Figure 2.7: Generation of torque in rotary VCM actuator.
geometry is fixed for a given actuator, the torque it generates is function of coil
current only and we can assume this to be K t I,whereK t and I are the torque
constant of the VCM and the coil current, respectively. In practice, the torque
constant may vary with the position of the coil, i.e., K t (θ) is a function of
actuator position θ. However, the change in the magnitude of torque constant
is usually very small and insignificant. We shall assume throughout this topic
a constant value for this parameter of VCM.
The motion of the actuator arm, defined according to the Newton's second
law of motion, can be modeled as
θ(t)= K t
where J is the moment of inertia of the rotating arm, and θ is the angular
acceleration of the actuator's motion. If the distance between the pivot center
and the read head is L inches, ‡ then the linear displacement of the read head
corresponding to an angular displacement (θ)isx = Lθ. It is very common in
the HDD industry to express the displacement of read head in units of track,
i.e., y = D trk Lθ,whereD trk is the track density in units of Tracks per Inch
(TPI). Taking all these factors into consideration, the rigid body dynamics of
the VCM actuator is given by
y(t)= D trk LK t
The corresponding transfer function model is G v (s)= s 2 .
If the VCM is driven by a voltage amplifier, shown on the left of Figure 2.8,
the output (V O ) of the amplifier is proportional to the input, i.e., V O = K VA u.
The current in the VCM coil and the applied voltage are related to each other
Imperial units of measurement are widely used in the HDD industry.