JS
the graphics with your opening post are something of a puzzle. At the foot of the first graphic, the ramp jerk is given as 'constant' whereas it is far from constant. The ramp velocity is nearer to constant, which is to be expected.
This may require a further graphic from JA that magnifies the ramp to better illustrate the 'constant' jerk.
Unless Jim has replaced some pictures, I don't see jerk at (inlet) lobe open/close ramp as requested to be constant - the boxes aren't ticked. Yes, the lifter velocity @ rotation angles defining the ramp (degree -> "A" parameter) is constant for a while, but the important parameter is the acceleration curve (the black one). Jim made a typo in his last posting - the black line is the follower's acceleration at the lobe.
Jim: At
www.tildentechnologies.com the following statement is made, quote:
We agree that the importance of jerk is grossly overstated.
Valve train dynamics theory shows that acceleration is the highest derivative that needs to be continuous, i.e. jerk remains finite, but can have jump discontinuities. Cubic splines are completely adequate. Most designers are using profiles that are much smoother than necessary. For example,
Norton's favorite spline uses quintic functions which have continuous snap (derivative of jerk). The use of overly smooth functions causes a slower opening cam or requires higher acceleration rates to compensate.
We have seen only one source (
Hollingsworth and Hodges) that have actually recommended limiting values. They recommend that jerk not exceed 0.0002 to 0.0004 in/deg3 for pushrod engines, whereas direct attack valve trains (OHC, flathead) can use values of 0.0004 to 0.0008 in/deg3. These values are quite large. When used with cubic splines, the profiles are very similar to those with infinite jerk <...>. We have profiled many OHV "performance" cams and typically find maximum jerk of 0.00003 to 0.00004, which is 5 to 10 times smaller. Overly smooth cams are poor performers.
The best way to establish acceptable values of jerk is to perform a
valve train dynamics analysis for the cam in question. (End of quote.)
The cited references are
Norton, R.L.:
Cam Design and Manufacturing Handbook, Industrial Press, 2002
Hollingsworth, P. and Hodges, R.A.: "The History and Mathematical Development of Cam Profile Design in Rover", paper SAE 914172, (1991).
Jim, in the analysis of the PW3 cam, maximum jerk (JMAX) at opening ramp was found to be 3.67E-4 in/deg^-3, very close to the recommended maximum, wherease at closing ramp JMAX was found to be only 1.81E-4. However, these figures appear to be unimportant. According to the tildentechnology site, the objective should be to obtain continuous acceleration at opening and closing ramps, and forget about jerk at the outset. The acceleration curves above are not continuous, neither at the opening ramp nor at the closing ramp. It seems to me there is still rom for improvements. Would you like to comment?
-Knut