THE INSTITUTIO~~.GINEERS SRI LANKA

PART III (A) EXAMINATION - October 2012

324 - MACHINE DESIGN

DArE: Time: From 9.00 am to 1.00 J?m DURATION: FOUR HOURS--------------------

READ THE FOLLOWING INSTRUCTIONS CAREFULLY BEFORE ANSWERING THE QUESTION PAPER

1 This question paper has two parts} PART A and PART B. Answer the question inPARTA} which is compulsory, and any three from PART B.

2 Use separate answer books to answer question/s in PART A and PART B} andsubmit them separately.

3 PARTA carries 50 marks} whereas each question in PART B 17 marks.

4 Attempt all parts in Question 1in that given order. Spend maximum three (03)hours to answer the question in PARTA and rest for questions in Part B.

5 Wherever appropriate} use the given catalogue} information} and data sheets}

provided to you in the examination hall. At the end of the examination return allsuch material to the examiner/supervisor of the examination hall.

6 Any missing data can be sensibly and reasonably assumed} but such assumptionsare not acceptable unless they are justified and clearly stated.

7 Wherever relevant use neatly drawn sketches to explain your answers.

8 Any result from calculations should have units} unless they are dimensionless.

9 All answers to the given questions should be underlined for the purpose of easyidentification.

-------11.9-Write the questi~No.to-vlhiel=l.t'ou answer on-the-cover page ap'jifopriaa.ute::.aIJ/-V _

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Figure.1. The raw coffee beans are fed into a cylindrical container, and hot air is directed through the

lower duct to the coffee beans. Used hot air is then expelled out through the upper duct by means of

suction fans, which are not shown in the figure. The coffee beans are agitated continuously inside the

cylinder using the rotor. The rotor arrangement is shown in the Figure.2.

The stainless steel cylindrical container R. into which the raw coffee beans are loaded. contains the

agitator (T) and it imparts violent and regular motion to the coffee beans. The agitator rotates in bothdirections (clockwise and anticlockwise) from time to time, governed by a timer, in order to maintain the

required agitation effect, while coffee beans are being heated up uniformly throughout by the hot air.

This would complete the roasting process of coffee beans.

Drive pulley C on the motor shaft drives the driven pulley 0 and transmits power to the gear box by

means of a suitable V-belt. The horizontal splined shaft F, which carries the cluster wheel with two

wheel segments G and W, is supported by two identical rolling element bearings E. The cluster wheel

can be axially moved to change the direction of rotation of the power output shaft. The shaft Q which

carries the wheels J, K and N is also supported by another pair of rolling element bearings. The direction

of rotation of the blade when the wheel segment G is in contact with wheel J, is opposite to that when

the segment W is in contact with H through K. The pair of bevel gears Nand U changes the drive

direction by 900. The shaft V, which is an integral part of the bevel gear U and whose axis is vertical,

holds the agitator in position. Two element rolling bearings P support this shaft. The container is firmly

held to the machine frame and the lateral movement of the shaft V is constrained with permitting only

its axial rotation. The wheels G, J, Q, H are enclosed in a gearbox.

Answer the following questions for the given configuration

1. Estimate the power required to drive the agitator.

2. Select a suitable motor, and specify the power rating and speed considering the pair of bevel gears

to have a speed ratio in the range of 1 to 2.

3. Find the number of teeth on the idler wheel H.

4. Select and specify a suitable belt drive system that includes number of belts and standard pulleys.

Recommend an initial belt tension, so that the belts can initially be tightened to this value.

5. Determine the minimum diameter of the splined shaft.

6. Determine the important parameters of wheels G and J selecting a suitable material.~~~'-"*'- {-"',jf''' -------~---~--~ "-,7. Serecta-s-urtabl~)ey for ttle::Od~dyenpulley.

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8. Recommend a suitable pair of rolling-element bearings to support the splined shaft on to the gearenclosure.

The /ollowtng information are proliTded in support 0/ the design analysis.

1. The dimensions of the blades of the agitator, blade arms and the container are as given in theFigure.2.

HOT AIR OUT

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HOT AIR IN

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Figure 2

PLAN VIEW OF BLADE (T)

• These blades rotate at 60 rev/min.• Amount of pressure that applies on a blade is 30 kN/m2 when the container is filled with the

mixture to its maximum capacity.• The projected area of a blade is 300 mm x 200 mm, on which the given pressure applies.

4. Diameter of the splined shaft refers to its minor diameter, and neglect the effects of splines whendesigning the shaft for strength. Shock and fatigue factors for bending and torsion are 2 and 1.5

. r~ctively. Shaft material has an allowable bending and,sh~stresses 50 MN/m2 and 40 MN/m2

--respeqively. ' -, --~-

2. All spur gears have a module of 4 mm.

3. Axes of all the shafts lie on same vertical plane.

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Machine Design IOctoberZ012

5. Splined shaft experiences maximum state of stresses when the pair of gears G and J transmits

power.

6. Mechanical Efficiencies relevant to different drives are:

Bevel gears 92%

Spur wheels 94%

Belt drive 90%

7. Ratio of the pulley diameters are in the range of 0.5 to 3 and the center distance between pulleys

can be in the range of 200 - 600 mm. This system is required to operate for over 10 hours a day

continuously.

8. Pressure angle for any spur gear is 20°.

9. The velocity ratio of the spur gears can be selected within the range of 0.5 to 2.

10. If necessary, select one of the following steels for the shaft material.

AISI Number Yield strength{MN/m2) Ultimate tensile strength

(MN/m2)

1010 303 366

1018 373 442

1045 532 626

4340 683 766

• If key ways are present then values are to be reduced by 25%.

• For ductile materials Yield stress in shear = 0.5 x yield stress in tension.

• A shaft having a diameter d, when subjected to combined bending and torsion theequivalent bending, and torsional stresses at any point on the shaft respectively are givenbelow in usual notations.

=; = :3[KbM + ~(KbMY + (K1TY ]

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--~rdi-T--=-""':';;~ . '-.L)2 ()2 -.-,;.._ all Ceq 1iS3 b·1VIJ +=K, T 2-·~-

--...•

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where the values of k, and k, are as follows:

Machine Design October2012

1.0

1.5 to 2.0

Kb Kt--1

--~.....•.

For Stationery shafts:Load Gradually applied

Load Suddenly applied

1.0

1.5 to2.0

For Rotating shafts:Load Gradually applied

Load Suddenly applied (minor shock)

v.shock)

1.5

1.5 to 2.01.0

1.0 to 1.5

2 0 to 3 0 I 1.5 to-l.O

• Principal stresses are given by

( ) _ (]' x + (]'Y I((]'x - (]' Y )2 2an max - 2 + ~ 2 + rxy

( . ) _ a x + a y _ ~(]' x - (]' y )2 2(]' n min - + T xy2 2

r(max)~,i( a, ;ay)' +r,,,'

11. For gear designs the following are useful

• For gears, basic Louis Equation is :F=sbPcY

• For ordinary design conditions, the face width is limited to a maximum of 4 times the circular pitch.

Letting b = kPc, where the factor, k::;; 4,

r, = 21V(bC+F) +F21V +.JbC+F

where, Fd= dynamic load, N

V = pitch line velocity, m/s

b = face width, m

F = gear torque = 2M / Dpitch diam. of gear I

C = a constant, in N/m~It;;",..

Fw(allowable wear load) = Dp b K Q

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Machine Design IOctober2012

Dp= pitch diameter of smaller gear (pinion), m

b = face width of gear, m

K = stress factor for fatigue, N/m_2_

Q = 2NJ{Np + Ng)

Ng= number of teeth on gear

Np= number of teeth on pinion

S;s(sin~XllEp +lIEg)K = -..:..::.....:--~-----.!=----~

1.4where, Ses = surface endurance limit of a gear pair, N/m2

-j Ep= modulus of elasticity of the pinion material, N/m2 .

Eg= modulus of elasticity of the gear material, N/m2

cj> = pressure angle.

The surface endurance limit may be estimated from,

where,

and

s., = [2.75 (BHN) - 70] MN/m2

where, BHN may be approximated by the average Brinell hardness number of the gear

and pinion up to a BHN of about 350 for steels.

The wear load Fwis an allowable load and must be greater than the dynamic load Fd.

Values of Deformation Factor C in kN/m - for dynamic load check.

Materials Involute tooth form Tooth Error - mm

Pinion Gear 0.01 0.02 0.04 0.06 0.08

cast iron cast iron 14 Yz 0 55 110 220 330 440

steel cast iron 14 Yz 0 76 152 304 456 608

steel steel 14 Yz 0 110 220 440 660 880

cast iron cast iron 200 full depth 57 114 228 342 456""

steel cast iron 200 full depth 79 158 316 474 632

steel steel 200 full depth 114 228 456 684 912

cast iron cast iron 200 stub 59 118 236 354 472

steel cast iron 200 stub 81 162 324 486 648

steel steel 200 stub 119 238 476 714 952

-"4>•.: T ~-.~...•......•----..

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/ Values for Sesas used in the wear load equation depend upon a combination of the gear and pinion""

/ materials. Some values for various materials for both Sesand K are tabulated.

j ~Average BrineJrHardness Number of steel Surface Endurance

,.,-f __0" .•,,:.-, " Stress Fatigue1.1

pinion and steel gear limitFactor K (kN/m2)

s., (MN/m2) 14 Yz0 200

150 342 206 282I

200 480 405 555I 250 618 673 919I

1 300 755 1004 1372

I 400 1030 1869 2553~

Brinnel Hardness Number BHN

Steel Pinion Gear

150 c.1. 342 303 414

200 c.1. 480 600 820

250 C.I. 618 1000 1310

150 Phosphor Bronze 342 317 427Phosphor Bronze 445 503 689200

c.1. Pinion C.I. Gear 549 1050 1420

c.I, Pinion C.I. Gear 618 1330 1960~

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Machine Design October2012

--f-~~~,~-=-

Form Factors y - for use in Lewis Strength Equation (transformed). F = s,(kym2 is given in th~~ollowing ~.table:I

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Number of Teeth

12

13

~ I14

"

15

16

17

18

19

20

21

23

25

27

30

34

38

43

50

60

75

100

150

300

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Rack

14 Yz0 Full-Depth

Involute of Composite

0.067

0.071

20° Full-DepthInvolute

0.078

0.083

0.0880.075

0.078

0.081

0.084

0.086

0.088

0.090

0.092

0.094

0.097

0.099

0.101

0.104

0.106

0.108

0.110

0.113

0.115

0.117

0.119

0.092

0.094

0.096

0.098

0.100

0.102

0.104

0.106

0.108

0.111

0.114

0.118

0.122

0.126

0.130

0.134

0.138

0.142

0.146

0:124

__ .~'~~.122 I 0.150 . ~

0-:154

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20° Stub Involute

0.099

1.103

0.108

0.111

0.115

0.117

0.120

0.123

0.125

0.127

0.130

0.133

0.136

0.139

0.142

0.145

0.147

0.151

0.154

0.158

0.161

0.165

~ 0.1»:»:0.175

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Machine Design 1October2012

PARTB

• Importance of investigating fatigue failures of engineering materials,• Causes of fatigue failures,• Fatigue failure initiation,

" L_ Quote at least-one world's occident, where fatigue-mechanism was responsibieftn causingfailure of the material of engineering components (provide sufficient evidence).

Question 2

Write a short note on fatigue failures of engineering components. Your answer should cover thefollowing:

Question 3

a. What are the basic considerations when selecting a bearing for a given application?

b. Identify two practical applications where each of the following rolling element bearings is in use.i. Cylindrical roller bearings.ii. Spherical roller bearings.

c. Explain clearly the following parameters within the context of rolling element bearings.i. L10 life.ii. Static Load Rating.Hi. Equivalent Dynamic Load.

Question 4

a. Explain preloading of a bolt. What is the advantage of preloading?

b. For a screw and nut pair with square threads, show that torque required to lift a vertical load isgiven by,

dT== Wtan(a+¢)-, where

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T = Torque required to overcome friction between the screw and nutW= Load to be lifted verticallya = Helix angle of the square thread

¢= Angle of friction

d = Mean diameter of the screwc. A power screw driven by an electric motor moves a nut in a horizontal plane against an axial

load of 75 kN at ~lJ.eed of 300 mm/min. The screw has a single square thread-sf 6 mm pitch onI . --a major diamet-er of40 mm. I he coefficient ottncbon-atscrew threaasrslJ.I. F!Qdlh~e~"':'po-w-_-eLO.-L:-------

the motor~~~' .

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b. Compare and contrast between friction clutch and a fluid coupling.

c. A single plate friction clutch, effective on both sides, is required to transmit 25 kW at 3,000rev/min.Dete-rm-'---in-e---:t-'--h-e-o-u-:-te-r-a-n-d~in-n-e-r-'dO;-ia-m-et:-e-r-s-o~ffrictIOnal surface if the coefficient of friction is 0.25,

ratio of diameters is 1.25 and the maximum pressure is not to exceed 0.1 Nfmm',Also, determine the axial thrust to be provided by springs. Assume the condition of uniform

wear.

Question 6

a. A mild steel rod of 12 mm diameter was tested for tensile strength with the gauge length of 60mm. Following observations were recorded.

Final length = 80 mm

Final diameter = 7 mm

Yield load = 3.4 kNUltimate load = 6.1 kN

Calculate the,

i. Yield stressii. Ultimate tensile stressiii. Percentage reduction in areaiv. Percentage elongation

b. A shaft is transmitting 100 kW power at 160 rev/min. Find a suitable diameter for the shaft, ifthe maximum torque transmitted exceeds the mean value by 25%. Take maximum allowableshear stress for shaft material as 70 MPo.

--~~. ~-·,67""

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