Gears & its Terminology
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- 2. Introduction • Gears are used to transfer motion and torque between machine components in mechanical devices. Depending on the design and construction of the gear pair employed, gears can change the direction of movement and/or increase the output speed or torque. • Let the wheel A be keyed to the rotating shaft and the wheel B to the shaft, to be rotated. • A little consideration will show, that when the wheel A is rotated by a rotating shaft, it will rotate the wheel B in the opposite direction as shown in Fig. (a). 3
- 3. TYPES OF GEARS 1.According to the position of axes of the shafts. a. Parallel 1.Spur Gear 2.Helical Gear 3.Rack and Pinion b. Intersecting Bevel Gear c. Non-intersecting and Non-parallel worm and worm gears 3
- 4. SPUR GEAR • Teeth is parallel to axis of rotation • Transmit power from one shaft to another parallel shaft • Used in Electric screwdriver, oscillating sprinkler, windup alarm clock, washing machine and clothes dryer 4
- 5. External and Internal spur Gear… 5
- 6. Helical Gear • The teeth on helical gears are cut at an angle to the face of the gear • This gradual engagement makes helical gears operate much more smoothly and quietly than spur gears • One interesting thing about helical gears is that if the angles of the gear teeth are correct, they can be mounted on perpendicular shafts, adjusting the rotation angle by 90 degrees 6
- 7. Herringbone gears • To avoid axial thrust, two helical gears of opposite hand can be mounted side by side, to cancel resulting thrust forces • Herringbone gears are mostly used on heavy machinery. 7
- 8. Rack and pinion • Rack and pinion gears are used to convert rotation (From the pinion) into linear motion (of the rack) • Aperfect example of this is the steering system on many cars 3/29/2016 8
- 9. Bevel gears • Bevel gears are useful when the direction of a shaft's rotation needs to be changed • They are usually mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well • The teeth on bevel gears can be straight, spiral or hypoid • locomotives, marine applications, automobiles, printing presses, cooling towers, power plants, steel plants, railway track inspection machines, etc. 3/29/2016 9
- 10. Straight and Spiral Bevel Gears 10
- 11. WORM AND WORM GEAR • 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 • Many worm gears have an interesting property that no other gear set has: the worm can easily turn the gear, but the gear cannot turn the worm • Worm gears are used widely in material handling and transportation machinery, machine tools, automobiles etc 11
- 15. NOMENCLATURE OF SPUR GEARS 15
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- 17. • Pitch circle: It is an imaginary circle which by pure rolling action would give the same motion as the actual gear. • Pitch circle diameter: 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: It is a common point of contact between two pitch circles. • Pressure angle or angle of obliquity: It is the angle between the common normal to two gear teeth at the point of contact and the common tangent at the pitch point. It is usually denoted by φ. The standard pressure angles are 14 1/2 ° and 20°. 17
- 18. • Addendum: It is the radial distance of a tooth from the pitch circle to the top of the tooth. • 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. Note : Root circle diameter = Pitch circle diameter × cos φ where φ is the pressure angle. 18
- 19. Circular pitch: 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. It is usually denoted by Pc ,Mathematically, A little consideration will show that the two gears will mesh together correctly, if the two wheels have the same circular pitch. Note : If D1 and D2 are the diameters of the two meshing gears having the teeth T1 and T2 respectively, then for them to mesh correctly, 19
- 20. Diametral pitch: It is the ratio of number of teeth to the pitch circle diameter in millimetres. It is denoted by pd. Mathematically, Module: It is the ratio of the pitch circle diameter in millimeters to the number of teeth. It is usually denoted by m. Mathematically, Clearance: It is the radial distance from the top of the tooth to the bottom of the tooth, in a meshing gear.Acircle passing through the top of the meshing gear is known as clearance circle. 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.
- 21. of the teeth due to tooth errors an Working depth: It is the radial distance from the addendum circle to the clearance circle. It is equal to the sum of the addendum of the two meshing gears. 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. Backlash: It is the difference between the tooth space and the tooth thickness, as measured along the pitch circle. Theoretically, the backlash should be zero, but in actual practice some backlash must be allowed to prevent jamming d thermal expansion. 21
- 22. Face of tooth: It is the surface of the gear tooth above the pitch surface. Flank of tooth: It is the surface of the gear tooth below the pitch surface. Top land: It is the surface of the top of the tooth. Face width: It is the width of the gear tooth measured parallel to its axis. Profile: It is the curve formed by the face and flank of the tooth. Fillet radius: It is the radius that connects the root circle to the profile of the tooth. 22
- 23. 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. Arc of contact: It is the path traced by a point on the pitch circle from the beginning to the end of engagement of a given pair of teeth. The arc of contact consists of two parts, i.e. (a)Arc of approach. It is the portion of the arc of contact from the beginning of the engagement to the pitch point. (b)Arc of recess: It is the portion of the arc of contact from the pitch point to the end of the engagement of a pair of teeth. 23
- 24. two types of teeth • In actual practice following are the commonly used 1. Cycloidal teeth ; and 2. Involute teeth. 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. • When 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. • On the other hand, if 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. 24
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- 26. Condition for Constant Velocity Ratio of Toothed Wheels–Law of Gearing • The law of gearing states the condition which must be fulfilled by the gear tooth profiles to maintain a constant angular velocity ratio between two gears. • Figure shows two bodies 1 and 2 representing a portion of the two gears in mesh. A point C on the tooth profile of the gear 1 is in contact with a point D on the tooth profile of the gear 2. The two curves in contact at points C or D must have a common normal at the point. Let it be n - n. Let, ω1= instantaneous angular velocity of the gear 1 (CW) ω2= instantaneous angular velocity of the gear 2 (CCW) vc = linear velocity of C vd = linear velocity of D 26
- 29. Each of two gears in a mesh has 48 teeth and a module of 8 mm. The teeth are of 20° involute profile. The arc of contact is 2.25 times the circular pitch. Determine the addendum. 29
- 30. 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. 30
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- 32. Two involute gears in mesh have 20o pressure angle. The gear ratio is 3 and the number of teeth on the pinion is 24. The teeth have a module of 6 mm. The pitch line velocity is 1.5 m/s and the addendum equal to one module. Determine the angle of action of the pinion (the angle turned by the pinion when one pair of teeth is in the mesh) and the maximum velocity of sliding. 32