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Unit-1 Spur Gears & Helical gears
Objective: It gives the basic knowledge about the principles of Spur & cross helical Gear design on the basis of static load, dynamic load, wear etc.
Objective type Questions
1. The gears are termed as medium velocity gears, if their peripheral velocity is
(a) 1-3 m/s (b) 3-15 m/s (c) 15-30 m/s (d) 30-50 m/s
2. The size of a gear is usually specified by
(a) pressure angle (b) pitch circle diameter (c) circular pitch
(d) diametral pitch (c) tooth thickness (f) none of the above
3. The radial distance from the ……..to the clearance circle is called working depth.
(a) addendum circle (b) dedendum circle
4. The product of the diametral pitch and circular pitch is equal to
(a) 1 (b) 1/ (c) (d) x no. of teeth
5. The backlash for spur gears depends upon
(a) module (b) pitch line velocity (c) tooth profile
(d) both (a) and (b) (e) both (b) and (c) (f) none of the above
6. The contact ratio for gears is:
(a) zero (b) less than 1 (c) greater than 1
7. If the centre distance of the mating gears with involute teeth is increased, then the pressure angle
(a) increases (b) decreases (c) remains the same
8. The allowable static stress for steel gears is approximately…….of the ultimate tensile stress.
(a) one-fourth (b) one-third (c) one-half (d) double (e) four times (f) six times
9. Lewis equation is applied
(a) only to the pinion (b) only to the gear
(c) to stronger of the pinion or gear (d) to weaker of the pinion or gear
10. The static tooth load should be …….. the dynamic load.
(a) less than (b) greater than (c) equal to
Theoretical questions
1. How are the gears classified and what are the various terms used in spur gear terminology?
2. Mention four important types of gears and discuss their applications, the materials used for them and their construction.
3. What condition must be satisfied in order that a pair o spur gears may have a constant velocity ratio?
4. State the two most important reasons for adopting involute curves for a gear tooth profile.
5. What is interference in gears? How can you remove it?
6. Write the expressions for static, limiting wear-load and dynamic load for spur gears and explain various terms used therein.
7. Discuss the design procedure for spur gears
8. How are the shaft and arms for spur gears designed?
9. Explain the following terms used in helical gears:
(a) Helix angle (b) normal pitch (c) axial pitch
Numerical Questions
1. A spur steel pinion (s0 =200 MN/m2) is to drive a spur steel gear (s0=140MN/ m2) . The diameter of the pinion
is to be 100mm and the center distance 200mm. The pinion is to transmit 5Kw at 900RPM. The teeth are to be 20o full depths.
Determine the necessary module and face width to give the greatest no of teeth.
2. Two spur gears are to be used for a rock crusher and are to be minimum size. The gears are to be design for following requirements:
power to be transmitted 18Kw, speed of pinion 1200RPM angular velocity ratio 3.5:1, tooth profile 20o stub, s0 value of pinion
100 MN/m2, s0 value for gear 70 MN/ m2. Design the gear.
3. A pair of spur gears transmitting power from motor to pump impeller shaft is to be designed with as small center distance as
possible. The forged steel pinion s0 =160MN/ m2) is to transmit 4Kw at 600 RPM to a cast steel gear (s0=100MN/ m2)
with a transmission ratio 9/2 to 1, and 20o full depth involute teeth are to be used. Determine the necessary
face width and module.
4. A cast steel 24-tooth spur pinion operating at 1150 RPM transmits 3Kw to a cast steel 56 Tooth spur gear. The gears have the
following specifications: module 3 , s0 =160MN/ m2, face width 35mm 14.5o tooth profile design the gear.
5. A cast steel pinion (s0=103MN/ m2) rotating at 900 RPM is to drive a cast iron gear (s0=55MN/ m2) at 144RPM.
The teeth are to have standard 20o stub involute profiles and maximum power to be transmitted is 25Kw. determine the
proper module, no. of teeth and face width for these gear for stand point of strength , dynamic load and wear. Pinion is surface hardened to BHN 250.
6. A 80mm diameter steel pinion (s0=140MN/ m2) drives a gray iron 240 mm diameter gear (s0=100MN/ m2). The pinion
operates at 1200 RPM and transmits 5Kw. The teeth are 20o stub. Determine the greatest no. of teeth and necessary face width
7. A Bronze spur gear (s0=83MN/ m2) is to drive a mild steel pinion (s0=103MN/ m2). The angular velocity
ratio is to be 3.5 to 1 . The pressure angle is to be 14.5o. Determine the smallest diameters gears that can be used
and the necessary face width to transmit 5Kw at 1800RPM of the pinion no less than 15 teeth are to be used on either gear. Design the gear.
8. A compressor running at 300RPM is driven by a 15Kw 1200RPM. Motor through a 20-degree full depth involute gear. The center distance
is 375. Choosing the suitable material for pinion and gear, Design the drive completely. Assume medium shock condition.
9. The counter shaft of lathe runs at 250RPM. The back gear (reverted train) of the lathe required to reduce the speed to 25RPM
approximately. Keeping the center distance between the axis of the lathe axis of the gear shaft 150mm, Determine module and no. of teeth of
gear wheels of the train. A set of gears having teeth from 20 to 120 rising by 4 available for the purpose.
10. A 45 Kw motor running at 100RPM is required to drive rotatary mill at 120RPM through a pair of spur gears. The distance between
axis of the motor and mill shaft is to be about 1m. Design the spur gear to go with the mill shaft. Assume a shaft diameter of 1000mm for
the mill. Gear material may be assumed to be cast steel.
11. A reciprocating compressor is to be driven by electric motor running at 900RPM. The compressor speed is 300RPM and it requires a
steady torque of 200N-m. Assuming a starting torque 25% greater than mean torque, design a suitable pair of spur gear for the drives. Assume
the motor shaft and compressor diameters as 30mm and 37mm respectively.
12. Design a pair of helical gear to transmit 40 Kw from a shaft running at 1500RPM .to another shaft with a speed reduction of 6.
Select the suitable materials for pinion and gear. Assume medium shock condition.
13. A 10 Kw, 750RPM induction motor is to drive a pump at 150 RPM through a pair of helical gear. The starting torque of the motor is
taken as 2.5times rated torque. Design the gear pair completely and check for dynamic and wear loads
14. A pair of straight spur gears are required to reduce speed from 500 to 100 RPM for 12 hours running time per day continuously.
The pinion is made of 40C8 steel normalized and has 20 teeth. The wheel is of cast iron of grade FG200 and has 100teeth. The gear is of
8mm module; 100mm face width and 20-degree pressure angle. Calculate the power rating.
15. A compressor running at 360RPM is driven by a 150 Kw, 1440-RPM motor through a pair of 20o full depth helical gears having
helix angle of 25 degree. The center distance is approximately 400mm. the motor pinion is to be forged steel and the driven gear is to be
cast steel. Assume medium shock conditions. Design the gear pair.
16. Two helical gears having 14.5-degree normal pressure angle and a helix angle of 23o connect two parallel shaft. The pinion
has 48 teeth, the gear has 240 teeth and the module is 3. The pinion has an BHN 250 and the gear has the BHN 200. The face width is 250mm.
Determine the wear load
17. Two parallel shafts are connected by a pair of steel helical gear. The pinion transmits 10Kw at 400RPM of the pinion. Both gear
made of same material, hardened steel with allowable stress (s0=100MN/ m2). If the velocity ratio is 4.5:1, determine the smallest
diameter gears that may be used having sufficient strength. No less than 30 teeth are to be used for either gear, the teeth are of 20 degree
stub in diametral plane and the helix angle is 45o.
18. For a helical gear drive an expression for the virtual no of teeth Nf in terms of helix angle φ and
actual no. of teeth N.
19. A pair of helical gears are used to transmit 15Kw. The teeth are 20o stub in diametral plane and have a helix angle of 45
degree. The pinion has an 80mm pitch diameter and operates at 10000RPM. The gear has a 320mm pitch diameter. If the gears are made of cast
steel (s0=100MN/ m2) , determine a suitable module and face width . The pinion is heat treated to BHN of 3000 and the
gear has a BHN of 200.
20. A pair of helical gears with a 23o helix angle is to transmit 2.5 Kw at 10000RPM of the pinion. The velocity ratio of 4:1.
Both the gear are made of hardened steel with an allowable stress (s0=100MN/ m2) fro each gear. The gears are 20o
stub and the pinion is to have 24 teeth. Determine the minimum diameter gear that may be used, and the required BHN.
Mini Project Problems
Spur gear problems
In the following problems, assume that :
- gears with any tooth number up to 120 are procurable ( constraints are more severe in practice)
- all gears are of steel, to the 20 degree full depth system unless otherwise indicated
- mid-range profile shifts apply, where relevant.
The program Steel Spur Gears should be used to assist solution of asterisked problems, and may be used to check longhand solution of other
fatigue problems.
1. Tooth numbers of certain gears in the epicyclic train are indicated; all gears are of the same module. Gear A rotates at 1000
rev/min clockwise while E rotates anticlockwise at 500 rev/min. Determine the speed and direction of rotation of the ring-gear D and of the
arm shaft F. If the power output through each of D and F is 1 kW, what are the power transfers through A and E?
[ 371 rev/min anticlockwise; 40 rev/min clockwise; 8.77 kW input; 6.77 kW output.
2. The arm of the epicyclic train is driven clockwise at 1450 rev/min by a 5 kW motor. What torque is necessary to lock the 33
teeth gear? What is the speed of the 31 tooth gear? Note the reduction[ 16.3 kNm clockwise, 2.92 rev/min clockwise ]
3. The sun wheels A and D are integral with the input shaft of the compound epicyclic gear illustrated, and the annular wheel C is
fixed. The planet wheel B rotates freely on an axle carried by the annular wheel F, and the planet E on an axle mounted on the output shaft's
arm. Given the tooth numbers indicated, find the speed of the output shaft when the input shaft rotates at 1000 rev/min.
Ans=524rev/min
4. In the epicyclic train illustrated, the gear C is fixed and the compound planet BD revolves freely on a spindle which is coaxial
with the input and output shafts.
(a) Show that if zb ze > zc zd then input and output shafts rotate in the same direction.
(b) 7.5 kW is fed into the input shaft at 500 rev/min, losses are negligible, and tooth numbers are sketched. Determine the torque on the output shaft.
Ans=15.5kNm
5. Select spur gears suitable for speed ratios of (i) 1/√2, and (ii) π , to four significant figures.
6. Determine the practical limits of profile shift on a 6 mm module gear with 19 teeth. If a profile shift of 0.4 is implemented, what are the dedendum, base, pitch, extended pitch and addendum circle diameters of the gear ?
Evaluate the base pitch and the angle γ of Fig A.
[ 103.8, 107.1, 114, 118.8 and 130.8 mm. 17.7 mm, 6.47o]
7. What is the practical range of centre distance for a pair of 4 mm module spur gears with 19 and 35 teeth ? If they are manufactured with profile shifts of 1.5 mm and 2 mm respectively, evaluate the extended pressure angle and the contact ratio.
[ 108.6 ≤ C ≤ 112.8 mm, 24.47o, 1.42 ]
8. Use the design procedure outlined in the Notes to determine gears suitable for a speed ratio of √ 2 ± 0.5 % and a centre
distance of 200 ± 1 mm.
[ 6 mm module, with 27 and 38 teeth, and profile shifts of 0.45 say, for pinion and correspondingly 0.38 for wheel ]
9. Evaluate the contact ratio and the fatigue geometric factors I and J for each of the following :
(a) the pairs 13:35, 23:62 and 36:97 (which approximate the ratio 0.3711 to within 0.1%);
(b)* 23:62 teeth, assuming the minimum practical profile shifts for both gears;
(c)* repeat (b) but use the maximum practical profile shifts.
Comment upon the trends suggested by these results.
10. The transmission accuracy level number of a pair of open gears is 6. Further particulars of the 25 mm module 300 mm facewidth gears are as follows :
| | number of teeth | allowable stresses, MPa | speed,
| | contact | bending | rev/min
| | pinion | 25 | 1100 | 290 | 150
| | wheel | 55 | 1000 | 280 | -
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11. What life may be expected of the gears whilst transmitting 1 MW uniformly? [ 39 khr ]
Shock loading of the foregoing drive results from unsuspected torsional vibration. If the effective application factor is in fact 1.25, what life may now be expected? [ 5.4 khr ]
12. Two mating gears of commercial quality are to hand with 18 and 56 teeth. Their common facewidth is measured as 50 mm and their addendum diameters as 83.2 and 233.6 mm. Metallurgical analysis reveals that the expected contact and bending stresses of the gears' common material are 1100 and 300 MPa respectively. Estimate the pair's capacity (kW) for a 10 khr life in a shock-free application in which the pinion speed is 300 rev/min. The transmission accuracy level number is 6. [ 9.1 kW ]
13. A gear pair transmits 75 kW with an application factor of 1.5 and reliability of 99%. Particulars of the commercial 6-accuracy level gears are :
| number of teeth | allowable stresses, MPa | speed,
| | | contact | bending | rev/min
| | pinion | 20 | 1300 | 180 | 90
| | wheel | 37 | 1250 | 175 | -
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14. Select a suitable module and facewidth for a life of 15 khr. [ 16, 144 mm ]
15. Details of a pair of commercial gears having a transmission accuracy level of 8 are as follows :
| number of teeth | allowable stresses, MPa | speed,
| | | contact | bending | rev/min
| | pinion | 10 | 1320 | 380 | 200
| | wheel | 36 | 1100 | 360 | -
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16. Select a suitable module and facewidth for a design life of 16 khr whilst transmitting a uniform 125 kW with a reliability of 99%. [ 16, 187 mm ]
17. A commercial gear pair having a transmission accuracy level of 8 is required to transmit 100 kW in a shockfree application with 99% reliability. The speeds of pinion and wheel are 1450 and approximately 470 rev/min. Allowable stresses for contact and for bending of the pinion are 1450 and 400 MPa respectively; for the wheel 1300 and 350 MPa.
Select suitable tooth numbers and profile shifts, along with a corresponding module and facewidth for a compact pair with a design life of 20 khr.
18. Estimate the life of a gear whose allowable contact stress is 1.2 GPa and which undergoes the stress spectrum:
| contact stress | σc | (GPa) | 1.0 | 1.1 | 0.9
| | speed | N | (rev/min) | 500 | 400 | 300
| | duration | t | (hours) | 2 | 1 | 3
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19. A pair of 8 mm module, 100 mm facewidth commercial gears is manufactured to a transmission accuracy level of 7 and employed in a
periodic duty of 1.25 application factor. The 23 tooth pinion's allowable contact stress is 1.2 GPa at 99% reliability, the 47 tooth wheel's
is 1.1 GPa.
If power is transmitted to the following cycle, what life may be expected of the pair?
| power | P | (kW) | 60 | 45 | 35
| | pinion speed | N1 | (rev/min) | 200 | 150 | 100
| | duration | t | (min) | 10 | 20 | 30
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Unit-2 Worm gears, Bevel gears
Objective: Student should have knowledge about the design of worm, Bevel and Hypoid gear and also have an idea about their different
engineering applications.
Objective type Questions
1. When bevel gears having equal teeth and equal pitch angle connect tow shafts whose axes intersect at right angle, then they are known as:
(a) angular bevel gears (b) crown bevel gears (c) internal bevel gears (d) mitre gears
2. The worm gears are widely used for transmitting power at ………velocity ratios between non-intersecting shafts.
(a) high (b) low
3. In worm gears, the angle between the tangent to the thread helix on the pitch cylinder and the Plane normal to the axis of worm is called:
(a) pressure angle (b) lead angle (c) helix angle
4. The number of starts on the worm for a velocity ratio of 40 should be
(a) single (b) double (c) triple (d) quadruple
Numerical Questions
1. Define the virtual no. of teeth for a bevel gear.
2. What are the advantages of spiral bevel gears over straight bevel gears?
3. Differentiate between the mitre and crown bevel gear.
4. A cast iron bevel gear has a pitch diameter of 600mm and a pitch angle of 30degree. The module is 2.5. Determine the permissible
endurance load. The teeth are 20-degree full depth.
5. Two cast iron bevel gears having pitch diameters of 80 mm and 100mm respectively and to transmit 11/4 Kw at 1100RPM of the pinion.
The tooth profile are of 20 degree full depth. Take (s0=55MN/ m2)
(a) determine the face width and the required module from
stand point of strength
(b) Check the design from stand point of dynamic load and wear C=110 kN/m
6. A cast steel (s0=100MN/ m2) bevel gear pinion has pitch diameter of 225mm and pitch angle of 30 degree. The module
is 4. The gear rotates at 600RPM. From the standpoint of strength only how much power should this gear be capable of transmitting?
7. Two steel bevel gears connects shaft at right angle. The pinion has a BHN of 300 and the gear has hardness 200. The teeth are 14.5
full depth and the module is 3. The number of teeth on pinion has 64. The face width is 40mm. determine the wear load.
8. A 100 kW, 750-RPM motor is required to drive a centrifugal pump continuously at 250 RPM by means of straight bevel gears connected
at 90m-degree shaft angle. The starting torque is 20% greater that rated torque (a) Design the gears. (b) Could the same pinion is use to
drive the another pump at 150RPM? Give brief explanation.
9. A pair of 4 pitch 20 degree involutes machine cut bevel gear have a2:1 reduction . The pitch diameter of the driver is 250mm
and runs at 200RPM. Selecting the suitable material for the pinion and the gear determine the various parameter of gear set.
10. A pair of bevel gear are mounted on shafts that are at 90 degree apart. The set is to transmit 90 Kw at 300RPM. The pinion has
150mm outside pitch diameter; 50 mm face width, a diametral pitch of 6, and 20 degree full depth. For a velocity ratio 0.4. Determine the forces acting on gear tooth.
11. Find the power transmitted by a pair of 20o bevel gears with Tp = 40 and Tg = 60 teeth.
Gears are made of steel and are hardened to 350BHN. Module is 6.5mm. width of face is 60mm but thickness of the blanks is 35mm. Pinion rotates
at 600rpm. The shaft angle is 90o. Safe static stress for gears = 105Mpa. Assume Kv =6 / (6 +v); C for dynamic
load calculation = 250 kN/m.
12. Design a pair of bevel gears to transmit 12kW at 600rpm. Gear ratio is 2: 1 and pinion has 24 teeth of 20o involute
full depth. The material for both the wheels is the same with safe static stress of 105Mpa. b = l/3. Find module, face width, cone distance
and pitch circle diameters of both the wheels.
Assume Kv =3.5/(3.5+ √V), Where V is peripheral velocity in m/sec. Shaft angle is 90o. Check the design for wear strength
and dynamic tooth load. Given that Ses = 600Mpa, Ep=Eg= 2x105 Mpa, c = dynamic load tooth factor = 300kN/m,
Y= Lawis form factor = 0.154 – (0.912/Tf).
13. For the above example determine the diameter of the shaft carrying gear if the mean plane of the gear is 150mm away from the bearing.
14. A pair of straight bevel gear is used to transmit 18.5kW at 600rpm. The gear ratio is 2 and shaft angle is 90o. Pinion has
28 teeth of 20o involute profile. The safe static stress for the pinion as well as gear material may be taken as 105Mpa. The module
is 6mm. Determine the necessary face width b of the gears to carry the given safety.
15. A spindle of a drilling machine is to be driven by means of a pair of 20o straight bevel gears. The pinion is to be mounted
on horizontal drive shaft. The reduction ratio is 3.5:1. The drilling operation requires 195Nm at 350rpm design the gear pair, if the safe static
stress for the gears is limited to 145Mpa.
16. A double threaded worm has a pitch circle diameter of 84mm with a axial pitch of 20 mm determine the helix angle
17. A hardened steel worm transmits power to a phosphor bronze with a velocity ratio 20 the centre ceutic distance is 400 mm determine,
a)Axial module
b) Lead Angle (helix angle) c)Power rating based on heat dissipation criterion d)Power rating based on wear if worm
rotates at750 rpm
18. For a worm and worm wheel the a centre distance is given as 225mm worm is made of hardened steel and rotates at 1250 rpm worm
transmits power to a phosphor bronze gear (σb=35 Mpa with a transmission ratio of 15 the tooth on gear are
20 degree full depth involute(y=0.125) determine all the design parameters and recommitted safe power that the drive can transmit.
19. Or the above example , determine the diameter of the shaft of worm as well as the worm gear for the arrangement of the bearing
assume coefficient of friction M=0.1
20. Design a pair of bevel gears for two shafts whose axes are at right angles. Speed of pinion shaft is 300 rpm and that of Gear
shaft is 120 rpm. The power transmitted is 80 kW.
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Unit-3 Antifriction bearing
Objective: Student should have knowledge about different type of bearings its engineering applications and methods of designing of Ball
and roller bearings from design charts
Theory and Numerical Problems
1. What is a bearing?
2. How will you classify the bearings?
3. On what factors does the selection of a bearing for a particular application depend?
4. Describe the various stages of friction in the case of plain bearings.
5. Differentiate between ‘Hydrodynamic’, ‘Wedge film lubrication’ and ‘Squeeze film lubrication’.
6. Distinguish between ‘Hydrodynamic bearings’ and ‘Hydrostatic bearings’.
7. What are the factors to be considered while selecting the material for plain bearing?
8. Name various bearing metals.
9. What is the function of lubrication in bearings?
10. Give the advantages and disadvantages of oils and greases.
11. Describe the various lubrication devices.
12. What s the importance of oils grooves in bearings?
13. Define ‘Bearing modulus’.
14. Define ‘Sommerfeld number’.
15. What is meant by ‘Self contained bearings’?
16. Give the applications and limitations of sliding bearings.
17. Enumerate the advantages and disadvantages of rolling contact bearings.
18. How will you classify the rolling contact bearings?
19. What are four main parts of a ball bearing?
20. Compare ball and roller bearings.
21 How are the rolling contact bearings manufactured?
22 What bearings are called ‘Needle bearings’? Give their applications.
23 What is the primary characteristic difference between a deep groove ball bearing and angular contact bearing?
24 here do we prefer to use taper roller bearing?
25 What is antifriction bearings. Discuss the materials that are used for manufacturing of bearings.
26 Explain rating life and basic load rating.
27 Where do we use thrust bearing? Explain the basis for bearing failure.
28 What is approximate friction power loss in a single radial ball bearing having a bore diameter of 55mm and subjected to a radial
load of 225KN? The shaft rotates at 600RPM.
29 Determine the approximate friction torque expected in single deep groove ball bearing under a radial load of 30KN. The bore of the
bearing is 50mm.
30 A bearing has a specific dynamic radial capacity of 24.5KN. What radial load the bearing can carry at 1200RPM if the desired life
is 2000hours (for 90% group of bearing).
31 A radial load of 5Kn acts for 5 revolutions and reduces to 4.5Kn for 10 revolutions . The load variations then repeat itself. What
is the mean cubic load?
32 Determine the 6200 series bearing which will be suitable for a radial load of 1.8Kn with the operation at 1200RPM for 2000hours.
Loading is steady. Basic load capacity of various series can be see from DDB.
33 A 300 mm bore (dimension series 02) single row angular contact ball bearing has a 30 degree contact angle. If the bearing carries a 3.5 KN radial load and a 6 KN thrust load and the inner ring rotates at 1500 RPM, Determine the rating life in hours.
34 Mention the relative advantages of rolling bearings and sliding bearing. What do you understand by static capacity and dynamic capacity of ball bearing? Explain how you will determine the equivalent load on a bearing when simultaneously acting radial and thrust load are known.
35 A certain bearing is to carry a radial load of 5 at KN a speed of 10RPM of 20% of the time, a load of 30 KN at a speed of 60RPM for 50% of time and a load of 30 KN at 100RPM during 30% of the time with a desired life of 5,000 hours. No thrust load acts on bearing. What will be dynamic capacity of the bearing?
36 A shaft is subjected to the varying load cycle as follows; 3KN for 1 Sec, 1 KN for 1s and 0.5KN for 3s. If the shaft rotates at the constant speed of 500RPM, What basic load rating for each fraction of cycle should be used in selecting the ball bearing with a life of 15000 hours?
37 A 6203 single row deep groove ball bearing has a basic load rating of 4500 n and a basic dynamic capacity 7350N. What is the life expectancy (that 90% bearing reach or exceed) for a radial load of 1350N and a thrust load of 1260N? The outer ring is stationary.
38 Select bearing for a60m diameter shaft that rotates uniformly at 1800RPM. Due to bevel gear mounted on the shaft, the bearing will have to withstand a 5KN radial load and a 2KN thrust load. With any restriction of the type of a bearing select one that is satisfying for a rating life of 20,000 hours.
39 A single row deep groove ball bearing has a specific dynamic capacity of 46.3Kn(for 1000000 revolutions or 500hours at 33.3RPM , That90% of group of bearing will complete or exceed) if the speed of rotation is 1800RPM and the actual radial load applied to the bearing is 9 KN what is the life in revolutions
40 In the above problem how many hours of operation can be expected for the above?
41 What is the average life that can be expected in prob. 7
42 An SKF self aligning ball bearing no.1310 has a specific capacity 33.5KN (that is the rating of 33.5Kn such that 90% of group of bearing will last 500hours at 33.3RPM). If the equivalent radial load actually applied to the bearing is P=44.5KN determine the life in millions of revolutions expected (such that 90% of a group of bearing of same nos. will survive) the speed of rotation being 1800RPM. & the life in hours for 90% of the bearings.
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Unit-4 Lubrication and sliding bearing
Objective: This chapter able the students to understand requirements of lubrication, method of lubrication in journal bearing and design of journal bearing.
Theory and Numerical Problems
1. Define a journal and the bearing.
2. What is the hydrostatic bearing?
3. What are the various type of lubricants used in bearings?
4. What is a hydrodynamic bearing? Define viscosity and viscosity index.
5. Define a short bearing and long bearing.
6. Define sommerfeld number. What is the bearing modulus?
7. What is the condition for full film lubrication How should be the minimum oil film thickness.
8. Name few of the bearing materials. What is the effect of small increase in bearing clearance on film temperature?
9. A 75mm long full journal bearing of diameter 75mm support a load of 12 KN on a journal rotating at 1800RPM. Assume D/C ratio of 1000, and a oil having viscosity 0.01kg/ms at the operating temperature Determine the coefficient of friction. Take L?D ratio 1.
10. In the above problem determine the amount of heat generated
11. A journal bearing 75MM long supports a load of 7.3KN on a 50mm diameter journal turning at 750RPM. The dimeteral clearance is 0.07mm. What should be the viscosity of oil if the operating temperature of the bearing surface is to be limited to 75degree centigrade when in still air at 20 oC.
12. A 100 diameter shaft operating at 2000RPM is supported by means of a 150mm long full journal bearing which is subjected to a radial load of 43KN . Operating temperature of the oil is limited to 80oC and the surrounding air temp. Is 38oC. Assume P=30*10-6 determine the coefficient of friction, bearing pressure, heat generated, heat dissipated, oil use. Is artificial cooling is required.
13. A 50mm medium weight full journal bearing has a length of 100mm and support a load of 2.5KNwhen the shaft rotates at 800RPM. Assuming a temperature difference of 40oC between the operating temps. Of the bearing surface and the surrounding still air , which coefficient of friction .00432,.00615,.00715,.00816 or.00256 will be required in order to eliminate the need for artificial cooling?
14. Explain the mechanism of film lubrication.
15. A full journal bearing has the following specifications
Journal diameter = 75mm
Bearing length = 55mm
Radial clearance = .055mm
Journal speed = 22,000RPM
Radial load = 1 KN
The power loss in the bearing was found to be 3KW find (a) viscosity of the lubricant at effective film temp. (b) The coefficient of friction at the given operating temp.
16. An electric motor whose speed is 1750RPM has bearing 100mm long and 75mm diameter. The oil used has an absolute viscosity of 15 cp
under running conditions. The clearance is .0015mmpermm and the load is 0.7MN/m2 . If φ = 90 degree,
Determine total power loss in the bearing and the minimum oil film thickness.
17. Design a bearing and journal to support a load of 4KN at 600RPM using a hardened steel journal and a bronze backed Babbitt bearing.
The oil viscosity is 250s Saybolt at 37.7oC and specific gravity is 0.90 at 15.6oC . The bearing is relived for 20 degree
from normal to the load line. Abundance supply of oil is maintained.
18. Determine the necessary length of bearing, running clearance, side relives, and loss of power due to friction for a journal
which has 60mm diameter and rotates at 175RPM. The total load on bearing due to belt pull and the weight of the pulley is 6KN and the load
is steady. Use a lubricating oil which has a Saybolt viscosity of 270s at 37.7oC and for which gamma =0.905 at 15.5oC.
19. Design a bearing and journal to support a load of 4900KN at 600RPM using a hardened steel journal and bronze backed Babbitt bearing.
An abundance of oil is supplied by means of oiling rings. The oil viscosity is 250s Saybolt at 37.8oC and the specific gravity is
0.90 at 15.6oC . The bearing is relived for 20 degree from normal to the load line.
20. A pressure fed bearing with an annular central groove has a length of 45mm and diameter of 45mm. The bearing supports a load
of 4400N at the journal speed of 1000RPM. The radial clearance is 0.025mm and the oil’s SAE30. Determine the equilibrium temperature and
minimum oil film thickness. Assume attitude angle 70o.
Master problems
1. In a journal bearing of 100 mm diameter with a bearing clearance of 0.2 mm, it is found suitable to use lubricating oil with
viscosity 60 cP. The shaft runs at 375 r.p.m. and develops a bearing pressure of 1.5 N/mm2. Determine (a) bearing pressure
when the shaft speed is increased to 500 rpm, other parameters remaining same. (b) Viscosity at 0.15 mm bearing clearance, 450 rpm of
shaft and 2.0 N/mm2 bearing pressure.
2. Following data refers to a 360o(full) hydrodynamic bearing;
Journal diameter d = 75 mm, bearing length l = 75mm, radial clearance C = 0.05 mm, minimum film thickness ho= 0.02 mm, Journal
speed N =420 rpm, radial load W = 3500 N, Cp for oil = 1.75 kJ/ KgoC, ρ of oil = 0.9 gm/cc.
Calculate
(a) Required viscosity of oil, Z
(b) The coefficient of friction μ ,
(c) The heat generated, Hg
(d) The amount of oil pumped through the bearing.
3. A 360o hydrodynamic bearing is subjected to a radial load of 10kN. The journal
speed is 1500 rpm.The diameter of journal and length of bearing are 60 mm each. The class of fit between journal and bearing is H7e7 (fine), normal running fit with the limits as 60+0.00, +0.03 mm and 60-0.06, -0.09. The minimum oil film thickness is 0.009 mm. Specify the viscosity of lubricating oil required for this application.
4. A 100 mm diameter shaft operating at 2000 rpm is supported in a 150 mm long
Full journal bearing subjected to a radial load of 43 kN. Operating temperature of oil is limited to 80oC and surrounding temperature is 38oC, assume ZN/P = 30 x 10-6. Using Mckee and Lasche equation, determine coefficients of friction, bearing pressure, Hg and Hd and viscosity Z of the lubricant.
5. Following data are given for a 360 degree hydrodynamic bearing with usual notations:
D = 50 mm, l =50 mm, C = 0.06 mm, ho = 0.012 mm, N = 1440 rpm, Z = 20 x 10-9 Nsec/mm2,
ρ of oil = 900 Kg/m3, Cp of oil = 1.75 KJ/ Kg degreeC . Calculate the maximum radial load that the journal can carry and
still operate under hydrodynamic conditions. For this load, calculate power lost in friction and resultant temperature rise.
6. A 50 mm diameter and 75mm long journal bearing is loaded with a bearing pressure 2 Mpa. The journal speed is 500rpm. The heat
lost from the bearing surface at the rate of 1.16 x 10-5 (J/s) / ( mm2oC). The housing area is 8 times
projected area. If the room temperature is 28oC, Determine the surface temperature of bearing. Co-efficient of friction is 0.0015.
Assume Hg = Hd
7. A 90mm shaft rotating at 1200 rpm is supported by 110 mm long bearing. The journal carries 50kN load. Given that
To = 70oC , Ta = 250C and ZN/P = 20 x 10-6
Specify the viscosity of the lubricating oil to be used and calculate heat generated. State weather external cooling is required for the bearing.
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Unit-5 Engine parts
Objective: It gives the basic knowledge about the design of different engine parts like connecting rod crank shaft, Piston etc
1. What are the main function of the piston of an internal combustion engine.
2. Why the rings provided in the piston .What are the various type of liners ?
3. What are the various type of crankshafts.
4. Why the area of inlet valve port is made larger than the area of the exhaust port?
5. A horizontal four stroke diesel engine has the following specifications
Brake power = 5KW
Speed = 1200RPM
I.M.E.P. = 0.35N/mm2
Mechanical efficiency = 80%
Calculate the dimension of the cylinder and the cylinder head.
6. Design the piston. Piston rings and gudgeon pin for single acting four stroke engine for the following given data.
Cylinder bore = 100mm
Stroke = 125mm
Maximum gas pressure = 5MPa
B.M.E.P. = 0.6MPa
Fuel consumption = 0.15kg/BrakekW/h
Speed = 2000RPM
7. Design and draw a piston for a single acting four stroke engines from following data using design data book.
Cylinder bore : 75 mm
Stroke: 125mm speed : 2000RPM
Maximum gas pressure : 5N/mm2
Indicated mean effective pressure: 0.75N/mm2
Mechanical efficiency : 80%
Fuel consumption : 0.15 kg per brake power
Higher calorific value of fuel : 42 *103 KJ/ Kg
Any other data required for the design may be assumed.
8. Design and draw a connecting rod of a petrol engine from following data using design data book. Also generate the program in c language.
Dia of Piston : 110 mm
Mass of reciprocating parts : 2 Kg
Length of connecting rod : 325 mm
Stroke : 150mm
Speed : 1500RPM
Maximum explosion pressure : 2.5 Mpa.
Any other data required for design may be assumed.
9. A connecting rod is to be designed for a four stroke petrol engine having the following specifications:
Piston diameter = 150mm
Stroke length = 150mm
Length of connecting rod = 320mm
Mass of reciprocating parts = 2 Kg
Speed = 1500RPM
Compression ratio = 4:1
10. Design a center crank shaft for a single acting four stroke single cylinder engine for the following data:
Piston diameter = 400mm
Stroke = 600mm
Speed = 200RPM
I.M.E.P. = 0.5MPa
Maximum combustion pressure = 2.5MPa
Gas pressure at maximum torque = 1MPa at 35 degree crank angle
Ratio of length of CR to Crank radius = 5
Total belt pull = 6.5KN
Assume any other missing data
11. Design a crankshaft for a 400mm* 600mm single acting four stroke single acting four stroke single cylinder engine to operate at 200RPM. The mean effective pressure is 0.5 MPa and the maximum combustion pressure is 2.75MPa. The maximum torque is at 35degree of crank angle when gas pressure is 1MPa. The ratio of length of connecting rod to the radius of crank is 4.8. The flywheel is used as a pulley whose weight is 55KN. The total belt pull is 6750N.
12. Design and draw the exhaust valve gear for a horizontal diesel engine for following Data using Design Data book.
Brake power : 8 Kw
Bore : 140 mm
Stroke : 270mm
Speed : 475 RPM
Maximum gas pressure : 3.5 Mpa
Back pressure : 0.4 Mpa
Suction pressure : 0.025 Mpa
Mean velocity of gas through the port : 2100 RPM
The valves open 33 degree before outer dead center and closer 1 degree after inner dead center. It opens and closes with constant acceleration and deceleration for each half of the lift. The length of the rocker arm on either side of the fulcrum is 150mm and the included angle is 60 degree the weight of the valve is 3N..
13. Design the various components of a valve gear mechanism for a horizontal diesel engine having the following specifications:
Brake power = 10KW
Bore = 140mm
Stroke = 270mm
Speed = 500RPM
Maximum gas pressure = 3.5Mpa
The valves open 33 degree before top dead center and closer 20 degree after bottom dead center. It opens and closes with constant acceleration and deceleration for each half of the lift. The length of the rocker arm on either side of the fulcrum is 150mm and the included angle is 135 degree . The mass of the valve is 300g.
14. Design a plain carbon steel centre crankshaft for a single acting four stroke single cylinder engine for the following data:
Ore = 400 mm; Stroke = 600 mm; Engine speed = 200rpm; Mean effective pressure = 0.5 N/mm2; Maximum combustion pressure = 2.5 N/ mm2; Weight of flywheel used ad a pulley = 50 kN; Total belt pull = 6.5 kN.
When the crank has turned through 35 degree from the top dead centre, the pressure on the piston is 1N/mm2 and the torque on the crank is maximum. The ratio of the connecting rod length to the crank radius is 5. Assume any other data required for the design.
15. The conical valve of an I.C. engine is 60mm in diameter and is subjected to a maximum gas pressure of 4N/mm2. The safe stress in bending for the valve material is 46Mpa. The valve is made of steel for which k= 0.42. The angle at which the valve disc seat is tapered is 30 degree
16. Design a rocker arm, and its bearings, tappet, roller and valve spring for the exhaust valve of a four stroke I.C. engine from the following data:
Diameter of the valve head = 80mm; Lift of the valve =25 mm; Mass of associated parts with the exhaust valve opens is 0.4 N/mm2 and the greatest suction pressure is 0.02 N/mm2 below atmosphere.
The rocker arm is to be I-section and the effective length of each arm may be taken as 180mm; the angle between the two arms being 135 degree.
The motion of the valve may be assumed S.H.M., without dwell in fully opened position. Choose your own materials and suitable values for the stresses.
Draw fully dimensioned sketches of the valve gear.
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