R05320304-dynamics-of-machinery

Set No. 1

Code No: R05320304

III B.Tech Supplimentary Examinations, Aug/Sep 2008 DYNAMICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Discuss the equilibrium of two and three force members. (b) In a four link mechanism the dimensions of the links are given below. Fixed link AD=60mm, driving link AB=50mm, coupler BC=100mm, driven link DC=80mm, and DE=40mm. The driving link is making an angle 1200 with AD. The driven link is acted upon by a force of 80 6 1500 N on link DC at E. Determine the input torque T on the link AB. [4+12] 2. (a) What is a wedge and where is it used? What is a self-locking wedge mechanism? (b) The shaft of a collar thrust bearing rotates at 200 r.p.m. and carries an end thrust of 100kN.The outer and the inner diameters of the bearing are 480 mm and 280 mm respectively. If the power lost in friction is not to exceed 8 kW, determine the coefficient of friction of the lubricant of the bearing. [6+10] 3. (a) Describe with neat sketch the belt transmission dynamometer. (b) A single block brake is shown in figure 3 the diameter of drum is 250mm and the angle of contact is 120 degrees. If the operating force of 600N is applied at the end of a lever and the coefficient of friction between the drum and the lining is 0.5 determine the torque that may be transmitted by the block brake. [6+10]

Figure 3 4. A gas engine is provided with 2 flywheels of 5kN each and the radius of gyration of each is 60 cm. Cylinder diameter is 20 cm. stroke 25 cm. and the mean rpm is 200 the mean pressure above the atmospheric during the firing stroke is 0.6 M Pa during the compression stroke is 0.11 MPa. During the exhaust stroke is 0.03 MPa. During the suction stroke is 0.016 MPa below atmospheric. If the engine has 1 of 2

Set No. 1

Code No: R05320304

one working stroke during four strokes and if the resistance is constant determine the % fluctuation of speed. [16] 5. In a Porter governor, the arms and links are each 25 cms long and intersect on the main axis. Each ball weighs 4 kgf and the central load is 20 kgf. The sleeve is in its lowest position when the arms are inclined at 300 to the axis. The lift of the sleeve is 5 cm. what is the force of friction at sleeve, if the speed at the beginning of ascent from the lowest position is equal to the speed at the beginning of the descent from the highest position? What is then the range of speed of governor, all other things remaining the same? [16] 6. Two weights of 8 kg and 16 kg rotate in the same plane at radii of 1.5 and 2.25 m respectively. The radii of these weights are 600 apart. Find the position of the third weight of the magnitude of 12 kg in the same plane which can produce static balance of the system. [16] 7. The following data relate to a single cylinder reciprocating engine. Mass of reciprocating parts = 40 kg Mass of revolving parts = 30 kg at 180mm radius. Speed = 150 rpm Stroke length = 350 mm If 60% of the reciprocating parts and all the revolving parts to be balanced, determine the (a) Balanced mass required at a radius of 320 mm. (b) The unbalanced force when the crank has turned 450 from the top dead center. [16] 8. A shaft 50 mm diameter and 3 m long . It is simply supported at the ends and carries three masses 100 kg, 120 kg and 80 kg at 1.0 m, 1.75 m and 2.5 m respectively from the left support. Taking E = 20 GN/m2 . Find the frequency of transverse vibrations using Rayleigh’s method. [16] ⋆⋆⋆⋆⋆

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Set No. 2

Code No: R05320304

III B.Tech Supplimentary Examinations, Aug/Sep 2008 DYNAMICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Differentiate between natural precision and forced precision. (b) Locomotive moving at a speed of 100 km/hr turns round a curve of 500m radius to the right. The pair of driving wheels is 2m in diameter and along with the axle weigh 20KN. The radius of gyration of wheels together with the axle may be taken as 0.6m. Find the gyro effect on the pair of driving wheels. [6+10] 2. (a) Derive the expression for the friction torque in flat collar bearing considering uniform pressure. (b) A shaft has a number of collars integral with it. The external diameter of the collars is 400 mm and the shaft diameter is 250 mm. If the intensity of pressure is 0.35 N/mm2 (uniform) and the coefficient of friction is 0.05.,estimate : i. Power absorbed when the shaft runs at 105 r.p.m. carrying a load of 150kN: and ii. Number of collars required. [6+10] 3. (a) Describe with neat sketch the prony brake dynamometer. (b) A single block brake is shown in figure 3 the diameter of drum is 250mm and the angle of contact is 120 degrees. If the operating force of 900N is applied at the end of a lever and the coefficient of friction between the drum and the lining is 0.45 determine the torque that may be transmitted by the block brake. [6+10]

Figure 3 4. (a) Draw the turning moment diagram for a single cylinder double acting steam engine. 1 of 3

Set No. 2

Code No: R05320304

(b) The crank effort diagram for a four stroke cycle gas engine may be assumed simplicity to consist of four triangles, the areas of which, from the line of zero pressure, are: power stroke, 60 sq cm; exhaust stroke, 5 sq cm; suction stroke 3 sq cm; compression stroke 15 sq cm; each square cm represents 1kN-m. Assuming the resistance to be uniform, find: i. The power of the Engine ii. The energy to be stored by the flywheel iii. Weight of the rim of a flywheel of 100 cm radius to limit the total fluctuation of speed to 4% of mean speed which is 150 rpm. [6+10] 5. A governor of the Proell type has each arm 250 mm long. The pivots of the upper and lower arms are 25 mm, from the axis. The central load acting on the sleeve has a mass of 25 kg and each rotating ball has a mass of 3.2 kg when the governor sleeve is in mid position, the extension link of the lower arm is vertical and the radius of path of rotation of the masses is 175 mm. the vertical height of the governor is 200 mm. if the speed of governor is 160 rpm, when in mid position, find: (a) Length of the extension link and (b) Tension in the upper arm.

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6. Four masses m1 , m2 , m3 and m4 having 100, 175, 200 and 25 kg are fixed to cranks of 20 cm radius and revolve in places 1, 2, 3 and 4. The angular position of the cranks in planes 2, 3 and 4 with respect to the crank in plane 1 are 750 , 1350 and 2000 taken in the same sense. The distance of planes 2, 3 and 4 from plane 1 are 60 cm, 186 cm and 240 cm respectively. Determine the position and magnitude of the balance mass at a radius of 60 cm in plane L and M located at middle of the plane 1 and 2 and the middle of the planes 3 and 4 respectively. [16] 7. A four coupled-wheel locomotive with two inside cylinders has reciprocating and revolving parts per cylinder as 300 kgf and 250 kgf respectively. The distance between planes of driving wheels is 150 cms. The pitch of cylinders is 60 cms. The diameter of tread and driving wheels is 190 cms and the distance between planes of coupling rod cranks in 190 cms. The revolving parts for each coupling rod crank are 125 kgf. The angle between engine cranks is 900 and the length of coupling rod crank 22 cms. The angle made by coupling rod crank with adjustment crank is 180 . The distance of center of gravity of balance weights in planes of driving wheels from a scale center is 75 cms. Crank radius is 32 cms. Determine: (a) The magnitude and position of balance weights required in leading and trailing wheels to balance2/3 of reciprocating and whole of revolving parts if half of the required reciprocating parts are to be balanced in each pair of coupled wheels. (b) The maximum variation of tractive force and hammer blow when locomotive speed is 100kmph. [16] 2 of 3

Set No. 2

Code No: R05320304

8. A vibrating system consists of a mass 50 kg, a spring of stiffness 30 KN/m and a damper. The damping provided is only 20% of the critical value. Determine: (a) The damping factor. (b) The critical damping coefficient. (c) The logarithmic decrement. (d) The natural frequency of damped vibrations. (e) The ratio of two consecutive amplitudes. ⋆⋆⋆⋆⋆

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Set No. 3

Code No: R05320304

III B.Tech Supplimentary Examinations, Aug/Sep 2008 DYNAMICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Discuss about the friction circle and friction axis of mechanisms. (b) In a slider crank mechanism the crank is making an angle of 450 with IDC. The crank and connecting rod lengths are 100mm and 300mm respectively. The driving moment on the crank is 50Nm. Determine the force on the slider that is necessary to be applied for the equilibrium of the linkage. [6+10] 2. (a) State the laws of kinetic friction. (b) An electric motor driven power screw moves a nut in a horizontal plane against a force of 75kN at a speed of 300 mm/min. The screw has a single square thread of 6mm pitch on a major diameter of 40 mm. The coefficient of friction at the screw threads is 0.1. Estimate power of the motor. [4+12] 3. (a) What are the advantages of the heenan and froude water vortex dynamometer? (b) A single block brake is shown in figure 3 the diameter of drum is 250mm and the angle of contact is 60 degrees. If the operating force of 1000N is applied at the end of a lever and the coefficient of friction between the drum and the lining is 0.40 determine the torque that may be transmitted by the block brake. [4+12]

Figure 3 4. A gas engine is provided with 2 flywheels of 5kN each and the radius of gyration of each is 60 cm. Cylinder diameter is 20 cm. stroke 25 cm. and the mean rpm is 200 the mean pressure above the atmospheric during the firing stroke is 0.6 M Pa during the compression stroke is 0.11 MPa. During the exhaust stroke is 0.03 MPa. During the suction stroke is 0.016 MPa below atmospheric. If the engine has one working stroke during four strokes and if the resistance is constant determine the % fluctuation of speed. [16] 1 of 2

Set No. 3

Code No: R05320304

5. In a Porter governor, the arms and links are each 25 cms long and intersect on main axis. Each ball weighs 3kgf and the central load 27.25 kgf. The sleeve is in the lowest position when the arms are inclined at 270 with the axis. The lift of the sleeve is 5 cm. What is the force of the friction at the sleeve if the speed at the beginning of ascent at the lowest position is equal to the speed at the beginning of descent from the highest position? [16] 6. A, B, C and D are four masses carried by a rotating shaft at radii of 10 cm, 12.5 cm, 20 cm and 15 cm respectively. The planes in which the masses revolve are 60 cm apart and the mass of B, C and D are 10 kg, 5 kg and 4 kg respectively. Find the required mass A and the relative angular setting of the four masses so that the shaft is in complete balance. (Assuming the plane of mass as the reference plane.) [16] 7. A four coupled-wheel locomotive with two inside cylinders has reciprocating and revolving parts per cylinder as 300 kgf and 250 kgf respectively. The distance between planes of driving wheels is 150 cms. The pitch of cylinders is 60 cms. The diameter of tread and driving wheels is 190 cms and the distance between planes of coupling rod cranks in 190 cms. The revolving parts for each coupling rod crank are 125 kgf. The angle between engine cranks is 900 and the length of coupling rod crank 22 cms. The angle made by coupling rod crank with adjustment crank is 180 . The distance of center of gravity of balance weights in planes of driving wheels from a scale center is 75 cms. Crank radius is 32 cms. Determine: (a) The magnitude and position of balance weights required in leading and trailing wheels to balance2/3 of reciprocating and whole of revolving parts if half of the required reciprocating parts are to be balanced in each pair of coupled wheels. (b) The maximum variation of tractive force and hammer blow when locomotive speed is 100kmph. [16] 8. A shaft 50 mm diameter and 3 m long . It is simply supported at the ends and carries three masses 100 kg, 120 kg and 80 kg at 1.0 m, 1.75 m and 2.5 m respectively from the left support. Taking E = 20 GN/m2 . Find the frequency of transverse vibrations using Rayleigh’s method. [16] ⋆⋆⋆⋆⋆

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Set No. 4

Code No: R05320304

III B.Tech Supplimentary Examinations, Aug/Sep 2008 DYNAMICS OF MACHINERY ( Common to Mechanical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Discuss about the friction circle and friction axis of mechanisms. (b) In a slider crank mechanism the crank is making an angle of 450 with IDC. The crank and connecting rod lengths are 100mm and 300mm respectively. The driving moment on the crank is 50Nm. Determine the force on the slider that is necessary to be applied for the equilibrium of the linkage. [6+10] 2. (a) Derive the expression for the friction torque in conical pivot bearing considering uniform pressure. (b) A conical pivot bearing supports a vertical shaft of 200 mm diameter. It is subjected to a load of 30kN. The angle of cone is 120 degrees and the coefficient of friction is 0.025. Find the power lost in friction when the speed is 140 r.p.m, assuming i. uniform wear ii. uniform pressure.

[6+10]

3. (a) Derive the expression for the torque transmitting capacity of a cone clutch by considering uniform wear. (b) A cone clutch is to be designed to transmit a torque of 1000rpm. The outside and inside radii are 75mm and 45mm respectively. The semi cone angle is 15 degrees. The coefficient of friction of friction lining is 0.35. Using the uniform wear theory, find the required clamping force. If the friction lining wears out by 0.4mm, what reduction in the torque capacity of the clutch. [4+12] 4. (a) Derive the expression of the following for a reciprocating engine. i. Piston Effort ii. Thrust on cylinder walls. iii. Force along connecting rod (b) A single Cylinder, single acting, four cycle gas engine develops 5kW at 300 rpm. The flywheel weighs 10kN and has a radius of gyration of 0.8 m. The speed variation on either side is one percent of mean speed. Determine the ratio of the expansion and compression strokes if the work done during admission and exhaust stroke is negligible. [6+10] 5. In a Porter governor, the links and arms are each 30 cms long. Each ball weighs 2.5 kg and the central load is 25 kg. For the lowest and highest of the sleeve the arms 1 of 2

Set No. 4

Code No: R05320304

are inclined 300 and 400 respectively to the vertical. The friction at the governor and the mechanism connecting it to the valve is equivalent to a force of 2.5 kg at the sleeve. Assuming the links and arms intersect on the axis, find: (a) The travel of the sleeve (b) The minimum ascending speed (c) The maximum descending speed (d) Range of speed of the governor.

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6. A shaft 3 m span between the bearings carries two masses of 5 kg and 10 kg acting at the extremities of the arms 0.45 m and 0.6 m long respectively. The planes in which the masses rotate are 1.2 m and 2.4 m respectively from the left hand bearing and the angle between the arms is 600 . If the speed of rotation is 100 rpm. Find the displacing force on the two bearings of the machine. If the masses are balanced by two additional rotating masses acting at a radius 0.3 and placed 0.3 m from each bearing, Estimate the magnitude of the two balanced masses and the angles at which they may be set with respect to the two arms. [16] 7. The following data relate to a single cylinder reciprocating engine. Mass of reciprocating parts = 40 kg Mass of revolving parts = 30 kg at 180mm radius. Speed = 150 rpm Stroke length = 350 mm If 60% of the reciprocating parts and all the revolving parts to be balanced, determine the (a) Balanced mass required at a radius of 320 mm. (b) The unbalanced force when the crank has turned 450 from the top dead center. [16] 8. A machine mounted on springs and fitted with a dashpot has a mass of 60 kg. There are three springs, each of stiffness 12 N/mm. The amplitude of vibrations reduces from 45 to 8 mm in two complete oscillations. Assuming that the damping force varies as the velocity. Determine: (a) The damping coefficient. (b) The ratio of frequencies of damping and undamped vibrations and (c) The periodic time of damped vibrations. ⋆⋆⋆⋆⋆

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