1. SPUR GEAR

2. SPUR GEAR
Introduction- Gear can be defined as the mechanical element used for transmitting power and rotary motion from one shaft to another by means of progressive engagement of projections called teeth.
Smaller of the pair is called PINION and the larger of the pair is called the GEAR.

3. ADVANTAGES OF GEAR DRIVES
1- Compact as compared to belt and chain drives.
2- Positive drives.
3- wide range of speed ratios.(6:1 to 4900:1)
4- High speed ratio than belt drives
5- Used for shafts parallel, intersecting, non-parallel, non-intersecting.
6- Large power transmission
7- Transmits power at higher speed.

4. LIMITATIONS OF GEAR DRIVES
1- Costly.
2- Can’t be used over a long distance.
3- Requires precise alignment of shafts.
4- Requires continuous lubrication.

5. CLASSIFICATION OF GEARS.
1- Parallel axis Gears Spur Gears.
Helical Gears.
Herringbone Gears.
Rack and pinion.
Internal gears.
2- intersecting axis Gears- Bevel Gears.
3- Non intersecting and Worm Gears
perpendicular axis Gears
4- Non intersecting and Crossed
Non parallel axis Gears- Helical Gears

6. Parallel axis Gears SPUR GEAR

7. SPUR GEAR

8. Parallel axis Gears Helical gear

9. Parallel axis Gears Rack and pinion

10. Intersecting axis Gears- Bevel gear

11. Non-intersecting and perpendicular axis Gears-worm

12. WORM GEAR BOX

13. Non-intersecting, Non-parallel-CROSSED HELICAL GEAR

14. SELECTION OF TYPE OF GEARS

15. 1- Relative position of Input and output shafts.
2- Speed Ratio.
3- Efficiency.
4- Input speed.
5- Power to be transmitted.
6- Cost.

16. SPEED RATIO Sr. no Gear Drive Red. Ratio 1
Single stage spur/ Helical Gear
6:1 2
Two stage spur or Helical gear
35:1 3
Three stage spur or Helical gear
200:1 4
Bevel gear drive 5
Single stage worm gear
70:1 6
Two stage worm gear
4900:1

17. worm gear and worm wheel
EFFICIENCY
Sr. No.
Gear Drive
Efficiency 1
spur or Helical gear
96-99% 2
Bevel gear drive
95-98% 3
worm gear and worm wheel
45-97%

19. TERMINOLOGY IN SPUR GEAR

20. The common normal at the point of contact between a pair of teeth must always pass through the pitch point it is known as Law of gearing
Law of Gearing

21. COMMON TERMINOLOGY
Pitch circle- It is an imaginary circle on gear which by pure rolling action would produce the same motion as the actual gear.
Pressure Angle- ( Ø) Angle between the common normal to the two meshing teeth at the point of contact and common tangent to the two pitch circles at the pitch point
Pitch Circle Dia.(d)- or PCD- It is the dia. of pitch circle.
Circular pitch- It is the dist. measured along the circumference of the pitch circle, from the point of one tooth to the corr. Point on the next tooth.
z= No. of teeth.

22. COMMON TERMINOLOGY Module (m)- Ratio of PCD to the no. of teeth,
First choice- 1.0,1.25,1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40 and 50.
Second choice ,1.375,1.75,2.25,2.75,3.5, 4.5, 5.5, 7, 9, 11, 14, 18, 22, 28.
Dimetral pitch (Pd)- Ratio of no. of teeth to PCD.
Speed Ratio(Gear Ratio)-G- Ratio of pinion speed to Gear speed

23. Centre Distance (a) :
It is the distance between the axes of the two mating gears. It is given by
Substituting in above equation
Hunting Tooth:
In gear pair if gear ratio is an integer number like 1, 3/2, 4/3, same tooth on gear will come in contact with same tooth on pinion which increases the wear on teeth & reduce the life of teeth.
In such case extra tooth on the gear is added to spread the wear evenly. This extra tooth is called Hunting tooth.

24. INTERFERENCE
The Phenomena when the tip of the tooth undercut the root on its mating gear is known as interference

25. MINIMUM NO. OF TEETH TO AVOID INTERFERENCE
The contact portions of the tooth profile which are not conjugate is called interference.
Interference is the meshing of two non-conjugate profiles.
Where ha= Addendum of meshing rack.
m = module in mm.
Ø= Pressure angle.

26. STANDARD SYSTEMS OF GEAR TOOTH
A tooth system is a standard which specifies the pressure angle and the relations for addendum, dedendum, working depth, tooth thickness and a fillet radius in terms of module.
Objective- To attain interchangeability of gears of all tooth number but of the same pressure angle and module.
1) 14.5° composite system.
2) 14.5° full depth involute.
3) 20° full depth involute.
4) 22.5° full depth involute.
5) 20° stub tooth involute.

27. GEAR MATERIAL Desirable properties of gear material-
Sufficient endurance strength in bending.
Sufficient surface endurance strength.
Low coefficient of friction.
Low and consistent thermal distortion.

28. TYPES OF GEAR MATERIALS
1) Cast Iron.- Large size and complicated shapes
Advantages of cast irons-
Cheap
Good damping property
Good surface endurance strength but low bending endurance strength.
Graphite presents in C.I. works as lubricant.
Easily cast in complicated shapes
Good machinability
Disadvantages of C.I.-
Brittle, low bending strength.

29. TYPES OF GEAR MATERIALS
2) Steel-
High bending endurance strength.
High surface endurance strength.
Ductile
Expensive
Poor damping property.
Sensitive to thermal distortion during heat treatment.
Steel pinion and C.I. gear.

30. TYPES OF GEAR MATERIALS
3) Non- Ferrous metals- copper, Zink, tin, aluminum,
bronze- worm gear.
4) Sintered Metals low cost gears
5) Non-metals Bakelite, Nylon
Cheap, easy to manufacture,
Light weight, tolerate errors in tooth profile.
Do not have sufficient strength.

31. Force analysis of spur gears

32. Force analysis of spur gears
1) Tangential force Ft-Responsible for power transmission.
Ft=Tangential force.
P= Power transmitted, W
V= Pitch line velocity,m/s
Tp= torque acting on pinion.
Tg= torque acting on Gear.
dp= P.C.D. of pinion.
dg= P.C.D. of Gear.
np= pinion speed, rpm.
ng= Gear speed, rpm.
Tangential force acting on the driving gear opposes the rotation of the driving gear whereas assists the rotation of driven gear.

33. Force analysis of spur gears
2) Radial Force- (Fr) Not useful component.
Tends to separate two gears.
Acts along the radial line through the pitch point and towards the centre.
3)Resultant force (F)=

34. GEAR TOOTH FAILURE Gear tooth failure ..
Wear failure or surface destruction
Bending failure or breaking of tooth
Pitting
Abrasive Wear
Scoring
Corrosive wear
Destructive Pitting
Initial Pitting

35. TYPES OF GEAR TOOTH FAILURE
Bending failure or tooth breakage.-
Gear tooth is like a cantilever and subjected to repetitive bending stresses.
Tooth breakage happens when total load exceeds beam strength.
Avoided by adjusting module, face width, providing fillet radius.
2) Wear failure-
Removes complete surface layer.
i) Pitting- Fatigue failure due to repetitive contact stresses.
A) Initial pitting- Because of high spots, surface irregularities, errors in tooth profile. It is a temporary phenomena.
Can be minimized by improving surface finish and proper alignment of gears.

36. B) Destructive pitting- Due to repetitive contact stresses.
Depends upon Hertz contact stress, surface endurance strength, number of cycles.
Can be avoided by improving surface endurance strength.(Hardness).
Spalling-It is another surface fatigue failure in which the cracks originates below the gear tooth surface due to sub surface stresses.
Spalling can be avoided by providing sufficient case depth in surface hardening.

37. INITIAL PITTING

38. DESTRUCTIVE PITTING

39. TYPES OF GEAR TOOH FAILURE
ii Scoring- (scuffing or galling)
Metal to metal contact due to lubrication failure. Excessive frictional heat and overheating of teeth. Welding and Tearing action. (stick-slip phenomena)
iii Abrasive Wear-
Damage caused by particles like dirt, dust in lubricant. Surface injury caused by particles trapped between mating teeth. Can be avoided by proper filtration of lubricant, use high viscosity oils, increasing surface hardness.
iv Corrosive wear-
Due to chemical action by improper lubricant, surrounding atmosphere.

40. INITIAL SCORING

41. MODERATE SCORING

42. DESTRUCTIVE SCORING

43. POLISHING WEAR

44. MODERATE WEAR

45. BEAM STRENGTH OF SPUR GEAR TOOTH
Beam strength of the spur gear tooth is the maximum tangential load
the gear tooth can take without tooth failure.
Lewis Equation for Beam strength of spur Gear tooth
Each tooth is considered as a cantilever beam fixed at the base.
Radial force Fr- Induces a direct compressive stress of small
magnitude and can be neglected.
Tangential Force Ft- Induces a bending stress which tends to break
the tooth.

46. M = Max. bending moment at section BC = Ft. l
Ft = tangential force acting on gear tooth
l = Length of tool
y = Half the thickness of the tooth
t = Thickness of tooth section at
b = Face width of the gear tooth
I = 1 . b . T3 /12
Max. bending stress at pt. B

47. Max. bending stress at section BC
From Equation tangential force acting on gear tooth
The variables ‘t’ & ‘l’ depends upon the size of the gear tooth and its profile.
Let t = K1pc and l= K2pc
pc = Circular pitch
K1 , K2 = Constants

48. Substitute the value in above equation we getOr
y = Lewis form factor based on circular pitch
Equation can be written as
Y = Lewis form factor =
When bending stress reaches the limiting value
The corresponding tangential force is called the beam strength
= Bending endurance strength
Fb = Beam strength of gear tooth
Lewis equation for Spur gear

49. BEAM STRENGTH OF SPUR GEAR TOOTH

50. BEAM STRENGTH OF SPUR GEAR TOOTH

51. LEWIS FORM FACTOR Y= 0.484- 2.87/Z For 200 full-depth involute.
The Lewis form factor Y is the function of tooth shape and the
point of application of load. Lewis form factor depends upon
1) Number of teeth.
2) Tooth system.
3) Point of application of load.
Y= /Z For 200 full-depth involute.
Y= /Z For 200 stub involute.
Y= /Z For full depth involute
and composite.

52. Permissible Bending Stress
The gear tooth is subjected to repeated bending stress.
The bending endurance strength,
σb = Ka. Kb.Kc. Kd. Ke. Kg. S’e
(S’e= Endurance limit for test specimen)
σb = Ka. Kb.Kc. Kd. Ke. Kg. x(0.5 Sut).
Where ka= surface finish factor
Kb= size factor
Kc= load factor
Kd= temp. factor.
Ke= Modifying factor for stress concentration.
Kg= reliability factor.

53. Permissible Bending Stress
For Gears, Ka. Kb.Kc. Kd. Ke. Kg. . = 0.66
σb = 0.66x0.5 Sut
σb = 0.33 Sut
σb = Sut/3
Face Width- (b) Face width is taken between 9 to 15 times
the module.(9m to 15m)
Weaker of Gear or Pinion-
The product (σb x Y) decides the weaker member. If
(σb x Y) pinion < (σb x Y) gear, pinion is weaker in bending.
When gear and pinion material is same, then Y is less for pinion and pinion is weaker.

54. WEAR STRENGTH OF SPUR GEAR TOOTH
Wear strength of the Gear tooth is the maximum tangential load the gear tooth can take without pitting failure.
Buckinghams equation for wear strength of a gear tooth-
Wear strength, Fw= dp. b. Q. K
dp = pitch circle diameter of pinion.
b = face width of teeth.
K= Load- stress factor
Q= Ratio factor.

55. WEAR STRENGTH OF SPUR GEAR TOOTH
σc = Surface indurance strength of weaker element.
The expression for the ‘K’ can be simplified for different pinion & gear material and 200 pressure angle
K= 0.16 [BHN/100]2 N/mm2 for steel pinion and steel gear.
K= 0.21 [BHN/100]2 N/mm2 for C.I. pinion and steel gear.
K= 0.18 [BHN/100]2 N/mm2 for steel pinion and C.I. gear.

56. EFFECTIVE LOAD ON SPUR GEAR TOOTH
Effective load on the gear tooth is the total maximum tangential force
acting on the gear tooth.
Theoretical Tangential Force (Ft)- The theoretical tangential force acting on the gear tooth due to power transmission-
P= Power Transmitted in Watt
V= Pitch line velocity, m/sec. = (π d.n. / 60x 1000)
Maximum Tangential Force-(Fmax.)-
Ft max. = Ka. Km. Ft
= Ka. Km. P/V
Application or Service factor (service factor/ overload factor) (Ka)-
Load distribution factor (Load conc. Factor) (Km)-

57. Application factor- (Ka)
Accounts for increase in the tangential force due to fluctuation of the torque by prime mover or load machine. It also known as service factor or overload factor.
Varies from 1.00 to 2.5.
Load distribution factor-( Km)-
Accounts for non-uniform distribution of load across the face width. Depends on-
Alignment of gears.
Bearing mounting.
Gear tooth manufacturing accuracy.

58. Dynamic Load on Gear Tooth
The tooth errors combined with the mass of the pinion and gear result in inertia forces.
Additional forces arising out of the inertia effects are known as
dynamic loads.
Dynamic loads arises due to
Inaccuracies in tooth profile.
Errors in tooth profile.
Run out of the gear.
Inertia of the rotating masses.
Deflection of the teeth.
Stiffness of the rotating parts.
Depends upon tooth error and pitch line velocity.

59. Dynamic Load on Gear Tooth

60. IS GEAR GRADES
Based on the accuracy of gear tooth IS has classified the gears into twelve different grades
IS Grade
Accuracy level
Manufacturing Method
Application
Pitch line velocity 12
Very low
Casting
Low speed, Light load
V≤ 10 m/s
10,11
Low
Hobbing
Low speed
V≤ 20 m/s
8,9
Medium
Fine hobbing
Vehicle gears
20≤ V ≤ 25
6,7
Medium, High
Shaving, grinding
Ind. gears
25≤ V ≤ 30
4,5
High accuracy
Shaving, finish grinding
Turbine gears
V > 30
1,2, 3
Ultra high
Finish grind, honing
Master gears
40 ≤ V ≤ 200

61. METHODS OF ESTIMATION OF DYNAMIC LOAD
Preliminary estimation by velocity factor-
The effective load between the meshing teeth in tangential
direction is given by
Kv= Velocity factor-Barth factor. Depends upon gear accuracy
and pitch line velocity.

62. 2) Precise Estimation by Buckinghams Equation-
The Buckingham equation for the dynamic load in the tangential direction is given by
Fd = Dynamic load.
Ft max. = Maximum tangential force= Ka. Km. Ft
Ft =Tangential force
Ka = Application factor or service factor.
Km = Load distribution factor or Load concentration Factor
V = Pitch line velocity.
C = Deformation factor or Dynamic factor.

63. Ep, Eg = modulii of elasticity for pinion & gear material.
e = sum of error on meshing teeth.
K =Tooth form factor.
Deformation factor( Dynamic factor) C- Depends upon the accuracy of gear teeth
Steel pinion and steel gear-C = 11500e N/mm
C.I. pinion and C.I. gear- C = 8900e N/mm.
Steel pinion and C.I. gear- C = 10000e N/mm
Pitch errors on meshing teeth-(e)- Sum of pitch errors between two meshing teeth, mm.
e =ep + eg
ep = pitch error for pinion teeth, mm
eg= pitch error for gear teeth, mm
Depends upon gear grade, size, tooth size

64. SAFETY OF GEAR PAIR 1) Safety against bending failure.
Beam strength of the gear tooth ≥ Effective load.
Fb ≥ Feff.
Fb = F.S X Feff.
2) Safety against Wear Failure.
Wear strength of the gear tooth ≥ Effective load.
Fw ≥ Feff.
Fw = F.S X Feff.
Recommended factor of safety is 1.5 to 2. It may extend up to 3

65. OBJECTIVES IN GEAR DESIGN
High power transmission.
Compact arrangement.
High efficiency.
Low initial cost.
Low maintenance and running cost.
Noise and vibration free operation.

66. DESIGN OF SPUR GEAR PAIR
Selection of tooth system.
Selection of the number of teeth.
Selection of material
Selection of gear grade.
Estimation of module, face width, pitch circle diameters, addenda and dedenda.
The procedure for design of spur gear is as follows:

67. Select Ø, Zp, Zg, Sup, Sug, BHN, Nf, Ka, Km & Gear Grade
Start
Input P,np, G
Select Ø, Zp, Zg, Sup, Sug, BHN, Nf, Ka, Km & Gear Grade
Calculate σbg, σbpYp, σbpYg, and σbg Yg Is
σbp.Yp< σbg.Yg
Yes No
Gear is weaker in Bending
Gear is weaker in Bending
Calculate fb=σbg.b.Q.Yg
In terms of ‘m’
Calculate fb=σbp.b.Q.Yp
In terms of ‘m’

68. Calculate Kv In terms of ‘m’
Calculate fw=dp.b.Q.K
In terms of ‘m’
Calculate
V = π m np Zp / 60x 1000
In terms of ‘m’
Calculate
Ft=P/V In terms of ‘m’
Calculate Kv In terms of ‘m’
Calculate
feff = Ka Km ft / Kv
In terms of ‘m’

69. Design based on Beam strength Design based on Wear strengthIs
fb< fw
Design based on Beam strength
Design based on Wear strength
Calculate fw=Nf . Feff Calculate ‘m’ by Trial & error Method
Calculate fb=Nf . Feff Calculate ‘m’ by Trial & error Method
Select Next standard module ‘m’
Increase m
Select strong material
Increase b
Increase accuracy of pinion & gear teeth
Increase m
Increase b
Increase BHN
Increase accuracy of pinion & gear teeth
Calculate dp, dg, b, ha, hf
Calculate hf, fb, & fw

70. Calculate fd by Buckingham’s equation
Calculate feff = Ka Km ft + fd
Gear pair is unsafe against Pitting
Gear pair is unsafe against bending
Yes
Is fb<fw No
Is fb>=Nf. feff
Is fw>=Nf. feff No No
Yes
Yes
Gear pair is safe
Stop

71. DESIGN OF SPUR GEAR PAIR
1) Input- Power, Gear ratio, rpm of pinion.
2) Select pressure angle (Ø), No. of teeth on pinion (zp) and gear(zg) , ultimate strength of pinion(Sup) and gearSug), surface hardness BHN), application factor(Ka), Load factor(Km).
3) Calculate bending stress (σb), Lewis form factor (Y), product of (Lewis form factor x bending stress σbxY ).
4) if it is less for pinion, pinion is weak.
5) Calculate Beam strength Fb= σb. b.m.Y in terms of module.
6) Calculate Wear strength Fw=dp.b.Q.K in terms of module.

72. DESIGN OF SPUR GEAR PAIR
7)Calculate pitch line velocity, V in terms of module.
8) Calculate tangential force, Ft= P/V. in terms of module
9) Calculate velocity factor, kv in terms of module.
10) Calculate effective load, Feff= ka.km.Ft/kv in terms of module.
11)If beam strength is less than wear strength, Design for beam strength.
12) Fb= Feff x f.s.
13) If wear strength is less than beam strength, Design for wear strength. Fw= Feff x f.s
14)Calculate m, dp, dg, b, ha, hf.

73. DESIGN OF SPUR GEAR PAIR
15) Calculate Fd, Dynamic load by Buckinghams equation. Fd=21V(bC+Ftmax.)/21V+√bC+Ftmax.
16) Calculate Feff.= Ka.Km.Ft+Fd
17) If Fb ≤ Fw and Fb ≥ Feff xF.S, Gear pair is safe in bending. If not, gear pair is unsafe in bending.then increase next module, change material, increase accuracy.
18) If Fw ≤Fb and Fw ≥ Feff xF.S, Gear pair is safe in pitting. If not, gear pair is unsafe in pitting. Then increase next module, increase BHN, increase accuracy.
STOP.

74. POWER TRANSMITTING CAPACITY OF SPUR GEAR
0) Given- m, Zp, Zg, b, ha, hf, np, grade, Sup, Sug, BHN, Ka, Km, F.S.
1)Decide weaker part in bending .
2) Calculate bending strength based on step 1
3) Calculate Wear strength ,Fw= dp.b.Q.K
4) Calculate V (pitch line velocity), Kv(velocity factor)
5)Calculate Feff.= Ka.Km.Ft/ Kv in terms of Ft.
6) If Fb is less than Fw, power rating is based on Beam strength and if it is more than Fw, power rating is based on wear strength.
7)Equating Fb or Fw with Feff x f.s, calculate Ft.
8)P= Ft x V

75. GEAR LUBRICATION Objectives of gear lubrication-
1) To reduce the possibility of scoring failure.
2) to reduce the wear of the teeth.
3) to reduce the power loss.
4) to act as coolant by dissipating heat.
4) to carry away the worn-out particles.
5) to minimise noise, vibration and shock.
6) to prevent corrosion.

76. LUBRICANTS USED IN GEARS.
Grease.
Straight mineral oil.
Motor oil.- SAE
Gear oils.

77. MODES OF LUBRICATION Grease lubrication. Drip-feed lubrication.
Splash lubrication.
Spray or jet lubrication.

78. MULTI-STAGE GEAR REDUCER
1) Splitting of reduction ratio by geometric progression.
2) Splitting of reduction ratio for compact arrangement.- Higher reduction in earlier stages.