Engineering Mechanics Statics Chapter 6 Friction Introduction Ideal

Engineering Mechanics: Statics Chapter 6: Friction

Introduction ¡ ¡ Ideal assumption – forces between contacting surfaces act normal to the surfaces Real surfaces – there are tangential forces between contacting surfaces = “Friction forces” ¡ Friction force occurs when one contacting surface tends to slide along another. l Minimize the effects: bearings, screws, gears, flow of fluids in pipe l Maximize the effects: brakes, clutches, belt drives, wedges

Types of Friction ¡ Dry friction - unlubricated surfaces in contact under a tendency to slide - friction occurs in the direction opposite to the impending motion - called Coulomb friction ¡ Fluid friction - adjacent layers in a fluid are moving at different velocity ¡ Internal friction –solid material under cyclical loading

Dry Friction ¡ Mechanism of Dry Friction ¡ Static friction: Fmax = ms. N limiting value for impending motion!!! ¡ Kinetic friction: Fk = mk. N

Dry Friction ¡ The direction of R is specified by tan a = F/N ¡ When the friction force reaches Fmax, the angle a reaches a maximum value fs. Thus, tan fs = ms ¡ ¡ When slippage is occurring, tan fk = mk The angles fs and fk are called angle of static friction and angle of kinetic friction which define the limiting direction of the total reaction R for each case.

Cone of Friction ¡ If motion is impending, R must be one element of the cone of static friction ¡ If motion is not impending, R is within the cone. The cone vertex angle is 2 fs ¡ If motion occurs, the angle of kinetic friction is applied. The reaction R must lie on the surface of cone of vertex angle 2 fk

Types of Friction problems 1. Motion is impending (body about to slip) Fmax = ms. N 2. Condition of motion is not known –find friction force F from equilibrium equation ¡ If F < Fmax (= ms. N) – body is in equilibrium and friction force = F ¡ If F = Fmax (= ms. N) – body is in equilibrium motion is impending ¡ If F > Fmax (= ms. N) – impossible not in equilibrium 3. Relative motion exist Fk = mk. N

Sample Problem 6/2 Determine the range of values which the mass m 0 may have so that the 100 -kg block will neither start moving up the plane nor slip down the plane The coefficient of static friction for the contact surfaces is 0. 30

Sample Problem 6/5 The three flat blocks are positioned on the 30 degree incline as shown, and a force P parallel to the incline is applied to the middle block. The upper block is prevented from moving by a wire which attaches it to the fixed support. The coefficient of static friction for each of the three pairs of mating surfaces is shown. Determine the maximum value which P may have before any slipping takes place.

Problem 6/9 The 30 -kg homogeneous cylinder of 400 -mm diameter rests against the vertical and inclined surfaces as shown. If the coefficient of static friction between the cylinder and the surfaces is 0. 30, calculate the applied clockwise couple M which would cause the cylinder to slip.