Black Magic and the Conical Spring Design
Spring Design Tips and Tricks
By Gary Van Buren
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wenty-five years ago, I sat in a spring design class in Bristol, Connecticut taught by Loren Godfrey. There were probably 15 young, eager engineers ready to soak up all the knowledge we could from Mr. Godfrey. In front of us was a bulky keyboard and, as I remember, a 13-inch, four color CRT monitor. For you younger readers, CRT means Cathode Ray Tube. The keyboard and monitor took up a lot of desk space and the onscreen program contained a lot of basic black and white numbers. This was the original DOS (disk operating system) version of the SMI software which was called Spring Designer. Now the SMI software is called Advanced Spring Design (ASD). The original software, commonly called SD2 and its successor SD2.1, helped design three types of springs: compression, extension and torsion. The compression mode allowed you to toggle between straight compression and conical compression. We spent two days learning from one of the best minds in our industry. One clear memory from that time occurred during the conical spring portion of instruction on the final day. Mr. Godfrey said that conical springs were kind of a “black magic.” We could get an output from the software that gave us IDs, ODs, coils, free length and a spring rate. The black magic happened at the coiling machine. The person running the coiler would play with coil diameters and pitches to make our mathematics into a working spring. Back in the old DOS days, the software was not capable of doing the complicated work that today’s ASD7 software can handle. Today’s software puts a tremendous amount of power in our
When all the geometry inputs are supplied, a unique solution is always possible. But when one or more key geometric variable is not provided, the nonlinear equations involved in the design of constant pitch (axial and radial) conical compression springs lead to scenarios where multiple solutions are possible. hands and can help take some of the black magic out of conical designs. Todd Piefer from Universal Technical Systems, Inc. (UTS), the developers of our ASD software, has put together some scenarios to show us the power of ASD7.
increases after that. A three dimensional (3D) image of this spring is shown in Figure 1.
Conical Compression Springs: Multiple Solutions Are Possible in ASD When all the geometry inputs are supplied, a unique solution is always possible. But when one or more key geometric variable is not provided, the nonlinear equations involved in the design of constant pitch (axial and radial) conical compression springs lead to scenarios where multiple solutions are possible. One such scenario is presented here. Inputs: Music wire; ends closed and ground; small coil ID = 0.4”; large coil OD = 1.0”; free length = 1.2”; total coils = 7. Assuming the spring is preset, the stress at solid must be at least 45 percent of the minimum tensile strength (MTS) but no more than 60 percent. We will use an input of 50 percent. ASD iteratively solves the system of equations and computes the wire size as 0.0727”. The load to solid is 37.6418 lbf. The solid length is 0.4341”. The transition load (the point at which the largest coil begins to go solid) is 9.1228 lbf. The deflection at that point is 0.4317”. The spring rate until that point is 21.1337 lbf/in. The rate continuously
Figure 1. 3D image of the first spring design (wire diameter: 0.0727”).
A second solution is possible. That is, there is a second wire size value that will result in the stress percentage at solid being 50. If we remove the input for the stress percentage at solid and input the wire size, ASD’s Incremental Solver tool can be used to repeatedly solve as the wire size changes. Eventually, we would see the second solution. Looking under the hood at the mathematical model in TK Solver, we can see a plot of the stress percentage at solid versus wire size as shown in Figure 2.
SPRINGS / Fall 2020 / 25
