Module 4 gears

Introduction to Spur Gears

1. Department of Mechanical Engineering JSS Academy of Technical Education, Bangalore-560060 Kinematics of Machines (Course Code:17ME42 ) Gears

2. Gear terminology Classification Law of gearing Path of contact and Arc of contact Contact ratio of spur, helical, bevel and worm gears Interference in involute gears . Methods of avoiding interference Back lash Content

3. The slipping of a belt or a rope is a common phenomenon in the transmission of motion or power between two shafts . The effect of slip is to reduce the velocity ratio of the Drive / System . In precision machine, in which a definite velocity ratio is important (as in watch mechanism) the only positive drive is by means of Gears or toothed wheels. Introduction

4. Belt/Rope Drives - Large center distance of the shafts. Chain Drives - Medium center distance of the shafts. Gear Drives - Small center distance of the shafts. T ransmission of motion or power between two shafts. Introduction

5. Gears or toothed wheels are used to transmit motion or power between two shafts with exact / definite or constant angular velocity ratio. Introduction

6. Advantages 1. Transmits exact velocity ratio. 2. Used to transmit large power . 3. H igh efficiency & reliability. 5. It has compact layout . Disadvantages 1. The manufacture of gears require special tools and equipment . 2. The error in cutting teeth may cause vibrations and noise during operation. Introduction

7. Classification of Toothed Wheels / Gears

8. Classification of Toothed Wheels / Gears

9. Classification of Toothed Wheels / Gears Gears have teeth parallel to the axis of the wheel, are called as spur gears .

10. H elical gears in which the teeth are inclined to the axis used for connecting parallel shafts. The double helical gears are known as herringbone gears . Helical gears

11. Intersecting Axes The two non-parallel or intersecting , but coplanar shafts connected by gears are called bevel gears and the arrangement is known as bevel gearing . The bevel gears, like spur gears, may also have their teeth inclined to the face of the bevel, in which case they are known as helical bevel gears.

12. The two non-intersecting and non-parallel i.e. non-coplanar shafts are connected by gears and are called skew bevel gears or spiral gears or Skewed Gears The arrangement is known as skew bevel gearing or spiral gearing .

13. Gears - Types and Classification

14. Gears - Types and Classification

15. Worm Drive Bevel Gears Spur Gears Gears - Types and Classification Rack Gears

16. Adjustable Pitch Rotor Gears - Types and Classification

17. Spur Gear terminology

18. Spur Gear terminology Pressure angle ( ϕ ) / Angle of Obliquity

19. Spur Gear terminology Significance of Pressure angle ( ϕ ) / Angle of Obliquity Increasing pressure angle improves the tooth strength. Increasing pressure angle result in smaller base circle so more portion of tooth becomes involute thus can eliminate interference. Increasing pressure angle will improve power transmission but at the same time will increase gear wear and meshing noise Decreasing the Pressure Angle will require more teeth on the pinion to avoid undercutting Low pressure angle will decrease power transmission capacity but will improve gear meshing properties like reduced noise

20. Law of Gearing (Condition for Constant Velocity Ratio of Toothed Wheels)

21. Forms of Teeth 1. 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. Tooth form Cycloidal Gears

22. Locus of a point on a straight line which rolls without slipping, on the circumference of the circle. Example: An involute profile is generated by the end of the string/tape being unwound from a cylinder or by a point on a line as the line rolls on the circumference of a circle without slipping. 2. Involute Teeth Tooth form Involute gears in Action

23. Comparison Between Involute and Cycloidal Gears Involute Cycloidal Centre distance for a pair of involute gears can be varied within limits without changing the velocity ratio. Requires exact centre distance to be maintained Pressure angle, from the start of the engagement of teeth to the end of the engagement, remains constant . Pressure angle is maximum at the beginning of engagement, reduces to zero at pitch point, starts decreasing and again becomes maximum at the end of engagement. Interference exists Interference does not occur at all Strength of the teeth is Low Teeth have wider flanks, therefore the cycloidal gears are stronger

24. Length of Path of Contact

25. O 1 P = Pitch circle radius of pinion = r 1 = Driver O 2 P = Pitch circle radius of Gear = r 2 = follower O 1 C = Base circle radius of pinion = r b1 O 2 D = Base circle radius of gear = r b2 O 1 B = Addendum circle radius of pinion= r a1 O 2 A = Addendum circle radius of gear = r a2 AP = Path of approach PB = Path of recess Consider a pinion driving the wheel as shown in Fig . When the pinion rotates in clockwise direction, the contact between a pair of involute teeth begins at A (on the flank near the base circle of pinion or the outer end of the tooth face on the wheel) and ends at B. C D is the common normal at the point of contacts and is common tangent to the base circles. The point A is the intersection of the addendum circle of gear and the common tangent. The point B is the intersection of the addendum circle of pinion and common tangent.

26. Interference in Involute Gears When addendum of gear 1 meet with the base circle of another gear 2, due to this strength of the gear reduces. If the portion of the gear exists below the base circle , then it results in interference & leads to undercutting of the tooth. Mating of two non-conjugate profiles results in a phenomena called interference.

27. Interference in Involute Gears The power transmission through a pair of teeth is along the path of contact, CD. This path is the common tangent to the two base circles and passes through pitch point, P. For this path not to deviate, the portions of the tooth profiles in contact must be involute . If not, the two surfaces (profiles) would not touch tangentially and the power transmission may not be proper. Mating of two non-conjugate profiles results in a phenomena called interference. Teeth in contact will not slide but mate roughly causing a bend in the teeth or dig out the non involute flank.

28. Methods to avoid Interference 1. Height of the teeth may be reduced. 2. Under-cut of the radial flank of the pinion. 3. Centre distance may be increased, but It leads to increase in pressure angle. 4. By tooth correction / Modification : The pressure angle, centre distance and base circles remain unchanged , but tooth thickness of gear will be greater than the pinion tooth thickness. 5. Increasing the number of teeth on the pinion.

29. Minimum No. of teeth to avoid Interference Consider a pinion driving Gear as shown in Fig. CD is the common tangent to base circle. The points C & D are called Interference points. If the path of contact does not extend beyond either of these points, interference is avoided.

30. Minimum No. of teeth to avoid Interference

31. Max. addendum circle radius of gear to avoid interference is From right angle triangle O 2 CD

32. Backlash Circumferential clearance – Backlash is the distance between mating teeth measured along the pitch circle circumference. In practical aspect gears must have some backlash due to tolerances, thermal expansion, wear, etc. One must minimize backlash for smooth operation . Example : robot joints which must be driven both directions . Changing direction, nothing happens until the backlash is overcome, and then impact – bad for dynamics.

33. End of Module