上海文通大 RDFD Cam Design SHANGHAI JIAO TONG UNIVERSITY Motion is between two dwells s.What should we use for our rise otio凯 and fall functions? mm or in 。What qualities High should we look for? dwell 1 Low dwell Rise Fall 0 90 180 270 360 Cam angle日deg 0 0.25 0.50 0.75 1.0 Time t sec ME357 Design Manufacturing ll
RDFD Cam Design Motion is between two dwells • What should we use for our rise and fall functions? • What qualities should we look for? ME357 Design & Manufacturing II
上游充通大学 RDFD Cam,Naive Cam Design SHANGHAI JIAO TONG UNIVERSITY Connect points using High Rise dwell Fall straight line Low dwell Constant velocity 0 e deg Infinite acceleration 0 e deg and jerk ⑧Not an acceptable cam program e deg ● e deg 90 180 270 360
RDFD Cam, Naïve Cam Design Connect points using Connect points using straight line Constant velocity /Infinite acceleration and jerk and jerk /Not an acce ptable cam program ME357 Design & Manufacturing II
上游充通大学 Fundamental Law of Cam Design SHANGHAI JLAO TONG UNIVERSITY 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). ME357 Design Manufacturing ll
Fundamental Law of Cam Design Any cam designed for operation at other than very low speeds must be designed with the following constraints following constraints The cam function must be continuous through the first and second derivatives of displacement across the entire interval (360 degrees). across the entire interval (360 degrees). Corollary: The jerk must be finite across the entire interval (360 degrees) (360 degrees). ME357 Design & Manufacturing II
上潘文通大学 RDFD Cam Sophomore Design SHANGHAI JIAO TONG UNIVERSITY Simple Harmonic Motion Sin function has continuous derivatives w ds hπ π0 V= sin do 2B B dv a= cos do 2B2 B da π0 j= do 2B3 B ⑧Acceleration is discontinuous,jerk is infinite(Bad Cam Design) cam angle 0 ME357 Design Manufacturing Il
RDFD Cam Sophomore Design Simple Harmonic Motion Simple Harmonic Motion Sin function has continuous derivatives h continuous derivatives 1 cos 2 h s - πθ β ⎡ ⎤ ⎛ ⎞ = ⎢ ⎥ ⎜ ⎟ 2 ⎣ ⎦ ⎝ ⎠ sin 2 ds h v d θ β π πθ β β ⎣ ⎦ ⎝ ⎠ ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠ 2 2 2 cos 2 d θ dv h a d β β π πθ θβ β ⎜ ⎟ ⎝ ⎠ ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠ ∞ ∞ 2 3 3 2 sin d da h j θβ β π πθ ⎜ ⎟ ⎝ ⎠ − ⎛ ⎞ = = ⎜ ⎟ ⎝ ⎠ ∞ ∞ /Acceleration is 3 2 j dθ β β ⎜ ⎟ ⎝ ⎠ discontinuous, jerk is infinite (Bad Cam Design) ME357 Design & Manufacturing II (Bad Cam Design)
上海文通大粤 RDFD Cam,Cycloidal SHANGHAI JIAO TONG UNIVERSITY h Need to start with acceleration and integrate 2π0 a=Csin B 2π0 V= CBcos 2π since v=0 at 0-B, a k二 CB 2π V= s= Bo-c 2π0 sin 0 B ME3 cam angleθ
RDFD Cam, Cycloidal h Need to start with acceleration and integrate and integrate 2 a Csin⎛ ⎞ πθ = ⎜ ⎟ sin 2 a C C k β β πθ ⎜ ⎟ ⎝ ⎠ ⎛ ⎞ + ⎜ ⎟ since v =0 at θ=β 1 cos 2 v k β π β = − + ⎜ ⎟ ⎝ ⎠ since v 0 at θ β, 1 2 C k β π = 2 2 1 cos 2 C v π β πθ β ⎡ ⎤ ⎛ ⎞ = ⎢ ⎥ − ⎜ ⎟ ⎣ ⎦ ⎝ ⎠ 2 2 2 i C C k π β β β πθ θ ⎢ ⎥ ⎜ ⎟ ⎣ ⎦ ⎝ ⎠ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ + ⎜ ⎟ ME357 Design & Manufacturing II 2 s i n 2 2 s C k β β θ π πβ ⎛ ⎞ = − ⎜ ⎟ + ⎜ ⎟ ⎝ ⎠ ⎝ ⎠