hap 5.2 The fundamental law of gearing(2) Ow ON OP ON, OO,P T ON OP K The fundamental law of gearing The angular velocity ratio between the gears of a gearset remains constant throughout the mesh O, O,P
The fundamental law of gearing: The angular velocity ratio between the gears of a gearset remains constant throughout the mesh. O P O P O N O N m in out V 1 2 1 1 2 2 1 2 = = = = O P O P O N O N T T m out i n i n out T 2 1 2 2 1 1 2 1 = = = = = Chap.5.2 The fundamental law of gearing(2) r1 r2 . 1 2 1 1 2 2 1 2 const O P O P O N O N m i n out V = = = = = 1 1 1 2 2 2 O N = O N
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 r, and r or diameter d, and d Two circles whose centers are at 0, and o and through pitch point p are termed pitch circles Pitch circles Pitch point Pitch circle Constant Angular Velocity Ratio
▪ 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. Chap.5.2 The fundamental law of gearing(3) Pitch circles r1 r2 Pitch point Pitch circle Constant Angular Velocity Ratio P
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 发生线 as a path traced by the end of a 渐开线 string which is originally involute B wrapped on a circle when the 6 string is unwrapped from the circle. The circle from which the involute is derived is called Base circle the base circle
2. The Involute Tooth 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. Chap.5.2 The fundamental law of gearing(4) What is the involute? How does the involute form? involute Base circle
Chap, 5.2 The fundamental law of gearing(5) 2. The involute tooth form 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 发生线 the cylinder. 3. A tangency to the involute is 渐开线 then always normal to the involute string, the length of which is the instantaneous radius of curvature of the involute curve KB= AB base circle 4. There is no involute curve within the base circle
2. The Involute Tooth Form involute base circle 1. The line(string) is always tangent to the basic circle. 4. There is no involute curve within the base circle. Chap.5.2 The fundamental law of gearing(5) 2. The center of curvature of the involute is always at the point of tangency of the string with the cylinder. 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
hap. 5.2 The fundamental law of gearing(6) 2. The involute tooth form Involute function 发生线 渐开线 cos a k involute inVa k tan a a B k k 64 base circle
2. The Involute Tooth Form involute base circle Involute function Chap.5.2 The fundamental law of gearing(6) k k k k k b k inv r r = = − = tan cos