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 r2 F2 T2 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. Shafts farther apart than spec.
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 Helical 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 Worm 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 Diametral Pitch Module Pressure Angle
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 and Chains
Belts are essentially the same as spur gears but they have the ability to have large offsets 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 This is the key to doing well in the transmission contest
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. Used to reduce stress concentrations in the shaft
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 ” – ”
Hole ” – ”
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
Bushings have sliding contact and rely on low friction at the point or line of contact 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 V ωb rb 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 Specifying Electric 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