The solid height of conical compression springs are defined as the length of the spring when under sufficient load to bring all coils into contact with the adjacent coils and additional load causes not further deflection. Solid height should be specified by the user as a maximum, with the actual number of coils in the compression spring design to be determined by the spring manufacturer.
As square or rectangular wire is coiled, the wire cross-section deforms slightly into a keystone or trapezoidal shape, which increased the solid height considerably. The dimensional change is a function of the spring index and the thickness of the material.
Conical Compression Pitch
A uniform pitch in a conical spring is far easier to make then a variable pitch. During testing, if no coil bottoms, a straight-line force curve versus deflection occurs similar to that of a compression spring. When the largest active coil bottoms, an upward slope of the force curve occurs. The maximum force occurs when all coils have bottomed. The calculation to determin the force at the solid position can be easily performed by using the regulary formula for compression springs and using the mean diameter of the smallest active coil only; N equals 1.
Grinding the end coils of conical springs is done in a different manner. Some specifications call for grinding only the small end coil. Others require grinding on both ends. Grinding in either case is difficult and expensive. Grinding small, medium and large quantities may be done as explained for regular compression springs except that when using double wheel grinders it is necessary to make special turntables with holes shaped like the conical springs. Making a large amount of tapered holes to hold the springs is not easily done and may require makeing special coned reamers to cut the holes. For this reason, hardwood platens, in palce of steel are often used.
1. Extra time for all manufacturing operations should be considered when estimating the costs of making coned conical compression springs or for any springs requiring special material, square or rectangular wire, or special testing.
2. Variable pitches in a conical spring are occasionally specified so that all active coils bottom simultaneously, but this is seldom achieved.
3. Grinding is especially difficult and time-consuming. Special fixtures may be required. The cost of grinding discs should be included for large quantities of springs.
4. Tangling of highly pitched springs made from small diameters of wire up to 1/16 inch (1.5 mm) having rather large base diameters often occurs and may require special handling during secondary operations and for packaging.
Conical Compression Spring Design
There are several methods of analyzing the complex stresses in conical compression springs depending upon the type of pitch, angular relationship of the coils, constant slope, currving contours, and other factors. Analyzing all of the variables and solving for stresses, deflections, and forces can be a mathematician's delight and a playground for higher mathematics, but spring manufacturers can ill afford to devote valuable time to such matters and many use a simplified solution that quickly and easily provides a suitable conical spring design, including wire size and number of active coils, as follows:
First, calculate the average outside diameter. This can be done in several ways depending upon the diameters specified. The easiest way is to add the outside diameter of the top end to the outside diameter of the base and divide by 2. Adding the OD of the base to the ID at the top of dividing by 2 will provide the average D. Second, calculate the approximate force at the solid height. Third, locate the average OD and find a force, deflection per coil and a wire size and proceed with calculations in the same manner as for regular coned compression springs. This method should be used with care if large deflections cause coils to bottom early.
MA more exact method is first to determine the wire size and number of coils by the approximate method and then analyze the force, deflection, and stress of each individual coil and make adjustments to the design to meet the requirements. This may require a large number of individual calculations for each spring, but should be done for large, important springs and where a long fatigue life may be needed.
Graphic layout of Specificiations for Conical Compression Springs