The Shape Factor accounts for urethane blocks or cylinders bulging at their sides when under a compressive load. Increasing the area that is free to bulge decreases vertical displacement, or for the same displacement requires greater force.
The concept of Shape Factor is numerically defined as the area of one loaded surface divided by the total area of the unloaded surfaces that are free to bulge.
These equations are limited to:
- Pieces which have parallel loading faces.
- Pieces whose thickness is not more than twice the smallest lateral dimension.
Modulus of Elasticity
The Modulus of Elasticity, E, is defined as the force per unit area (stress) divided by the percentage of the change in height (strain); or:
For many of the common engineering materials, such as steels, E is a specific value that remains consistent within the elastic range of the material. With urethane, however, the E value changes with each specific compound. (See curve on page 9).
The test data for those curves was determined over a two year period. Testing was conducted under controlled conditions, and the data reflects the variation of E vs. Shape Factor for three K•Prene® grades with dry and lubricated surfaces.
The curves represented a statistical average of the test results, and are offered as a guide to help the engineer predict his forces, size and grade of urethane required, or percent deflection.
Other Engineering Considerations
Heat build -up, due to internal friction (hysteresis effect), is the most common cause of premature failure of urethane. The amount of heat generated is a direct function of degree of deflection. Thus, in selecting K•Prene® materials minimize the percentage of deflection for longer life.
K•Prene® urethane can withstand temperatures up to 250° F., although it may soften before that point and lose some load-bearing capacity. However, upon cooling, it will return to its original physical characteristics. The urethane will also withstand temperatures down to -80° F.
Lubricated or dry condition of load-bearing area is another factor that affects the stress-strain relationship. For urethane compressed between parallel plates, there is a tendency for the surface to spread laterally. While a clean, dry loaded surface offers some resistance to this lateral movement, a lubricated surface will offer essentially none. If extremely high pressures are required, lateral movement can be prevented by bonding the urethane to metal with double-faced tape or K-20 adhesive. Cut resistance of K•Prene® urethane is very high. However, placing it near a sharp metal edge or permitting it to bulge over a sharp edge should be avoided. With forces involved, the urethane may fail due to cutting or fracturing.
How to use the Curves
In solving problems, the engineer should first determine the Shape Factor using the formula previously introduced, and assume a particular size of urethane pressure pad.
Having once determined the Shape Factor, the engineer can then select the appropriate grade of K•Prene® urethane, and come horizontally across on the chart to find E. With the Modulus of Elasticity known, one can then apply the basic formula of E to solve for either force or percentage of deflection.
*For deflections more than 20%, E must be modified by the multiplier derived from the small curve. For deflections equal to or smaller than 20%, this multiplier is one.
Note: Solutions for “force” or “percentage of deflection” using these equations should be accurate to within ± 10% of actual values. Be sure to allow for this margin of error in problem solving.
Example problems of how to calculate the Modulus of Elasticity
We have created three sample problems in regards to deflection on different shapes of urethane materials that we commonly sell. This should be of some help and useful when trying to calculate the deflection for metalworking with urethane. We encourage you to try the formulas for your particular application.