A few years ago, 'awake' posted his algebraic and CAD drawing solutions of the geometry of a three arc cam here: Cam Calculations SOLVED! (But is there an easier way??). He asked if there was a simpler method. Well, yes there is. I've attached the .pdf file below.
The article concentrates on the design of the three arc cam using a new to us concept, Acceleration Ratio, which is an older concept used in cam design in the 1930's and possibly earlier. Originally, cam design was done at the drafting board - this was a defined shape method. During the 30's articles were published giving methods of calculating the motion of the lifter and it was increasing clear that acceleration was the most important parameter. While cams were still designed by their shape - their lift, duration, base circle radius, flank radii, and nose radius - the design was then evaluated by the acceleration of the lifter. Someone developed the new parameter Acceleration Ratio. I have not yet found the source of that concept. It is at the core of the defined acceleration method.
Designing a cam by either the defined shape or defined acceleration ratio begins with the values of three initial parameters: cam lift, cam duration and base circle radius. A fourth initial parameter is necessary to begin the design process and this is where the methods diverge. For the defined shape method, the fourth parameter is nose radius and at this stage is a guess. The design is completed using the equations in p. 5 of the pdf. The acceleration ratio is computed and the suitability of the cam design is determined by a rule of thumb. The nose radius may then be changed to bring the acceleration ratio within the guidelines.
In the defined acceleration ratio method, the acceleration ratio is assigned based upon the desired performance of the engine and the design process is completed using the equations in p. 4. These equations are simpler than those for the defined shape method and there is no need for further validation of the design.
At one time spreadsheets based upon both methods were available on the Model Engine Builder Magazine website and on my personal website. They are no longer available on either site. They may become available on the MEB website at some time. I have submitted an article to MEB with the information necessary for a reader to build his/her own spreadsheet(s) and if perchance this is not published, I will post this information on HMEM.
CarlW
The article concentrates on the design of the three arc cam using a new to us concept, Acceleration Ratio, which is an older concept used in cam design in the 1930's and possibly earlier. Originally, cam design was done at the drafting board - this was a defined shape method. During the 30's articles were published giving methods of calculating the motion of the lifter and it was increasing clear that acceleration was the most important parameter. While cams were still designed by their shape - their lift, duration, base circle radius, flank radii, and nose radius - the design was then evaluated by the acceleration of the lifter. Someone developed the new parameter Acceleration Ratio. I have not yet found the source of that concept. It is at the core of the defined acceleration method.
Designing a cam by either the defined shape or defined acceleration ratio begins with the values of three initial parameters: cam lift, cam duration and base circle radius. A fourth initial parameter is necessary to begin the design process and this is where the methods diverge. For the defined shape method, the fourth parameter is nose radius and at this stage is a guess. The design is completed using the equations in p. 5 of the pdf. The acceleration ratio is computed and the suitability of the cam design is determined by a rule of thumb. The nose radius may then be changed to bring the acceleration ratio within the guidelines.
In the defined acceleration ratio method, the acceleration ratio is assigned based upon the desired performance of the engine and the design process is completed using the equations in p. 4. These equations are simpler than those for the defined shape method and there is no need for further validation of the design.
At one time spreadsheets based upon both methods were available on the Model Engine Builder Magazine website and on my personal website. They are no longer available on either site. They may become available on the MEB website at some time. I have submitted an article to MEB with the information necessary for a reader to build his/her own spreadsheet(s) and if perchance this is not published, I will post this information on HMEM.
CarlW
