圈上海文通大华 Motion Diagram Example ▣ Problem: Consider the following cam design CEP specification > Dwell Low:at zero displacement for 900 >Rise:25mm in 900 >Dwell High:at 25mm for 900 >Fall:25mm in 900 >Cam rotation speed: 2πrad/s Solution:Using polynomial displacement function High Is good? Rise dwell Fall h Low dwell 0 0 圈上泽夫道大学 Example High ▣Naive Cam Design: Rise dwell Fall Low >Connect points using dwell 0 straight line e deg >Constant velocity Infinite acceleration and jerk Not an acceptable camo program 11
11 Motion Diagram Example Problem: Consider the following cam design CEP specification Dwell Low: at zero displacement for 900 Rise: 25mm in 900 Dwell High: at 25mm for 900 Fall: 25mm in 900 Cam rotation speed: 2π rad/s Is good? Solution: Using polynomial displacement function Example Connect points using straight line Constant velocity Infinite acceleration and jerk Not an acceptable cam program Naive Cam Design:
圈上克大峰Fundamental Law of Cam Design Any cam designed for operation at other than very low speeds must be designed with the following constraints The cam function must be continuous through the first and second derivatives of displacement across the entire interval(360 degrees). Corollary: The jerk must be finite across the entire interval(360 degrees). 圈上泽夫道大学 Motion Diagram Example ▣ Problem: Consider the following cam design CEP specification > Dwell Low:at zero displacement for 900 >Rise:25mm in 900 >Dwell High:at 25mm for 900 >Fall:25mm in 900 >Cam rotation speed:2n rad/s Solution:Using simple harmonic motion h is the rise,0 is the camshaft angle,B is the total angle of the rise interval 0 22 45 78 90 12
12 Fundamental Law of Cam Design Any cam designed for operation at other than very low speeds must be designed with the following constraints The cam function must be continuous through the first and second derivatives of displacement across the entire interval (360 degrees). Corollary: The jerk must be finite across the entire interval (360 degrees). Problem: Consider the following cam design CEP specification Dwell Low: at zero displacement for 900 Rise: 25mm in 900 Dwell High: at 25mm for 900 Fall: 25mm in 900 Cam rotation speed: 2π rad/s Solution: Using simple harmonic motion Is good? Motion Diagram Example h is the rise, θ is the camshaft angle, β is the total angle of the rise interval
圈上泽文通大华 Motion Diagram Example svaj Plots for Simple Harmonic Rise -m Psπh sin 45 衣 90 A dwell has the zero velocity and zero acceleration v,a must match the dwell's zero value of any nondwell segments and adjoin them. Acceleration is discontinuous,jerk is infinite(Bad Cam Destgn) 圈上泽夫道大学 Outline ④ Cam Introduction © Cam Motion Diagrams 雪 Cam Synthesis ©Sizing the Cam 13
13 Motion Diagram Example A dwell has the zero velocity and zero acceleration v, a must match the dwell’s zero value of any nondwell segments and adjoin them. Acceleration is discontinuous, jerk is infinite (Bad Cam Design) Outline Cam Introduction Cam Motion Diagrams Cam Synthesis Sizing the Cam