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Mchine Riddle No.38 - Speed torque curves of DC motors
I need to know a few thing about the speed torque curves of DC motors. Firstly, what's the formula of Stall torque and that of no-load speed of motor...??
And secondaly, how to plot the speed torque curve for a motor...!!
Thanking in advance...!!
Author : Jawad Ahmed - From: Pakistan
Sun, September 11th, 2011 - 13:32
The fundamental principles of a DC variable speed drive, with a shunt wound DC motor, are relatively easy to understand and are covered by a few simple equations as follows:
• The armature voltage VA is the sum of the internal armature EMF VE and the volt drop due to the armature current IA flow through the armature resistance RA.
Armature Voltage V A = V E+I A RA
• The DC motor speed is directly proportional to the armature back EMF VE and indirectly proportional to the field flux Φ, which in turn depends on the field excitation current IE. Thus, the rotational speed of the motor can be controlled by adjusting either the armature voltage, which controls VE, or the field current, which controls the Φ.

                     Motor Speed     n ∝ V E / Φ

• The output torque T of the motor is proportional to the product of the armature current and the field flux.
                     Output Torque T ∝ I AΦ

• The direction of the torque and direction of rotation of the DC motor can be reversed either by changing the polarity of Φ, called field reversal, or by changing the polarity of IA, called armature current reversal. These can be achieved by reversing the supply voltage connections to the field or to the armature.
• The output power of the motor is proportional to the product of torque and speed.
Output Power P ∝ T n
From these equations, the following can be deduced about a DC motor drive:
• The speed of a DC motor can be controlled by adjusting either the armature voltage or the field flux or both. Usually the field flux is kept constant, so the motor speed is increased by increasing the armature voltage.
• When the armature voltage VA has reached the maximum output of the converter, additional increases in speed can be achieved by reducing the field flux. This is known as the field weakening range. In the field weakening range, the speed range is usually limited to about 3:1, mainly to ensure stability and continued good commutation.
• The motor is able to develop its full torque over the normal speed range. Since torque is not dependent on VA, the full-load torque output is possible over the normal speed range, even at standstill (zero speed).
• The output power is zero at zero speed. In the normal speed range and at constant torque, the output power increases in proportion to the speed.
• In the field weakening range, the motor torque falls in proportion to the speed.
Consequently, the output power of the DC motor remains constant.

Although a DC machine is well suited for adjustable speed drive applications, there are some limitations due to the mechanical commutator and brushes, which:
• Impose restrictions on the ambient conditions, such as temperature and humidity
• Are subject to wear and require periodic maintenance
• Limit the maximum power and speed of machines that can be built

Generally, the torque-speed curve is obtained by increasing torque with a fixed value of speed in current mode. However, this torque-speed plot does not show whether it takes the deteriorated effect in several different kinds of loads such as sinusoidal, ramp, arbitrary nonlinear periodic loads. Given one of these loading types, several tests will be performed with different magnitudes and frequencies. The whole loading period will be at least one minute for each test in order to see the trajectory with different torque profiles.
The generated torque will be recorded as a state at each time to compare the value of the measured state with the monitored state values obtained from a Condition Based Maintenance system in real time. In all of the tests with different dynamic loadings, it should be noticed that both amplifier and motion controller influence the performance of the test motor. 
Author : Hamid - From: Iran
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