Transmission Machine Components

1. Transmission Machine Components

2. Gears • Gears simply change the parameters of mechanical power Pitch-Line Velocity P r1 r2 gear pinion

3. Tooth Forces T2 F2 r2 T1 r1 F1

5. Normal velocity must match. Using similar triangles v2 cosθ2   =   v1 cosθ1 where   v1 = ω1 . O1C   ;       v2 = ω2 . O2C  Want constant rotation rate ratio ω2 /ω1   =   v2 . O1C/v1 . O2C   =   O1C.cosθ1 /O2C.cosθ2               =   O1 C1 /O2 C2   =   O1 P / O2 P  Point P must be fixed

7. Effect of Errors Shafts at spec. distance Shafts farther apart than spec.

8. Involute Tooth Profile • The two curved surfaces of mating teeth, contact as a line

9. Types of Gears • Spur Gears • Teeth are parallel to rotation axis • Transmit power between shafts with parallel axes • Helical Gears • Teeth inclined to the axis of rotation • Used for the same applications as spur gears, but have less noise due to gradual tooth engagement

10. Types of Gears, cont. • Bevel Gears • Teeth on a conical Surface • Used with intersecting shafts • Worm Gears • Similar to a screw • Used with non-parallel and non-intersecting shafts typically with high speed ratios

11. Rack and Pinion • A rack is an unwound spur gear • Turns rotary motion in to linear motion

12. Anatomy of a Gear • Pitch Circle • Theoretical circle upon with all calculations are based • Diametral Pitch • Module • Pressure Angle • For gears to work together they must have the same pitch (or module) and pressure angle

13. Multiple Gear Stages • Gear ratios from a multi-stage gear train multiply together T3 T2 T4 T1 2:1 reduction 2:1 reduction 2:1 reduction Overall a 8:1 reduction

14. Efficiency • In reality gears are not 100% efficient • Good quality spur gears are typically in the 90+ % efficiency range • This can be a problem with multiple (large) gear reductions Each a 2:1 reduction with 95% efficiency Overall a 32:1 reduction, but only 77% efficient

15. Belts are essentially the same as spur gears but they have the ability to have large offsets Belts and Chains P1 P2

16. Slip • Belts rely on friction and to prevent slip tension must be maintained • Chains and timing belts that have teeth with positive engagement can help prevent slip

17. Shafts Energy used to overcome the forces resulting from misalignment will reduce the overall efficiency of your system Parallel misalignment Angular misalignment This is the key to doing well in the transmission contest

18. Pins • Pins hold two parts together based upon the shear strength of the pin • Pins are good when the joint must take both thrust and shear • Pinned joints are easy to analyze and reliable • Pinned joints can be used as a mechanical fuse • Pinned joints are difficult to assemble and disassemble because pins are typically press fit into place shaft gear pin

19. Keys • Keys transmit torque in shear across the length of the key • Keys have all the advantages of pins, but they are easy to install in remove • Keys do not take any axial load Woodruff key Used to reduce stress concentrations in the shaft

20. Clamp Fit • Clamps depend upon friction and the bolted connection between two parts (or a single part with a flexure) to develop the clamping force • Clamped connections can be easy and reliable for low torque applications

21. Press (Interference) Fits • Two parts can be pressed together if the hole is manufactured smaller than the shaft that is installed • The load between these two parts is taken in friction developed by the strain of the press fit • Manufacturing tolerances are very tight for this type of connection • For a 0.25” diameter shaft with a class FN2 fit • Shaft 0.2510” – 0.2514” • Hole 0.2500” – 0.2506” • Difficult to disassemble without damage to the parts

22. Splines • Splines are essentially matching internal and external gears used to transmit torque • Splines are extremely reliable and efficient • Splines are difficult to manufacture

23. Retaining Rings • Retaining rings are used to constrain things axially in one direction on a shaft • Installed by machining a groove into one of the mating parts • Can be made external or internal External E-Style External Internal

24. Shaft Connections Coupler transmits torque and allows for misalignment Key or set screw transmits torque

25. Couplers • Bellows • Spider Coupling • Helical • Universal Joint

26. Bearing and Bushings

27. Bushings have sliding contact and rely on low friction at the point or line of contact Bushings r F

28. Rolling Element Bearings • Replace sliding contact with rolling contact which is much more efficient Outer Race Ball Separator (retainer) Inner Race Image courtesy of Barden Precision Bearing

29. Rolling Contact ωb rb V ω1 ri ro rLi rLo

30. Spherical Bearings • Allows for misalignment in all rotational degrees of freedom • Constrains in all translational degrees of freedom • Good for low speed / high load applications

31. A Brief Into to SpecifyingElectric Motors

32. Electric Motors • Torque is proportional to current • Speed is proportional to voltage • An electric motor generates an Electromotive Force (back EMF) as it spins • A portion of the input voltage goes to doing work and a portion goes to overcome the back EMF

33. Kt Ke

34. Electric Motors For a given voltage

35. Electric Motor Power Can’t always operate here due to heat

36. Continuous Operating Range