Figure 1 illustrates the basic geometry of the spring, essentially a continuous clover-shaped ribbon of equal width (W) and formed into three equally spaced disc segments (S) which can deflect radially when side-stressed (F) at the aperture or vertically, when formed into a dome. Characteristic of Clover®Dome geometry is the relationship of radial point P1 at the inner edge of the disc’s outer segments (S) to radial point P2 at the inner edge of cutouts (A). For standard dome, P2 is located on or inside the diameter determined by the radius at point P1.

The unique spring rate of the Clover®Dome bridges the large gap between very stiff Belleville disc springs and resilient coil springs. To demonstrate the different spring rates between Clover®Dome, Belleville, Curved, Wave and Finger springs, a simple equation referred to as “Coefficient of Compliance” (CC) is shown in Table 1. The Coefficient of Compliance (CC) can be determined by experimental means or if the material thickness has been determined.

The equation below shows how to calculate the CC when the material thickness has previously been determined. Generally the CC is approximated using data derived experimentally. The CC is a relative method for comparing springs. The common disc spring is stiffer and would have a very low CC while highly compliant coil springs will have a higher CC. The coefficient is calculated as follows:

The angle of the conical form will determine the amount of total deflection the Clover®Dome will yield. This cone angle is dependent upon the ratio of the OD to the ID and the thickness of the material. Testing has shown that as material thick-ness increases the cone angle decreases. OD to ID ratios of 2.0 will also yield a lower cone angle when compared to OD to ID ratios of 2.5 and higher. The actual cone angle is difficult to predict and these calculations should only be used as ap-proximations. The following figure is a guide to approximating the height of the formed part. OD to ID ratios approximately 2.0 with material thickness greater than .030” should use an angle of approximately 13º. While OD to ID ratios of 2.5 and greater with material thickness less than .030” should use angles of approximately 14º.

The desired spring rate is used for calculating the material thickness. To determine the spring rate we must know what the desired loads are for the Clover®Dome as well as the OD and ID. First we must determine the amount of deflection a particular OD and ID combination will generate. This can be determined from the previous section on calculating deflection. Once the deflection is calculated we can then determine the spring rate by dividing the desired load by the calculated deflection. This will approximate the spring rate as if it were linear. We know from figure 3 that the spring characteristics are very often non-linear. This approximation is necessary to calculate the properties of the Clover®Dome. This spring rate is theoretical and should only be used to approximate designs.

The shape of the force versus deflection curves (FD curves) can be approximated using figure 3 below. The ratio h to t is used to determine the shape of the particular curve. Ratios of 3.5 and higher yield a regressive curve while ratios of .5 yield a progressive curve.

Series stacking of Clover®Domes is utilized when the deflection of a single spring is not sufficient. Equation 3 illustrates the effects of placing Clover®Domes in series stacks. The force for the stack remains constant while the number of parts in the stack multiplies the deflection.

Parallel stacks of Clover®Domes can be used to achieve forces that can not be reached using single springs. Equation 4 illustrates the effects of adding springs in parallel. The force of each spring added to the stack is added to the total load while the total deflection of the stack remains constant.

 

The thickness of Clover®Domes is calculated using the spring rate, approximated CC and the OD. The following equation shows how to determine the material thickness required.

There are limitations to material thickness. Pre-tempered material, that is required for the Clover®Dome, is available in thickness’ up to .060” (1.52mm). Generating parts thicker than this is generally avoided. At this time designing parts over .050” (1.27 mm) should be avoided due to manufacturing limitations and material availability. Figure 6 (below) is an example of the variation in FD curves for parts with the same OD/ID and varying thicknesses.

The trend of force / deflection curve for a thick “t” disc tends to be linear. For a thin “t” disc the curve is linear for the first portion of the curve but tends to flatten out and regress at its apex.

Fiction is generated when Clover®Domes are in contact with any other surface. The friction is roughly equivalent to 3% of the total load. When stacking Clover®Domes friction of each part stacked in parallel is taken into account. The friction generated by series stacks is much lower than parallel stacks. Hysteresis is the difference in force from loading to unloading. Hysteresis results in an increase in force during loading and loss of force during unloading. Figure 7 illustrates hysteresis, which can be equivalent to 3% of the maximum force. The effects can be reduced using lubrication on the friction surfaces.

In considering an application it is important to ask the following questions:

    * Size limitations on OD & ID
    * Space limitations, max height (O.H.)
    * Pre-load (load at initial deflection)
    * Final load (load at full deflection)
    * Initial deflection (measured from O.H. )
    * Distance from initial to final deflection
    * Static or dynamic application
    * No. of cycles if dynamic
    * Environment (Chemical, temperature)

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