1. GEC, RAJKOT GEARS & GEARS TRAIN

2. INTRODUCTION:
The belt or rope drive we have seen that the velocity ratio transmitted can not be exact due to the slip of rope or belt on the pulley. Also due to frictional losses the efficiency of power transmission in such drives is less.
The power may be transmitted from one shaft to another by means of mating gears with high transmission efficiency.
This leads to the formation of teeth on both discs and the discs with teeth on their periphery are knows as Gears.

3. Advantages and Disadvantages of Gear Drive: Advantages:
It transmits exact velocity ratio.
It may be used to transmit large power.
It has high efficiency.
It has reliable service.
It has compact layout.
Disadvantages:
The manufacture of gears require special tools and equipment.
The error in cutting teeth may cause vibrations and noise during operation.

4. CLASSIFICATION OF GEARS:
1. According to the position of shaft axes:
a. Parallel
1.Spur Gear
2.Helical Gear
3.Rack and Pinion
b. Intersecting
1. Bevel Gear
c. Non-intersecting and Non-parallel
1. worm and worm gears
2. Spiral or Skew gears

5. SPUR GEAR:
If teeth of the gear wheels are parallel to the axis of wheel, the gears are called spur gear.
Transmit power from one shaft to another parallel shaft.
Used in Electric screw driver, windup alarm clock, washing machine and clothes dryer etc.

6. HELICAL GEAR:
The teeth of the gear are cut in the form of helix around gear. Their teeth are not parallel to the shaft axis.
This gradual engagement makes helical gears operate much more smoothly and quietly than spur gears.
HERRINGBONE GEARS:
To avoid axial thrust, two helical gears of opposite hand can be mounted side by side, to cancel resulting thrust forces.

7. RACK & PINION GEARS:
A rack and pinion is a special case of spur gear in which one gear is having infinite diameter called Rack.
The rack and pinion is used to transmit the rotary motion into reciprocating motion.

8. BEVEL GEARS:
The two non-parallel or intersecting, but coplanar shafts connected by gears. Teeth of the gear are cut on conical surfaces. Teeth having varying in cross section along the tooth width.
These gears are called bevel gears and the arrangement is known as bevel gearing.
Bevel gear are used to power transmit at perpendicular direction.

9. WORM AND WORM GEARS:
The two non-parallel and non intersecting, but non coplanar shafts connected by gears.
Worm gears are used when large gear reductions are needed. It is common for worm gears to have reductions of 20:1, and even up to 300:1 or greater.
Worm gears are used widely in material handling and transportation machinery, machine tools, automobiles etc.

10. External Gear: The teeth of gears mesh externally with each other.
2. According to types of meshing of gears:
External Gear: The teeth of gears mesh externally with each other.
The larger gear is called as wheel and the smaller gear is called as pinion.
Internal Gear: The teeth of gears mesh internally with each other.
The larger gear is called as annular wheel and the smaller gear is called as pinion.

11. 3. According to the peripheral velocity of the gears.
The gears, according to the peripheral velocity of the gears may be classified as :
(i) Low Velocity Gear: The gears having velocity less than 3 m/s are termed as low velocity gears.
(ii) Medium Velocity Gear: The gears having velocity between 3 and 15 m/s are known as medium velocity gears.
(iii) High Velocity Gear: The velocity of gears is more than 15 m/s are called high speed gears.

12. Gear Trains:
A Gear train is the combination of gear wheels which is used to transmit motion & power from one shaft to another shaft.
A Gear train are used to transmit large velocity ratio within a small space.
Types of Gear Trains:
Following are the different types of gear trains, depending upon the arrangement of wheels :
1. Simple gear train, 2. Compound gear train, Reverted gear train, 4. Epicyclic gear train.
Gear trains are widely used in modern machines like in automobile, ships, clocks, watches, lathes, milling etc…

13. Simple Gear Train:
In a simple gear train each shaft carries only one gear it is known as simple gear train.
The gear A drives the gear D, therefore gear A is called the driver and the gear D is called the driven or follower.
Gear B & C are called intermediate gears which are required if the distance between the driving and driven shafts is large and to obtain the required direction of rotation of driven shafts.
Let NA, NB, NC, ND are speed in rpm of the gear wheel A, B, C, D.

14. Consider wheel A drives the wheel B
Consider wheel A drives the wheel B. The pitch line velocity at the point of contact of two wheels must be same.
On multiplying each equations,

15. Compound Gear Train:
In a Compound gear train are more than one gear on the shaft these known as Compound gear train.
The gear A drives the gear B. Gear C rigidly mounted on the axis of gear B so that they will have the same speed.
Finally gear C drives the gear D mounted on the driven shaft.
The velocity ratio can be determined,
Multiplying equations,

17. Reverted Gear Train:
When the axes of the first gear (first driver) and the last gear ( last driven) are co-axial, then the gear train is known as reverted gear train
The gear A is mounted on the driving shat and drives the gear D through compound gear B & C while the axes of driving and driven shaft are coincide.
The velocity ratio can be determined,

18. The distance between the centers of the shafts are same.
The circular pitch or module of all the gears is assumed to be same. therefore number of teeth on each gear is directly proportional to its circumference or radius.
TA + TB = TC + TD
The reverted gear trains are used in automotive transmissions, lathe back gears, industrial speed reducers, and clocks in minute and hours hands.

19. Epicyclic Gear Train:
When the axes of the first gear (first driver) and the last gear ( last driven) are co-axial, then the gear train is known as reverted gear train
The gear A is mounted on the driving shat and drives the gear D through compound gear B & C while the axes of driving and driven shaft are coincide.
The velocity ratio can be determined,

20. Gear Tooth Terminology: [Gtu-04 Marks]
Pitch circle. It is an imaginary circle which by pure rolling action would transfer the same motion and power as the actual gear.
Pitch circle diameter (D). It is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter. It is also known as pitch diameter.
Pitch Point (P).It is a common point of contact between two pitch circles.

21. Gear Tooth Terminology:
Module. It is the ratio of the pitch circle diameter to the number of teeth.
Module, m = D /T
Circular Pitch (Pc). It is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth.
Pc = π D/T

22. Gear Tooth Terminology:
Diamentral Pitch (Pd). It is the ratio of number of teeth to the pitch circle diameter.
Addendum. It is the radial distance of a tooth from the pitch circle to the top of the tooth.

23. Gear Tooth Terminology:
Dedendum. It is the radial distance of a tooth from the pitch circle to the bottom of the tooth. Addendum circle. It is the circle drawn through the top of the teeth and is concentric with the pitch circle. Dedendum circle. It is the circle drawn through the bottom of the teeth. It is also called root circle.

24. Gear Tooth Terminology:
Clearance. It is the radial distance from the top of the tooth to the bottom of the tooth, in a meshing gear. Total depth. It is the radial distance between the addendum and the dedendum circles of a gear. It is equal to the sum of the addendum and dedendum.

25. Gear Tooth Terminology:
Working depth. It is the radial distance from the addendum circle to the clearance circle.
Tooth thickness. It is the width of the tooth measured along the pitch circle.
Tooth space. It is the width of space between the two adjacent teeth measured along the pitch circle.

26. Gear Tooth Terminology:
Backlash. It is the difference between the tooth space and the tooth thickness, as measured along the pitch circle.
Face of tooth. It is the surface of the gear tooth above the pitch surface.
Top land. It is the surface of the top of the tooth.

27. Gear Tooth Terminology:

28. Law of Gearing (Condition for Cons. Vel. Ratio): [Gtu-07 Marks]
Consider the portions of the two gear in mesh, let two teeth are in contact at point K and the teeth are rotating in directions as shown.
T T be the common tangent & N'N' be the common normal to the curves at the point of contact K. The Centers O1 & O2 of gear.
Draw O1M and O2N perpendicular to N'N'.
V1 and V2 be the velocities of the point K
on the gear 1 and 2. The components of
these velocities along the common normal
MN must be equal.
V1 cos α = V2 cos β
(ω1 x O1K ) cos α = (ω2 x O2K ) cos β
∆ O1MK, cos α = O1M / O1K
∆ O2NK, cos β = O2N / O2K
(i)

29. Contu…
Consider triangle O1MP and O2NP in which Pitch point P lies on intersection of common normal and line joining the centres of gears.
(ii)
Combining equations (i) and (ii),
The angular velocity ratio is inversely
proportional to the ratio of the distances
of the point P from the centre O1 and O2.
A constant angular velocity ratio for all
positions of the mating gears, the point
P must be the fixed point for the two wheels.

30. Contu…
“The common normal at the point of contact between a pair of teeth must always pass through the pitch point.”

31. Gear Tooth Profile: Cycloidal Teeth:
Actual practice following are the two types of teeth commonly used :
Cycloidal Teeth:
A cycloid is the curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line.
A circle rolls without slipping on the outside of a fixed circle, the curve traced by a point on the circumference of a circle is known as epi-cycloid.
A circle rolls without slipping on the inside of a fixed circle, then the curve traced by a point on the circumference of a circle is called hypo-cycloid.

32. Involute Teeth:
The involute is defined as the curve generated by the end point of a cord which is unwound over the circle.
Generation of the Involute curve

33. Comparison Between Involute and Cycloidal Gears:
Involute Teeth Gear
Cycloidal Teeth Gear
The profile of involute gears is the single curvature.
The profile of gears is the double curvature i.e. epi cycloid & hypocycloid.
The pressure angle from start to end of engagement remains constant, which result is smooth running.
The pressure angle varies from start to end of engagement, which result is less smooth running.
The centre distance for a pair of involute gears can be varied within limits without changing the velocity ratio.
The centre distance between cycloidal gears is to be kept constant to keep velocity ratio constant.
The involute gears have interference problem.
This gear do not have any interference problem.
Easy manufacturing
Difficult manufacturing

34. Standard Tooth Profiles or Systems:
141°/2 Composite system:
This type of profile is made with cycloidal curves at the top and bottom portion and involute curve at the middle portion.
This profile used for general purpose gears.
141°/2 full depth involute system:
This type of profile is made straight line except for the filled arcs.
The whole profile corresponds to the involute profile.
Manufacturing of such profile is easy but interference problem.

35. 20° full depth involute system:
This type of profile is same as 141°/2 full depth involute system, but increase of pressure angle from 141°/2 to 20°.
So the results in a stronger tooth, because the tooth acting as a beam is wider at the base.
20° Stub involute system :
The problem of interference in 20° full depth involute system is minimized by removing extra addendum of gear tooth which causes interference.
Such modified tooth profile is called stub tooth profile.
This type of gear are used for heavy load.

36. Length of Path of Contact:
Path of contact. It is the path traced by the point of contact of two teeth from the beginning to the end of engagement.
Length of the path of contact. It is the length of the common normal cut-off by the addendum circles of the wheel and pinion.
When the pinion rotates in clockwise direction, the contact between a pair of involute teeth begins at K and end at L.
MN is the common normal at the point of contacts and the common tangent to the base circles.
The point K is the intersection
of the addendum circle of wheel
and the common tangent.
The point L is the intersection
of the addendum circle of pinion
and common tangent.
KL is called as path of contact.

37. KP is called as path of Approach .
PL is called as path of Recess.

39. Length of Arc of Contact:
Arc of contact. It is the path traced by the point on the pitch circle from the beginning to the end of engagement.
Length of the Arc of contact. It is a sum of length of arc of approach and length of arc of recess.
Arc GPH is called as arc of contact.
Length of the arc of approach (arc GP) & Length of the arc of recess (arc PH).

40. Involute curve generated by rolling a straight line over a base circle without slipping.
The involute curves GKC & LHD can be considered to have been generated by points K & L on straight line MN.
Point K coincides with C and Point L coincides with D on the base circle. So arc CD is equal to length KL.
Length of the arc of contact,

41. Length of the arc of approach (arc GP), Length of the arc of recess (arc PH), Length of the arc of contact,

42. Contact Ratio or No. of Pairs of Teeth in Contact:
The contact ratio or the number of pairs of teeth in contact is defined as the ratio of the length of the arc of contact to the circular pitch.
Contact ratio =
Where,
Gear Ratio (G):
It is the ratio of no. of teeth of wheel to the no. of teeth of pinion.
G = T / t
Where, T = No. of wheel teeth,
t = No. of Pinion teeth

43. Velocity of Sliding of Teeth:
The velocity of sliding is the velocity of one tooth relative to its mating tooth along the common tangent at the point of contact.
Let V1 and V2 be the velocity of the point K on gear teeth 1 and 2.
Velocity of sliding,
Vs = (ω1 + ω2) KP
“Velocity of Sliding of two meshing teeth is
Proportional to the distance from the point
of contact form the pitch point and angular
Velocities of the two gears”.

44. Example: A pinion having 30 teeth drives a gear having 80 teeth
Example: A pinion having 30 teeth drives a gear having 80 teeth. The profile of the gears is involute with 20° pressure angle, 12 mm module and 10 mm addendum. Find the length of path of contact, arc of contact and the contact ratio.
Example: Two involute gears of 20° pressure angle are in mesh. The number of teeth on pinion is 20 and the gear ratio is 2. If the pitch expressed in module is 5 mm and the pitch line speed is 1.2 m/s, assuming addendum as standard and equal to one module,
Find: 1. Length of arc of contact,
2. The angle turned through by pinion when one pair of teeth is in mesh ; and
3. Velocity of sliding at the point of contact.

45. Example: Two mating involute spur gear of 20° pressure angle have a gear ratio of 2. The number of teeth on the pinion is 20 and its speed is 250 r.p.m. The module pitch of the teeth is 12 mm. Assume pinion to be driver.
Find : 1. the addendum for pinion and gear wheel ;
2. the length of the arc of contact ; (GTU-07)

46. Interference in involute Gears: [Gtu-03 Marks]
A pinion with centre O1, in mesh with wheel or gear with centre O2. MN is the common tangent to the base circles and KL is the path of contact between the two mating teeth.
Let, The radius of the addendum circle of pinion is increased to O1N, the point of contact L will move from L to N.
When this radius is further increased, the point of contact L will be on the inside of base circle of wheel and not on the involute profile of tooth on wheel.

47. contu…
The tip of tooth on the pinion will then undercut the tooth on the wheel at the root and remove part of the involute profile of tooth on the wheel.
This effect is known as interference, and occurs when the teeth are being cut. In brief, the phenomenon when the tip of tooth undercuts the root on its mating gear is known as interference.
The radius of the addendum circle of the wheel & pinion increases beyond O2M & O2N. The points M and N are called interference points.

48. contu…
Interference may be avoided if the path of contact does not extend beyond interference points M & N.
The Condition to avoid interference is that the path of contact KL should always be less than or equal to length MN.

49. Minimum Number of Teeth on Wheel to Avoid Interference :
Let t = Number of teeth on the pinion, T = Number of teeth on the wheel,
m = Module of the teeth, r = Pitch circle radius of pinion = m.t / 2,
G = Gear ratio = T / t = R / r, φ = Pressure angle
From triangle O2MP,
Let aw be the maximum standard addendum of wheel to avoid interference,
aw = Aw . M
Where, Aw = Addendum Coefficient of Wheel

50. Minimum number of teeth on pinion, If wheel and pinion have equal teeth, then G = 1,

51. Example: Determine the minimum no of teeth required on pinion and wheel to avoid interference.
(i) when gear ratio is 3 and
(ii)when number of teeth on pinion and wheel is equal. Take pressure angle= 200 and addendum of wheel is 1 module (GTU-07)
Example: Two 200 involute spur gears have a module of 6 mm. the addendum is equal to one module. The larger gear has 36 teeth, while the pinion has 16 teeth will the gear interfere with the pinion? What will be the effect , if the number of teeth on pinion are reduced to 14.

52. Methods of Avoid Interference: [Gtu-05 Marks]
The interference can be eliminated if we select correct minimum number of teeth on pinion and wheel.
But if we not possible then following methods are used to avoid interference.
(1) Modified Profile of Teeth:
When the base circle of gear is more than the radius of dedendum circle then portion of the profile below base circle is non-involute. In such case interference will occurs.
To avoid the interference when the portion of the flank of pinion and the portion of the face of wheel teeth are made cycloidal instead of involute shape.

53. (2) Modified Addendum of Pinion and Wheel:
The length of path of contact KL is less then MN, then there is no interference.
But the length of path of contact KL is larger than MN, then interference occurs.
When addendum of wheel is reduced and addendum of pinion is increased then avoid the interference.

54. (3) Modified Center Distance between Pinion and Wheel:
The center distance of involute gear can be varied within limits without affecting the law of gearing then avoid the interference.
If the center distance is increased then the pressure angle also increases. So the interference point M & N changes with M′ & N′.
But path of contact KL is not extend up to new interference point.

55. Example: An epicyclic gear train consists of sun wheels S, a stationary internal gear E and three identical planet wheels P carried on a star-shaped planet carrier C. The size of different toothed wheels are such that the planet carrier C rotates at 1/5th of the speed Of the sun wheel S. The minimum number of teeth on any wheel is 16. The driving Torque On the sun wheel is 100N-M. Determine
1. Numbers of teeth on different wheels of the train.
2.Torque necessary to keep the internal gear stationary