the same centralized location each time the carrier block is mounted into the housing.
The uncertainty in the sensor mirror offset uc(dv,H) is given a value of 50 gnm based on
machining tolerances believed to be used in the manufacturing of the carrier block and
housing [34].
Finite element analysis was performed on the flexure used in these experiments to
investigate the influence of applied load on the slope of the flexure at the mirror. In a
similar manner to the schematic in Figure 4-10, the end of each flexure was given a fixed
boundary condition. Four different simulated loads were applied in the vertical and
horizontal directions. The deflection of the flexure was measured at four points along the
mirror location to establish the slope of the flexure under each applied load. The slopes
of the flexures were examined as a function of the zero error point deflection. This
examination showed that for a given direction on a single flexure the value of the slope
defined in Figure 4-10 is a constant multiple (Gv,H) of the zero error point deflection (So).
This value of (Gv,H) is constant for a single direction on a particular flexure.
slope = 8oG,, eqn 4.70
This expression can be substituted into eqn 4.69.
F,,,, = KY,H 8oH, d HySoG, ) eqn 4.71
Substituting eqn 4.68 into eqn 4.71 yields an expression for the measured force.
F. V,H = Fo (1-dy,vG,) eqn 4.72
The force measured by the tribometer in the vertical and horizontal directions is the
product of the optical sensor voltage (VV,H), the displacement-voltage sensor constant
(CV,H), and the flexure stiffness (Kv,H).