# Dynamic mechanical characteristic of an induction motor - Electric drive

## Dynamic mechanical characteristic of an asynchronous motor

The dynamic mechanical characteristic of an asynchronous motor is the relationship between the instantaneous values ​​of the speed (slip) and the moment of the electric machine for the same time moment of the transient operation mode.

The graph of the dynamic mechanical characteristic of an induction motor can be obtained from the joint solution of the system of differential equations of electric equilibrium in the stator and rotor circuits of the engine and one of the equations of its electromagnetic moment, which are given without their derivation: (5.35)

The following notation is adopted in the system of equations (5.35): - component of the vector of the stator winding voltage, oriented along the axis a of the fixed coordinate system; - component of the vector of the stator winding voltage, oriented along the axis b of the fixed coordinate system; - equivalent inductive resistance of the stator winding, equal to the inductive resistance of the stator winding and the inductive resistance from the main field; - equivalent inductive resistance of the rotor winding, reduced to the stator winding, equal to the inductive resistance of scattering of the rotor winding and the inductive resistance from the main field; - inductive resistance from the main field (magnetizing circuit), created by the total action of the stator currents; - component of the vector of the flux linkage of the stator winding, oriented along the axis a of the fixed coordinate system; - component of the vector of the flux linkage of the stator winding, oriented along the axis b of the fixed coordinate system; - component of the rotor winding flux link vector, oriented along the axis a of the fixed coordinate system; - component of the rotor winding flux linkage vector, oriented along the b axis of the fixed coordinate system; - the component of the current vector of the rotor winding, oriented along the axis a of the fixed coordinate system; - component of the current vector of the rotor winding, oriented along the axis b of the fixed coordinate system.

Electromechanical processes in an asynchronous electric drive are described by the equation of motion. For the case of  (5.36)

where - the torque of the load resistance applied to the motor shaft, - the total moment of inertia of the drive driven to the motor shaft. >

The analysis of the dynamic processes of energy conversion in an asynchronous motor is a complex task due to the substantial nonlinearity of the equations describing the asynchronous motor due to the product of the variables. Therefore, it is advisable to study the dynamic characteristics of an asynchronous motor with the use of computer facilities.

The simultaneous solution of the system of equations (5.62) and (5.63) in the MathCAD software environment makes it possible to calculate the graphs of the transient processes of the velocity ω and the moment M for numerical values ​​of the parameters of the induction motor replacement circuit defined in Example 5.3.

Since the dynamic mechanical characteristic of an asynchronous motor can be obtained only from the results of calculations of transient processes, first we give the graphs of the transient processes of the velocity (Figure 5.9) and the moment (Figure 5.10) when the induction motor starts up by direct inclusion in the network. Fig. 5.9. The speed transient process when a squirrel-cage asynchronous motor is started by direct connection to the network while simulating in a fixed coordinate system Fig. 5.10. The transient process of the electromagnetic moment when a squirrel-cage asynchronous motor is started by direct connection to the network during simulation in a fixed coordinate system Fig. 5.11. Mechanical characteristics of a squirrel cage induction motor: 1 - dynamic: 2 - static

Graphs and of transient processes make it possible to construct a dynamic mechanical characteristic of an asynchronous motor (Figure 5.1 I, curve I) inclusion in the network. For comparison, the same figure shows the static mechanical characteristic - 2, calculated from the expression (5.7) for the same parameters of the induction motor replacement circuit.

Analysis of the dynamic mechanical characteristic of an asynchronous motor shows that the maximum shock moments at the start exceed the nominal torque L/N of the static mechanical characteristic by more than 4.5 times and can reach unacceptably high mechanical strength values. The impact moments during start-up, and especially when the induction motor is reversed, lead to the failure of the kinematics of the production mechanisms and of the asynchronous motor itself.

Modeling in the MathCAD software environment allows you to easily conduct research on the dynamic mechanical characteristics of an asynchronous motor. It is established that the dynamic characteristic is determined not only by the parameters of the induction motor replacement circuit, but also by the parameters of the electric drive, such as the equivalent moment of inertia , the moment of resistance on the motor shaft. Consequently, the asynchronous motor with the given parameters of the supply network and the substitution circuit has one static and a lot of dynamic mechanical characteristics.

As follows from the analysis of the dynamic characteristics of Fig. 5.9-5.10, the transient process of starting a short-circuited asynchronous motor can have an oscillatory character not only at the initial, but also in the final section, and the engine speed exceeds the synchronous ω0. In practice, fluctuations in the angular velocity and the motor torque in the final part of the transient are not always observed. In addition, there is a large number of production mechanisms for which such fluctuations need to be eliminated. A typical example is the mechanisms of winches and the movement of cranes. For such mechanisms, asynchronous motors with soft mechanical characteristics or with increased slip are produced. It is established, the softer the working section of the mechanical characteristic of an asynchronous motor and the greater the equivalent moment of inertia of the electric drive, the smaller the amplitude of oscillations upon reaching a steady speed and the faster they decay.

Studies of dynamic mechanical characteristics are of theoretical and practical importance, since, as shown in Section 5.1.1, taking into account only static mechanical characteristics can lead to incorrect conclusions and distortion of the nature of dynamic loads when starting asynchronous motors. Studies show that the maximum values ​​of the dynamic torque can exceed the nominal torque of the engine when starting up directly into the network 2-5 times and 4-10 times when the engine is reversed, which must be taken into account when designing and manufacturing electric drives.

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