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Int: 6 th Session: ENGINEERS MECHANICS ENGINEERS MECHANICS STATICS STATICS CHAPTER6CHAPTER6 Lecture Notes: Lecture Notes: Professor A. Salam Al-Ammri Suhad Ibraheem Mohammed Al-Khwarizmi College of Engineering University of Baghdad Professor Dr. A.Salam Al-Ammri & Suhad Ibraheem Mohammad 2/17/2012

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Int: 6 th Session: Contents

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Int: 6 th Session: Journal Bearings. Axle Friction Journal bearings provide lateral support to rotating shafts. Thrust bearings provide axial support Frictional resistance of fully lubricated bearings depends on clearances, speed and lubricant viscosity. Partially lubricated axles and bearings can be assumed to be in direct contact along a straight line.

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Int: 6 th Session: Forces acting on bearing are weight W of wheels and shaft, couple M to maintain motion, and reaction R of the bearing. Reaction is vertical and equal in magnitude to W. Reaction line of action does not pass through shaft center O; R is located to the right of O, resulting in a moment that is balanced by M. Physically, contact point is displaced as axle “climbs” in bearing. Journal Bearings. Axle Friction

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Int: 6 th Session: Journal Bearings. Axle Friction Angle between R and normal to bearing surface is the angle of kinetic friction k. May treat bearing reaction as force- couple system. For graphical solution, R must be tangent to circle of friction.

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Int: 6 th Session: Thrust Bearings. Disk Friction Consider rotating hollow shaft: For full circle of radius R,

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Int: 6 th Session: Wheel Friction. Rolling Resistance Point of wheel in contact with ground has no relative motion with respect to ground. Ideally, no friction. Moment M due to frictional resistance of axle bearing requires couple produced by equal and opposite P and F. Without friction at rim,wheel would slide. Deformations of wheel and ground cause resultant of ground reaction to be applied at B. P is required to balance moment of W about B. P r = W b b =coef. of rolling resistance

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Int: 6 th Session: Sample Problem SOLUTION: With the load on the left and force P on the right, impending motion is clockwise to raise load. The perpendicular distance from center O of pulley to line of action of R is A pulley of diameter 4 in. can rotate about a fixed shaft of diameter 2 in. The coefficient of static friction between the pulley and shaft is Determine: the smallest vertical force P required to start raising a 500 lb load, the smallest vertical force P required to hold the load, and the smallest horizontal force P required to start raising the same load.

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Int: 6 th Session: Sample Problem The perpendicular distance from center O of pulley to line of action of R is again 0.20 in. Summing moments about C, Impending motion is counter-clockwise as load is held stationary with smallest force P. With the load on the left and force P acting horizontally to the right, impending motion is clockwise to raise load. Line of action of R must pass through intersection of W and P and be tangent to circle of friction which has radius r f = 0.20 in.

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Int: 6 th Session: The collar bearing uniformly supports an axial force of P = 800 lb. If the coefficient of static friction is µ s = 0.3, determine the torque M required to overcome friction. Sample Problem 6.4.2

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Int: 6 th Session: The disk clutch is used in standard transmissions of automobiles. If four springs are used to force the two plates A and B together, determine the force in each spring required to transmit a moment of M = 600 lb – ft,across the plates. The coefficient of static friction between A and B is μ s = 0.3. Sample Problem 6.4.3

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Int: 6 th Session: The shaft of radius r fits loosely on the journal bearing. If the shaft transmits a vertical force P to the bearing and the coefficient of kinetic friction between the shaft and the bearing is μ k, determine the torque M required to turn the shaft with constant velocity. Sample Problem 6.4.4

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Int: 6 th Session: Sample Problem The 10 Mg crate is lowered into an underground storage facility on a two screw elevator designed as shown.Each screw has a mass of 0.9 Mg,is 120 mm in mean diameter, and has a single square thread with a lead of 11 mm. The entire mass of the crate,screws,and 3 Mg elevator platform is supported equally by flat collar bearings at A, each of which has an outside diameter of 250 mm and an inside diameter of 125 mm.If the coefficient of friction for the collar bearing and the screws at B is Calculate the torque M which must be applied to each screw (a) to raise the elevator and (b) to lower the elevator

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Int: 6 th Session: Sample Problem For the flat sanding disk of radius a,the pressure ( P ) developed between the disk and the sanded surface decreases linearly with ( r ) from a value P o at the center to P o /2 at (r = a). If the coefficient of friction is µ,derive the expression for the torque ( M ) required to turn the shaft under an axial force ( L ).

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