Syllabus

NME-501 : MACHINE DESIGN-I

UNIT I

Introduction Definition, Design requirements of machine elements, Design procedure, Standards in

design, Selection of preferred sizes, Indian Standards designation of carbon & alloy steels, Selection of

materials for static and fatigue loads. 3 Design for Static Load Modes of failure, Factor of safety,

Principal stresses, Stresses due to bending and torsion, Theory of failure.

UNIT II

Design for Fluctuating Loads Cyclic stresses, Fatigue and endurance limit, Stress concentration factor,

Stress concentration factor for various machine parts, Notch sensitivity, Design for finite and infinite life,

Soderberg, Goodman & Gerber criteria.

Riveted Joints Riveting methods, materials, Types of rivet heads, Types of riveted joints, Caulking and

Fullering, Failure of riveted joint, Efficiency of riveted joint, Design of boiler joints, Eccentric loaded

riveted joint.

UNIT III

Shafts Cause of failure in shafts, Materials for shaft, Stresses in shafts, Design of shafts subjected to

twisting moment, bending moment and combined twisting and bending moments, Shafts subjected to

fatigue loads, Design for rigidity.

Keys and Couplings Types of keys, splines, Selection of square & flat keys, Strength of sunk key,

Couplings, Design of rigid and flexible couplings.

UNIT IV

Mechanical Springs Types, Material for helical springs, End connections for compression and tension

helical springs, Stresses and deflection of helical springs of circular wire, Design of helical springs

subjected to static and fatigue loading.

Power Screws Forms of threads, multiple threads, Efficiency of square threads, Trapezoidal threads,

Stresses in screws, Design of screw jack

Note: Design data book is allowed in the examination Books and References

UNIT-I

MEERUT INSTITUTE OF TECHNOLOGY MEERUT

B.Tech (Mechanical) (V semester)

Subject-Machine Design-1

Assignment No-1

1. What is Machine Design? What are the steps in Machine Design process?

2. What do you mean by need analysis? Write its importance in design. (U.P.T.U

2008-09)

3. Explain the brain storming. What are their rules?

4. What is standardization? Give the advantages of standardization. (U.P.T.U

2007-08)

5. What is interchangeability?

6. Explain Concurrent Engineering.

7. What is preferred number? Derive the R-10 series.

8. Explain the importance of preferred size in design process. (U.P.T.U

2004-05)

9. Find out the number of R-20/4 (10…100) derived series.

10. Discuss the effect of silicon, manganese, sulphur and phosphorus on cast iron.

11. Designate the following materials

(a) Grey cast iron with minimum tensile strength of 300 N/mm2.

(b) Designate plain carbon steel with 0.5 % carbon and 0.85 manganese

(c) Carbon= 0.35 - 0.45 %, chromium= 0.90 - 1.1 %.

(d) Carbon 0.12 - 0.20 % , Ni= 0.8 -1.2 %, Cr= 0.6 – 1.0 %

(e) C=0.15 -0.25 %, Si=0.10 – 0.50 %, Mn= 0.3 – 0.5 %, Ni=2.5 – 3.5 %, Cr= 18-

24 %

(f) 50Cr1V23 U.P.T.U 2005-06)

12. Define these definitions

(a) Ductility (b) Brittleness (c) Creep (d) Fatigue (e) Elasticity (f) Plasticity (g)

Toughness (h) Resilience

13. What are the reasons for the use of alloy steel in machine parts? (U.P.T.U

2004-05)

14. What are the three basic mode of failure of mechanical component?

15. What is factor of safety? Why is it necessary to use factor of safety.

16. What are the factors to be considered for deciding the magnitude of factor of safety?

17. Explain different types of theories of failure in machine design.

18. Explain the importance of material selection decision in machine design. (U.P.T.U

2008-09)

19. Discuss the factors which are considered in the selection of a material for a machine

component.

20. Enumerate advantages and disadvantages of plastic material over metals. (U.P.T.U

2007-08)

UNIT-II

MEERUT INSTITUTE OF TECHNOLOGY MEERUT

B.Tech (Mechanical) (V semester)

Subject-Machine Design-1

Tutorial No-1

1. A forged steel bar 50 mm in diameter is subjected to

reversed bending stress of 250 N/mm2. The bar is made

of steel 40C8 (Sut=600 N/mm2). Calculate the life of the

bar for a reliability of 90 %. Ans=23736 Cycle

2. A rotating beam made of steel 45C8 (Sut=630 N/mm2) is

subjected to completely reversed bending stress. The

corrected endurance limit of the bar is 315 N/mm2.

Calculate the fatigue strength of the bar for a life of

90,000 cycle.

3. A machine component is subjected to a flexural stress

which fluctuates between + 300 MN/m2 and – 150

MN/m2. Determine the value of minimum ultimate

strength according to 1. Gerber relation; 2.Goodman

relation; and 3. Soderberg relation. Take yield strength

= 0.55 Ultimate strength; Endurance strength = 0.5

Ultimate strength; and factor of safety = 2.

4. A bar of circular cross-section is subjected to alternating

tensile forces varying from a minimum of 200 kN to a

maximum of 500 kN. It is to be manufactured of a

material with an ultimate tensile strength of 900 MPa

and an endurance limit of 700 MPa. Determine the

diameter of bar using safety factors of 3.5 related to

ultimate tensile strength and 4 related to endurance limit

and a stress concentration factor of 1.65 for fatigue load.

Use Goodman straight line as basis for design.

5. Determine the thickness of a 120 mm wide uniform

plate for safe continuous operation if the plate is to be

subjected to a tensile load that has a maximum value of

250 kN and a minimum value of 100 kN. The properties

of the plate material are as follows: Endurance limit

stress is 225 MPa, and Yield point stress is 300 MPa.

The factor of safety based on yield point may be taken

as 1.5.

6. Determine the diameter of a circular rod made of

ductile material with a fatigue strength (complete

stress reversal), σe = 265 MPa and a tensile yield

strength of 350 MPa. The member is subjected to a

varying axial load from Wmin = –300×103 N to

Wmax=700×103

N and has a stress concentration

factor = 1.8. Use factor of safety as 2.0.

7.

8.

7. A steel rod is subjected to a reversed axial load of

180 kN. Find the diameter of the rod for a factor

of safety of 2. Neglect column action. The

material has an ultimate tensile strength of 1070

MPa and yield strength of 910 MPa. The

endurance limit in reversed bending may be

assumed to be one-half of the ultimate tensile

strength. Other correction factors may be taken as

follows:For axial loading = 0.7; For machined

surface = 0.8 For size = 0.85 ; For stress

concentration = 1.0.

8. A circular bar of 500 mm length is supported

freely at its two ends. It is acted upon by a central

concentrated cyclic load having a minimum value

of 20 kN and a maximum value of 50 kN.

Determine the diameter of bar by taking a factor

of safety of 1.5, size effect of 0.85, surface finish

factor of 0.9. The material properties of bar are

given by : ultimate strength of 650 MPa, yield

strength of 500 MPa and endurance strength of

350 MPa.

9. A piston rod of circular cross section is subjected

to a cyclic load fluctuating between 15 kN in

compression to 25 kN in tension. The endurance

limit for the piston rod material is 360 N/mm2.

While yield strength is 400 N/mm2. The impact

factor is 1.25 while fos is 1.5. The surface finish

factor and stress concentration factor are 0.88 and

2.25 respectively. Determine the diameter of

piston rod. d=20.70 mm

10. A 50 mm diameter shaft is made from carbon

steel having ultimate tensile strength of 630 MPa.

It is subjected to a torque which fluctuates

between 2000 N-m to – 800 N-m. Using

Soderberg method, calculate the factor of safety.

Assume suitable values for any other data Needed

11. A simply supported beam has a concentrated load

at the centre which fluctuates from a value of P to

4 P. The span of the beam is 500 mm and its

cross-section is circular with a diameter of 60

mm. Taking for the beam material an ultimate

stress of 700 MPa, a yield stress of 500 MPa,

endurance limit of 330 MPa for reversed bending,

and a factor of safety of 1.3, calculate the

maximum value of P. Take a size factor of 0.85

and a surface finish factor of 0.9.

UNIT-III

MEERUT INSTITUTE OF TECHNOLOGY MEERUT

B.Tech (Mechanical) (V semester)

Subject-Machine Design-1

Tutorial No-2

1. A solid shaft is transmitting 1 MW at 240 r.p.m.

Determine the diameter of the shaft if the maximum

torque transmitted exceeds the mean torque by 20%.

Take the maximum allowable shear stress as 60 MPa.

. Ans: d=160 mm

2. A cylindrical shaft made of steel of yield strength

700 MPa is subjected to static loads consisting of a

bending moment of 10 kN-m and a torsional moment

of 30 kN-m. Determine the diameter of the shaft

using two different theories of failure and assuming a

factor of safety of 2. Ans. 100 mm

3. Find the diameter of a solid steel shaft to transmit 20

kW at 200 r.p.m. The ultimate shear stress for the

steel may be taken as 360 MPa and a factor of safety

as 8.If a hollow shaft is to be used in place of the

solid shaft, find the inside and outside diameter when

the ratio of inside to outside diameters is 0.5.

Ans: d=50 mm do = 50mm di=25 mm

4. A line shaft rotating at 200 r.p.m. is to transmit 20

kW. The shaft may be assumed to be made of mild

steel with an allowable shear stress of 42 MPa.

Determine the diameter of the shaft, neglecting the

bending moment on the shaft . Ans: d=50 mm

5. A solid circular shaft is subjected to a bending

moment of 3000 N-m and a torque of 10 000 N-m.

The shaft is made of 45 C 8 steel having ultimate

tensile stress of 700 MPa and a ultimate shear stress

of 500 MPa. Assuming a factor of safety as 6,

determine the diameter of the shaft. Ans: d=90 mm

6. A line shaft rotating at 200 r.p.m. is to transmit 20

kW. The allowable shear stress for the material of the

shaft is 42 MPa. If the shaft carries a central load of

900 N and is simply supported between bearing 3

metre apart, determine the diameter of the shaft. The

maximum tensile or compressive stress is not to

exceed 56 MPa. Ans. d=50 mm

7. A propeller shaft is required to transmitted 45 KW

power at 500 r.p.m. its hollow shaft having an inside

diameter 0.6 times of outside diameter. It’s made of

plain carbon steel and the permissible shear stress is

84 N/mm2. Calculate the inside and outside diameter

of the shaft. Ans: di=23.47 mm do=39.12 mm

8. Derived the diameter of a hollow shaft with a ratio of

of 0.8, capable of transmitting 300 KW at 225

rev/min. when subjected to a maximum bending

moment of 5500 Nm, the load is suddenly applied with

minor shock for torsional moment the bending moment

is steady and the allowable shearing stress is 56 MPa.

Ans: di=120 mm do=150 mm

9. A shaft made of mild steel is required to transmit 100

kW at 300 r.p.m. The supported length of the shaft is 3

meters. It carries two pulleys each weighing 1500 N

supported at a distance of 1 metre from the ends

respectively. Assuming the safe value of stress,

determine the diameter of the shaft. Ans: d=70 mm

10. A hollow circular shaft of outer and inner diameter of

do and di respectively is subjected to a torsional

moment of M over a length l. The permissible angle of

twist is θ degree. Proved that the shaft diameter is

given by.

d0 =

11. A rotating shaft 40 mm in diameter, is made of steel

FeE 580 (Syt=580 N/mm2). It is subjected to a steady

torsional moment of 250 N-m and bending moment of

1250 N-m. Calculate the factor of safety available

based on Ans. (i) 2.89, (ii) 2.86

(i) Maximum principal stress theory

(ii) Maximum shear stress theory

12. A Propeller shaft is required to transmit 50 kW power

at 600 rpm. It is hollow shaft. Having inside diameter

0.8 times of the outer diameter. It is made of steel (Syt

= 380 N/mm2) and the factor of safety is 4. Calculate

the inside and outside diameter of the shaft.

13. Two 400 mm diameter pulleys are keyed to a simply

supported shaft 500 mm apart. Each pulley is 100 mm

from its support and has horizontal belts, tension ratio

being 2.5. If the shear stress is to be limited to 80 MPa

while transmitting 45 kW at 900 r.p.m., find the shaft

diameter if it is to be used for the input-output belts

being on the same or opposite sides. Ans. 40 mm

14. A line shaft is driven by means of a motor placed

vertically below it. The pulley on the line shaft is 1.5

metre in diameter and has belt tensions 5.4 kN and 1.8

kN on the tight side and slack side of the belt

respectively. Both these tensions may be assumed to be

vertical. If the pulley be overhang from the shaft, the

distance of the centre line of the pulley from the centre

line of the bearing being 400 mm, find the diameter of

the shaft. Assuming maximum allowable shear stress

of 42 MPa Ans: d=78mm

15. A shaft is supported by two bearings placed 1 m apart.

A 600 mm diameter pulley is mounted at a distance of

300 mm to the right of left hand bearing and this drives

a pulley directly below it with the help of belt having

maximum tension of 2.25 kN. Another pulley 400 mm

diameter is placed 200 mm to the left of right hand

bearing and is driven with the help of electric motor

and belt, which is placed horizontally to the right. The

angle of contact for both the pulleys is 180° and µ =

0.24. Determine the suitable diameter for a solid shaft,

allowing working stress of 63 MPa in tension and 42

MPa in shear for the material of shaft. Assume that the

torque on one pulley is equal to that on the other

pulley. Ans: d=51.7mm

16. A transmission shaft with keyway is subjected to a

maximum torsional moment of 750 M-m and

maximum bending moment of 1200 N-m.the loads are

suddenly applied minor shocks are encountered, and

the allowable shear stress is 42 MPa. Find the shaft

diameter Ans: d=68.3 mm

17. A mild steel shaft transmits 20 kW at 200 r.p.m. It

carries a central load of 900 N and is simply supported

between the bearings 2.5 meters apart. Determine the

size of the shaft, if the allowable shear stress is 42 MPa

and the maximum tensile or compressive stress is not

to exceed 56 MPa. What size of the shaft will be

required, if it is subjected to gradually applied loads?

Ans: d=53.4 mm, d=57.7 mm

18. Design a shaft to transmit power from an electric motor

to a lathe head stock through a pulley by means of a

belt drive. The pulley weighs 200 N and is located at

300 mm from the centre of the bearing. The diameter

of the pulley is 200 mm and the maximum power

transmitted is 1 kW at 120 r.p.m. The angle of lap of

the belt is 180° and coefficient of friction between the

belt and the pulley is 0.3. The shock and fatigue factors

for bending and twisting are 1.5 and 2.0 respectively.

The allowable shear stress in the shaft may be taken as

35 MPa. Ans: d=51.1 mm

19. The layout is a transmission shaft carrying two pulleys

B and C and supported on bearing A and D as shown in

fig. Power is supplied to the shaft by means of a

vertical belt on the pulley B. when id then transmitted

to the pulley C carrying a horizontal belt. The

maximum tension in the belt on the pulley is 2.5 KN.

The angle of wrap for the both pulley is 1800 and the

coefficient of friction is 0.24. The shaft is made of

plain carbon steel 30

C8 (Syt=400 N/mm2) and the factor

of safety is 3. Determine the shaft diameter on strength

basis. Ans: d=45.47 mm

20. The layout of a shaft carrying two pulleys 1 & 2 and

supported on two bearing A & B as shown in fig. The

shaft transmits 7.5 KW power at 360 r.p.m from the

pulley 1 to the pulley 2. The diameter of pulleys 1 & 2

are 250mm and 500 mm respectively. The masses of

pulley 1 & 2 are 10 kg and 30 kg respectively. The belt

tension act vertically downward and the ratio of belt

tension on the tight side to slack side for each pulley is

2.5:1. The shaft is made of plain carbon steel (Syt =380

N/mm2) and fos is 3. Estimate suitable diameter of

shaft. If permissible angle of twist is 0.50 per meter

length. Calculate the shaft diameter on the basis of

torsional rigidity. Assume G=79300 N/mm2.

Ans: d=41.37 mm Ans:41.37 mm

21. A line shaft supporting two pulleys A and B as shown.

Power is supplied to the shaft by means of a vertical

belt on the pulley A. Which is then transmitted to the

pulley B carrying a horizontal belt. The ratio of the belt

tension on tight and loose sides is 3:1. The limiting

value of tension in the belt is 2.7 kN. The shaft is made

of plain carbon steel 40

C8 (Sut=650 N/mm2) and

(Syt=380 N/mm2). The pulleys are keyed to the shaft.

Determine the diameter of the shaft according to the

ASME code if Kb=1.5and kt=1.0 Ans: d=42.53mm

22. A steel spindle transmits 4 kW at 800 r.p.m. The

angular deflection should not exceed 0.250 per meter of

the spindle. If the modulus of rigidity for the material

of the spindle is 84 GPa. Find the diameter of the

spindle and the shear stress induced in the spindle.

. Ans: d=35 mm, τ=5.67 N/mm2

23. A line shaft rotating at 200 r.p.m is required to transmit

25 kW. It carries a central load of 900 N and is simply

supported between bearing 3 meter apart. The

allowable tensile and shear stress for the shaft are 56

N/mm2 and 42 N/mm

2 respectively. Determine the

diameter of the shaft. If Kt=1.25 and Km= 1.5 Ans: d=63.5 mm

24. The layout of intermediate shaft of a gear box

supporting two spur gears B and C as shown. The shaft

is mounted on two bearing A and D. The pitch circle

diameters of gears B and C are 900 and 600 mm

respectively. The material of the shaft is steel FeE 580

(Sut=770 N/mm2) and (Syt=580 N/mm

2). The factor

Kb and Kt of ASME code are 1.5 and 2.0 respectively

Determine the shaft diameter. Assume that the gears

are connected to the shaft by means of keys .

. Ans: d=68.59 mm

25. The armature shaft of 40 kW, 720 rpm electric motor.

Mounted on two bearing A and B as shown. The total

magnetic pull on the armature is 7 kN and it can be

assumed to be uniformly distributed over a length of

700 mm midway between the bearing. The shaft is

made of steel with ultimate tensile strength of 770

N/mm2 and yield strength of 580 N/mm

2Determine the

shaft diameter using ASME code if kb=1.5and kt=1.0

Ans: d=45.13 mm

26. Figure shows a shaft carrying a pulley A and a gear B

and supported in two bearings C and D. The shaft

transmits 20 kW at 150 r.p.m. The tangential force F

on the gear B acts vertically upwards as shown. The

pulley delivers the power through a belt to another

pulley of equal diameter vertically below the pulley A.

The ratio of tensions T 1 /T2 is equal to 2.5. The gear

and the pulley weigh 900 N and 2700 N respectively.

The permissible shear stress for the material of the

shaft may be taken as 63 MPa. Assuming the weight of

the shaft to be negligible in comparison with the other

loads, determine its diameter. Take shock and fatigue

factors for bending and torsion as 2 and 1.5

respectively. Ans: 69.6 mm

27. A solid circular shaft of diameter d is subjected to

bending moment of M and torsional moment of T.

Prove that according to maximum shear stress theory.

=

28. A solid circular shaft of diameter d is subjected to

bending moment of M and torsional moment of T.

Prove that according to maximum principal r stress

theory.

=

29. The shaft of an axial flow rotary compressor is

subjected to a maximum torque of 2000 N-m and a

maximum bending moment of 4000 N-m. The

combined shock and fatigue factor in torsion is 1.5 and

that in bending is 2. Design the diameter of the shaft, if

the shear stress in the shaft is 50 MPa. Design a hollow

shaft for the above compressor taking the ratio of outer

diameter to the inner diameter as 2

Ans. 96 mm 98 mm, 49 mm

30. A shaft made of steel receives 7.5 kW power at 1500

r.p.m. A pulley mounted on the shaft as shown in Fig.

14.19 has ratio of belt tensions 4. The gear forces are

as follows : Ft= 1590 N, Fr = 580 N. Design the shaft

diameter by maximum shear stress theory. The shaft

material has the following properties: Ultimate tensile

strength = 720 MPa; Yield strength = 380 MPa; Factor

of safety = 1.5. Ans. d=20 mm

31. It is required to design a square key for fixing a gear

on a shaft of 25 mm diameter. The shaft is

transmitting 15 kW power at 720 rpm to the gear.

The key is made of steel 50C4 (Syt=460 N/mm2) and

the factor of safety is 3. For key material, the yield

strength in compression can be assumed to be equal

to the yield strength in tension. Determine the

dimension of the key. Ans: l=35 mm

32. The standard cross section for a flat key which is

fitted on a 50 mm diameter shaft is 16x10 mm. The

key is transmitting 475 N-m torque from the shaft to

the hub. The key is made of commercial steel

(Syt=Syc=230 N/mm2). Determine the length of the

key, if the factor of safety is 3. Ans: l=50 mm

33. A shaft, 40 mm in diameter is transmitting 35 kW

power at 300 rpm by means of Kennedy keys of

10x10 mm cross section. The keys are made of steel

45C8 (Syt=Syc=380 N/mm2) and the factor of safety is

3. Determine the required length of the key.

34. Design the rectangular key for a shaft of 75 mm

diameter. The shearing and crushing stresses for key

material are 50MPa and 75MPa respectively.

. (UPTU-2002)

35. Design the rectangular key for a shaft of 50 mm

diameter. The shearing and crushing stresses for key

material are 42MPa and 72MPa respectively

(UPTU-2004)

36. A square key is to be used to fix a gear to a 35 mm

diameter shaft. The hub length of the gear is 60 mm.

Both the shaft and key are to be made of the same

material, having an allowable shear stress of 55

N/mm2. If the torque to be transmitted is 395 N-m.

Determine the minimum dimension of key cross

section. Ans: b=6.84 mm, h=6.84 mm

37. Design a square key for fixing a gear on the shaft

having 25mm diameter. The gear rotates at 550 rpm

and transmits 12 kW power to the meshing gear. The

key is made of steel having yield stress in tension as

400 N/mm2. The yield stress in compression and

tension may be taken equal to each other. Assume

factor of safety is 2.5. (UPTU-2005) Ans:l=34mm

38. A standard splined connection 8x52x60 mm is used

for the gear and the shaft assembly of a gearbox. The

splines transmit 20 kW power at 300 rpm. The

dimension of the splines are as follow

Major diameter= 60 mm, Minor diameter = 52 mm

Number of splines = 8, Permissible normal pressure

on splines is 6.5 N/mm2. The coefficient of friction is

0.06. Calculate (i) Length of the hub (ii) The forced

require for shifting the gear.

Ans: l=110 mm, F= 1364.19 N

39. A steel shaft has a diameter of 25 mm. The shaft

rotates at a speed of 600 r.p.m. and transmits 30 kW

through a gear. The tensile and yield strength of the

material of shaft are 650 MPa and 353 MPa

respectively. Taking a factor of safety 3, select a

suitable key for the gear. Assume that the key and

shaft are made of the same material. Ans. l = 102 mm

40. A kennedy keys are used to transmit 30 kW power at

500 rpm from 40 mm diameter shaft to the hub. The

keys are made of steel 55C8 with yield strength of

400MPa and ultimate tensile strength of 700 MPa.

Ifnthe factor of safety required is 3 and over load

factor is 1.5, design the key. .

Ans: b=10 mm, h=10 mm l= 23 mm

41. Design a muff coupling which is used to connect two

steel shafts transmitting 40 kW at 350 rpm. The

material for the shaft and the key is plain carbon steel

for which allowable shear and crushing stresses may

be taken as 40 MPa and 80 MPa respectively. The

material for the muff is cast iron for which the

allowable shear stress may be assumed as 15 MPa.

42. Design of a muff coupling, which is used to connect

two steel shafts transmitting 25 kW power at 360

rpm. The shaft and key are made of plain carbon

steel 30C8 (Syt = Syc=400 N/mm2). The sleeve is

made of grey cast iron FG 200 (Sut=200 N/mm2).

The factor of safety for the shaft and key is 4. For

sleeve the fos is 6 based on ultimate strength.

43. Design a muff coupling to connect two mild steel

shafts to transmit 35 kW at 1440 r.p.m. The C.I

sleeve connects the shaft through two mild steel sunk

keys. The maximum torque transmitted is 25 %

greater than the average torque.Allowable shear

stress for C.I and mild steel are 15 N/mm2 and 65

N/mm2.and the allowable crushing stress for mild

steel= 160 N/mm2.

Ans: d=29 mm , D= 58 mm, L=102 mm, l=51 mm

44. Design a muff coupling to connect two shafts

transmitting 40 kW at 120 r.p.m. The permissible

shear and crushing stress for the shaft and key

material (mild steel) are 30 MPa and 80 MPa

respectively. The material of muff is cast iron with

permissible shear stress of 15 MPa. Assume that the

maximum torque transmitted is 25 per cent greater

than the mean torque.

45. It is required to design a split muff coupling to

transmit 50 kW power at 120 rpm. The shaft, key and

clamping bolts are made of plain carbon steel 30C8

(Syt =400n/mm2). The yield strength in compression

is 150% of tensile yield strength. The factor of safety

for the shaft, key and bolts is 5. The number of

clamping bolts is 8. The coefficient of friction

between halves and the shaft is 0.3.

46. Design a cast iron protective flange coupling to

connect two shafts in order to transmit 7.5 kW at 720

r.p.m. The following permissible stresses may be

used:

Permissible shear stress for shaft, bolt and key

material = 33 MPa, Permissible crushing stress for

bolt and key material = 60 MPa, Permissible shear

stress for the cast iron = 15 MPa

47. The shaft and flange of a marine engine are to be

designed for flange coupling in which the flange is

forged on the end of the shaft. The following

particulars are to considered in the design

Power of engine= 3MW

Speed of engine= 100 rpm

Permissible shear stress in bolt and shaft = 60 Mpa,

No of bolts used=8

Pitch circle diameter of bolts = 1.6 x diameter of

shaft. Find Diameter of shaft, diameter of bolts

Thickness of flange, diameter of flange.

48. Design a clamp coupling to connect two plain carbon

steel shafts to transmit 60 kW power at 500 r.p.m.

The C.I muff halves are clamped by four alloy steel

bolts. The key used has same material as that of the

shaft. The maximum torque transmitted is 20 %

greater than the average torque. Allowable shear

stress for shaft and key material are 55MPa and

allowable crushing stress for shaft and key material

=155 MPa.

Allowable crushing stress for C.I muff = 150 MPa,

Allowable Tensile stress for alloy steel bolts =130

MPa

49. Design a Cast Iron protective type flange coupling to

transmit 15 kW at 900 r.p.m from an electric motor

to a compressor. The service factor may be assumed

as 1.35. The following permissible stresses may be

used.

Shear stress for shaft, bolt and key = 40 MPa

Crushing stress for bolt and key = 80MPa

Shear stress for Cast Iron = 8 MPa

50. Two 35 mm shaft are connected by a flange

coupling. The flanges are fitted with 6 bolts on 125

mm bolt circle. The shaft transmits a torque of 800

N-m at 350 RPM. For the safe stresses mentioned

below, Calculate (i) diameter of bolts (ii0 thickness

of flanges (iii) Key dimension (iv) hub length and (v)

Power transmitted.

Safe shear stress for shaft material = 63 MPa

Safe stress for bolt material = 56 MPa

Safe stress for cast iron coupling = 10 MPa

Safe stress for key material = 46 MPa

51. Design a cast iron flange coupling for a mild steel

shaft transmitting 90 kW at 250 rpm. The allowable

shear stress in the shaft is 40 MPa and the angle of

twist is not to exceed 10 in a length of 20 diameters.

The allowable shear stress in the coupling bolts is 30

MPa.

52. A flexible coupling is used to transmit 15 kW power

at 100 rpm. There are six pins and their pitch circle

diameter is 200 mm. The effective length of the bush

(lb). The permissible shear and bending stress are 35

and 152 N/mm2

respectively Calculate the pin

diameter by shear consideration.

53. Design a bushed-pin type flexible coupling for

connecting a motor shaft to a pump shaft for the

following service conditions, Power to be transmitted

= 40 kW; speed of the motor shaft = 1000 r.p.m. ;

diameter of the motor shaft, = 50 mm; diameter of

the pump shaft = 45 mm. The bearing pressure in the

rubber bush and allowable stress in the pins are to be

limited to 0.45 N/mm2 and 25 MPa respectively

54. Design a Cast Iron protective type flange coupling to

connect two shaft of 36 mm diameter, transmitting at

720 r.p.m. The over load capacity 1.25 times the

average torque. The bolt and key are made of C20

steel and the flanges are made of Cast Iron. Assume

missing data suitable, if any U.P.T.U 2007-08)

55. Design a cast iron protective flange coupling to

connect two shafts in order to transmit 7.5 kW at 720

r.p.m. The following permissible stresses may be

used

Permissible shear stress for shaft, bolt and key

material = 33 MPa, Permissible crushing stress for

bolt and key material = 60 MPa, Permissible shear

stress for the cast iron = 15 MPa.

UNIT-IV

MEERUT INSTITUTE OF TECHNOLOGY MEERUT

B.Tech (Mechanical) (V semester)

Subject-Machine Design-1

Tutorial No-3

1. A compression coil spring made of an alloy steel is

having the following specifications :

Mean diameter of coil = 50 mm; Wire diameter = 5

mm; Number of active coils = 20. If this spring is

subjected to an axial load of 500 N; calculate the

maximum shear stress (neglect the curvature effect) to

which the spring material is subjected.

2. A helical spring is made from a wire of 6 mm

diameter and has outside diameter of 75 mm. If the

permissible shear stress is 350 MPa and modulus of

rigidity 84 kN/mm2, find the axial load which the

spring can carry and the deflection per active turn.

3. Design a spring for a balance to measure 0 to 1000 N

over a scale of length 80 mm. The spring is to be

enclosed in a casing of 25 mm diameter. The

approximate number of turns is 30. The modulus of

rigidity is 85 kN/mm2. Also calculate the maximum

shear stress induced.

4. A mechanism used in printing machinery consists of a

tension spring assembled with a preload of 30 N. The

wire diameter of spring is 2 mm with a spring index of

6. The spring has 18 active coils. The spring wire is

hard drawn and oil tempered having following

material properties:Design shear stress = 680 MPa,

Modulus of rigidity = 80 kN/mm2

Determine: 1. the initial torsional shear stress in the

wire; 2. spring rate; and 3. the force to cause the body

of the spring to its yield strength.

5. Design a helical compression spring for a maximum

load of 1000 N for a deflection of 25 mm using the

value of spring index as 5. The maximum permissible

shear stress for spring wire is 420 MPa and modulus

of rigidity is 84 kN/mm2.

6. Design a close coiled helical compression spring for a

service load ranging from 2250 N to 2750 N. The

axial deflection of the spring for the load range is 6

mm. Assume a spring index of 5. The

permissible shear stress intensity is 420 MPa and

modulus of rigidity, G = 84 kN/mm2.

Neglect the effect of stress concentration.

7. Design a valve spring of a petrol engine for the

following operating conditions

Spring load when the valve is open = 400 N

Spring load when the valve is closed = 250 N

Maximum inside diameter of spring = 25 mm

Length of the spring when the valve is open = 40

mm

Length of the spring when the valve is closed = 50

mm

Maximum permissible shear stress = 400 MPa

8. Design a helical spring for a spring loaded safety

valve (Ramsbottom safety valve) for the

following conditions :

Diameter of valve seat = 65 mm ; Operating

pressure = 0.7 N/mm2; Maximum pressure when

the valve blows off freely = 0.75 N/mm2;

Maximum lift of the valve when the pressure rises

from 0.7 to 0.75 N/mm2 = 3.5 mm ; Maximum

allowable stress = 550 MPa

Modulus of rigidity = 84 kN/mm2; Spring index =

6.

9. A safety valve of 60 mm diameter is to blow off at

a pressure of 1.2 N/mm2. It is held on its seat by a

close coiled helical spring. The maximum lift of

the valve is 10 mm. Design a suitable

compression spring of spring index 5 and

providing an initial compression of 35 mm. The

maximum shear stress in the material of the wire

is limited to 500 MPa. The modulus of rigidity for

the spring material is 80 kN/mm2.

Calculate: 1. Diameter of the spring wire, 2. Mean

coil diameter, 3. Number of active turns, and 4.

Pitch of the coil.

10. Its required to design a helical compression spring

subjected to a maximum force of 1250 N. The

deflection of the spring corresponding to the

maximum force should be approximately 30 mm.

The spring index can be taken as 6. The spring is

made of patented and cold drawn steel. The

ultimate tensile strength and modulus of rigidity

of the spring material are 1090 and 81370 N/mm2

respectively. The permissible shear stress for the

spring wire should be taken as 50 % of the

ultimate strength. Design the spring and calculate.

Wire diameter, mean coil diameter, Number of

active coil, free length of the spring, pitch of the

coil

11. It’s required to design a helical compression

spring for the mechanism. The axial force acting

on the spring is 300 N when the valve is open and

150 when the valve is closed. The length of the

spring is 30 mm when the valve is open and 35

mm when the valve is closed. The spring is made

of oil-hardened and tempered valve spring wire

and the ultimate tensile strength is 1370 N/mm2.

The permissible shear stress for spring wire

should be taken as 30% of the ultimate tensile

strength. The modulus of rigidity is 813770

N/mm2.Tyhe spring is fitted over a valve rod the

minimum inside diameter of the spring should be

20 mm Calculate:

Wire diameter, mean coil diameter, No of active

coil, total no of coil, free length of the spring,

pitch of the coil

(a) A helical tension spring is used in the spring

balance to measure the weights. One end of the

spring is attached to the rigid support while the

outer end, which is free, carries the weights to be

measured. The maximum weight attached to the

spring balance is 1500 N and the length of the

scale should be approximately 100 mm. The

spring index can be taken as 6. The spring is made

of oil hardened and tempered steel wire with

ultimate tensile strength opf 1360 N/mm2 and

modulus of rigidity of 81370 N/mm2. The

permissible shear stress in the spring wire should

be taken as 50 % of the ultimate tensile strength

Calculate : Wire diameter, mean coil diameter, no

of active coil, spring rate, actual spring rate

12. A helical compression spring made of oil

tempered carbon steel is subjected to a load which

varies from 400 N to 1000 N. The spring index is

6 and the design factor of safety is 1.25. If the

yield stress in shear is 770 MPa and endurance

stress in shear is 350 MPa, find: 1. Size of the

spring wire, 2. Diameters of the spring, 3. Number

of turns of the spring, and 4. free length of the

spring.

The compression of the spring at the maximum

load is 30 mm. The modulus of rigidity for the

spring material may be taken as 80 kN/mm2.

13. A helical compression spring of a cam-

mechanism is subjected to an initial preload of 50

N. The maximum operating force during the load

cycle is 150 N. The wire diameter is 3 mm, while

the mean coil diameter is 18 mm. The spring is

made of oil-hardened and tempered valve spring

wire of Grade-VW (Sut=1430 N/mm2). Determine

the FOS used in the diagram on the basis of

fluctuating stresses.

14. A closely coiled helical spring is made of 10 mm

diameter steel wire, the coil consisting of 10

complete turns with a mean diameter of 120 mm.

The spring carries an axial pull of

200 N. Determine the shear stress induced in the

spring neglecting the effect of stress

concentration. Determine also the deflection in the

spring, its stiffness and strain energy stored by it

if the modulus of rigidity of the material is 80

kN/mm2.