Table 1.

Summary of variables used in the reciprocating pump model.

Variables Used in the Model
F	Force
Q	Flow rate
R	Fluidic resistance due to fluid viscosity and component geometry
υd	Axial velocity of diaphragm center
vol	Displaced fluid volume due to diaphragm deflection
Ma	Mass of actuator armature, includes shaft and head
Mfeff	Effective mass of moving fluid
z	Diaphragm center deflection
V	Actuator coil voltage
B	Stiffness term
D	Empirical coefficient for non-linear actuator force response to input coil voltage
Initial Conditions
z0a	Actuator displacement offset
z0s	Spring deflection when fluid displacement volume is zero and actuator head is in contact with diaphragm
z0d	Diaphragm center deflection under no load (buckle displacement)
Pump Properties
Ad	Diaphragm area
Ac	Cross sectional area of flow channel
a	Diaphragm radius
t	Diaphragm thickness
k	Spring constant of actuator return spring
Material Properties
E	Tensile modulus of diaphragm
ν	Diaphragm Poisson ratio