This calculation will look at the force provided by a stack of belleville disk springs actuated by the instrument latches on the bottom of the Sloan 2.5m telescope. The goal is to determine the correct combination of springs in series and parallel to provide about 800 lbf at full deflection. The springs selected for the camera stirrup are Schnorr part number Z-12B, SWACO part number BS-1.102-0.500-1.25. Parameters are given below.
The following equation relates the load and deflection of disc springs without annular flats and comes from the Belleville Springs catalog:
If I have two springs in parallel (oriented the same way), the force will be about double for the same deflection as one spring.
The drawing of the camera stirrup from Jim Gunn shows eight sets of springs in series. Each set is made up of two springs in parallel. This arrangement provides for the load of 972lbs when all of the sets of parallel springs are deflected by .026". The total deflection of the stack comes from multiplying the number of sets in series by the deflection.
This number is the additional extension that the screw should stick out from the bottom of the stirrup aftertightening from the condition with the latch latched and the bellevilles initially uncompressed.
If we want to limit the force to 800 lbf, what would the deflection be?
The effective stroke of thelatch is only about 0.59". The bellevilles will still be under load when the latch has unlatched. What is the initial load of the belleville washers with the latch unlatched? I will assume that the full 75% deflection was the force while the latch is latched.
APPENDIX B: Check of disk spring linearity.
0 0 0
0.002 51.034 2.552-104 0.004 99.233 2.481-104 0.006 144.775 2.413-104 0.008 187.837 2.348-104 0.010 228.596 2.286-104 0.012 267.229 2.227-104 0.014 303.913 2.171-104 0.016 338.827 2.118-104 0.018 372.145 2.067-104 0.020 404.047 2.020-104 0.022 434.708 1.976-104 0.024 464.307 1.935-104 0.026 493.020 1.896-104
See the following page for graphs of force vs deflection and spring constant vs. deflection.
Last modified 04/28/99