Sunday, 11 September 2016

Question bank- Static Force Analysis-Unit 1-VTU Dynamics of Machines-10ME54

Vidya Vikas Institute of Engineering & Technology, MYSURU
SEPTEMBER 2016 - Nov 2016              5th Semester                  Dynamics of Machines 10ME54
Question Bank on       Static Force Analysis
Q 1.
The four bar linkage of shown in Fig. 1 below has crank 2 driven by an input torque T2. An external load P = 240 N acts at point O on the link 4. Find the required input torque to hold the mechanism in this position in equilibrium. Given = 50 mm, AB = 60 and = 70 mm,
O2O4 = 100 mm.
Fig. 1
Q 2
Determine the shaft torque T2 at O2 for  static equilibrium with the shown external force.
Given O2A= 40 mm, AB = 80 mm, O4B= 60 mm, and    AC = 30 mm. Refer fig. 2
Fig. 2
Q 3
Determine the torque T2, in Fig.3, required to overcome the force FE along the link 6.   AD=30 mm, AB=90 mm, O4 B=60 mm, DE=80 mm, O2 A=50mm, O2 O4 =70 mm
Fig. 3
Q 4
For the static equilibrium of the quick return mechanism shown in Fig. 4 determine the input torque T2 to be applied on link AB for a force of 300N on the slider D. The dimensions of the various links are OA= 400 mm, AB=200 mm, OC=800 mm, CD=300 mm.
Fig. 4
Q 5
Determine the torque T2, on link 2 shown in Fig. 5, required to keep the mechanism given in equilibrium. O2A = AB = O4B=30 MM,  O2O4 = 60 mm, Angle AO2O4 = 60º, BC = 19 mm, AD=15 mm.
Fig. 5
Q 6
A four bar linkage mechanism as shown in Fig.6 has the following dimensions and is acted upon by a force P = 80 N at an angle θ =150° on link DC.  Link dimensions are as follows: AD = 50 mm, AB = 40 mm, BC = 100 mm, DC = 75 mm and CE = 35 mm.  Determine the input torque T on the link AB for the static equilibrium of mechanism for the given configuration.
Fig. 6
Q 7
Determine the couple, T on link AB required for the equilibrium of the system shown in Fig. 7. AB = 200 mm; BC = 800 mm; BD = 300 mm.  Load P = 2000 N acts at angle of 45°to the connecting rod.
Fig. 7
Q 8
Determine the required input torque T1 for static equilibrium of the mechanism shown in Fig. 8. Torques T2 and T3 are pure torques, having magnitudes of 10 N-m and 7 N-m, respectively.
Fig. 8
Q 9
The dimensions of four bar link mechanism are AB = 400 mm, BC = 600 mm, CD = 500 mm, AD = 900 mm and DAB = 60°. AD is a fixed link, E is the point on link BC such that BE = 200 mm and CE = 400 mm. A force P of 150 N acts at 45° at a distance of 250 mm from D, as shown in Fig. 9. Another force Q = 100 N acts at E at an angle of 180°. Find the required input torque on link AB for static equilibrium of the mechanism.
Fig. 9
Q 10
For the slider crank mechanism shown in Fig. 10, determine the Torque T1 on link 1 required for static equilibrium.
Fig. 10
Q 11
For the four bar link mechanism shown in Fig. 11, determine the Torque on link 2 required for static equilibrium.
Fig.11
Q 12
For the four bar link mechanism shown in Fig. 12, determine the Torque on link 2 required for static equilibrium. AB = 30 mm, BC = 50 mm, CD = 70 mm, and AD = 80 mm.
Fig. 12
Q 13
For the mechanism shown in Fig. 13 find the required input torque for the static equilibrium. The lengths OA and AB are 250 mm and 650 mm respectively. F=500N
Fig. 13
Q14
To
Q22
14.  Define and explain principle of virtual work with help of a slider mechanism.
15.  Explain with a neat sketch static force analysis of two and three force members.
16.  Explain the procedure for static force analysis of a four bar mechanism.
17.  Figure below shows a quaternary link ABCD under the action of forces F1, F2, F3 and F4 acting at A,B,C and D respectively. The link is in static equilibrium. Determine the magnitude of forces F2 & F3 and the direction of F3.
18.  What are the implications of considering friction in static force analysis?
19.  A body shown in is subjected to three forces F1, F2 and F3. State the condition for equilibrium of the body. If force F1 is completely known, F2 is known in direction only and F3 is completely unknown, explain how the problem can be solved.
20.  Explain the procedure for static force analysis of a slider crank mechanism.
21.  Discuss the equilibrium of the following systems: 
i)                    Two force members
ii)                  Three force members, and
iii)                Member with Two forces and a torque.
22.  What is principle of Virtual work? Explain 

Compiled by Dr. N. S. SRIRAM, VVIET, Mysore 

 Compiled by N. S. SRIRAM, VVIET, Mysore
·       
I acknowledge that the above materials have been compiled from publications and contributions made by teachers, students of various institutions through different websites.
I thank all of them which made this compilation possible.
































Posted by at 1 comment:
Labels: ,

Dynamics of machines- Question Bank on Unit 3 - Friction in Bearings-10ME54

Question Bank on Friction in Bearings   Unit – III  
10 ME54 Dynamics of Machines (5th semester BE VTU)
Usually question in this unit consists of part a) which will be a theory or derivation and part b) will be a numerical problem.
Some typical Questions in part a) of question paper that appear or have appeared till now are:
1.                  Define static and dynamic friction and State Laws of dry friction.
2.                  Discuss the types of friction and laws of friction.
3.         Derive the expressions for frictional torque in a flat pivot bearing. Assume uniform pressure conditions.
4.                  Discuss briefly the various types of friction experienced by a body.
5.                  State the laws of (i) Static friction: (ii) Dynamic friction; (iii) Solid friction; and (iv) Fluid friction.
6.                  Explain the following: (i) Limiting friction, (ii) Angle of friction, and (iii) Coefficient of friction.
7.                  What is meant by the expression ‘friction circle’?
8.            Deduce an expression for the radius of friction circle in terms of the radius of the journal and the angle of friction.
9.                  From first principles, deduce an expression for the friction moment of a collar thrust bearing, stating clearly the assumptions made.
10.              Derive an expression for the friction moment for a flat collar bearing in terms of the inner radius R2, outer radius R1, axial thrust W and coefficient of friction μ. Assume uniform intensity of pressure.
11.              Derive from first principles an expression for the friction moment of a conical pivot bearing assuming (i) Uniform pressure, and (ii) Uniform wear
12.              A truncated conical pivot of cone angle φ rotating at speed N supports a load W. The smallest and largest diameter of the pivot over the contact area are‘d’ and ‘D’ respectively. Assuming uniform wear, derive the expression for the frictional torque.
13.              Derive from the first principles an expression for the friction moment of a conical pivot bearing assuming (i) Uniform pressure and (ii) Uniform wear.
14.              Derive an expression for ratio of tensions in flat belt drive.
15.              State the laws of dynamic friction.
16.              Derive an expression for frictional torque in a flat collar bearing assuming uniform pressure.
17.              Derive an equation to calculate the centrifugal tension in a flat belt drive.
18.              Explain: i) Slip, ii) Creep, iii) Initial tension and, iv) Centrifugal tension, in belt drive.
19.              Explain how centrifugal tension affects the maximum tension in the flat belt drive. Also derive the equation for centrifugal tension in a flat belt drive.
20.              Derive the expressions for frictional torque in a flat pivot bearing for uniform pressure and wear conditions.
21.              Derive the expressions for frictional torque in single collar bearings for uniform pressure conditions.
22.              Derive the expressions for frictional torque in flat collar bearings for uniform pressure and wear conditions
23.              Derive an expression for the ratio of tensions in a flat belt drive.
24.              Obtain condition for maximum power transmitted by a belt from one pulley to another.

Numerical Problems on friction in bearings
1.     Calculate the power lost in overcoming the friction and number of collars required for a thrust bearing whose contact surfaces are 20 cm external radius and 15 cm in internal radius. The coefficient of friction is 0.08. The total axial load is 30 kN. Intensity of pressure is not to exceed 3.5 x 105 N/m2. Speed of the shaft is 420 rpm.

2.    In a thrust bearing the external and internal radii of contact surfaces are 210 mm and 160 mm respectively. The total axial load is 60 kN and coefficient of friction is 0.05. The shaft is rotating at 380 rpm. Intensity of pressure is not to exceed 0.35 N/mm2. Calculate :
i)           Number of collars required for the thrust bearing.
ii)         Power lost due to friction.

3.         Find the power lost in friction assuming (i) uniform pressure and (ii) uniform wear when a vertical shaft of 100 mm diameter rotating at 150 r.p.m. rests on a flat end foot step bearing. The coefficient of friction is equal to 0.05 and shaft carries a vertical load of 15 kN.

4.         A conical pivot with angle of cone as 120° supports a vertical shaft of diameter 300 mm. It is subjected to a load of 20 KN. The coefficient of friction is 0.05 and the speed of shaft is 210 rpm. Calculate the power lost in friction assuming (i) uniform pressure and (ii) uniform wear.

5.         A load of 25 KN is supported by a conical pivot with angle of cone as 120°. The intensity of pressure is not to exceed 350 kN/m2. The external radius is 2 times the internal radius. The shaft is rotating at 180 rpm and coefficient of friction is 0.05. Find the power absorbed in friction assuming uniform pressure.

6.         In a collar thrust bearing the external and internal radii are 250 mm and 150 mm respectively. The total axial load is 50 KN and shaft is rotating at 150 rpm. The coefficient of friction is equal to 0.05. Find the power lost in friction assuming uniform pressure.

7.         A conical pivot bearing 150 mm in diameter has a cone angle of 120º. If the shaft supports an axial load of 20 kN and the coefficient of friction is 0.03, find the power lost in friction when the shaft rotates at 200 rpm, assuming (i) Uniform pressure, and (ii). Uniform wear.

8.         A vertical shaft supports a load of 20 kN in a conical pivot bearing. The external radius of the cone is 3 times the internal radius and the cone angle is 120º. Assuming uniform intensity of pressure as 0.35 MN/m2, determine the dimensions of the bearing. If the coefficient of friction between the shaft and bearing is 0.05 and the shaft rotates at120 rpm., find the power absorbed in friction.

9.         A plain collar type thrust bearing having inner and outer diameters of 200 mm and 450 mm is subjected to an axial thrust of 40 kN. Assuming coefficient of friction between the thrust surfaces as 0.025, find the power absorbed in overcoming friction at a speed of 120 rpm. The rate of wear is considered to be proportional to the pressure and rubbing speed.

10.     The thrust of a propeller shaft in a marine engine is taken up by a number of collars integral with the shaft which is 300 mm in diameter. The thrust on the shaft is 200 kN and the speed is 75 rpm. Taking μ constant and equal to 0.05 and assuming intensity of pressure as uniform and equal to 0.3 N/mm2, find the external diameter of the collars and the number of collars required, if the power lost in friction is not to exceed 16 kW

11.     A shaft has a number of a 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 rpm carrying a load of 150 kN and ii) number of collars required.

12.     A conical pivot bearing supports a vertical shaft of 200 mm diameter. It is subjected to a load of 30 kN. The angle of the cone is 120º and the coefficient of friction is 0.025. Find the power lost in friction when the speed is 140 rpm, assuming i). Uniform pressure and ii) uniform wear.

13.     A conical pivot supports a load of 18 kN, the cone angle is 100º and the intensity of normal pressure is not to exceed 300 kN/m2. The external radius is 2.5 times the internal radius. Find the outer and inner radii of the bearing surface. If the shaft rotates at 1500 rpm and the coefficient of friction is 0.05, find the power absorbed in friction. Assume uniform pressure.

14.     A vertical shaft 150 mm in diameter rotating at 100 rpm rests on a flat end foot step bearing. The shaft carries a vertical load of 20 kN. Assuming uniform pressure distribution and coefficient of friction equal to 0.05. Estimate power lost in friction.

15.     A shaft has a number of a 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 rpm carrying a load of 150 kN and ii) Number of collars required.

Compiled by N. S. SRIRAM, VVIET, Mysore

·         I acknowledge with thanks the contributions made by various teachers, students in the different websites, from which the above question bank materials have been compiled.


·         I thank all of them who made this compilation possible.
Posted by at No comments:

Dynamics of Machines - 10ME54 - UNIT 3 - Question Bank on belt drives

Question Bank on Belt Drives    Unit – III  
10 ME54 Dynamics of Machines (5th semester BE Mechanical VTU)
Usually question in this unit consists of part a) which will be a theory or derivation and part b) will be a numerical problem.
Some typical Questions in part a) of question paper that appear or have appeared till now are:
1.                  Define static and dynamic friction and State Laws of dry friction.
2.                  Discuss the types of friction and laws of friction.
3.              Derive the expressions for frictional torque in a flat pivot bearing. Assume uniform pressure conditions.
4.                  Discuss briefly the various types of friction experienced by a body.
5.                  State the laws of (i) Static friction: (ii) Dynamic friction; (iii) Solid friction; and (iv) Fluid friction.
6.                  Explain the following: (i) Limiting friction, (ii) Angle of friction, and (iii) Coefficient of friction.
7.                  What is meant by the expression ‘friction circle’?
8.             Deduce an expression for the radius of friction circle in terms of the radius of the journal and the angle of friction.
9.                  From first principles, deduce an expression for the friction moment of a collar thrust bearing, stating clearly the assumptions made.
10.              Derive an expression for the friction moment for a flat collar bearing in terms of the inner radius R2, outer radius R1, axial thrust W and coefficient of friction μ. Assume uniform intensity of pressure.
11.              Derive from first principles an expression for the friction moment of a conical pivot bearing assuming (i) Uniform pressure, and (ii) Uniform wear
12.              A truncated conical pivot of cone angle φ rotating at speed N supports a load W. The smallest and largest diameter of the pivot over the contact area are ‘d’ and ‘D’ respectively. Assuming uniform wear, derive the expression for the frictional torque.
13.              Derive from the first principles an expression for the friction moment of a conical pivot bearing assuming (i) Uniform pressure and (ii) Uniform wear.
14.              Derive an expression for ratio of tensions in flat belt drive.
15.              State the laws of dynamic friction.
16.              Derive an expression for frictional torque in a flat collar bearing assuming uniform pressure.
17.              Derive an equation to calculate the centrifugal tension in a flat belt drive.
18.              Explain: i) Slip, ii) Creep, iii) Initial tension and, iv) Centrifugal tension in belt drive.
19.              Explain how centrifugal tension affects the maximum tension in the flat belt drive. Also derive the equation for centrifugal tension in a flat belt drive.
20.              Derive the expressions for frictional torque in a flat pivot bearing for uniform pressure and wear conditions.
21.              Derive the expressions for frictional torque in single collar bearings for uniform pressure conditions.
22.              Derive the expressions for frictional torque in flat collar bearings for uniform pressure and wear conditions
23.              Derive an expression for the ratio of tensions in a flat belt drive.
24.              Obtain condition for maximum power transmitted by a belt from one pulley to another.

Numerical problems on Belt Drives:
1.         A belt 100 mm wide and 10 mm thick is to transmit power at speed of 1000 m/min. The net driving tension is 1.8 times the tension on slack side. If the safe permissible stress is 2 MPa, calculate the maximum power that can be transmitted at this speed. Assume the density of leather as 1000 kg/m3. Also determine (i) the absolute maximum power. (ii) Percentage increase in power.

2.         A leather belt is required to transmit 7.5 kW from a pulley 1.2 m in diameter, running at 250 rpm, the angle of contact is 165° and µ = 0.3. If the safe working stress for the leather belt is 1.5 MPa and density of leather is 1000 kg/m3 and thickness of belt is 10 mm, determine the width of belt taking centrifugal tension into account.

3.         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 centers of two pulleys is 3 m. The density of leather is 1000 kg/m3. The maximum allowable stress in leather is 2.5 MPa. The coefficient of friction between leather and pulley is 0.3. Assume open belt drive and neglect slip in belt drive.

4.         A flat belt is required to transmit 35 kW from a pulley of 1.5 m effective diameter running at 300 rpm. The angle of contact is spread over 11/24 of the circumference and the coefficient of friction between belt and pulley surface is 0.3. Determine width of the belt required taking centrifugal tension into account. It is given that the belt thickness is 9.5 mm, density of its material is 1.1x103 kg/m3 and the permissible working stress for belt is 2.5 N/mm2.

5.         An open belt drive is used to connect two parallel shafts, 4 m apart. The diameter of the larger pulley is 1.5 m and that of smaller pulley is 0.5 m. The mass of the belt is 1 kg/m length. The maximum tension is not to exceed 1500 N. The coefficient of friction is 0.25. The bigger pulley which is the driver runs at 250 rpm. Due to slip, the speed of driven pulley is 725 rpm. Calculate the power transmitted, power lost in frictions, and the efficiency of the drive.

6.         2.5 kW of power is transmitted by an open belt drive. The linear velocity of the belt is 2.5 m/s. The angle of lap on the smaller pulley is 165°. The coefficient of friction is 0.3. Determine the effect on power transmission in the following cases:
i)                     Initial tension in the belt is increased by 8%.
ii)                   Initial tension in the belt is decreased by 8%.
iii)                Angle of lap is increased by 8% by the use of an idler pulley, for the same speed and tension on the tight side.
iv)                Coefficient of friction is increased by 8% by suitable dressing to the friction surface of the belt.
7.         A shaft rotating at 200 rpm drives another shaft at 300 rpm and transmits 6 kW through a belt. The belt is 100 mm wide and 10 mm thick. The distance between the shafts is 4 m. The smaller pulley is 0.5 m in diameter. Calculate the stress in the belt, if it is :
i)                    An open belt drive, and        ii)   A cross belt drive.                   Take μ= 0.3

8.         An op en belt drive is required to transmit 10 kW of power from a motor running at 600 rpm. Diameter of the driving pulley is 250 mm. The speed of the driven pulley is 220 rpm. The belt is 12 mm thick and has a mass density of 0.001 g/mm3. Safe stress in the belt is not to exceed 2.5 N/mm2. The two shafts are 1.25 m apart. The coefficient of friction is 0.25. Determine the width of the belt.

9.      Two parallel shafts that are 3.5 m apart are connected by two pulleys of 1 m and 400 mm diameters, the larger pulley being the driver runs at 220 rpm. The belt weighs 1.2 kg per meter length. The maximum tension in the belt is not to exceed 1.8 kN. The coefficient of friction is 0.28. Owing to slip on one of the pulleys, the velocity of the driven shaft is 520 rpm only. Determine the:
i)                    Torque on each shaft
ii)                  Power transmitted
iii)                Power lost in friction
iv)                Efficiency of the drive.

10.  The maximum power transmitted by a belt is 60 kW. The belt is 250 mm wide and 10 mm thick and weighs 9.81 kN/m3. If the ratio of tensions on the tight and slack sides is 2, determine the maximum stress induced in the belt.

11.  In a belt drive, the mass of the belt is 1 kg/m length and its speed is 6 m/s. The drive transmits 9.6 kW of power. Determine the initial tension in the belt and the strength of the belt. The coefficient of friction is 0.25 and the angle of lap is 220°

12.  In an open belt drive the diameters of the larger and smaller pulleys are 1.2 m and 0.8 m respectively. The smaller pulley rotates at 320 rpm. The center distance between the shafts is 4 m. When stationary, the initial tension in the belt is 2.8 kN. The mass of the belt is 1.8 kg/m and the coefficient of friction between the belt and the pulley is 0.25. determine the power transmitted.

13.  The initial tension in a belt drive is found to be 600 N and the ratio of friction tensions is 1.8. The mass of the belt is 0.8 kg/m length. Determine:
i)                    Velocity of the belt for maximum power transmission
ii)                  Tension in the tight side of the belt when it is started, and
iii)                Tension in the tight side of the belt when the running at maximum speed.


14.  An open belt drive transmits 4 kW of power. The smaller pulley is the driver and rotates at 300 rpm. The diameters of the two pulleys are 280 mm and 640 mm and center distance is 3 m. The coefficient of friction between the belt and the pulley is 0.3. If the safe working stress is 8 N/mm widths, determine the minimum width of the belt. Also calculate the initial tension in the belt and the length of the belt required. The initial tension in a belt drive is found to be 600 N and the ratio of friction tensions is 1.8. The mass of the belt is 0.8 kg/m length. Determine:



Compiled by N. S. SRIRAM, VVIET, Mysore
·         I acknowledge with thanks the contributions made by various teachers, students in the different websites, from which the above question bank materials have been compiled.

·         I thank all of them who made this compilation possible.
Posted by at No comments:
Subscribe to: Posts (Atom)