Rack and Pinion Drive – Calculation and Selection - PDF document

Dimensions in mmZD … 11/2012 ChapterRacks Helical m = 1.5 ZA-30 m = 2 ZA-31 m = 3 ZA-32 m = 4 ZA-33 m = 5 ZA-34 m = 6 ZA-35 m = 8 ZA-36 m = 10 ZA-37 m = 12 ZA-38Racks Straight m = 1 ZB-36 m = 1.5 ZB-37 m = 2 ZB-38 m = 2.5 ZB-39 m = 3 ZB-40 m = 4 ZB-41 m = 5 ZB-42 m = 6 ZB-43 m = 8 ZB-44 m = 10 ZB-45 m = 12 ZB-46Integrated Racks m = 2 ZC-15 m = 3 ZC-16 m = 4 ZC-17 p = 5 mm ZC-18 p = 10 mm ZC-19 p = 13.33 mm ZC-20Calculation, Instruction Calculation Example Travelling Operation ZD-3 Actual size of modular gearing according to DIN 867 ZD-5 Dimensions in mmZD … 21/2012 The values given in the load table are based upon uniform, smooth operation, K=1.0 and reliable grease lubrication. Since, in practice, the applications are very diverse, it is important to consider the given conditions by using appropriate factors SFormulas for Determining the Tangential Force = [m/s²] = (for lifting axle) [kN] = (for driving axle) [kN] u perm. = [kN] Formula dimensions see page ZD-3Drive Type of load from the machines to be driven Uniform Medium Shocks Heavy ShocksUniform 1.00 1.25 1.75Light Shocks 1.25 1.50 2.00Medium Shocks 1.50 1.75 2.25The safety coef“cient should be allowed for according to experience (S u Tab Lubrication uous 0.5 30 0.85 0.95 1.0 60 0.95 1.10 from 1.5 90 1.00 1.20 3 2.0 120 1.05 1.30 to 3.0 180 1.10 1.50 10 5.0 300 1.25 1.90 The linear load distribution factor considers the contact stress, while it describes unintegrated load distribution over the to = 1.1 for counter bearing, e.g. Torque Supporter = 1.2 for preloaded bearings on the output shaft e.g. ATLANTA HT, HP and E servo-worm gear unit, BG bevel-gear unit = 1.5 for unpreloaded bearings on the output shaft e.g. ATLANTA B servo-worm gear unit Dimensions in mmZD … 31/2012 Your CalculationValues Given Travelling OperationMass to be Moved m = kgSpeed v = m/sAcceleration Time t = sAcceleration Due to Gravity g = 9.81 m/sCoef“cient of Friction µ = Load Factor K = Life-Time Factor f = Safety Coef“cient S = Linear Load LCalculation Process Results = a = = m/s= = kNPermissible Feed Forceu Tabu zul./per. u zul. /per. kNu zul./per.; �kN kN �= ful“lled Values Given Travelling Operation Mass to be Moved m = 820 kgSpeed v = 2 m/sAcceleration Time t = 1 sAcceleration Due to Gravity g = 9.81 m/sCoef“cient of Friction µ = 0.1Load Factor K = 1.5Life-Time Factor f = 1.05 Safety Coef“cient S = 1.2Linear Load LCalculation Process Results = = = 2 m/s= 8202 = 2.44 kNAssumed feed force: rack C45, ind. hardened, straight tooth, module 3, pinion 16MnCr5, case hardened, 20 teeth, u zul./per. u zul./per. u zul./per. ;� 4.05 kN 2.44 kN �= ful“lled Result: Rack 27 30 101 Page ZB-13 Pinion 24 35 220 Page ZB-23 case hardened tb uTab 21 11.5 kN u Tab 1000 1000 10001000 Dimensions in mmZD … 41/2012 Your CalculationValues Given Lifting OperationMass to be Moved m = kgSpeed v = m/sAcceleration Time t = sAcceleration Due to Gravity g = 9.81 m/s²Load Factor K = Life-Time Factor f = Safety Coef“cient S = Linear Load LCalculation Process Results = a = = m/s² a Fu erf./req. = = kNPermissible Feed Force Fu zul./per. u zul./per. kNu zul./per. ; �kN kN �= ful“lled Values Given Lifting OperationMass to be Moved m = 300 kgSpeed v = 1.08 m/sAcceleration Time t = 0.7 sAcceleration Due to Gravity g = 9.81 m/s²Load Factor K = 1.2 Life-Time Factor f = 1.1 Safety Coef“cient S = 1.2Linear Load L = 1.2Calculation Process Results = = = 4 m/s²= 300·9.81+300·4 = 4.1 kNAssumed feed force: rack C45, ind. hardened, helical, pinion 16MnCr5, case hardened, 20 teeth, page u zul./per. u zul./per. = u zul./per. ;� 6.0 kN 4.1 kN �= ful“lled Result: Rack 29 20 105 Page ZA-7 Pinion 24 29 520 Page ZA-24 tb tb 1.08 u Tab u Tab 1000 1000 10001000 11.5 kN1.2·1.2·1.1·1.2