The challenge of developing a conical disc-spring with increased deflection, while retaining a relatively high spring rate, has resulted in a line of disc spring products for use in appliance and other manufacturing and industrial applications.
The springs, made and sold by De-Sta-Co Manufacturing (Troy, MI, U.S.) provide new engineering and packaging solutions and alternatives to fasteners, snap-on components, structural, and hydraulic assemblies, vibration dampening, and "break-away" constructions.
Developed by Schwab-Koplin Associates (Port St. Lucie, FL, U.S.), CloverSpring™ products are engineered to provide four distinctive functions:
The CloverDome™: a disc-spring with a 15-degree cone angle for applications requiring substantial deflection.
The CloverGripDome™: a conical disc spring, which will grip and fit cylindrical or rectangular components.
The CloverDisc™: a bistable, snap-acting positioning device, friction-less, linear-bearing, or radial-spring support.
The CloverSnapDome™: a true overcenter snap-disc with extended deflection past its "flat" plane.
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 the disc spring's 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). This relationship defines three distinctive conditions. For standard dome and grip-dome applications, P2 is located on or inside the diameter determined by the radius at point P1. For disc spring applications involving side-stressing and resulting snap-action, point P2 may be moved much closer to the gravity center of the disc, with the inner diameter of the disc correspondingly reduced. The third condition, wherein P2 is located beyond radial point P1, results in higher stresses and is usually avoided.
The spring rate (K) and deflection (h) are determined by the geometry, cone angle (ß), material thickness (t), and type of material used.
To demonstrate the different spring rates between the CloverDome disc spring, Belleville, Curved, Wave, and Finger springs, a simple equation referred to as "Coefficient of Compliance" (CC) is applied.
The coefficient is calculated as follows:
Coefficient of Compliance CC=
t3 K x D2
Where: t = material thickness in thousands of an inch (i.e., .015 in = 15); K = spring rate (load / deflection in inches); and D = Outer diameter of the spring (footprint).
Example: Belleville Washer pt.# AM186204 K = 33 lb / 0.018 in = 1833 lb/in D = 0.709 in t = 16
4096 1833 x 0.502
CloverDome pt.# CD-0015-01 K = 20.22 lb / 0.041 = 493.170 lb/in D = 0.714 in t = 15
3375 491.17 x 0.5097
For applications where the requirements for diameter (D), load, and needed deflection are given, the equation allows to solve for t3 = CC x K x D3, providing a close approximation of what the material thickness should be for spring-grade materials with a relatively high tensile strength (see Table 1).
Example: Belleville-type Disc Spring: Outer diameter (O.D.) 0.709 in, K=33 lb/0.018 in = 1833 The applicable mean Coefficient of Compliance (CC) as given in Table 1 is 4.180. t3 = 4.180 x 1833 x 0.5026 = 3851, where t = 15.67 or 0.01567-in thick
Load Vs. Deflection
Figure 2 illustrates an ascending curve all the way to 100-percent compression. The shape and characteristic (C) of the curve is dependent on the relationship of height divided by the material thickness or C = (h/t), where h is the overall height (O.H.) of the dome minus its material thickness (t). The ratio for the curve (C) is, therefore, 0.033 in/0.011 in = 3. While non-linear, the curve is sufficiently flat to provide a near constant spring rate between 25 percent and 75 percent of compression.
Figure 3 illustrates a curve for a larger dome-spring with an h/t value equal to 0.080 in/0.020 in = 4. Here, the curve becomes positively non-linear after 50 percent of compression, and the spring rate varies accordingly. Obviously, the lower the ratio, the more linear the curve. For applications involving high loads such as for nuts and bolts, the h/t ratio may need to be less than 2, for "snap" or "grip" domes as high as 8.
While non-linear, the curve in figure 3 is sufficiently flat to provide a near constant spring rate between 25 percent and 75 percent of compression. Taking the load value and amount of deflection between 25 percent and 75 percent of compression, the result is L= 8 lb and displacement is 0.015 in. The spring rate is, therefore, 8 x 1000: 0.015 = 533 lb/in for a good portion of the curve.
Self-Calibrating Bolt Tension
Figure 4 and figure 5 illustrate how the disc spring is used to provide accurate tension control for the installation of bolts. A narrow, conically shaped calibration ring (circle) is bonded or fused to the underside of the dome (see figure 4). The cross section of the calibrating ring is dimensioned to restrict dome compression to 75 percent of h (see figure 5).
h = O.H. (0.070 in) - t (0.025 in) = 0.045 in, hence 75 percent = 0.033 in, thus the calibrating ring would be 0.012 in to arrest compression at 75 percent of h. Assuming the load to be 100 lb at h, then the calibrated load would be precisely 75 lb. As the nut is turned on the bolt, torque is relatively light but abruptly becomes high when bottoming out on the calibration ring.
Force F in figure 1 is dependent on the amount of mechanical interference between the disc's aperture and the diameter of the member pushing through it. The ability of each disc segment (S) to substantially deflect outwards (elasticity) allows to "Grip" on diameters 5-6 percent larger than the disc's aperture, making it suitable for use on plastics or even wooden dowels where tolerances on diameters can vary appreciably.
The "grip-force" of the disc increases as the load increases and prevents any slippage, providing the material hardness on which the disc is acting, which is slightly below the hardness of the disc itself. For example, a typical Stimpson rivet and GripDome assembly (see figure 7) does not require any riveting tool and allows for expansion, proportional to the deflection of the disc. The ability to expand can prevent rivet rupture due to fatigue. For square-grip assemblies, the disc of figure 1 is changed to a square aperture as illustrated in figure 6.
Stacking allows the design for high loads in a reduced space, where coil springs are not feasible. Combinations of series and parallel arrangements can be designed to accommodate a wide range of loads or deflections to provide customized characteristics for specific applications. In stacking, the friction between springs and the friction between springs and the guide rod must be considered, especially in stacks with parallel units, as the friction causes a damping effect which may result in an increase during loading and decrease during unloading in the order of 2-3 percent for each pair of parallel springs.
Figure 8 illustrates a typical parallel stack of springs. The total deflection of a parallel stack has a deflection equal to the deflection of a single spring. The total load of the stack equals the load of a single disc multiplied by the number of springs in the stack. It should be remembered that friction will affect the calculation, depending on how many discs are stacked.
figure 9 illustrates a series stack that replaces coil springs in applications where space is a premium and fail-safe operation is a must and the possible fracture of a coil spring cannot be tolerated. While a disc may fracture, the stack will be reduced by just one failing spring at a time. The chance of two failing simultaneously is remote. The total deflection of a series stack is equal to the deflection of a single spring multiplied by the number of springs in the stack. The total load is equal to the load of a single spring.
The disc spring has the following applications: fasteners (specifically panel fasteners), latching devices, oven /refrigerator door latch assemblies, clutch assemblies, and "break-away" partitions; vibration damping and shock protection, spring mounts for compressors and motors, fan housings; and grip-dome assemblies, eliminating screws, rivets, E-rings, and other fastening means.