1. Gears are used to change the torque and speed of rotating shafts in machines like marine engines. For example, a ship's main engine typically runs at 400 RPM but the propeller needs to turn at 100 RPM, so a gear reduction is used.
2. There are different types of gears that can be used for speed and torque conversions. Planetary gears allow for compact gear reductions and different speed ratios by fixing different combinations of the sun, planet, and ring gears.
3. For gears to operate smoothly, the fundamental law of gearing must be satisfied. This requires that the common normal between mating gear teeth pass through a fixed pitch point, ensuring the velocity ratio between gears remains constant during
1. Gears are used to change the torque and speed of rotating shafts in machines like marine engines. For example, a ship's main engine typically runs at 400 RPM but the propeller needs to turn at 100 RPM, so a gear reduction is used.
2. There are different types of gears that can be used for speed and torque conversions. Planetary gears allow for compact gear reductions and different speed ratios by fixing different combinations of the sun, planet, and ring gears.
3. For gears to operate smoothly, the fundamental law of gearing must be satisfied. This requires that the common normal between mating gear teeth pass through a fixed pitch point, ensuring the velocity ratio between gears remains constant during
1. Gears are used to change the torque and speed of rotating shafts in machines like marine engines. For example, a ship's main engine typically runs at 400 RPM but the propeller needs to turn at 100 RPM, so a gear reduction is used.
2. There are different types of gears that can be used for speed and torque conversions. Planetary gears allow for compact gear reductions and different speed ratios by fixing different combinations of the sun, planet, and ring gears.
3. For gears to operate smoothly, the fundamental law of gearing must be satisfied. This requires that the common normal between mating gear teeth pass through a fixed pitch point, ensuring the velocity ratio between gears remains constant during
1. Gears are used to change the torque and speed of rotating shafts in machines like marine engines. For example, a ship's main engine typically runs at 400 RPM but the propeller needs to turn at 100 RPM, so a gear reduction is used.
2. There are different types of gears that can be used for speed and torque conversions. Planetary gears allow for compact gear reductions and different speed ratios by fixing different combinations of the sun, planet, and ring gears.
3. For gears to operate smoothly, the fundamental law of gearing must be satisfied. This requires that the common normal between mating gear teeth pass through a fixed pitch point, ensuring the velocity ratio between gears remains constant during
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Gear trains (Chapter 6)
Change torque, speed Why we need gears Example: engine of a containership Optimum operating speed of the engine about 400 RPM Optimum operating speed of the propeller about 100 RPM Need reduction gear
2 Engine Gear Propeller, operates at about 100 RPM Output flange Engine operates at about 400 RPM Connecting the main engine to the propeller through a reduction gear 3 Types of gears 4 Gear box Synchronizers Stick shift The gear box is in first gear, second gear 5 Gear Nomenclature (6.1) 6 Important definitions Velocity ratio=m V =angular velocity of output gear/ angular velocity of input gear=pitch diameter of input gear/pitch diameter of output gear Torque ratio=m T =torque at output gear/torque at input gear m T =1/m V Gear ratio=m G =N gear /N pinion ,
m G is almost always greater than one
7 Fundamental law of tooth gearing (6.2 and 6.3): velocity ratio must be constant as gears rotate Angular velocity ratio= ratio of distances of P from centers of rotation of input and output gear.
If common normal were fixed then the velocity ratio would be constant. P O P O 3 2 2 3 = e e e 3 T 3 2 8 If gear tooth profile is that of involute curve then fundamental law of gearing is satisfied Involute curve: path generated by a tracing point on a cord as the cord is unwrapped from base cylinder 9 Generating gear teeth profile P Steps: Select base circles Bring common normal AB Draw involutes CD, EF
10 Gear action Angular velocity of Gear 3 / angular Velocity of gear 2 = O 2 P/O 3 P = constant 11 Fundamental law of gearing: The common normal of the tooth profiles at all points within the mesh must always pass through a fixed point on the line of the centers called pitch point. Then the gearsets velocity ratio will be constant through the mesh and be equal to the ratio of the gear radii. 12 Base circle radius = Pitch circle radius cos| 13 Path of approach: BP=u a =[(r 3 +a) 2 -r b3 2 ] 1/2 -r 3 sin| Path of recess: PC=u r =[(r 2 +a) 2 -r b2 2 ] 1/2 -r 2 sin| Final contact: C Initial contact: B 14 Standard gears: American Association of Gear Manufacturers (AGMA) (6.4) Teeth of different gears have same profile as long as the angle of action and pitch is the same.
Can use same tools to cut different gears. Faster and cheaper product. Follow standards unless there is a very good reasons not to do so. 15 Template for teeth of standard gears 16 AGMA Specifications Diametral pitch, p d =1, 1.25, 1.5,,120 Addendum of pinion = addendum gear Observations The larger the pitch, the smaller the gear The larger the angle of action: the larger the difference between the base and pitch circles, the steeper the tooth profile, the smaller the transmitted force. 17 AGMA Standard Gear Specifications Parameter Coarse pitch (p d =N/d<20) Fine pitch (p d =N/d>20) Pressure angle, | 20 0 or 25 0 (not common) 20 0 Addendum, a 1/p d 1/p d Dedendum, b 1.25/p d 1.25/p d Working depth 2.00/p d 2.00/p d
Whole depth 2.25/p d 2.2/p d +0.002 Circular tooth thickness 1.571/p d (~circular pitch/2) 1.571/p d Fillet radius 0.30/p d Not standardized Clearance 0.25/p d 0.25/p d +0.002
Minimum width at top land 0.25/p d
Not standardized
Circular pitch t/p d t/p d
18 1/p d 1.25/p d 1.571/p d t/p d Min: 0.25/p d 0.3/p d 0.25/p d d=N/p d 19 Planetary (or Epicyclic) Gears (10.4) Gears whose centers can move Used to achieve large speed reductions in compact space Can achieve different reduction ratios by holding different combinations of gears fixed Used in automatic transmissions of cars 20 Planetary gear 21 Planet Carrier Input shaft Sun gear Ring gear Components of a planetary gear 22 A variant of a planetary gear Carrier 23 Planetary gears Planetary gears in automotive transmission 24 Velocity Analysis Of Planetary Gears (10.6, 10.7) Two degrees of freedom Given the velocities of two gears (e.g. sun and carrier) find velocities of other gears Approach Start from gear whose speed is given Use equation e gear = e car + e gear/car
25 Velocity analysis of planetary gear 26 This program finds the velocities of the remaining links given the velocities of two links in a planetary gear. Input: Number of teeth of sun, planet and ring gears, N1, N3, N4, respectively. N1 30 := N3 35 := N4 100 := Velocities of two links: specify the known values of the inputs and guess the values of the outputs: e 3 100 := e 4 120 := e 1 100 := e 2 100 := e 12 100 := Given e 3 0 e 4 1 e 1 e 2 e 12 + 27 12 2 4 12 2 3 12 2 1 4 1 3 1 e e e e e e e e e N N N N = = + = 28 Find e 1 e 2 , e 3 , e 4 , e 12 , ( ) 3.333 1.538 0 1 1.795 |
ME 3670: Design and Analysis of Machine Elements 1: Part I: Kinematics and Mechanisms Lecture 16-19 Cam Motion Program and Profile Design Read 8.1-8.10, Kinzel