A Novel Method of Stabilizing the Vibration Velocity at the End of Piezoelectric Transducers - Advanced Research on Computer Education, Simulation and Modeling - page 40

2 The Traditional Constant Current Method and Its Shortages

The equivalent circuit of a transducer near its mechanical resonant frequency is
shown in Fig.1 [5][6].

Fig. 1. Equivalent circuit of a piezoelectric transducer

( tI are the transducer's exciting voltage and its current at time t . L m , C m
and R m compose the mechanical arm. C e is named as the electrical arm.

and

)

U ( t )

I ( t )

may be

described below.

U ( t ) U ( t )

. (1)

I ( t ) = I ( t ) + I ( t ) = +

m e

Z ( ω ) Z ( ω )

m e

In which is the exciting frequency of the transducer, Z ( ω ) is the impedance of

ω

m

the mechanical arm, Z is the impedance of the electrical arm.

Assuming that the transducer is excited at the resonant frequency

( ω )

e

ω

, which satis-

s

fies the equations below:

Z ( ω ) << Z ( ω )

m s e s

(2)

I ( t ) ≈ I ( t ) >> I ( t )

m e

ω

is to stabilize the vibration
velocity, which is the basis of the traditional current-based stabilizing vibration veloc-
ity method.
Assuming that

Equation (2) shows that keeping

I ( t )

constant at

s

is far away from

ω , the equations below are satisfied: ω

s

Z ( ω ) >> Z ( ω )

m e

I ( t ) ≈ I

e t

( )

(3)
Equation(3) implies that the vibration speed is nearly zero at

I ( t ) ≈ 0

m

ω . Therefore, the vi-
bration velocity could be stabilized using the traditional method only after the reso-
nant frequency being successfully traced.

3 The Novel Method of Stabilizing the Vibration Velocity

The impedance Z ( ω )

and the conductance

of the transducer [7][8] are given

G [ ω ( t )]

in equation (4)