Session #3 Gears: Force Transmission & Gear Trains Dan Frey
Today s Agenda Pass out second reading packet Pass out loaner laptops Introduce project teams Gears Force Transmission Gear Trains Survey
HW 1 Problem 1 A 17-tooth spur pinion paired with a 50 tooth gear has a diametral pitch of 2½ teeth/in and a 20o pressure angle. Make a drawing of the gears showing one tooth on each gear (you may use a CAD program or other techniques as appropriate, you may choose a scale for your drawing as appropriate). Estimate the contact ratio. Among other things, it is necessary that you be able to actually draw the teeth on a pair of meshing gears. You should understand, however, that you are not doing this for manufacturing or shop purposes. Rather, we make drawings of gear teeth to obtain an understanding of the problems involved in meshing of the mating teeth. -Shigley and Mischke
Involute Profile How it is constructed Demo Properties Conjugate action Allows design of whole sets of compatible gears Conjugate action not sensitive to center distance variations
Concept Question Are the teeth on a matching rack and pinion set the same shape? 1. Yes 2. No, never 3. It depends on Courtesy of OSHA.
Pressure Line Where the teeth contact, the surface normal defines a pressure line The force transmitted acts along this line The pressure line always includes the point of tangency between the pitch circles With the involute gear profile, the pressure line is constant Figure removed for copyright reasons. Source: Shigley and Mischke, Figure 13-17. From Shigley and Mischke
Pressure Angle The pressure line acts at some angle to the tangent of the pitch circles This angle can be chosen by the designer It affects Separation forces Tooth shape Figure removed for copyright reasons. Source: Shigley and Mischke, Figure 13-17. From Shigley and Mischke
Gear Terminology Line of action & pressure line & generating line are all synonymous Source: Buchsbaum, Frank, Design and Application of Small Standardized components Data Book 757 Vol. 2, Stock Drive Products, 1983. See Handbook of Gears. http://www.sdpsi.com/d190/d190cat.htm (accessed 28 June 2006.) Courtesy of Stock Drive Products/Sterling Instrument.
Concept Question A pair of gears are mated. One is driven at a set torque, the other is regulated at a set speed. The gears are the ones circled. What is the ratio of the separation forces and the total force on the bearing? 1. << 0.3 2. About 0.3 3. About 0.5 4. >> 0.5 Courtesy of W. M. Berg, Inc. Used with permission.
Discussion Questions Image removed for Copyright reasons. Are there any disadvantage to a helical gear as compared to a spur gear? How can the disadvantages be remedied? Is a helical gear set stronger than a spur gear of the same diameter, pitch, face width, & material?
Simple Gear Trains A simple gear train has only one gear on each shaft How does this arrangement behave? ω 1
Compound Gear Trains A compound gear train has at least one shaft with multiple gears How does this arrangement behave? Figure removed for copyright reasons. Source: Figure 9-29 in Norton, R. L. Design of Machinery. 3rd edition. Burr Ridge, IL: McGraw-Hill, 2003.
Discussion Question State a relationship one would normally apply in choosing radii for gears 3, 4, and 5 Figure removed for copyright reasons. Source: Figure 9-29 in Norton, R. L. Design of Machinery. 3rd edition. Burr Ridge, IL: McGraw-Hill, 2003.
Manual Transmissions Diagram of manual transmission components removed for copyright reasons. If you find just two axles in a machine, does that mean there are just two stages?
Discussion Questions How many stages in this device? How do you suppose this number is chosen? Are the reduction ratios typically all nearly the same in all successive stages? 72 teeth 10 teeth on pinion gear 42 teeth 16 teeth 10 teeth 48 teeth 10 teeth 36 teeth
Planetary Gear Trains One or more of the gear axes are allowed to rotate aka epicyclic Used in Power tools Automatic transmissions Gear boxes
Analysis of Planetary Gear Trains Figure removed for copyright reasons. Source: Shigley and Mischke, Figure 13-28.
Differentials Allows shafts to move at different speeds Applies same torque to both Slippage problem What can be done? See animations at http://auto.howstuffworks.com/differential3.htm
Next Steps On Thurs 16 FEB (right here) next session on gears Finish HW#1 On Fri 17 FEB, the first lab in the lab