Mech 324

Lab 9: Cam Testing

Lab 06 Group 01

Sam McCreery, Abdullah, Alex Larson, Marco Martinez

Due December 5th, 2014

1. Executive Summary

This lab was primarily focused on utilizing a series of polynomial expansion functions and differential equations in which a cam lobe was initially designed virtually. Thereafter, the cam was physically manufactured using a Computer Numerical Controlled machine. This model was built out of an acrylic compound. With the physical model, iterative data points could be successfully measured with the cam running at a specified constant RPM. The cam was tested upon a follower, which tested how well the Rise-Fall and Dwell durations were executed. Additionally, special care was taken in ensuring that the cam did not encounter dirac delta functions or severe discontinuities.

2. Background

Design Considerations

In designing cams, there must be a multitude of mathematical considerations made. When choosing any calculus or differential equation based functions, which may be thought of as piecewise functions in sectors of rise, fall, and dwell, in any given displacement model, one must choose a function which will not "run out" of derivatives. Initializing from displacement in which ds/dt yields velocity, in which dv/dt is acceleration, and da/dt results in jerk. It is then sometimes necessary to select a sinusoidal or cosine type function which derives and integrates between cosine and sine, and therefore does not encounter a "Dirac delta function", which results in something referred to as “infinity spikes” starting at acceleration and passing on to jerk. This theoretically states that the cam lobe is experiencing zero stress and force. This is the opposite of the truth, however, as this would result in a sharply pointed cam lobe, which would experience massive stress concentration at its tip. This tip would resultantly rub off into a blunter normal shaped cam over time, as a result of the incredible stress buildup at this sharp tip. In calculus, these "Infinity spikes" are the design results of vertical lines in the velocity diagram which creates discontinuities.

A dwell is a location where a cam lobe has zero velocity and acceleration. Non-dwell piecewise functions at non-zero velocity and acceleration must be linked continuously to dwells with zero velocity and acceleration according to the fundamentals of cam design.

Cam lobe design relies primarily on solving a number of unknowns with given boundary conditions as inputs. With these, one can specify and custom tailor the polynomial expansion for cam design to the proper final exponential, which is one integer lower than the number of given boundary conditions. The polynomial expansion represents an initial function for displacement, in which derivatives may be taken to derive polynomial expansion equations for velocity, acceleration, and jerk, if needed. The following may be solved by hand, though would be very intensive, and is rather ideally solved computationally by a matrix set up. The angular term “Beta” represents the sum of the rotational angle of the rise and fall phase of the cam lobe, and may be related to the term “theta”, which is dimensionally homogeneous with beta. Theta represents the angle of interest or the angle specified.

Flat Faced Followers vs. Roller Followers

From a design standpoint, roller followers are often preferred for an ease of replacement and a vast availability from a multitude of suppliers, which makes replacement cost effective and relatively easy. Additionally, grooved and tracked cams require the use of roller followers. However, flat-faced followers are largely favored in the automotive industry, where enough mass-production volume allows adequate quantity and market for easy replacement. Additionally, there is a limitation of free space inside the valve cover, and flat-faced followers allow better and more efficient packaging atop the engine head. Lastly, roller followers have the advantage of accepting negative radii of curvature. Roller followers are often utilized in mass production machinery which allows very rapid replacement of worn followers.

Figure 1 Flat Faced Follower

Real Life Example

Figure 2 Flat faced followers are often used in automotive engines, such as this Toyota 5sFE I-4

Figure 2 represents an inline four-cylinder engine cutaway, with a “DOHC” or “Dual Overhead Cam” layout. This allows the removal of a need for rocker arms or pushrods, and allows a direct cam lobe to valve contact via flat faced followers. This is widely used in modern automotive powertrains. Additionally, the oil sump of the engine above holds two balance shafts, which equilibrates the inherent imbalances of inline 4-cylinder engines.

Figure 3 Roller follower

Optimizing and therefore minimizing cam lobe size has a number of advantages. Specifically, there is usually a desire for space efficiency in machinery design, and a minimally optimized cam size can make efficient use of valuable space in a machine. Additionally, machinery such as automotive engines must fit in a certain environment, such as an engine bay. Nowadays, there is a push for maintaining compact dimensions of vehicles while maximizing interior volume while engine bay packaging becomes more and more packed with increasingly advancing specifications.

3. Results

0 5 10 15 20 25 30 35

-2

-1.5

-1

-0.5

0

0.5

1

Acceleration

Acceleration

Figure 4

0 5 10 15 20 25 30 35

-4.00E-02-3.00E-02-2.00E-02-1.00E-020.00E+001.00E-022.00E-023.00E-02

Velocity

Velocity

Figure 5

0 5 10 15 20 25 30 35

-1.50E-03

-1.00E-03

-5.00E-04

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

Displacement

Displacement

Figure 6

4. Appendix

Hello Seth Davies!

Toyota 5sFE engine diagram http://nlp.ilsp.gr/soaplab2-results/93dbfb32-d55f-4619-8454-5f45fe923856/xml/11577.html

Flat Faced Follower diagram http://www.engr.colostate.edu/~dga/mech324/Labs/Lab%207/MECH324%20-%20Lab%207.htm

Stansloski, Mitchell, Laboratory 7, Cam Design, Online, Colorado State University

http://www.engr.colostate.edu/~dga/mech324/Labs/Lab%207/MECH324%20-%20Lab%207.htm