Suppose we've got the setup as shown in the figure (see attachment).(adsbygoogle = window.adsbygoogle || []).push({});

The idea is that the motor transfers its speed and force (rotary) to the actuator force and speed (linear) via some gears and a spindle.

Here:

R = radius [m]

J = inertia [kg m^2]

n = rotary to linear transmission [---]

If Im not mistaken, then the speed of the motor [tex] \phi_{motor} [/tex] is related to the speed of the actuator [tex] \phi_{actuator} [/tex] as follows:

[tex] \phi_{actuator} = \phi_{motor} \left( \frac{R_{motor}}{R_{spindle}} n_{actuator} \right) [/tex]

The force of the actuator [tex] F_{actuator} [/tex] is related to the torque of the motor [tex] T_{motor} [/tex] as

[tex] F_{actuator} = T_{motor} \left( \frac{R_{spindle}}{R_{motor}} \frac{1}{n_{actuator}} \right) [/tex]

And my main problem is the following: what is the total inertia [tex] J_{tot} [/tex] seen by motor? Is that

[tex] J_{tot} = J_{motor} + \frac{J_{spindle}}{ \left( \frac{R_{spindle}}{R_{motor}} \right)^2 } [/tex]

or

[tex] J_{tot} = J_{motor} + \frac{J_{spindle}}{ \left( \frac{R_{spindle}}{R_{motor}} \frac{1}{n_{actuator}} \right)^2} [/tex]

If someone could confirm/correct my formula, that would be very helpful.

Thanks in advance.

Bob

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# Refreshing gear ratio and total inertia

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