Dynamic Equations and System-model of a Simple System

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Dynamic Equations and System-model of a Simple System

It is quite necessary to analyze electro-mechanical conversion system for predicting the performance and/or for monitoring the system. A simple system is being taken up here to deal with dynamic equations and a simple model with its components is being related to the system. The details will vary from system to system, and accordingly the equations will vary.

Fig. 25.7 shows different components of such a system meant for electrical to mechanical conversion. On one side, an electrical source feeds the device at the ‘electrical port’. On the other side, a force fe is developed at the ‘mechanical port’. Mechanical load is connected to this port.

(a) At Electrical Port : A voltage source is shown to feed the device. r is its effective internal resistance. At the electrical port, the inputs are l (= flux linkage with the coil) and i. From l , the voltage induced in the coil can always be evaluated.

(b) Role of the Conversion device: With these inputs, the device converts the energy into mechanical form, and is available as a force fe (in case of linear motions), and, displacement x measured from a suitable reference.

(c) At the Mechanical Port: The possible items are: spring, damper, mass and an applied mechanical force. Their natural and simple dependence on displacement x and its derivatives are indicated below:

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The second term on the right-hand side is statically induced emf (or transformer-emf), since change of current with time is responsible for it. This cannot produce any force (or torque) and hence cannot convert energy from electrical to mechanical form (or vice-versa).

The third term on the right hand side includes the speed (= dx/dt) and dependence of L (x) on x. Any of these, if non-existent, will mean that third term reduces to zero. This term relates dynamically induced emf (= speed emf) and is the main indicator of the process of electro-mechanical energy conversion. So, for conversion, there must be an inductance which varies with the system position, and a motion must be there. In addition, coil must carry a current.

Having understood the linear-motion-system, it is easier to understand the system with rotary motion, with due modifications.

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