enme110_lecture_22

enme110_lecture_22 - CHAPTER 8 FRICTION Wedges Wedges are...

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Unformatted text preview: CHAPTER 8 FRICTION Wedges Wedges are inclined planes used to increase the application of a force. The two force equilibrium equations are used to relate the 'forces acting on the wedge. An‘applied force P must push on the wedge to move it to the right. If the coefficients of friction between the surfaces are large enough, then P can be removed, and the wedge will be self-locking and remain in place. Screws Square-threaded screws are used to move heavy loads. They represent an inclined plane, wrapped around ‘a cylinder: ' 7 The moment needed to turn a screw . depends upon the coefficient of friction and the screw’s lead angle 9. , If the coefficient of friction between the surfaces is large enough, then the screw - will support the load without tending to turn, i'.e_., it will be self-locking. Flat Belts The force'needed to move a flat belt over a rough curved surface depends only on the angle of belt contact, [3, and the coefficient of friction. M = Wr tan(6 + 4):) Upward Impending Screw Motion M‘ = Wrtan(9 — (:55) Downward Impending Screw Motion. 9>¢9 i M” = Wr tan(qb — 5) _ Downward Screw Motion #5: > 9 Motion or impending motion of belt relative to surface _,_.__.—.-...._ NR ~l50» Collar Bearings and Disks The frictional analysis of a collar bearing or disk requires looking at a differential element of the contact area. The normal force acting on this element is determined frOm force equilibrium along the shaft, and the moment needed .to turn the shaft at a constant rate'is determined from moment equilibrium ‘ about the shaft’s axis. If the pressure on the surface of a collar bearing is uniform, then integration gives the result shown. . Journal Bearings When a moment is applied to a shaft in a nonlubricated or partially lubricated journal bearing, the shaft will tend to roll up the side of the bearing until slipping occurs This defines the radius of a friction circle, and from it the moment needed to turn the shaft can be determined. I Rolling Resistance The resistance of a wheel to rolling over a surface is caused by localized deformation of the two materials in Contact. This causes the resultant normal force acting on the rolling body to be inclined so that it provides a component that acts in the opposite direction of the applied force P causing the motion.'Ihis effect is characterized using the Coefficient of rolling resistance, a, which is determined from experiment. M = Rr sin (bk QiMA;¢ Mr W (Riga-359 Z W'Cb' 'P.~r'_".’wei.. A- pproxi Maire...” “\JWEON“ CHAPTER REVIEW Rotation 15!» .—..—. ,, I. gL‘naoswery a . . ._._..... n e. , .o :MQ , .. ,, ,, ,%.&n.eca\, ,o A, C056 “‘1'? 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enme110_lecture_22 - CHAPTER 8 FRICTION Wedges Wedges are...

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