voltage varied with spring force. The nominal spring force was calculated from the spring constant and  the geometry of the brake assembly. Starting with the friction plate pulled in against the solenoid, the  voltage to the brake was lowered until the plate mo ved under the force of the springs. Reducing the  number of springs in the brake assembly decreased the spring force pushing on the friction plate until the  brake plate no longer dropped out at zero voltage (Table 2). At this condition, the residual magnetic force  is greater than the spring force attempting to push the brake plate off the solenoid. An additional test was  performed with no springs in the brake assembly. The voltage to the brake was reduced to zero and a  measurement of the force required to separate the friction plate from the solenoid was recorded (Table  3). The same measurements were taken after adding a second non-magnetic 0.051 mm shim between  the solenoid and the friction plate (Tables 2 and 3). Adding the second shim raised the drop-out voltage  significantly (Figure 8) without changing the pull-in  voltage substantially. These tests enabled a method to  determine the force margin and illustrated a rewo rk path that could increase that margin. 

Table 2.  Drop-out v oltage v s. spring force as measured on a spare brake 

0.051-mm shim 2x 0.051-mm shim # of Springs  Nominal  Force (N) Voltage (V) Nominal Force  (N) Voltage (V)  6 9.012 1.27 8.910 3.60  5 7.508 0.92 7.428 3.21  4 6.005 0.22 5.943 2.12  3 4.506 No release(b) 4.457 1.51  2   2.971 0.35  1   1.486 No release 

(b)No release at zero volts, released with –0. 3 volts (reverse polarity voltage of 0.3 volts) 

Table 3.  Force required to separate the friction plate from the solenoid at zero v olts   as measured on a spare brake 

0.051-mm shim 2x 0.051-mm shim # of Springs  Nominal Force  (N) Voltage (V) Nominal Force  (N) Voltage (V)  0 4.706 0 2.224 0 

The required margin point for each shim condition was determined using the spring force test data and a  tolerance analysis of spring force. A quadratic equation wa s fit to the test data in Figure 8 since force in  the solenoid is a quadratic function of current and t herefore voltage. Regression results in equations of  the form: 

  (3) c bV aV FM ++=2

with , , and  all constants. Setting c equal to the minimum possible spring force of three springs  minus the maximum possible friction force from the ali gnment pins shifted the cu rves. This ensures that  when six springs are present, there is a minimum factor  of safety of 2.0 on the force required to create  drop-out at the zero voltage condition. The two shi fted regression curves are plotted in Figure 9, one  curve for a single, non-magnetic 0.051-mm shim and one for a double, non-magnetic shim or a 0.102 mm  total shim thickness. The final margin point for eac h shim thickness was calculated from the regression  curves as the drop-out voltage values corresponding to  the maximum possible force from 6 springs plus  an additional two times the friction force. An additi onal 0.1 VDC was added to account for measurement  scatter resulting in required minimum drop-out vo ltage values of 2.05 VDC for the 0.051-mm shim  thickness and 3.81 VDC for the 0.102-mm shim thickne ss. It should be noted that the drop-out voltage of  0.6 measured during acceptance testing of the failed LPA works out to a force factor of safety of 0.97.  This was a unit that clearly should have failed.  ab c 228