4.2.1 Damper Design

4.2.1 Damper design

A simplified cross section of the damper is shown in Figure 18. It can be modeled as a linear bearing if the gap size is small compared to radius (see Figure 19).

Figure 18. Simplified cross section of a rotary viscous damper.

is the radius of the vane,

the radius of the cup, and

the angle around the damper from some fixed reference. The vane is rotating such that the velocity at

is U. Note that the gap size has been exaggerated for clarity.

Figure 19. Linearized model of a rotary viscous damper. Note that the boundary conditions must be identical at the two ends, since they represent the same point on the damper. Again, the gap size has been exaggerated for clarity.

This model assumes that Navier-Stokes equations are dominated by the viscous terms (in this case, ), so that the x-component of the momentum equation reduces to (16) :

(16)

where is the viscosity, u is the velocity in the x-direction and P is the pressure. Since the velocity is independent of x, we can integrate twice with respect to y to obtain the velocity profile. Enforcing the no-slip condition at y=0 and y=h, we obtain :

(17)

Since the gap is uniform in this case, the pressure remains constant, and (17) reduces to a linear velocity profile.

(18)

The damping torque is found by integrating shear stress over surface area of the vane times R, the moment arm (19). Note that the torque is actually the torque per unit length of the damper, so that its units are those of force.

(19)

Finally, substituting (18) into (19), we obtain the force on the damper vane applied by the fluid :

(20)

This is the signal we wish to measure using a strain gauge force sensor. In 4.2.2, we will show how this torque is converted into a voltage using the strain gauge circuitry.

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