上海交通大学：《Design and Manufacturing》课程教学资源（讲义）Lecture10 gears

图 上泽充大￥ ta2b口 SHANCHAI HAD TONG UNVERSIY LECTURE 10-I Gears-Introduction 齿轮机构设计 上泽克夏大粤 outline Where can we find gears? ©Common Types of Gears Fundamental Law of Gearing Involute profiles Gear tooth nomenclature How to manufacture a gear? Interference and undercutting ME357 Design Manufacturing ll

1 Gears-Introduction 齿轮机构设计 LECTURE 10-I ME357 Design & Manufacturing II outline Where can we find gears? Common Types of Gears Fundamental Law of Gearing Involute profiles Gear tooth nomenclature How to manufacture a gear? Interference and undercutting

国 上泽充大￥ Where can we find gears? SHANCAAI IAD TONG UNVERSIE 圈上泽大学 Where can we find gears? Gear Selector Fork A manual transmission is essentially a set of compound FROM ENGINE gear trains in which the driver selects the gear ratio

2 Where can we find gears? A manual transmission is essentially a set of compound gear trains in which the driver selects the gear ratio. Where can we find gears?

图 上泽充大￥ ACA4AlLs0IC0七sn Why Use Gears? 1.Reduce speed 2.Increase torque 3.Move power from one point to another 4.Change direction of power 5.Split power Generally this functionality is accomplished by many gears mounted in a gear box! 图 上泽文通大学 Torquet Power Curves 公 nnl Speed

3 1. Reduce speed 2. Increase torque 3. Move power from one point to another 4. Change direction of power 5. Split power Generally this functionality is accomplished by many gears mounted in a gear box! Why Use Gears? Speed Torque nnl Tb Power Curves

国 上泽充大￥ Common Types of Gears SHANCAAI IAD TONG UNVERSIY 图 上泽克夏大粤 Common Types of Gears

4 Common Types of Gears Common Types of Gears

国 上泽充大￥ Common Types of Gears SHANGHAI JAD TONG UNYERSIE Type Shaft Orientation Advantages Disadvantages Spur Parallel,Non-Intersecting High efficiency Noisy Helical Parallel,Non-Intersecting Lower Noise More expensive Non-Parallel,Non- Intersecting Bevel Any angle,intersecting or Shaft Greater Thrust and non-intersecting Orientation Loads Hypoid change Worm Perpendicular,non- High Gear Ratio, Low Efficiency intersecting not back drivable 图 上泽文大学 (o)External set (b)Internal set

5 Common Types of Gears Type Shaft Orientation Advantages Disadvantages Spur Parallel, Non-Intersecting High efficiency Noisy Helical  Parallel, Non-Intersecting  Non-Parallel, Non￾Intersecting Lower Noise More expensive Bevel and Hypoid Any angle, intersecting or non-intersecting Shaft Orientation change Greater Thrust Loads Worm Perpendicular, non￾intersecting High Gear Ratio, not back drivable Low Efficiency

图 上泽充大￥ Fundamental Law of Gearing AA4AIL0ICo七Ys Why Involute? 票郵國民華中 REPUBLIC OF CHINA 350卓水博牛 图 上泽文通大学 Fundamental Law of Gearing Assuming roll without slip at the pitch point,what is the relationship between the angular velocities of the cylinders? From previous knowledge: 02=-1 033 From Instant Centers: Instant Center(2,3)must be located at point of contact. S0, 02 (1,3-2,3 03 1,2-2,3

6 Fundamental Law of Gearing Why Involute? Fundamental Law of Gearing Assuming roll without slip at the pitch point, what is the relationship between the angular velocities of the cylinders? From previous knowledge: 2 3 3 2 r r     From Instant Centers: Instant Center (2,3) must be located at point of contact. So,     2 3 3 2 1,2 2,3 1,3 2,3 r r      

上浒充大学 Fundamental Law of Gearing SHANCHAI HAD TONG UNVERSIY ©For a pair of gears to maintain a constant angular velocity ratio, VK2 n VK2K1 C K Pitch circle the common normal of 节圆 both contacting Pitch circle surfaces must pass 2 节圆 through the fixed "pitch 02 point". The angular velocity ratio between 2 meshing gears remains constant 01 throughout the mesh 上泽充夏大粤 Fundamental Law of Gearing Angular velocity ratio(my) ©Torque ratio(mt)is n mechanical advantage(mA) VK2K1 Pitch circle 节圆 Pitch circle 节圆 y ot=± =士 din in Iout mr out= Tin out din

7 1 2 O1 O2 C2 1 2 C1 n n P vK1 vK2 v K K2K1 Pitch circle 节圆 Pitch circle 节圆 Fundamental Law of Gearing For a pair of gears to maintain a constant angular velocity ratio, the common normal of both contacting surfaces must pass through the fixed “pitch point”. The angular velocity ratio between 2 meshing gears remains constant throughout the mesh 1 2 O1 O2 C2 1 2 C1 n n P vK1 vK2 v K K2K1 Pitch circle 节圆 Pitch circle 节圆 Fundamental Law of Gearing Angular velocity ratio (mV) Torque ratio (mT) is mechanical advantage (mA) in out in out out in in out T out in out in in out V d d r r ω ω T m d d r r ω ω m            T

上浒充大学 Fundamental Law of Gearing SHANCHAI HAD TONG UNEVERSI Involute curve "String” There are 2 common tangent to profiles that give base circle constant angular and normal velocity ratios to inyolute ·Cycloidal ·Involute The involute profile can maintain the same velocity ratio even if there is some misalignment in the distance between the shafts. ·We can equate the angular velocity ratio to Cpe-pov) the gear ratio! Base circle or evolute ® 上泽充夏大粤 Fundamental Law of Gearing Meshing Action 2000-Q0UG WRIGHf,UWA

8 There are 2 common profiles that give constant angular velocity ratios • Cycloidal • Involute The involute profile can maintain the same velocity ratio even if there is some misalignment in the distance between the shafts. • We can equate the angular velocity ratio to the gear ratio! Fundamental Law of Gearing Meshing Action Fundamental Law of Gearing

合的率单：互相啮合传动的一对齿廓在任一位置时的传动比，等于其 连心线O1O2被固定的节点所分成的两线段之反比。 The common normal of the tooth profiles,at all contact points within the mesh,must always pass through a fixed point on the line of centers,called the pitch point pressure angle rotated in direction of driven gear pitch circles line of action pitch point (common normal) leaving contact (length of action Z angle of recess) angle of approach driving (cw) driven (cew) Care of action beginning contact center distance C addendum circles 上泽克夏大粤 8 Pressure angle (angle between force and motion Pressure angle rotated in direction of driven gear Velocity at pitch point Axis of transmission or line of action (common normal)is tangent to Addendum of pinionp both base circles Pitch radius of pinion p 09 Common tangent- gear Pitch radius of gear g Pitch point Driven(CCW) Driving (CW) Base circle of pinion Base circle of gear- Pitch circles Addendum of gear ag

9 The common normal of the tooth profiles, at all contact points within the mesh, must always pass through a fixed point on the line of centers, called the pitch point Fundamental Law of Gearing 齿廓啮合的基本定律：互相啮合传动的一对齿廓在任一位置时的传动比，等于其 连心线O1O2被固定的节点所分成的两线段之反比。 Pressure angle (): angle between force and motion

上泽充大￥ Involute profiles HANCAAI HAD TONG UNVEESIY How involute profile constructed? What are its geometric properties? Advantages using involute profiles ME357 Design Manufacturing ll 上泽充夏大粤 Involute profiles How involute profile constructed? Involute VK 逝开线 PressureOlk K Angle rx向径 String 压力角 String 发生线 Inyolute angle Base circle 展角 Base circle Rolling without slipping 基圆

10 ME357 Design & Manufacturing II Involute profiles How involute profile constructed? What are its geometric properties? Advantages using involute profiles Involute profiles How involute profile constructed? Involute 渐开线 String 发生线 Base circle 基圆 F 向径 Pressure Angle 压力角 K K K K vK rK rb Involute angle Base circle 展角 String Rolling without slipping