# Torque and voltage relationship

### New Relation to Improve the Speed and Torque Characteristics of Induction Motors

rotational speed is proportional to voltage applied * torque is proportional to current What is the relation between a load current and a torque in shunt motor ?. Relation between motor's torque/speed and its voltage/current 23 Jan The torque of a motor is proportional to the current flowing through it (τ ∝ i). Can someone please help me understand the relation between volts, amps and torque? I understand with Ohm's law that voltage and current.

It depends on the accuracy of your assembly, sensor position, friction, alignment of the motor and generator axles etc.

If you want to get meaningful numbers you might use a second generator kit as explained in Torque and Efficiency Calculation section. Speed, torque, power and efficiency of the motors are not constant values.

Usually the manufacturer provides the following data in a table like this one sample data from one of the motors used in generator kit: Also the manufacturers usually provide power curves for the motor at nominal voltage: These curves are generated by plotting motor speed, consumed current, and efficiency as functions of the motor torque.

## Relation between motor's torque/speed and its voltage/current. :: 23 Jan 2010

Sometimes there might be also a curve representing mechanical output power. As you can see from the graph speed and current are linear functions of torque so you might need only two measurements to draw these graphs.

- Calculations

Efficiency and power will need more data. While it is technically better to follow the same format and create similar curves for your motor it is not absolutely necessary for a good science project.

You may take all measurements, calculate unknown values and plot the graphs where for example speed and torque are represented as functions of applied voltage or current etc. Simple formulas and calculations described here are essential for calculating most common motor parameters. However this is a simplified approach that does not take into consideration many factors.

If you want to extend your research further — see Links section and search the Internet. There is tons of information with more complex calculations. See other pages at Experiments section on how to measure motor parameters. This equation indicates that rotor speed can be adjusted with the frequency of the IM source.

The frequency of the induced EMF in the rotor changes in inverse proportion to Sr. The frequency of the rotor induced EMF is expressed by equation 5: The rotor bars have low electrical resistance, as well as an inductance Lr and inductive reactance Xr properties.

The inductive reactance of the rotor is computed with the rotor blocked [3, 16]. The EMF induced in the rotor, when its blocked, is defined by equation 7 [5]: The torque with the rotor blocked can be determined by the current in the rotor according to equation 9 [5]: The equivalent circuit of the single cage IM is shown in figure 2. The circuit is a model in steady state and allows obtaining the equations that define the IM behavior [17, 18].

The mutual reactance jXm represents the difference between stator and rotor inductances. The impedance of the stator is represented by Rs and Xs. The s term takes into account the apparent increment of Rr when the rotor is moving.

From figure 2 ait can be seen that the rotor current magnitude Ir, with the rotor blocked, is expressed according to equation 10 [5]: By substituting equation 10 into equation 9 and considering that equation 11 expresses the initial value of the rotor torque [5]: For any value of s, considering equations 6 and 8equation 12 indicates that rotor current is: The term, at any value of s, is Hence, equation 13 expresses that, for a given sliding the torque of the IM is [5]: The equation 14 can be derived considering equations 7 and 8: Therefore, the stator magnetic field, expressed by equation 15is: By substituting equation 15 into equation 13the torque magnitude is expressed by quation 16 as: As stated before, a region of constant torque is demanded for speeds below the nominal.

Commonly, the voltage magnitude of the motor power source is modified in direct proportion to the frequency.

### Motor Voltage, Amps and Torque Relationship

When the frequency is larger than the nominal, the voltage magnitude is the nominal value. To determine the real value of E1rand the real value of the torque, Rs and Ls should be considered.

The equivalent circuit of the IM can be reduced to the circuit shown in figure 2 b. The magnitude of the equivalent impedance is expressed by equation According to the circuit of figure 2 bthe magnitude of V can be expressed by equation Hence, by substituting equation 20 into equation 19Er is given by equation 21 as: The equation 22 expresses Er when the rotor is blocked: Figure 3 shows the torque-speed profile described by equation The torque is normalized with respect to the nominal torque value and E1r is obtained with equation The rotor starts blocked and is subsequently released, allowing the rotor speed to attain the synchronous speed.

The IM ratings are shown in table 1. The torque-speed profile in figure 3 shows that the motor torque capacity decreases in direct proportion with velocity decrements.

### Calculations | Simple Electric Motors

The proposed relationship This section describes the method to compute the proposed relationship, which allows the IM to approach the torque-speed profile shown in figure 1 and to improve the speed response. The frequency factor must be calculed each operation speed of the IM, in order to include the frequency influcence in the elements of the equivalent circuit shown in figure 2.

Hence, this factor appears in the calculation of the magnitud of V. Then, the induced EMF in the rotor E1rm for a given frequency is expressed by equation From equation 22the power source voltage magnitude required to produce E1rm at the nominal frequency is obtained with equation Hence, the power source voltage magnitude required for any given frequency is expressed by equation 29 as: Where equation 30 must be considered: Equations 27 and 30 are defined by the IM parameters.

There exist several methods to determine the IM parameters [5, 15, 16]. Figure 4 shows the torque-speed profile described by equation The torque is normalized with respect to the nominal torque value.

Each curve represents the torque response for a given frequency with the voltage computed by equation 29where the variables X, E1rm and the losses are computed according to the given frequency. In the case of the ''Proposed '' plot, the magnitude voltage is computed acording to equation 29where stator and rotor losses are considered according to operation frequency and factor frequency. The IM used has the ratings listed in table 1. The experimental tests were made implementing a sudden acceleration until the rotor speed attains the set value, with and without a 5 Nm load.

A motor-brake coupled to the IM shaft is part of the equipment. The control console allows set the required load expressed in Newton-meters.

The inverter supplies the voltage and frequency to the IM in order to produce a three phase balanced system. The frequency of the voltage source is established in the PSoC 5.

**Motor production: Speed, Torque and Horsepower**

In the rotor of the IM, an encoder and DAC were mounted to measure the speed response with the help of a fluke scopemeter. The scopemeter allows, using an isolated USB cable, to capture the voltage generated by DAC; this voltage matches with the speed response of motor.

The IM speed responses for rpm are presented in figure 9.

Similarly, the results at rpm, rpm, rpm and rpm are shown in figures 101112 and 13respectively. Table 2 shows the summary of the IM responses. The results obtained for the open loop system figure 6 using the relation proposed show a settling time reduction in all cases and a significant error decrement with load, especially at low speeds.