Spring Calculator

Subj: Design tool for vertical seismometer, "SpringCalc.exe", version
November, 2004

This program allows the user to model a spring-supported pendulum constrained to move in a vertical plane, and is a design aid for building a vertical seismometer.

There are a lot of data entry boxes to fill in, as you will see. There are two boxes for characterizing the spring, two for point of attachment of the spring to the pendulum arm, one for pendulum mass, one for pendulum length, two for trial limits on spring angle, and one for the angle decrement step size. The picture, "SchematicA.gif", shows the model for the sensor. "SchematicB.gif" show an alternate configuration, where the spring is suspended downward from a boom attachment point on the other side of the boom hinge. In this case, Xp is negative, and the spring angle is greater than 180 degrees. A third configuration is shown in "SchematicC.gif", where a spring in compression pushes upward on the pendulum arm. One embodiment of this arrangement allows a leaf spring, approximately assuming a sideways "U" shape, to be used. This program assumes that such a spring is free to pivot at each end.

Trial design numbers are already filled in. You can modify any of the entries using mouse and keyboard, and store them for future use. The data is stored in file "SeisData.bin". What the program does is to stretch the spring in the spring angle direction to balance the pendulum. The X, Y coordinates are the resulting upper attachment point of the spring. It then displaces the pendulum from horizontal by one degree up and down to determine the restoring torque on the pendulum, and from that information, calculates a natural period of oscillation. You will note that the restoring torque can be negative, indicating a non-stable solution. If you should want to save the displayed results, you will have to select the text with the mouse, and use Ctrl-C to copy it to the clipboard, and from there to a Notepad document. The program starts with the highest spring angle entered, and iterates downward one step angle at a time until either the lower limit, instability, or an iteration limit of 50 is reached, whichever occurs first.

Note that if you specify a spring angle of 90 degrees, and put the mass at the same distance as Xp, you have the very nearly the equivalent of a mass dangling from a spring. The resulting period is what you would expect from the combination of spring constant and mass. At lesser spring angles, the period gets longer, until a limiting angle is reached, below which the pendulum is in unstable equilibrium.

If you try a zero length spring for your model, you will find the tuning up of the sensor will be very easy. It gets harder as the relaxed length of the spring gets longer, and the value of "X" goes more negative (the upper spring attachment is farther behind the vertical drawn from the hinge).

Download "springcalc.zip" here.

Bob McClure