Chapter 8: Friction - CAU

1 Chapter 8: FrictionSchool of Mechanical Engineering of Dry Friction . Coefficients of of FrictionProblems Involving Dry FrictionSample Problem Problem ScrewsSample Problem Bearings. Axle Bearings. Disk Friction . Rolling Problem Problem of Mechanical Engineering8 -2 IntroductionLaws of Dry Friction . Coefficients of of FrictionProblems Involving Dry FrictionSample Problem Problem ScrewsSample Problem Bearings. Axle Bearings. Disk Friction . Rolling Problem Problem In preceding chapters, it was assumed that surfaces in contact were either frictionless(surfaces could move freely with respect to each other) or rough(tangential forces prevent relative motion between surfaces).

2 Actually, no perfectly frictionless surface exists. For two surfaces in contact, tangential forces, called Friction forces, will develop if one attempts to move one relative to the of Mechanical Engineering8 -3 However, the Friction forces are limited in magnitude and will not prevent motion if sufficiently large forces are applied. The distinction between frictionless and rough is, therefore, a matter of degree. There are two types of Friction : dryor Coulomb frictionand fluid Friction . Fluid Friction applies to lubricated mechanisms. The present discussion is limited to dry Friction between nonlubricated Laws of Dry Friction .

3 Coefficients of Friction Block of weight Wplaced on horizontal surface. Forces acting on block are its weight and reaction of surface N. Small horizontal force Papplied to block. For block to remain stationary, in equilibrium, a horizontal component Fof the surface reaction is required. F is a static- Friction of Mechanical Engineering8 -4 Small horizontal force Papplied to block. For block to remain stationary, in equilibrium, a horizontal component Fof the surface reaction is required. F is a static- Friction force. As Pincreases, the static- Friction force Fincreases as well until it reaches a maximum value Further increase in P causes the block to begin to move as Fdrops to a smaller kinetic- Friction force Laws of Dry Friction .

4 Coefficients of Friction Maximum static- Friction force:NFsmm= Kinetic- Friction @=School of Mechanical Engineering8 -5 Maximum static- Friction force and kinetic- Friction force are:-proportional to normal force-dependent on type and condition of contact surfaces-independent of contact areaThe Laws of Dry Friction . Coefficients of Friction Four situations can occur when a rigid body is in contact with a horizontal surface:School of Mechanical Engineering8 -6 No Friction ,(Px= 0) No motion,(Px< Fm) Motion impending,(Px= Fm) Motion,(Px> Fm)Angles of Friction It is sometimes convenient to replace normal force Nand Friction force Fby their resultant R.

5 School of Mechanical Engineering8 -7 No Friction Motion impending No motionsssmsNNNF mfmf===tantan MotionkkkkkNNNF mfmf===tantanAngles of Friction Consider block of weight Wresting on board with variable inclination angle of Mechanical Engineering8 -8 No Friction No motion Motion impending MotionProblems Involving Dry FrictionSchool of Mechanical Engineering8 -9 All applied forces known Coefficient of static Friction is known Determine whether body will remain at rest or slide All applied forces known Motion is impending Determine value of coefficient of static Friction .

6 Coefficient of static Friction is known Motion is impending Determine magnitude or direction of one of the applied forcesSample Problem : Determine values of Friction force and normal reaction force from plane required to maintain equilibrium. Calculate maximum Friction force and compare with Friction force required for equilibrium. If it is greater, block will not of Mechanical Engineering8 -10A 100 N force acts as shown on a 300 N block placed on an inclined plane. The coefficients of Friction between the block and plane are ms= and mk= Determine whether the block is in equilibrium and find the value of the Friction force.

7 Calculate maximum Friction force and compare with Friction force required for equilibrium. If it is greater, block will not slide. If maximum Friction force is less than Friction force required for equilibrium, block will slide. Calculate kinetic- Friction Problem : Determine values of Friction force and normal reaction force from plane required to maintain equilibrium.:0= xF()0N 300 - N 10053=-FN 80-=F:0= yF()0N 300 - 54=NSchool of Mechanical Engineering8 -11:0= yF()0N 300 - 54=NN 240=N Calculate maximum Friction force and compare with Friction force required for equilibrium.

8 If it is greater, block will not slide.() 240 N 60 NmsmFNFm===The block will slide down the plane. Sample Problem If maximum Friction force is less than Friction force required for equilibrium, block will slide. Calculate kinetic- Friction force.()N 48=actualFSchool of Mechanical Engineering8 -12 Sample Problem : When Wis placed at minimum x, the bracket is about to slip and Friction forces in upper and lower collars are at maximum value. Apply conditions for static equilibrium to find minimum of Mechanical Engineering8 -13 The moveable bracket shown may be placed at any height on the 3-cm diameter pipe.

9 If the coefficient of Friction between the pipe and bracket is , determine the minimum distance xat which the load can be supported. Neglect the weight of the bracket. Apply conditions for static equilibrium to find minimum Problem : When Wis placed at minimum x, the bracket is about to slip and Friction forces in upper and lower collars are at maximum Apply conditions for static equilibrium to find minimum of Mechanical Engineering8 -14 Apply conditions for static equilibrium to find minimum x.:0= xF0=-ABNNABNN=:0= yFWNWNNWFFABABA==-+=-+ :0= BM()()()()()()()() Wedges-simple machines used to raise heavy loads.

10 Force required to lift block is significantly less than block weight. Friction prevents wedge from sliding out. Want to find minimum force Pto raise block. Block as free-body Wedge as free-bodySchool of Mechanical Engineering8 -15 Wedges-simple machines used to raise heavy loads. Force required to lift block is significantly less than block weight. Friction prevents wedge from sliding out. Want to find minimum force Pto raise block. Block as free-body0:00:02121=+--==+-= NNWFNNF sysxmmor021=++WRRvrr()()06sin6cos:006sin 6cos:03232= - +-==+ - --= syssxNNFPNNFmmm Wedge as free-bodyor032=+-RRPrrrSquare-Threaded Screws Square-threaded screws frequently used in jacks, presses, etc.