PI P-843, User Manual

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3. Calculate the effective mass m
eff
of the unloaded piezo actuator and m
eff
' of the loaded
piezo actuator using the formulas in the figure above.
7.1.2 Calculating the Maximum Operating Frequency of the Loaded Piezo
Actuator
Information
In the following calculation, the maximum permissible operating temperature of the piezo
actuator is not taken into account. During operation without cooling, the maximum
operating temperature may already be exceeded when the operating frequency is still below
the limit value calculated in the following.
►
For the maximum permissible operating frequency without cooling, see column B of the
table in
"Maximum Ratings" (p. 29) .
1. Calculate the resonant frequency of the loaded piezo actuator with the following formula:
Variables:
f
0
' = Resonant frequency of the loaded piezo actuator [Hz]
f
0
= Resonant frequency of the unloaded piezo actuator [Hz]; see "Data Table" (p. 28) .
m
eff
= Effective mass; approx. 1/3 of the mass of the piezo actuator [kg]
m
eff
' = Effective mass m
eff
+ additional load M [kg]
See also "Calculating the Effective Mass" (p. 18) .
2. Calculate the maximum operating frequency of the loaded piezo actuator with the
following formula:
f
max
= f
0
'/3
Variables:
f
max
= Maximum operating frequency of the loaded piezo actuator [Hz]
f
0
' = Resonant frequency of the loaded piezo actuator [Hz]
7.1.3 Calculating the Forces that Occur During Dynamic Operation
1. Use the following formula to calculate the dynamic forces acting on the piezo actuator
during sinusoidal operation with the frequency f:
Variables:
F
dyn
= Dynamic force [N]
m
eff
' = Effective mass m
eff
(approx. 1/3 of the mass of the piezo actuator) + additional load
M [kg], see also "Calculating the Effective Mass" (p. 18)
Δ
L = Displacement in the application (peak-to-peak) [m]
f = Frequency [Hz]
Example: The dynamic forces are approximately ±40 N at 1000 Hz, 2 µm displacement
(peak-peak) and 1 kg effective mass.
7.1.4 Calculating the Power Requirement for Sinusoidal Operation
1. Calculate the average current requirement for sinusoidal operation using the following
formula:
7 STARTUP AND OPERATION P843M0001EN
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2/23/2021
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