UNIT - 3 Friction and Belt Drives 1.State the laws of dynamic or kinetic friction (03 Marks) (June 2015) Laws of Kinetic or Dynamic Friction Following are the laws of kinetic or dynamic friction: 1. The force of friction always acts in a direction, opposite to that in which the body is moving. 2. The magnitude of the kinetic friction bear a constant ratio to the normal reaction between the two surfaces. But this ratio is slightly less than that in case of limiting friction. 3. For moderate speeds, the force of friction remains constant. But it decreases slightly with the increase of speed. 2.Derive an expression for frictional torque in a single collar bearing assuming uniform pressure. (5 marks) (June 2015) Single collar bearing: Dept of Mechanical Engineering, SJBIT Page 30
Consider a single flat collar bearing supporting a shaft as shown in Fig. 10.20 (0). Let r( = External radius of the collar, and r; = Internal radius of the collar. 3.An open belt drive connects two pulleys 1.5 m and 0.5 m diameter on parallel shafts 3.5m apart. The belt bas a mass of lkg/m length and maximum tension in the belt is not to exceed 2 kn. The 1.5 m pulley, which is the driver runs at 250 rpm. Due to belt slip, the velocity of the driven shaft is only 730 rpm. If the coefficient of friction between the belt Dept of Mechanical Engineering, SJBIT Page 31
and the pulley is 0.25 find,i) The torque on each shaft ii) Power transmitted iii) The power lost in friction and iv) The efficiency of the drive. (12 Marks) (June 2015) d, = 1.5 m; r, =0.75 m d2 = 0.5 m ; r2 = 0.25 m c = 3.5 m ; m = I kg/rn length T = 2kN = 2000 N M = 0.25 n, = 250 rpm, 112 = 730 rpm 4.State the laws of dry friction. (05 Marks) (Dec 2014) Laws of solid Friction: Solid or dry friction obeys approximately the following laws. I. The friction force is directly proportional to the normal load between the surfaces for given pair of materials. 2. The friction force depends upon the material of which the contact surfaces are made (i.e., it depends upon the roughness of the material) 3. The friction force is independent of the area of contact. 4. The friction force is independent of the velocity of sliding. 5. The friction force opposes the sliding motion and it acts in the direction opposite to which the body tends to move. Dept of Mechanical Engineering, SJBIT Page 32
5.Derive an expression (or the ratio of tensions in a flat belt drive. (05 Marks) (Dec 2013) Dept of Mechanical Engineering, SJBIT Page 33
6.A 8mm thick belt is required to transmit 15 kw running over a pulley at a speed of 15 metres per second. If the coefficient of friction between the belt and the pulley is 0.3 & the angle of lap is 1800, find the width of belt required. The maximum tension in the belt material is not to exceed 20 N/mm width of the blet. The density of belt material is 1000 kg/m". (10 Marks) (Dec 2013) A leather belts required to transmit 7.5 I{W from a pulley 1.2min diameter running at 250rpm. The angle embraced is 1650 and the coefficient of friction between the belt and the pulley is 0.3. If tbe safe working stress for the leather belt is 1.5 MPa denssity of leather Dept of Mechanical Engineering, SJBIT Page 34
1000 kg/m" and thickness of belt 10mm determine the width of the belt taking centrifugal tension into account. (15 Marks) (Dec 2014) Dept of Mechanical Engineering, SJBIT Page 35
Derive an expression of total friction torque for a private bearing subjected to uniform pressure. (08 Marks) (June 2015) Dept of Mechanical Engineering, SJBIT Page 36
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A pulley is driven by a flat belt; the angle if lap being 120. The belt is 100 mm wide, 6 mm thick and density of 1000 kg/m'. If the coefficient offriction is 0.3 and the maximum stress in the belt is not to exceed 2 MPa, find the greatest power which the belt can transmit and the corresponding speed of the belt. (12 Marks) (Jan 2014) Explain (i) Slip, (ii) Creep, (iii) Initial tension, and (iv) Centrifugal tension in belt drive. (6 marks) (June 2013) (i) Slip: Slip is the term used to describe the sliding motion between the belt and pulley surfaces. Slip can take place either on the driving pulley or driven pulley or both. The effect of slip is to reduce the velocity ratio, and consequently, power loss in transmission. (ii) Creep: Any material when subjected to tension elongates, and so is the belt material. This elongation is directly proportional to the tension in the belt. Tensions on the two sides of the belt passing over the pulley are different. on the tight side the tension is more, and on the slack side, the tension is less. On the driven pulley, the tension on the belt entering the pulley is less than the tension on the belt, which is leaving the pulley. The belt entering the pulley is stretched less than Dept of Mechanical Engineering, SJBIT Page 38
the belt that is leaving the pulley. Hence, there is a gradual increase in the length of belt over the surface of the pulley. This stretching results in relative motion between the belt and pulley surfaces. This phenomenon is called creep. A similar effect is there on the driving pulley as well. Creep results in loss of power and decrease in velocity ratio. (Hi) Initial tension: When the belt drive is not running, the belt is kept under tension known as initial tension. When the drive is set into motion, the tension on the tight side of the belt increases due to friction, and that on the slack side decreases. Assum ing that the length of belt remains the same before and after the drive was set into operation, the increase in tension on the tight side of the belt over the initial tension should be same as the decrease in tension on the slack side of the belt. Let To = initial tension in the belt when the drive is not running T = increase in tension on the tight side = decrease in tension on the slack side. (iv) Centrifugal tension: Part of belt which is in contact with the pulley surface undergoes circular motion. Each element of belt which undergoes this motion experiences centrifugal force which is directed radially outwards. The effect is same on both the driver and driven pulleys and the net result is that the belt is subjected to an extra tension called the centrifugal tension. An open belt drive is required to transmit 10 kw from a motor running at 600 rpm. The belt is 12 mm thick and has a mass density of 0.001 gm/rnrrr', Safe stress in tbe belt is not to exceed 2.5 Nz mm. Effective diameter of the driving pulley is 250 mm whereas the speed of the driven pulley is 220 rpm. The two shafts are 1.25 m apart. If the coefficient of friction is 0.25, determine the widtb of the belt. (14 marks) (June 2013) Dept of Mechanical Engineering, SJBIT Page 39
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Derive an equation to calculate centrifugal tension in a flat belt drive.(05 Marks)(Jan 2014) Determine the width of a 9.75 mm thick belt required to-transmit 15 kw from a motor running at 900 rpm. The diameter of the driving pulley of the motor is 300 'mm. The driven pulley runs at 300 rpm and distance between centres of two pulley is 3 mts. The density of leather is 1000 kg/m", The maximum allowable stress in leather is 12.5 MPa. The coefficient of friction between leather and pulley' is 0.3. Assume open belt drive and neglect' slip in belt drive. (15 Marks) (Jan 2014) Given t = 9.75mm=9.75 x 1O-3m P= 15kw. NI = 900 rpm d, = 300 mm=oj m Nz = 300 rpm x = 3 m = 1000kg / rrr' O"max = 2.5mPa = 2.5x106Pa Dept of Mechanical Engineering, SJBIT Page 41
A leather belt is req uired to transmit 7.5 kw from a pulley 1.2 m in diameter, running at 250rpm, the angle of contact is 1650 and,t = 0.3. Jf the safe working stress for the Dept of Mechanical Engineering, SJBIT Page 42
leather belt is 1:5 MPa and density ofleather is 1000 kg/m" and thickness of belt is 10mm, determine the width of belt taking centrifugal tension into account. (10 Marks) (June 2014) Dept of Mechanical Engineering, SJBIT Page 43