Session #3Gears: 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 actuallydraw 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. Yes2. No, never3. 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 involutegear 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.sdp-si.com/D190/D190cat.htm (accessed 28 June 2006.) Courtesy of Stock Drive Products/Sterling Instrument.

Concept QuestionA 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. << 0.32. About 0.33. About 0.54. >> 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 be remedied?

• Is a helical gear set stronger than a spur gear of the same diameter, pitch, face width, & material?

Image removed for Copyright reasons.

Simple Gear Trains

• A “simple” gear train has only one gear on each shaft

• How does this arrangement behave?

ω1

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 meanthere 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?10 teeth on pinion gear72 teeth

10 teeth

36 teeth10 teeth

48 teeth

16 teeth42 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