F V C K
F = FmVH V, CV,HKV,H eqn 4.73
H = (1- dVHGV ) (1- dVdyHGV )
Eqn 4.73 is the same functional form as the relations used in eqns 4.47, 4.54, and 4.61.
4.3.5.4 (K): Flexure stiffness
A calibration certificate is supplied by the manufacturer with values for horizontal
and vertical cantilever stiffness values (KH, Kv). For this uncertainty analysis the
manufacturer provided values of stiffness are used. These values are also entered into the
software interface any time a new flexure is used. These stiffness values are
manufacturer calculated by mounting each flexure into a similarly designed housing to
that used in the tribometer (Figure 4-3). Known masses are hung from the flexure and the
deflection at the mirror is measured using the same type of optical light intensity sensor
as it in the tribometer. This manufacturer calibration method is examined to determine
the uncertainty in the stiffness values. The maximum measurement displacement for the
optical sensors is 1000 gm. The horizontal stiffness is found by applying the maximum
force (MgmHooom) that would cause the maximum measurable horizontal displacement
(8HlOOOm)-
KHIoooPm Mg mo m eqn 4.74
SHlOOOpm
The variance in the KH expression can be found using eqn 4.74.
2u (KHiooopm) = U2 (M 00pm HIOOpm-- +,2 ( 5H0"0' H0 eqn 4.75
Tuh alt p a d at mgHIOOOum 4 OOOm i 4HlOOO6Im
The evaluated partial derivatives in eqn 4.75 are expressed in eqns 4.76 and 4.77.