MACHINE DESIGN(1)

(1)Bending Moment

1- Find the reactions at the supports and plot the hear-force and bending- moment diagrams for each of the beams shown in Figure.

2- The shaft shown in figure is supported in bearings at O and C and is subjected to bending loads due to the force components acting at A and B.Sketch two diagrams for each plane of bending, and compute the moment components at A and B. Also compute the maximum bending moment.

2- The figure illustrates an over hanging shaft in bearings, assumed to be self-aligning, at O and B. The shaft is loaded by external forces at A and C. If the diameter of the shaft section at B is 30 mm, what is the bending stress at this section? Is the stress likely to be higher at section A and B?

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(2) Fatigue Stress

1-The endurance limit of a steel member is 112 MPa and the tensile strength is 385 MPa. What is the fatigue strength corresponding to a life of 70(103) cycles?.

2-(a)Corresponding to a reliability of 99 percent, estimate the endurance limit of a round cold drawn steel shaft 3o mm in diameter (Sut = 430 MPa and HB = 125). (b)- What is the endurance limit of a non-rotating bar of the same material and dimensions? Take ka = 0.82, kb = 1.189d-0.097 , kc = 0.814 and assume that kd = ke = kf = 1

3-A 40mm round bar has been machined from AISI 1050 colddrawn round bar (Sut= 400 MPa). This part is to withstand a fluctuating tensile load varying from 0 to 100 KN. Because of the design of the ends and the fillet radius, a fatigue stress-concentration factor of 1.85 exists. The remaining Marin factors have been worked out, and are ka=0.797, kb=kd=1, and kc=0.923. Find the factor of safety using the Goodman interaction line.

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4- Given:Kt = 1.4 , Sut = 420 MPa notch sensitivity q = 0.3Will the beam have infinite life?

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(3) Shaft Design

1- A section of commercial steel shafting 2.0 m long between bearings carries a 1000 N pulley at its midpoint, as shown in Fig.1. The pulley is keyed to the shaft and receives 30 KW at 150 rev/min, which is transmitted to a flexible coupling just outside the right bearing. The belt drive is horizontal and the sum of the belt tensions is 8000 N. Assume Kt = Kb =1.5. Calculate the necessary shaft diameter and determine the angle of twist between bearings. G = 80000 MN/m2.

Fig.12-Fig.2 shows the forces acting on a steel shaft carrying two gears. The gears are keyed to the shaft at B and D. A and C are journal bearing centers. Six KW is transmitted at 650 rev/min of the shaft. The allowable stress for an unkeyed section is 80 MN/m2, and Kb = Kt = 1.5. a)- Sketch horizontal, vertical and

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30 30Pmax=10 kNPmin = 3 kN

50 mm dia

3 mm rad100 mm dia

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100100

resultant bending moment diagrams, shows values at change points. B)- Determine the necessary shaft diameter to the nearest mm. Indicate the critical section.

Fig.23- A machine shaft turning at 600 rev/min is supported on bearings 750 mm apart as shown in Fig.3 below. Fifteen KW is supplied to the shaft through a 450 mm pulley located 250 mm to the right of the right bearing. The power is transmitted from the shaft through a 200 mm spur gear located 250 mm to the right of the left bearing. The belt drive is at an angle of 60 0 above the horizontal. The pulley weighs 800 N to provide some flywheel effect. The ratio of the belt tensions is 3:1. The gear has a 20 0 tooth form and mates with another gear located directly above the shaft. If the shaft material selected has an ultimate strength of 500 MN/m2 and a yield point of 310 MN/m2 determine the necessary shaft diameter using Kb = Kt = 1.0

Fig.3

4- A hollow shaft, 500 mm outside diameter and 300 mm inside diameter, is supported by two bearings 6 m apart. The shaft is driven by a flexible coupling at one end and drives a ship propeller at 100 rev/min. The maximum trust on the propeller is 5000 KN. The shaft transmits 6000 KW and it weighs 800 KN. Determine the maximum shear stress in the shaft considering the weight of the shaft and the column effect. Assume Kb= 1.5 and Kt= 1.0.

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250500250

A

B

C

D

1500N2000N

2500N1000N

800N

500N 2200N

1900N75200100

5- Fig.4 shows an arrangement for a motor and exciter with a pinion on the same shaft. The pinion drives a gear with the gear directly below the pinion. The motor develops 55 KW at 200 revs/min. The exciter absorbs 5 KW, the remainder goining to the pinion. The motor and the exciter are assembled to the shaft by means of a force fit while the pinion is keyed to the shaft. What is the required diameter of the shaft, if the shaft material selected has an ultimate strength of 520 MN/m2 and a yield point of 330 MN/m2 determine the necessary shaft diameter using Kb = 1.5 and Kt = 1.5, the pressure angle of the gear is 20 0 .

Fig.4

6- A 600 mm diameter pulley driven by a horizontal belt transmits power through a solid shaft to a 300 mm diameter pinion, which drives a mating gear.

Fig.5The pulley weighs 1200 N. The arrangement of elements, the belt tensions, and the components of the gear reactions on the pinion are indicated in Fig.5. Determine the necessary shaft diameter using Kb =2.0, Kt = 1.5 and the allowable torsional stress = 40 MN/m2.

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250500500500

pinionExciter motorMotor rotor

1500N

500N

250

375225

800N

2000N

7- The figure (6)is a schematic drawing of a shaft that supports two V-belt pulleys. The loose belt tension on the pulley at A is 15% of the tension on the tight side. The shaft material has a yield strength of 300 MN/m2 and an ultimate tensile strength of 520 MN/m2. Calculate the shaft diameter.

Fig.6

8-Two bearings located 900 mm apart support a section of commercial shafting. A 2000 N, 750 mm diameter, 20 degree involute gear is keyed to the shaft 200 mm to the right of the right bearing. A 300 mm diameter pulley is keyed to the shaft 500 mm to the right of the left bearing. The weight of the pulley is 800 N and the belt tension ratio is 5:1. The gear receives 7 kW at 210 rev/min from a gear located above. Four kW is taken from the shaft at the pulley and the remainder is taken from the shaft through a flexible coupling located 150 mm to the left of the left bearing. Figure(7) shows an end view of the arrangement as observed from the right.

a)- Draw the bending moment diagrams showing values at the change points

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b)- Calculate the diameter of the steel shafting based on strength

Figure 7_______________________________

(4) Coupling Design

1- A rigid coupling has a bore diameter of 50 mm. Four machined bolts on a bolt circle of 125 mm diameter and fitted in reamed holes. If the bolts are made from the same material as the shaft, with an ultimate tensile strength of 550 MN/m2 and a yield point in tension of 345 MN/m2, determine the necessary size of bolts to have the same capacity as the shaft in torsion.

2- Assume that a flange coupling has the following specifications:Number of bolts, 6 Size of bolts, 12 mm diameterPreloading of bolts, 22 KN in each bolt Inner diameter of contact, 175 mmOuter diameter of contact, 200 mm Speed of rotation of coupling, 300 rpm Coefficient of friction, 0.15 Shaft diameter, 50 mmShaft material, annealed steel with an ultimate tensile strength of 586 MN/m2 and a yield point in tension of 310 MN/m2 The bolts are set in large clearance holes in the coupling. Determine:1) The maximum power capacity based upon friction such that slip occurs

between faces of contact2) Compare the shaft horsepower capacity with the friction horsepower

capacity. Assume steady load conditions and that the shaft is in torsion only.

3- Set up the equations or relations necessary to determine:a) the hub diameter DH

Ft

T1

T2

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Fr

b) the web thickness tc) the flange thickness h

4- A flange coupling connects two 50 mm diameter lengths of commercial shafting. The coupling webs are bolted together with four bolts of the same material as the shaft. The bolts are set in clearance holes. The diameter of the bolt circle is 240 mm and the web thickness is 22 mm. Determine

a) the minimum bolt diameter required transmitting the same torque that the shaft can transmit.

b) What power may be transmitted at 200 rev/min under steady state conditions?

(5) Belt Drives

1- A shaft transmits maximum power from a pulley to a flexible coupling. The shaft rotates at 900 rev /min, the pulley is 400 mm in diameter, the belt stands horizontal, and the leather belt 50 mm wide and 6 mm thick. Maximum stress in the belt is 2 MN/m2 and the coefficient of friction is 0.3. If the shaft is to be checked for strength at section A-A, what bending moment and what torque should be used? Leather has a density of p= 970 Kg/m3.

2- A fan is driven by a belt from a motor which runs at 880 rev/min. a leather

belt 8 mm thick and 250 mm wide is used. The diameter of the motor pulley and driven pulley are respectively 350 and 1370 mm. The center distance is 1370 mm, and both pulleys are made of cast iron. Coefficient of friction is 0.35. The allowable stress for the belt is 2.4 MPa. The belt mass is 970 Kg/m3. What is the power capacity of the belt?

3- A crossed belt drive is to transmit 7.5 KW at 1000rev/min of the smaller pulley. The smaller pulley has diameter of 250 mm, the velocity ratio is 2, and the center distance is 1.25 m. It is desired to use a flat belt 6 mm thick with an expected coefficient of friction 0.3. If the maximum allowable stress

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in the belt is 1.7 MN/m2, determine the necessary belt width b. The leather has a density of 970 Kg/m3.

4- A V-belt drive is to transmit 18.5 KW from a 250 mm pitch diameter pulley at 1800 rev/min to a 900 mm diameter flat pulley. The center distance between the input and the output shafts is 1.0 m. The groove angle is 400, and the coefficient of friction between the belt and the pulley is 0.2. The cross section of the belt is b2 = 38 mm wide at the top and b1 = 19 mm wide at the bottom by d = 25 mm deep. Each belt weighs 11 KN/m3 and the allowable tension per belt is 900 N. How many belts are required?

5- A 1.35 m diameter steel flywheel is to be connected to a 0.4 m diameter rubber faced motor pulley by means of double ply leather belt which has a thickness of 8 mm. The center distance is 3.0 m. The coefficient of friction for leather on steel is 0.20 and for leather on rubber is 0.4. The leather has an allowable stress of 2.75 MN/m2. Density of leather is 970 kg/m3. If 45 kW is transmitted with a belt speed of 24.5 m/sec, determine:a)- ef for the pulley which governs the designb)- the necessary belt width** Available widths of belt are:2.5 mm increments from 10 to 25 mm5.0 mm increments from 25 to 100 mm10 mm increments from 100 to 200 mm25 mm increments from 200 to 300 mm

6- An open belt drive delivers 15 KW when the motor pulley, which is 300 mm diameter, turns at 1750 rev/min. The belt is 10 mm thick and 150 mm wide and has a density of 970 Kg/m3. The driven pulley, which is 1.2 m diameter, has an angle of contact of 2000.What is the maximum stress in the belt assuming a coefficient of friction 0.3 for both pulleys? (1.37MPa)

7- A V-belt drive transmits 11 KW at 900 rev/min of the smaller sheave. The sheaves pitch diameters are 173 mm and 346 mm. The center distance is 0.76 m. If the maximum permissible working force per belt is 560 N, determine the number of belts required if the coefficient of friction is 0.15 and the groove angle of the sheaves is 340. The belt mass is 0.194 Kg/m.

(3.16 use 4 belts)-------------------------------------------------------------

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(6) POWER SCREWS AND THREADED FASTENERS

1- The screw shown in fig.(1) is operated by a torque applied to the lower end. The nut is loaded and prevented from turning by guides. Assume friction in the ball baring to be negligible. The screw has a 48 mm outside diameter and triple ISO trapezoidal thread. The pitch is 8 mm. Thread coefficient of friction is 0.15. Determine:1)- The load which could be raised by a torque T of 40 Nm.2)- Would the screw be overhauling.3)- The average bearing pressure between the screw and the nut thread surfaces.

2-The following data apply to the C-clamp shown in fig.(2).ISO metric threads, Pitch = 1.75 mm (single thread)Outside diameter = 12 mm, Root diameter = 9.85 mm, Root area = 76.25 mm2

Coefficient of thread friction f = 0.12, Coefficient of collar friction fc = 0.25Mean collar radius rc = 6 mm, Load W = 4000 NOperator can comfortably exert a force of 80 N at the n of the handle.A)- What length of handle, L, is needed?B)- What is the maximum shear stress in the body of the screw and where does this exist?C)- What is the bearing pressure P on the threads?

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3-Estimate the maximum wrench torque which can be applied in tightening a 20 mm bolt if the shear stress in the body of the bolt is not to exceed 140 MN/m2.Outside diameter = 20mm Root diameter = 16.72 mmThread angle = 300 Pitch = 2.5 mmEffective friction radius rc = 12 mm Thread and collar coefficient of friction = 0.10

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(7) CLUTCHES

1- Drive the torque capacity for one pair of surfaces pressed together with an axial force F, assume uniform pressure.

2-Drive the torque capacity for one pair of surfaces pressed together with an axial force F. Assume uniform wear. 3-Determine the maximum, minimum, and average pressure in a plate clutch where the axial force is 4000 N, the inside radius of contact is 50 mm, the outside radius of contact is 100 mm. Uniform wear is assumed.

4-A multiple disk clutch, steel and bronze, is to transmit 4 KW at 750 rev/min. The inner radius of contact is 40 mm and the outer radius of contact is 70 mm. The clutch operates in oil with an expected coefficient of friction 0.10. (Oil is

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used to give smoother engagement, better dissipation of heat, even though the capacity is reduced). The average allowable pressure is 350 KN/m2 maximum. 1)- How many total disks of steel and bronze are required?2)- What axial force required?3)- What is the average pressure?4)- What is the actual maximum pressure? Assume uniform wear.

5-A multiple disk clutch is composed of 5 steel and 4 bronze disks. The clutch is required to transmit 16 Nm torque. If the coefficient of friction may be taken as 0.10, the average pressure is not to exceed 350 KN/m2 and the inner diameter is restricted to 50 mm, assuming uniform wear, determine:

1-the necessary outer diameter of the disks 2-the necessary axial force

6-A soft cone clutch must handle 200 Nm of torque at 1250 rev/min. the large diameter of the clutch is 350 mm, the cone pitch angle is 6.250, the face width b is 65 mm, and the coefficient of friction is 0.20, determine:

1- the axial force F required to transmit the torque2- the axial force Fe required to engage the clutch3- the average normal pressure p on the contact surfaces 4- the maximum normal pressure, assuming uniform wear.

8- Consider the same clutch and conditions as the above problem, but assume uniform pressure. Determine:

1- the axial force F required to transmit the torque2- the axial force Fe required to engage the clutch3- the average normal pressure p on the contact surfaces

9- A cone clutch is to transmit 100 Nm after engagement. If the maximum force is 850 N, what is the required width of faces? The total included cone angle is 240, and the maximum average pressure is limited to 100 KN/m2, and the coefficient of friction is 0.20. Assume uniform wear.

10- A soft cone clutch has a cone pitch angle of 100, a mean diameter of 300 mm, and a face width of 100 mm. Using a coefficient of friction of 0.20, the assumption that uniform wear exists, and the average pressure is 70 KN/m2 for a speed of 500 rev/min, determine:

1- the force required to engage the clutch2- the power that can be transmitted.

(8) Keys, Pins, and Splines

1- Determine the required length of a square key if the key and the shaft are made of the same material and of equal length.

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2- A feather key is 12 mm wide and 9 mm deep and is to transmit 680 Nm of torque from a 38 mm diameter shaft. The steel key has an allowable stress in tension and compression of 110 Mpa and an allowable stress in shear of 57.5 Mpa. Determine the required length of the key.

3-A pin in knuckle joint is subjected to an axial load of 90 KN. Assume that the thickness of the eye to be 1.5 times the diameter of the pin. The allowable stress of the material in tension and compression due to bending is 60 MN/m2 and the allowable stress in shear is 30 MN/m2 . The allowable stress in bearing is 20 MN/m2 . Determine the required pin diameter.

4- A splined connection in an automobile transmission consists of 10 splines cut in a 58 mm diameter shaft. The height of each spline is 5.5 mm and the keyways in the hub are 45 mm long. Determine the power that may be transmitted at 2500 rev/min, if the allowable normal pressure on he splines is limited to 4.8 MN/m2 .

5- A flat key is used to key a gear on a 30 mm shaft made of 0.3%C cold drawn steel. The key is made of the same material as the shaft (σu = 634 MPa and σy = 538 MPa). Determine the torque capacity of the shaft in accordance with the ASME shafting code. Calculate the torque capacity of the key using a factor of safety of 1.5 based upon the yield strength of the material, and assuming that σs =0.6 σy . Shear and compression areas are 115 mm2 and 22 mm2.

5- If the key in Problem 2 had 9 mm wide and 12 mm deep, what would have been the required length for the same load and material?

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