## Electric Motor Speed Control, Formula And Calculator Motor speed

## What does motor speed mean?

The motor speed defines the rotation of the axial connected with the rotating part of the motor. To define it further we have to introduce another term called RPM.

Motor RPM (Revolution Per Minute) is the rate at which the rotor is revolving. It is the number of cycles in which the rotor shaft completes a full rotation each minute.

It is used for measuring the speed of turbines, motors, centrifuges, conveyors & other equipment’s. We will discuss the two types of motors here. i.e. Induction motor and DC motor. Let’s discuss.

## Induction Motor Speed

Induction motors speed not only depends upon the supplied voltage but also on the number of poles of the motor, and frequency of the system. The numbers of poles in an AC motor are either two or four.

Another factor that affects the speed of the Induction motor is slip. Which is the difference between the synchronous speed of the stator and the actual operating speed.

To get a motor running torque is necessary. For this purpose, a rotor rotates slightly slower than the stator magnetic field.

### Is an induction motor a constant speed motor?

Constant speed motors do not change speed and run at a uniform speed. Normally, the induction motor runs at a constant speed.

So, it is a constant speed motor. There is a slight slip caused by the lagging of the rotor flux rate from the stator flux rate. As the value of inductive load increases, the slip decreases.

Finally, at the rated value, the slip becomes negligible. At this time the change in speed of the motor is negligible. So, the induction motor speed is constant. The normal slip value of the induction motor is from 3% to 5%.

### Induction Motor Speed Formula?

We can calculate the an induction motor speed using the speed formula as given below.

Motor Speed (RPM) = (f *60*2)p

Where f is source frequency in Hz.

p is the number of poles of the motor.

This formula is the synchronous speed while the motor at full load will be slightly lower in speed than this.

### Motor Speed Calculation Example and Calculator:

A Three phase induction motor works on 50Hz power source and number of poles of this motor is 4, Then, Motor Speed Formula = (f *60*2) /  p = 120*50 / 4 = 1500 RPM, Use the below online motor speed calculator for more calculations.

## How to control induction motor speed?

Controlling speed of induction motors is slightly difficult because it is a constant speed at the firs place. But controlling its speed is possible and can be done by one of the following methods.

• Adding rheostat to the stator circuit.
• Number of poles of the motor changing, as induction motor speed if function of poles number (Speed = 120 Frequency / poles number)
• V/ f controlling or frequency control
• Voltage controlling, but reducing voltage reduces motor torque

### Adding rheostat to the stator circuit

Adding rheostat in the stator circuit gives us a facility to control the speed of the motor. The speed can be decreased and increased. But the torque has to remain the same. The same equation number 2 can be used for this method’s concept.

The stator rheostat decreases the voltage that slows down the motor. We can speed up the motor by changing the sliding contact from a lower end to the upper (the lower has higher resistance and vice versa).

### Frequency control or (V/f) control

The speed of the motor is function of the frequency. This is clear from the formula Speed (RPM) = (f *60*2)p

By reducing the frequency of the source the speed will reduced as a result. But this reduction of the frequency causes flux to increase causing rotor and stator cores saturation which increase motor no load current of.

To overcome this issue the voltage to frequency ratio should be kept constant (V/F) from here comes the name of the method V/F.

By using electronic controllers consisting of inverters and converters we can control the V/F and then the speed of AC induction motor.

The drive which controls the motor is called VFD (variable frequency drive) or VSD is (variable speed drive), this drive is used from smal applications to large ones.

VFD drive is based on power electronics and is programmable, while motor parameters such as motor speed, voltage, frequency and connection type are set to the VFD.

Electrical drives, what exactly is a drive? An electrical drive is an electronics control system of electrical motor speed and torque. In many industrial applications its important to control electrical motors speed in the production process.

Electrical drive is used in factories, electrical trains, robotics and many other industrial applications such as assembly lines must run at different speeds.

#### What types of motors’ speed can be changed with a VFD?

Some motors that we can generally use with a Vfd for speed changing are:

• Brushless AC Sync. Motors
• Wound rotor AC Sync. Motors
• Permanent magnet AC Sync. Motors
• Squirrel cage AC Sync. Motors.

Let’s know the logic using which we can say that the motor can be either operated with a Vfd or not, for speed control. Some general rules for motors built in different eras are:

Built before 1992:

• Insulation class F
• Constant Torque Ratio <=2.1
• Should be Vfd rated.

Built after 1992:

• Constant torque ratio 2.1
• Variable torque ratio 4:1-10:1

(A motor built after 1992 but if it is either a 56-frame motor or fractional motor, it should not be used with Vfd from speed changings.)

NEMA motors:

• Constant torque ratio 4:1-20:1
• Variable torque ratio 10:1-20:1

### Number of poles Changing

From the speed formula of induction motor the changing of poles number changes the speed. This method can be achieved by mounting two different windings with different poles number. And by switching connection we apply power to only one winding and get the speed of the motor changing.

This method doesn’t provide smooth speed control and costs much as two windings are in the same motor.

### Voltage controlling of speed

Controlling speed of induction motor by changing the voltage is possible but this method affects the motor torque because T ∝ V2

While T is the torque and V is the supply voltage. By reducing the voltage the torque will be reduced also and the motor may not be able to drive the load any more. Also reducing the voltage will cause the current to increase and then the motor will overheated.

I have written a detailed article about motor temperature rise. You can find it here.

### How to run an induction motor at constant speed on variable load?

A feedback control block/ controller can be used to control the frequency of the motor in a variable load case. A feedback controller is attached to the power supply and the power to the motor is passed through the feedback controller.

The Feedback controller detects the load at the motor end and changes the frequency of the induction motor according to that load.

Feedback is general information from a Hall sensor, a resolver, or an encoder. There are two types of feedback controllers. Open-loop and Closed-loop feedback controllers. The Closed-loop feedback controller gets feedback from the load side and adjusts the frequency.

A wire takes the feedback back to the controller. In Open-loop feedback controller, there is no loop but it is a simplified version of the closed-loop feedback controller. Both the controllers work just fine. If we observe this system, there are 3 major blocks in this system.

The first block is the Induction motor that has PWM controlled and 3-phase input power supply. So, the motor itself, PWM generator, 3-phase supply system, and a position sensor are the constituents of this block. The next block i.e., block number 2 is the block that applies a Frequency Shift Keying modulator and a Frequency Shift Keying de-modulator.

Between this modulator and the de-modulator is a wireless channel. The modulator and de-modulator both have one antenna each. The modulator has a PLL modulator and an RF amplifier. The de-modulator has a PLL de-modulator and a Data Slicer.

The position sensor of block 1 sends the digitally encoded signal to the Modulator part and de-modulator sends another digital signal to the controller. The controller is block number 3. The controller gets the value of digitally encoded position feedback (θop). The θopis sent as an input to the feedback controller.

This controller is the driver of the angular velocity ω. We know that the angular frequency is ω = d(θ)/dt. The value of this term is compared to the reference velocity. The error signal is then sent as an input to the PI (proportional-integral) controller that gives a value we call “slip”. (Keep in mind that the error signal is the reference velocity – angular velocity we got). This slip is used to get the desired reference voltage.

That is fed to the motor. So, conclusively, the crux of this whole concept is that when a PWM is applied now to the induction motor, the position sensor will detect the change in position, and block 2 (modulator and demodulator) will help in calculating the θop.

That further gets us the value of the slip and eventually the value of the desired voltage. So, a change in PWM will change the speed. An increase in the duty cycle will increase the speed.

## How Can We Change Single-Phase Induction Motor Speed?

We change the speed of a Single-Phase induction motor by several methods. One of the most effective methods is changing the speed using the high-frequency triangular wave oscillator, a PWM controller, a driver circuit, and a MOSFET. In this method, a capacitor is introduced parallel to the induction motor.

The normal single-phase supply is 240 V AC. If we want to change/control the speed of the induction motor, this supply is not connected directly to the motor. Instead of directly connecting the power supply, the power supply is connected to a bridge rectifier.

The output of the bridge rectifier is fed to the control circuit. After this stage, a high-frequency PWM is introduced into the circuit. Increasing the speed is actually done by increasing the duty cycle of the PWM.

The purpose of the capacitor that is connected in parallel combination with the motor is to perform freewheeling. The control of the speed of the motor or the RMS output voltage of the motor is performed collectively by the PWM generator and the controller.

After the PWM and the controller, a single MOSFET switch is there in the circuit. This circuit has 4 operating modes.

1,2: Conduction and freewheeling mode for the positive cycle.

3,4: Conduction and freewheeling mode for the negative cycle.

The control circuit generates the high-frequency triangular wave. Then PWM generator i.e., the duty ratio controller gives high-width Pulse width modulated signal. There are various ICs in the control circuit that generate pulses from -12V to +12V. Using this method, we don’t only get the speed control but also the overall efficiency of the motor is improved.

The improvement is in the sense that the copper losses are reduced because the power factor is increased due to which lesser current flows through the stator windings.

## DC Motor control

The speed of DC motor is dependent upon the voltage available to it and the flux. Speed is directly proportional to supply voltage and inversely to the flux. Thus, controlling the DC motor speed can be done by one of the following ways:

• Flux control and varying the field winding current.
• Armature voltage and resistance varying.
• Controlling the voltage of the supply.

### DC Motor Speed Control

Before we discuss the methods of speed control for the dc motor, let’s have a brief intro about, what parameters include in the speed of the dc motor. We can define it from the formula.

N= (V-IaRa)/kφ

Hence from the formula, we easily decide that the speed of a motor can vary if we change the following parameters.

• Applied Terminal Voltage of the armature, V.
• External resistance in Armature circuit. i.e. Ra
• Flux Per Pole, i.e.

### Voltage Control Method

As discussed above that if we can change the speed of dc motor by changing the voltage applied at the terminal of the armature. We also refer to this method as the armature voltage control method. A dc motor can be either connected in series or a shunt.

In this method, we connect a shunt field to a fixed exciting voltage. While applying variable voltages to the armature. Using switchgear, we can change the applied armature voltage, and hence the speed can either increase or decrease. In case of sensitivity, we can use Ward-Leonard System for dc motor speed control.

### Armature Control Method

Basically, this method involves a variation of resistance in the armature circuit. And sometimes we call it the Rheostat control method. As we know that dc motor speed is directly proportional to the back emf Eb while

Eb = V – IaRa.

So in case When V and Ra are constant, then speed will be directly proportional to the Armature current Ia. So if we add a resistance in series with the armature. It will decrease armature current and as a result, the speed of the dc motor will decrease. This type of DC motor speed control method is less operational due to some drawbacks.

### Flux Control Method

Another method through which we can perform DC motor speed control is the flux control method. From the equation of speed, we see that speed of the dc motor is inversely proportional to the flux per pole. Hence if we increase flux the speed will decrease or vice versa.

To control flux, we add rheostat with field windings in series. Adding resistance in series will decrease the flow of current and similarly less amount of flux will be produced. As result, the speed of the dc motor will increase. Similarly, we can decrease the speed of the motor by increasing flux. The addition and subtraction of resistance can be done with a variable resistor perfectly.

## How do you slow down a DC motor?

The output voltage of a DC motor is as:

V = Eb + IaRa

Where Ia is the Armature current, Ra is the armature resistance, and Eb is the back EMF. This implies that speed of the speed that is directly proportional to the output voltage of the motor depend upon:

1. Armature voltage, and
2. Back EMF

But we study the formula of Eb closely, Eb is:

Eb = (PøNZ)/60 [A]

Where A is the amperes, p is the number of poles,ø is the flux, z is the speed of the motor, and N is the number of conductors.

A few algebraic steps and we will get:

N = K (V – IaRa)/ ø,

Where K is a constant value.

Looks like the factor 1,2 have a newcomer in the list. Now, we can say that the speed of the motor is directly proportional to:

1. The Armature voltage,
2. The Back EMF, and
3. Inverse of the flux

So, by decreasing the armature voltage, and back emf or increasing the flux due to the field.

## Which motors’ speed control is easier, AC or DC?

The speed of the DC motor is easier to control than AC motor speed. The Voltage Regulation can be used to control the speed. In Voltage Regulation, the armature voltage changes the speed of the motor.

The other method of voltage control of DC motor is by speed-regulated method. It is the same method as the voltage regulation is but with a little fashion. A feedback loop is added that gives feedback on the speed of the motor. A speed measuring device such as a tachometer can be employed for the feedback control device with some changing in it.

On the other hand,controlling the speed of an AC motor is a little complicated thing. Normally, the speed of the AC motor is set to a value during the construction period of the motor. For changing of speed of the AC motor there are several methods. These methods include using a voltage/frequency method, a micro-controller, a feedback controller, or a PWM (ed) signal along with the feedback controller.

The application of any of these solutions needs ophisticated methods. That deals with a lot of calculations. These methods often need expensive hardware. If you just look for a feedback control device price, it is sometimes, even greater than the price of the motor.

And then completing these circuits and then keeping them using pose another cost normally known as M&O (maintenance and operational) cost.

So, conclusively, we can say that controlling the speed of the DC motors is easier than controlling the speed of the AC motors at runtime.

Read my detailed article Motor types.

## How to measure motor RPM?

Using a device called tachometer you can measure motor RPM, and the RPM of any rotating machine. This device has two ways of measurement. The first is by direct contact between motor shaft and the tachometer shaft and the RPM of the motor will show up on the device screen.

The second method is by laser ray. We set a small reflective piece sticky paper on the motor shaft and then we direct the laser to the shaft while it is rotating. The device will count the RPM and show it on the screen.

## Can a VFD damage a motor?

Yes, a VFD can damage a motor. There are different ways in which VFD can damage the motor like damaging the bearings of motors and burning the windings.

A VFD (Variable Frequency Drive) is produced using Pulse-Width-Modulation (PWM) of sine wave applied on a VFD motor. When a pulse width modulated sine wave is applied to the VFD motor, peak voltages are generated. These peak voltages often get high enough that the temperature of motor windings increases.

This increase in temperature often reaches a certain value that is more than what insulation of the windings of the motor can tolerate. An increase in the temperature melts off the insulation on the windings and becomes a cause of a short circuit between different windings.

The other major damage VFD can do to the motor is damaging the bearings of the motor. VFD causes shaft currents. Due to VFD, a small voltage occurs at the ends of the shaft that produces a current. This is called shaft current.

Shaft currents produce arcs. Pitting occurs due to the current flowing through the shaft and damages the bearing. Also, the phenomenon of frosting and fluting occurs. These two also damage the bearing of the motors.