2m n x tan α n When working with a pair of gears the subscript 1 & 2 denotes input (drive) and output (driven) gear. Tip diameter is the theoretical diameter of the gear without tooth thickness tolerance applied. For s n at 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. d a1 d 1 d r1 s n p n a 1.US Corp. 51771
Spur Gears Gear Quality Standard metal gears are supplied to quality Grade 7 DIN 31 based on Pitch total deviation Fp, Pitch deviation fp, Radial runout Fr and Pitch error fu. Skive hobbed gears are supplied to quality Grade DIN 31. GG25 Cast Iron, PEEK GF3 and Delrin (POM) are supplied to quality Grade DIN 31. 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 Standards Standard DIN 31 DIN 31 ISO 132 AGMA Example 3 mod, 5 teeth, 3mm face width spur gear Grade 7 7 1 Pitch total deviation F p µm 32 5 51 Pitch deviation f p µm 13 13 Radial runout F r µm 22 31 1 Pitch error f u µm 1 Double flank composite transmission error F i " µm 2 3 1 1 Double flank toothtotooth transmission error f i " µm 11 21 2 Torque Stated value for metal spur gears is maximum torque (T 2 ) 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. Materials Input Speed Bending Stress Factor S b Surface Stress Factor S c 17M 32 3 5M2 33 Stainless 31 Stainless GG25 Cast Iron 1 rpm Uniform, hours running per day 5 11 2 1 7 135 Stated value for plastic spur gears is maximum torque (T 2 ) 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/suface temperature using method from BS :17. 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. Materials Input Speed / No. of Load Cycles Limiting Bending Stress Limiting Surface Stress Initial Temperature Max. Bulk or Surface Temperature Coefficient of Friction Delrin POM (White) 1 rpm / 1 22. N/mm 2 13.5 N/mm 2 2 C C. (Dry) PEEK GF3 (Light Brown) 1 rpm / 1 3 N/mm 2 * N/mm 2 * 2 C C.25** * Reference Only ** Approximate value based on initial light greasing. Maximum torque for titanium gears is approximatey 3% of 17M steel gears. Due to lack of stress factors we are unable to offer specific values. Testing in application is required. Torque for antibacklash 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. T 2 > T required x K a Application factor K a Working characteristics of driven machine Working characteristics Light Moderate Heavy of driving machine Uniform Shocks Shocks Shocks Uniform 1. 1.25 1.5 Light Shocks 1.1 1.35 1. 1.5 Moderate Shocks 1.25 1.5 2. Heavy Shocks 1.5 2. 2.25+ 51771.US Corp. 2
Parallel Helical Gears Description Symbol Unit Equation Normal Module m n Transverse Module m t = m n / cos β Axial Module m x = m n / sin β Normal Pressure Angle α n degrees = 2 Transverse Pressure Angle α t degrees = tan 1 (tan α n / cos β) Helix Angle β degrees = Lead Angle λ degrees = β Number of Teeth z Profile Shift Coefficient x = zero for Ondrives standard gears Addendum h a mm = 1. m n (for Ondrives standard gears) Dedendum h f mm = 1.25 m n (for Ondrives standard gears) Tooth Depth h mm = 2.25 m n (for Ondrives standard gears) Gear Ratio u = z 2 / z 1 Centre Distance a mm = (d 1 +d 2 ) / 2 Pitch Circle Diameter d mm = z m t = (z m n ) / cos β Tip Diameter d a mm = d + (2m n x) + (2 m n ) Root Diameter d r mm = d a (2 h) Normal Pitch p n mm = π m n Transverse Pitch p t mm = π m t = (π m n ) / cos β Axial Pitch p x mm = π m x = (π m n ) / sin β Normal Tooth Thickness in Pitch Circle s n mm = (p n / 2) + 2m n x tan α n Transverse Tooth Thickness in Pitch Circle s t mm = (p t / 2) + 2m n x tan α t When working with a pair of gears the subscript 1 & 2 denotes input (drive) and output (driven) gear. Tip diameter is the theoretical diameter of the gear without tooth thickness tolerance applied. For s n & s t, 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. d a1 d 1 d r1 p t s t a β 3.US Corp. 51771
Parallel Helical Gears Gear Quality Standard gears are supplied to quality grade 7e25 DIN 31 based on the following parameters Radial Runout F r = Pitch Deviation f p = Total Pitch Deviation F p = Pitch Error f u = 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 Standards Example 3 mod, 5 teeth, 3mm face width helix parallel helical gear Standard DIN 31 ISO AGMA Grade 7 7 1 Pitch total deviation F p µm 7 5 55 Pitch deviation f p µm 13 Radial runout F r µm 31 Pitch error f u µm Double flank composite transmission error F i " µm 3 1 5 Double flank toothtotooth transmission error f i " µm 21 2 Torque Stated value is maximum torque (T 2 ) 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. Materials Input Speed Bending Stress Factor S b Surface Stress Factor S c When selecting gears application factors should be applied to required torque. T 2 > T required x K a Application factor K a Working characteristics of driving machine Uniform Light Shocks Moderate Shocks Heavy Shocks 17M 5M2 33 Stainless 31 Stainless 1 rpm Uniform, hours running per day 32 3 5 11 2 1 Uniform 1. 1.1 1.25 1.5 Working characteristics of driven machine Light Moderate Shocks Shocks 1.25 1.5 1.35 1. 1.5 2. Heavy Shocks 1.5 2. 2.25+ 51771.US Corp.
Crossed Axis Helical Gears Description Symbol Unit Equation Normal Module m n Transverse Module m t = m n / cos β Axial Module m x = m n / sin β Normal Pressure Angle α n degrees = 2 Transverse Pressure Angle α t degrees = tan 1 (tan α n / cos β) Helix Angle β degrees = 5 Lead Angle λ degrees = β Number of Teeth z Profile Shift Coefficient x = zero for Ondrives standard gears Addendum h a mm = 1. m n (for Ondrives standard gears) Dedendum h f mm = 1.25 m n (for Ondrives standard gears) Tooth Depth h mm = 2.25 m n (for Ondrives standard gears) Gear Ratio u = z 2 / z 1 Centre Distance a mm = (d 1 +d 2 ) / 2 Pitch Circle Diameter d mm = z m t = (z m n ) / cos β Tip Diameter d a mm = d + (2m n x) + (2 m n ) Root Diameter d r mm = d a (2 h) Normal Pitch p n mm = π m n Transverse Pitch p t mm = π m t = (π m n ) / cos β Axial Pitch p x mm = π m x = (π m n ) / sin β Normal Tooth Thickness in Pitch Circle s n mm = (p n / 2) + 2m n x tan α n Transverse Tooth Thickness in Pitch Circle s t mm = (p t / 2) + 2m n x tan α t When working with a pair of gears the subscript 1 & 2 denotes input (drive) and output (driven) gear. Tip diameter is the theoretical diameter of the gear without tooth thickness tolerance applied. For s n & s t, 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. d a1 d 1 p t s t p x a β λ 5.US Corp. 51771
Crossed Axis Helical Gears Direction of Rotation Torque Stated value is maximum torque (T 2 ) 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. Materials Input Speed Bending Stress Factor S b Surface Stress Factor S c Lubrication Lubrication Viscosity When selecting gears application factors should be applied to required torque. T 2 > T required x K a Application factor K a Right Hand Helix Working characteristics of driving machine Uniform Light Shocks Moderate Shocks Heavy Shocks Uniform 1. 1.1 1.25 1.5 Left Hand Helix 17M 5M2 (SAE 2) Case Hd. 1 rpm Uniform speed 32 5 3 11 Mineral Oil Between mm 2 /s and 13mm 2 /s at C Working characteristics of driven machine Light Moderate Shocks Shocks 1.25 1.5 1.35 1. 1.5 2. Heavy Shocks 1.5 2. 2.25+ 51771.US Corp.
Worms & Wheels Description Symbol Unit Equation Axial Module m x Normal Module m n = m x cos λ Normal Pressure Angle α n degrees = 2 Transverse Pressure Angle α t degrees = tan 1 (tan α n / cos λ) Lead Angle λ degrees = tan 1 ((m x z 1 ) / d 2 ) Helix Angle β degrees = λ Number of Starts on Worm z 1 Number of Teeth on Wheel z 2 Profile Shift Coefficient x = zero for Ondrives standard worms Addendum h a mm = 1. m x (for Ondrives standard worms) Dedendum h f mm = 1.25 m x (for Ondrives standard worms) Tooth Depth h mm = 2.25 m x (for Ondrives standard worms) Gear Ratio u = z 2 / z 1 Centre Distance a mm = (d 1 +d 2 ) / 2 Reference Diameter of Worm d 1 mm = (m x z 1 ) / tan λ Reference Diameter of Wheel d 2 mm = m x z 2 Tip Diameter of Worm d a1 mm = d 1 + (2 m x ) Root Diameter of Worm d r1 mm = d a1 (2 h) Tip Diameter of Wheel d a2 mm = d 2 + (2 m x ) Root Diameter of Wheel d r2 mm = d a2 (2 h) Outside Diameter of Wheel d e2 mm = d a2 + m x Normal Pitch p n mm = π m n Axial Pitch p x mm = π m x Normal Tooth Thickness in Pitch Circle s n mm = s x cos λ Transverse Tooth Thickness in Pitch Circle s x mm = (p x / 2) Gear Quality: Steel and Stainless Steel Worm = DIN 37, Bronze Wheel = 7 DIN 37. PEEK and Delrin Worms 7 DIN 37, PEEK and Delrin Wheel = DIN 37. When working with a gear set the subscript 1 denotes a worm and 2 a wheel. Tip diameter is the theoretical diameter of the gear without tooth thickness tolerance applied. For s n & s x, 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. d 2 d r2 d 1 d a2 d e2 a X N N X λ 7.US Corp. 51771
Worms & Wheels p n Normal Section Torque Stated 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 17M worm. Value is output torque T 2 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. Surface Durability Tooth Root Strength Input Speed Life Limiting Stress N/mm 2 (CA1) Limiting Stress N/mm 2 (GG25) Lubrication Lubrication Viscosity Application Factor s n p x s x.2.1 Maximum torque as % of CA1 Aluminium Bronze Wheel Maximum Wheel Temperature Working characteristics of driving machine Uniform Light Shocks Moderate Shocks Heavy Shocks h f Uniform 1. 1.1 1.25 1.5 h a Axial Section 1 rpm Uniform Speed 25, hours d r1 d 1 d a1 Mineral Oil Between mm 2 /s and 13mm 2 /s at C 1. Delrin POM 5%* C PEEK GF3 55 5%* C * 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 worm application factors should be applied to required torque. T 2 > T required x K a Application factor K a Working characteristics of driven machine Light Moderate Shocks Shocks 1.25 1.5 1.35 1. 1.5 2. Heavy Shocks 1.5 2. 2.25+ 51771.US Corp.
Worms & Wheels Efficiency The following allows an approximate value for the efficiency of the gears to be found allowing required input torque and gear forces 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) / (1. tan λ) T1 = (T2 / u) * η Coefficient of friction µ (Mineral Oil) Velocity Range (m/s).. 1.1. 2.2. 3.3... 5.5... 7.7..... 1.1. 11.11... 13.13. 1.1... 1.1. 17.17... 1.1. 2.2. 21.21. 22.22. 23.23. 2.2. 25.25. 2.2. 27.27. 2.2. 2.2. 3...3.32.27.22.21.22.7.17.1.11.5.1.1.13.11.13.137.135.13.132.131.13...7..5..3.3.1.3.23.322.272.23.217.2..175..1..1.1.13.11.13.13.13.133.131.13....7..5..3.2..1.31.2.23.2.1.5.17.1...1.1.13.11.13.13.13.133.131.13...7..5...3 T1= Input Torque (Nm) T2= Output Torque (Nm) u = Ratio η = Efficiency λ = Lead Angle (degrees) µ = Coefficient of Friction pz = Angle of Friction vg = Sliding Speed (m/s) n1= rpm of Worm d1= Pitch Diameter of Worm (mm) µ for Velocities 3m/s.3.23.3.3.25.23.21.17..173.1..3.1..12.1.13.13.13.133.131.13...7..5...3..53.32.3.21.232.2.1.3.173.1..3.1..12.1.13.13.13.133.131.13...7..5...3.5.53.3.27.257.22.21.1.2.172.1..2.17.1.12.13.13.13.13.133.131.13...7..5...3..521.35.23.25.22.2.13.1.172.1.7.1.17.1.12.13.137.135.13.132.131.13...7..5...3.7.5.352.2.251.22.27.12.17.17.13..1.17.1.12.13.137.135.13.132.131.13...7..5...3...3.2.2.223.25.1.17.1....1.1.11.13.137.135.13.132.131.13...7..5..3.3..5.33.2.25.221.23..177.1....1.1.11.13.137.135.13.132.131.13...7..5..3.3.US Corp. 51771
Worms & Wheels Gear Forces and Direction of Rotation F tm1 = F xm2 Ftm1 = 2*(T1 / d1) = Fxm2 Ftm2 = 2*(T2 / d2) = Fxm1 Frm1 = Ftm1*[tan 2 / (sin λ + pz) ] = Frm2 F rm1 = F rm2 pz = arctan (µ) Ftm = Tangential force (N) Fxm = Axial force (N) Frm = Radial force (N) The subscript 1 and 2 relate to the worm and wheel. Ondrives worm and wheel gears are supplied right hand lead as standard. The black arrows show the direction of rotation. F tm2 = F xm1 51771.US Corp. 1
Bevel Gears Description Symbol Unit Equation Normal Module m n Pressure Angle α degrees = 2 Shaft Angle Σ degrees = ( for Ondrives standard gears) Number of Teeth z 1, z 2 Gear Ratio u = z 2 / z 1 Pitch Diameter of Worm d 1, d 2 mm = z m n Pitch Cone Angle δ 1 degrees = δ 1 = tan 1 (sin Σ / (u + cos Σ)) Pitch Cone Angle δ 2 degrees = δ 2 = Σ δ 1 Cone Distance R e mm = d 2 / 2 sin δ 2 Addendum h a mm = 1. m n (for Ondrives standard gears) Dedendum h f mm. to 1.m n = 1.25 m n (standard gears) 1.5 to 2.m n = 1.22 m n (standard gears).m n = 1.2 m n (standard gears) Outside Diameter d a mm = d + 2 ha cos δ Pitch Apex to Crown X mm = R e cos δ h a sin δ Quality Grade 7 DIN 35 d a d X δ 2 Torque Stated value is maximum torque (T 2 ) 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. Materials Input Speed Bending Stress Factor S b Surface Stress Factor S c δ 1 h ahf F R e 17M 5M2 33 Stainless 31 Stainless 1 rpm Uniform, hours running per day 32 3 5 11 2 1 11.US Corp. 51771
Materials 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. 5M2 17MT M 722M2T 33S21 31S1 17PH CA1 PB2 Brass CZ1 PEEK GF3 Delrin POM Cast Iron GG25 Titanium TiALV Case Hardened Nitride Hardened Cold Drawn Cold Drawn Condition A Sand Cast Continuous Cast Grade 5 Material Equivalents B.S. 7 17MT 5M2 33S21 31S1 M 55M13 722M2 PB2 CA1 Brass CZ1 B.S. 2 Cast Iron 25 Titanium TiALV En 2T 32 5 5J 3 B ISO CuSn11 GZCuAL1Ni CuZn3Pb3 En ENGJL25 B.S. 2TA11 Density (Kg/m 3 ) 75 75 75 75 77 75 7 1 11 72 2 Elongation after Fracture 11% 513% 717% 13% 355% % 1% % 5% 2% 2.7% 3% 1% DIN NiCrMo / 3CrNiMo 2NiCrMo22 / 2NiCrMo2 X1CrNiS X5CrNiMo17133 C 1NiCr1 32CrMo CuSn CuAL1Ni DIN DIN 11 GG25 UNS R5 Tensile Strength (N/mm 2 ) 51 51 51 51 5 113 75 35 1 7 51 Werkstoff 1.52, 1.52 1.523 1.35 1.3 1.511 1.5752 1.731 Werkstoff 3.7.2% Proof Stress (N/mm 2 ) 75 3 5 2 25 1 3 172 2 21 SAE/AISI 3, 337 2 33 31 1 3, 331, 31 SAE ASTM B UNC C32 UNC C35 AMS 11/2 51771.US Corp.
Materials Delrin POM (White) DIN EN ISO 131: POM C polyacetal comopolymer. Very good dimensional stability compared 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/oiled to improve wear. General Properties Density Absorption of Moisture Mechanical properties Yield Stress/ Tensile Strength Elongation at Break Tensile Modulus of Elasticity Ball Indentation Hardness Shore Hardness Coefficient of Friction against hardened and ground steel (dry) Thermal Properties Melting Temperature Thermal Properties Coefficient of Linear Thermal Expansion Service Temperature, long term (min.) Service Temperature, long term (max.) Service Temperature, short term Heat Deflection Temperature Electrical Properties Dielectric Constant Dielectric Dissipation Factor Specific Volume Resistivity Surface Resistivity Comparative Tracking Index (test solution A) Dielectric Strength PEEK GF3 (Light Brown) DIN EN ISO 131: 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. Selfextinguishing. 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. kg/m 3 N/mm 2 N/mm 2 N/mm 2 Skala D C W / (m K) 1 K 1 C C C C Ω cm Ω kv/mm Delrin POM 11.2% 7 3.% 2 1.1.3.31 11 5 1 1 11 3..2 113 113 PEEK GF3 1.1% 2.7% 7 23.3. 33.3 3 2 25 31 3 3.2.1 11 113 175 2 13.US Corp. 51771
Backlash 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 2 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 37 Ondrives 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 Gear Type Spur Spur (Skive hobbed) Pinions Parallel Helical Crossed Axis Helical Worm & Wheel Bevel Module.5 to. 7e/e DIN 55 e DIN 55 7e DIN 55 7e DIN 55 7e DIN 55 7e/e DIN 55 Module 1. to 3. e25 DIN 37 e25 DIN 37 e25 DIN 37 e25 DIN 37 e25 DIN 37 e25 DIN 37 Module. to. 7f2 DIN 35/37 Centre Distance Tolerance Js7 Js7 Js7 Js Js A sn = 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 & 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. T sn = Tooth thickness tolerance measured in the normal section. (mm) A sne = S n S ne A sni = A sne T sn = S n S ni Circumferential Backlash j t This 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 j n This 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 Units = mm & degrees Spur Gear Parallel Helical Gear Crossed Axis Helical Gear Deviation from centre distance A s (mm).1.1..2.25.3.35..5.5 Change in Backlash j a (mm).1.7.11...22.25.2.33.3 Deviation from centre distance A s (mm).1.1..2.25.3.35..5.5 Change in Backlash j a (mm).1..11..1.23.2.3.3.3 Deviation from centre distance A s (mm).1.1..2.25.3.35..5.5 Change in Backlash j a (mm).1.1..21.2.31.3.1..51 j a 51771.US Corp. 1
Backlash Angular Backlash jθ 3 x Units = mm & degrees π x d2 d 2 = Reference diameter (mm) A s = centre distance tolerance (i.e. a = 3mm Js7, As = ±.mm α n = Normal pressure angle (α n = 2 ) β = Helix angle (β = zero for spur gears) Replace helix angle β with lead angle λ for worm and wheel. 1 = arc minutes e25 DIN 37 Reference Diameter d (mm) Over Upto 1 1 5 5 5 5 2 7e DIN 55 Reference Diameter d (mm) from 3 to above to above to 25 above 25 to 5 above 5 to 1 above 1 to 2 above 2 to Normal Module m n above.1 to.25 above.25 to. above. to 1. above.1 to.25 above.25 to. above. to 1. above.1 to.25 above.25 to. above. to 1. above 1. to 3 above.1 to.25 above.25 to. above. to 1. above 1. to 3 above.1 to.25 above.25 to. above. to 1. above 1. to 3 above. to 1. above 1. to 3 above. to 1. above 1. to 3 Upper Tooth Thickness Allowance A sne.22mm.3mm.mm.5mm Upper Tooth Thickness Allowance A sne.2.3.35.3.35..35..5.5..5.5.55.5.5.55.3.3.7.7. *A sne is converted from base tangent length allowance (A w) according to A w = A sn * cos 2 Tooth Thickness Tolerance T sn.2mm.3mm.mm.5mm Tooth Thickness Tolerance T sn.11..1..1.1.1.1..2.1..2.22..2.22.2.2.2.2.32.us Corp. 51771
Backlash Example for Calculating Backlash for Two NonIdentical Gears Input Gear PSG.52 7e Ouput Gear PSG.5 7e 1. Calculate the reference diameter d for each gear PSG.52 d1 = z * mn = 1.mm PSG.5 d2 = 2.mm 2. Find Asne and Tsn from the tables overleaf PSG.52 Asne =.35mm Tsn =.1mm PSG.5 Asne =.mm Tsn =.1mm 3. Calculate Asni for each gear PSG.52 Asni = Asne Tsn =.35.1 =.21mm PSG.5 Asni = Asne Tsn =..1 =.2mm. Calculate the centre distance of the two gears and the centre distance tolerance centre distance = (1 + 2) / 2 = mm Js7 = ±.mm 5. Calculate the change in backlash due to centre distance. Calculate the maximum backlash Remove the minus sign on Asn 7. Calculate the minimum backlash Remove the minus sign on Asn. Convert to angular backlash 3 x 1 = arc minutes π x d2 2.2 to 13.72 arc minutes 51771.US Corp. 1
Limits and Fits P R E C I S I O N G E A R S 51771 17.US Corp. Over Inc. F F7 G G7 H H7 H H H1 H11 J J7 J JS JS7 JS K M M7 3 1 22 1 1 3 75 5 3 1 2 1 1 22 13 2 13 1 5 2 5 22 3 5 5 7 1.5.5 7.5 7.5 11 11 2 7 3 1 27 1 3 1 17 2 11 27 3 7 11 5 1 5.5 5.5 13.5 13.5 2 3 33 2 1 2 2 7 2 7 13 21 33 52 13 5 2 13.5.5 1.5 1.5 1.5 1.5 2 11 17 21 3 5 5 5 5 1 1 1 1 1 3 3 3 3 1 5 1 25 3 1 1 25 7 2 1 1 22.5.5 2 2 31.5 31.5 21 33 1 2 2 225 7 5 5 1 2 72 1 5 2 22 7 3 1 7 25 1.5 1.5 23 23 3 3 5 2 37 225 25 1 25 5 25 25 3 1 25 3 2 1 1 1 1 11 2.5.5 1.5 1.5 3 13 2 25 3 3 2 1 1 1 3 7 1 13 2.5.5 23 23 5 2 3 5 3 71 3 3 7 22 35 5 7 1 22 1 22 13 3 2 11 11 17.5 17.5 27 27 2 35 Hole Sizes (mm) Micrometres (1 3 m)
Limits and Fits P R E C I S I O N G E A R S 51771.US Corp. Over Inc. f f7 g5 g g7 h h7 h h h1 h11 j j7 js5 js js7 k m m7 3 1 1 22 1 3 75 2 2.5 2.5 1 1 1 13 22 13 2 5 11 5 1 5 2 22 3 5 7 2 1 5 3 3.5.5 7.5 7.5 1 1 21 1 1 27 1 3 1 17 2 11 27 3 7 11 3 5.5 5.5 1 7 25 7 3 2 33 2 1 7 1 7 2 7 2 13 21 33 52 13 13.5.5.5.5 1.5 1.5 2 21 2 3 5 5 5 5 1 1 1 1 1 3 3 3 1 32 1 3 1 5 25 3 1 1 25 1 11 22.5.5 2 2 2 3 55 1 2 2 225 5 7 5 35 1 2 72 1 5 2 1 13 25 21 1 1 1.5 1.5 23 23 33 17 3 17 225 25 25 1 25 5 2 25 3 1 25 3 2 1 1 11 5 1 5.5 5.5.5.5 2 25 3 3 3 1 23 1 2 1 1 3 7 1 7.5.5.5.5 21 2 3 11 1 11 3 5 3 71 27 3 7 22 35 5 7 1 22 13 2 7.5 7.5 11 11 17.5 17.5 25 3 35 13 13 Hole Sizes (mm) Micrometres (1 3 m)
Modifications Bore Size d Over 1 17 22 3 3 Key bxh mm 2x2 3x3 x 5x5 x x7 1x x Bore Size d Including 1 17 22 3 3 5 Width Shaft b Bore b N Js./.2 +./../.2 +./. +./.3 +./. +./.3 +./. +./.3 +./. +./.3 +./. +./.3 +./. +./.3 +.21/.21 Keyway Size bxh 2x2 3x3 x 5x5 x x7 1x x 1x Boring out available. Keyways to DIN 5 Js Sliding Fit. D1 free fit and P Tight fit available on request. Woodruff keyways available on request. Standard bore tolerance H7 ISO 2. Other tolerances available. Special bore shapes available including square and hexagon. Nom 1.2 1. 2.5 3. 3.5. 5. 5. Depth Pin Hole 1.5 2. 3.. 5... 1. 1. 1. Shaft t 1 Bore t 2 Tolerance Nom +.1/. 1. +.1/. 1. +.1/. 1. +.1/. 2.3 +.1/. 2. +.2/. 3.3 +.2/. 3.3 +.2/. 3.3 Tolerance +.1/. +.1/. +.1/. +.1/. +.1/. +.2/. +.2/. +.2/. Tapped Hole M3x.5 M3x.5 M3x.5 Mx.7 M5x. Mx1. Mx1.25 M1x1.5 M1x1.5 Mx Radius r Max Min.1..1..1..25.1.25.1.25.1..25..25 b r t t 2 h 1 r 1.US Corp. 51771