Dwell-Rise-Fall-Dwell and Dwell-Fall-Rise-Dwell cam laws. Sections 1 to 8: segments having equal rise and fall periods.
Abstract:ESDU 06002 provides guidance on the selection of cam laws suitable for Dwell-Rise-Fall-Dwell (DRFD) and Dwell-Fall-Rise-Dwell (DFRD) output motions having equal rise and fall periods, including ones having an intermediate constant-velocity component in both the rise and fall actions. The Item extends the scope of Item 82006 that deals with the selection of DRD cam laws. This Item can be used to define DRFD or DFRD motions formed from either a single cam law or from blended components of suitable cam law. The displacement curve for the follower rise is a mirror-image of that for the fall. The procedure used for blending cam profiles ensures continuity of follower displacement, velocity and acceleration with infinte jerk throughout the motion. The approach of deriving a DRFD motion from a DRD rise succeeded immediately by a DFD fall is inferior because the follower acceleration of DRD motions must be zero at both limits of travel to avoid infinite jerk. Hence these motions would have unnecessarily high accelerations and be liable to induce vibration. Instead, the DRFD and DFRD cam laws given in this Item make the output acceleration an absolute maximum at the cam angle where the follower displacement equals the lift, co-incident with the reversal of velocity. The cam laws to be found in ESDU 06002 generate the equations of motion for the rise or fall segment of a DRFD motion as continuous functions and include: Double Harmonic Motion, Triple Harmonic Motion, 2-4-5 Polynomial, 3-4-5-6 Polynomial and 3-5-6-7-8 Polynomial motions. Additionally, but suitable only for Components controlling the reversal of velocity at the maximum follower displacement of blended motion, the Constant-Cosine-Constant Acceleration Motion is included. Output motions having asymmetric rise and fall periods are analysed in companion ESDU 06003 and examples are provided in ESDU 06004. The use of an associated computer program, described in ESDU 06005 (to be issued), is recommended for all calculations including sensitivity analyses to optimise the motion.
|Data Item ESDU 06002|