Gears: Force Transmission & Gear Trains

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 Courtesy of OSHA. 2. No, never 3. It depends on _____ Pressure Line

• Where the teeth contact, the surface normal defines a pressure line • The force transmitted Figure removed for copyright reasons. acts along this line Source: Shigley and Mischke, Figure 13-17. • The pressure line always includes the point of tangency between the pitch circles • With the involute gear profile, the pressure line is constant From Shigley and Mischke Pressure Angle

• The pressure line acts at some angle to the tangent of the Figure removed for copyright reasons. pitch circles Source: Shigley and Mischke, Figure 13-17. • This angle can be chosen by the designer • It affects – Separation forces – Tooth shape

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.sdp- si.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

• Are there any disadvantage to a helical gear as compared to a spur gear? • How can the disadvantages Image removed for Copyright reasons. 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 ω only one gear on each 1 shaft • How does this arrangement behave? Compound Gear Trains

• A “compound” gear train has at least one

shaft with Figure removed for copyright reasons. Source: Figure 9-29 in Norton, R. L. Design of Machinery. 3rd edition. Burr Ridge, IL: multiple gears McGraw-Hill, 2003. • How does this arrangement behave? Discussion Question

• State a relationship one would

normally apply Figure removed for copyright reasons. Source: Figure 9-29 in Norton, R. L. Design of Machinery. 3rd edition. Burr Ridge, IL: in choosing McGraw-Hill, 2003. radii for gears 3, 4, and 5 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