Gear Trains(齿轮)

O1 N1 1 O2 N 2 2
Chap.5.2 The fundamental law of gearing(2)
O1 N1 1 O2 N 2 2
mV
out 2 O2 N 2 O2 P in 1 O1 N 1 O1 P
mT
Tout O N OP in 1 1 1 1 Tin out 2 O2 N 2 O2 P
r1
The fundamental law of gearing:
The angular velocity ratio between the gears of a gearset remains constant throughout the mesh.
mV
r2
out 2 O2 N 2 O2 P const. in 1 O1 N 1 O1 P
Chap.5 Gear Trains
Chap.5.1 Introduction Chap.5.2 The fundamental law of gearing Chap.5.3 Gear tooth nomenclature Chap.5.4 Condition for Correct Meshing Chap.5.5 Contact Ratio Chap.5.6 Interference and undercutting Chap.5.7 Gear types and Application Chap.5.8 Ordinary gear trains Chap.5.9 Epicyclic or planetary gear trains Chap.5.10 Applications of gear train
Chap.5.1 Introduction(4)
Gears for connecting intersecting shafts
1. Straight bevel gears 2. Spiral bevel gears
Chap.5.1 Introduction(5)
Neither parallel nor intersecting shafts
out 2 r2 rb 2 mV Const. in 1 r1 rb1 #39; cos ' a' ' cos ' ' const. a' ' cos ' ' rb1 rb 2
Chap.5.2 The fundamental law of gearing(10)
r2
The fundamental law of gearing
The ratio of the driving gear radius to the driven gear radius remains constant as the teeth move into and out of mesh.
4. Changing Center Distance
Conclusion： 1. To the gear with an involute form, center distance errors do not affect the velocity ratio, for the base circle diameters are unchanging once the gear is cut. 2. But the pressure angle is affected by the change in center distance. 3. The pitch point and pitch circles are changed
2. Parallel helical gears
3. Herringbone gears (or double-helical gears)
Chap.5.1 Introduction(3)
Gears for connecting parallel shafts
4. Rack and pinion (The rack is like a gear whose axis is at infinity.)
Chap.5.1 Introduction(1)
Gears for connecting parallel shafts
1. Spur gears
external contact
internal contact
Chap.5.1 Introduction(2)
Gears for connecting parallel shafts
5. Backlash
Chap.5.2 The fundamental law of gearing(1)
1. The Fundamental Law of Gearing
Tooth profile 1 drives tooth
profile 2 by acting at the instantaneous contact point K. N1N2 is the common normal of the two profiles. velocities V1 and V2 at point K, along N1N2 are equal in both magnitude and direction. Otherwise the two tooth profiles would separate from each other.
Important lines
Tangency of the both base circles （基圆公切线）is the common normal .
Line of action（力作用线） Axis of transmission(啮合线或传动线)
rbg rg
rbp
rp
Conclusion: these three lines are the same line.
Chap.5.1 Introduction
Can you give some example the gearsets? Gears are machine elements that transmit motion by means of successively engaging teeth. Gears may be classified according to the relative position of the axes of revolution. The axes may be 1. parallel 2. intersecting 3. neither parallel nor intersecting
Chap.5.2 The fundamental law of gearing(7)
out 2 O1 N 1 O1 P r1 in 1 O2 N 2 O2 P r2
r1
mV
r r1 b1 Const. r2 rb 2 mV
out 2 r1 rb1 Const. in 1 r2 rb 2
1. Crossed-helical gears
2. Hypoid gears 3. Worm and worm gear
Chap.5.2 The fundamental law of gearing
1. The Fundamental Law of Gearing 2. The Involute Tooth Form 3. Pressure Angle 4. Changing Center Distance
Standard value of the pressure angle are 14.50, 200 and 250. 200 is the most commonly used.
Chap.5.2 The fundamental law of gearing(9)
4. Changing Center Distance
3.
A tangency to the involute is then always normal to the string, the length of which is the instantaneous radius of curvature of the involute curve.
4. There is no involute curve within the base circle.
involute
Base circle
Chap.5.2 The fundamental law of gearing(5)
2. The Involute Tooth Form
1. The line(string) is always tangent to the basic circle. 2. The center of curvature of the involute is always at the point of tangency of the string with the cylinder. involute
Pitch point Pitch circle Constant Angular Velocity Ratio
r1
P
r2
Chap.5.2 The fundamental law of gearing(4)
2. The Involute Tooth Form
What is the involute? How does the involute form? The involute curve is the path traced by a point on a line as the line rolls without slipping on the circumference of a circle. It may also be defined as a path traced by the end of a string which is originally wrapped on a circle when the string is unwrapped from the circle. The circle from which the involute is derived is called the base circle.
base circle
Chap.5.2 The fundamental law of gearing(6)
2. The Involute Tooth Form
Involute function
rb rk cos k
k inv k tan k k
involute
base circle
Chap.5.2 The fundamental law of gearing(8)
3. Pressure angle（节圆压力角）
The pressure angle in a gearset is defined as the angle between the axis of transmission or line of action(common normal) and the direction of velocity at the pitch point. Meshing angle(啮合角)
Chap.5.2 The fundamental law of gearing(3) Point P is very important to the velocity ratio, and it is called the pitch point. For a constant velocity ratio, the position of P should remain unchanged. The motion transmission between two gears is equivalent to the motion transmission between two imagined slipless cylinders with radius r1 and r2 or diameter d1 and d2. Two circles whose centers are at O1 and O2, and through pitch point P are termed pitch circles. Pitch circles