Md-17 Shaft Design

1 1 August 15, 2007 August 15, 2007111717.. Shaft DesignShaft DesignObjectivesObjectives Compute forces acting on shafts from gears, pulleys, and Compute forces acting on shafts from gears, pulleys, and Find bending moments from gears, pulleys, or sprockets that Find bending moments from gears, pulleys, or sprockets that are transmitting loads to or from other transmitting loads to or from other devices. Determine torque in shafts from gears, pulleys, sprockets, Determine torque in shafts from gears, pulleys, sprockets, clutches, and , and couplings. Compare combined stresses to suitable allowable stresses, Compare combined stresses to suitable allowable stresses, including any required stress reduction factors such as stress including any required stress reduction factors such as stress concentration factors and factors of factors and factors of safety.

2 Determine suitability of Shaft Design and/or necessary size of Determine suitability of Shaft Design and/or necessary size of 15, 2007 August 15, 200722 IntroductionIntroduction Shaft must have adequate Shaft must have adequate torsionaltorsionalstrength to strength to transmit torque and not be over torque and not be over stressed. Shafts are mounted in bearings and transmit power Shafts are mounted in bearings and transmit power through devices such as gears, pulleys, cams and through devices such as gears, pulleys, cams and Components such as gears are mounted on shafts Components such as gears are mounted on shafts using keys.

3 Shaft must sustain a combination of bending and Shaft must sustain a combination of bending and 15, 2007 August 15, 200733 Standard diameters of shaftsStandard diameters of shafts1/41/45 to 85 to 81/81/83 to 53 to 51/161/16 UptoUpto33 Diameter Diameter increments (in.)increments (in.)Diameter (in.)Diameter (in.)August 15, 2007 August 15, 200744 Torsion of circular shaftsTorsion of circular shaftsAugust 15, 2007 August 15, 200755 Torsion of circular shaftsTorsion of circular shafts = the angle of twist (radians)= the angle of twist (radians) T = the applied torque (inT = the applied torque (in--lb.)lb.) L = Shaft length (in.)

4 L = Shaft length (in.) J = polar moment on inertia of the Shaft cross section J = polar moment on inertia of the Shaft cross section (in(in44)) G = shear modulus of elasticity of the Shaft material G = shear modulus of elasticity of the Shaft material (lb/in(lb/in22))JGLT twist,of Angle=August 15, 2007 August 15, 2007662 August 15, 2007 August 15, 200777 TorsionalTorsionalShear StressesShear Stresses TorsionalTorsionalshear stress, Sshear stress, SSS== J = Polar moment of inertia = J = Polar moment of inertia = c = radius of the Shaft c = radius of the Shaft T = TorqueT = Torque d = diameter of shaftd = diameter of shaftTorqueJcT32d 4 August 15, 2007 August 15, 200788 Shear Stress in a shaftShear Stress in a Shaft Shear stress, SShear stress, SSS==WhereWhere T = torqueT = torque D = diameter of the Shaft = D = diameter of the Shaft = Torque3 T16D3SS T16 August 15.

5 2007 August 15, 200799 Forces on spur gear teethForces on spur gear teeth FFtt= Transmitted force= Transmitted force FFnn= Normal force or separating = Normal force or separating forceforce FFrr= Resultant force = Resultant force = pressure angle= pressure angle FFnn= F= Ftttan tan cosFFtr=August 15, 2007 August 15, 20071010 Forces on spur gear teethForces on spur gear teeth Power, orPower, or Torque, T = FTorque, T = Fttr and r = r and r = DDpp/2 /2 Combining the above we can writeCombining the above we can write63,000nTP=nD63,000P2DT2 Fppt ==n P63,000T=August 15, 2007 August 15, 20071111 Loads from Bevel gearsLoads from Bevel gears An additional axial force will be acting on the Shaft An additional axial force will be acting on the Shaft because of the bevel anglebecause of the bevel angle For the pinion it is relatively small, and can be For the pinion it is relatively small, and can be For the larger gear it will be significant and will be For the larger gear it will be significant and will be larger than the radial separating than the radial separating from Bevel gearsLoads from Bevel gears Force transmitted.

6 FForce transmitted, Fn n = F= Ftttan tan coscos = Pressure angle= Pressure angle = Cone angle= Cone angle Axial Force, Axial Force, FFaa= F= Ftttan tan sin sin Resultant Force, FResultant Force, Frr= = F = FF = Fnnor or FFaadepending on whichever is largerdepending on whichever is larger22tFF+3 August 15, 2007 August 15, 20071313 Loads from worm gearsLoads from worm gearsAxialDrivingSeparatingAugust 15, 2007 August 15, 20071414 Loads from worm gearsLoads from worm gears Driving force on the worm gear , FDriving force on the worm gear , Ftt= = TToo= Output torque= Output torque Separating force, FSeparating force, Fss==wherewhere = lead angle= lead angle = normal pressure angle= normal pressure angle f = coefficient of frictionf = coefficient of frictionwgorT sinf- cos cos sinFtAugust 15, 2007 August 15, 20071515 Loads from worm gearsLoads from worm gearsAugust 15, 2007 August 15, 20071616 Loads from worm gearsLoads from worm gears Axial force on the worm gearAxial force on the worm gearwherewhere = lead angle= lead angle = normal pressure angle= normal pressure angle f = coefficient of frictionf = coefficient of friction += sinf- cos cos cosf sin cosFFt( gear )a( gear )

7 August 15, 2007 August 15, 20071717 Loads from Belts and ChainsLoads from Belts and Chains For a belt, Total load, FFor a belt, Total load, Ftt= F= Fff+ + FFbb Net driving force, Net driving force, FFdd= F= Fff FFbb Driving torque, TDriving torque, T= = FFddrr r = effective radius of pulley or sprocketr = effective radius of pulley or sprocket For a chain For a chain FFbb= 0= 0 August 15, 2007 August 15, 20071818 Bending of circular shaftsBending of circular shafts Shafts transmit power through gears and Shafts transmit power through gears and pulleyspulleys These produce bending load in addition to These produce bending load in addition to torsiontorsion Use strength of material approach to calculate Use strength of material approach to calculate the reaction forces and bending momentsthe reaction forces and bending moments4 August 15, 2007 August 15, 20071919 Bending of circular shaftsBending of circular shaftsAugust 15, 2007 August 15.

8 20072020 Bending of circular shaftsBending of circular shaftsAugust 15, 2007 August 15, 20072121 Shaft Design ProblemsShaft Design Problems Step 1:Step 1:Calculate the torque on the Shaft from powerCalculate the torque on the Shaft from power Step 2:Step 2:Find the Find the torsionaltorsionalstress in the shaftstress in the Shaft Step 3:Step 3:Calculate the loads coming from gears, belts Calculate the loads coming from gears, belts or chainsor chains Step 4:Step 4:Calculate the bending moment due to the Calculate the bending moment due to the acting forces. If necessary combine the forces. If necessary combine the forces.

9 Step 5:Step 5:Calculate the bending stress in the shaftCalculate the bending stress in the Shaft Step 6:Step 6:Combine the bending stress and the Combine the bending stress and the torsionaltorsionalstress using the theories discussed in chapter 4stress using the theories discussed in chapter 4 August 15, 2007 August 15, 20072222 Shaft shown drives a gear set that is transmitting 5 hp at 1750 rpm. Shaft is supported in self-aligning ball bearings and gears are both 10 pitch, 40 tooth, 20 spur gears. Find torsional and bending stresses in Problem 17-1: Design Stresses in ShaftsAugust 15, 2007 August 15, 20072323 Find the torsion in the Shaft :(2-6)hp = Tn63,000 then:(17-1)T = 63,000 hpn T = 63,000 (5)1750 T = 180 in-lbExample Problem 17-1: Design Stresses in Shafts (cont d.)

10 August 15, 2007 August 15, 20072424 Find the torsional stress in the Shaft . First find Z':(Appendix 3)Z' = D316 Z' = (.75 in)316 Z' = .083 in3(3-6)Ss = TZ' Ss = 180 in3 Ss = 2170 lb/in2 Example Problem 17-1: Design Stresses in Shafts (cont d.)5 August 15, 2007 August 15, 20072525 Find the load at the gear pitch circle:(11-4)Dp = NTPd Dp = 4010 Dp = 4 inches(12-3)Ft = 2 TDP Ft = 2 (180 in-lb)4 in Ft = 90 lbExample Problem 17-1: Design Stresses in Shafts (cont d.)August 15, 2007 August 15, 20072626 Find the resultant force on the Shaft :(12-2)Fr = Ftcos Fr = 90 lbcos 20 Fr = 96 lb Find the maximum moment:(Appendix 2)Mm = FL4 Mm = 96 lb (15 in)4 Mm = 360 in-lbExample Problem 17-1: Design Stresses in Shafts (cont d.)