# Motor Sizing Principles

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1 1. General Concepts Motor Sizing Principles Motor: Converts electrical energy into mechanical energy. In this course we will be considering motors which rotate (spin) Mechanical Power: The mechanical output of the motor (P) measured in Watts. Older motors and USA motors measure power in Horse Power (Hp). Conversion Factor: 1 Hp = 746 W For reference: A Litre petrol Engine at full throttle can produce around 90 kw A fit human on a bicycle produces a maximum of about 400W. Sample Problem: i)how many horsepower is a typical litre petrol engine? ii) How many Watts is 15 Hp? Speed: The number of revolutions per minute of the motor. Usually denoted N and measures in rpm (revs per minute). In some formulae speed is measured in revs per second and denoted n. In academic works a different units called radians per second is often used and denoted ω The reason this unit I sused is becaue it simplifies some of the formulae. Conversion Factors: n=n/60 ω=πn/60 : The force with which a motor turns is called measured in Newton metres (Nm). A motor with high accelerates quickly and can drive a heavy load. In the USA torque is often measured in foot-pounds (ft-lb). The relationship between Power, Speed and The higher the speed the more power, the higher the torque the more power. In fact the power depends on multiplied by Speed. Important Formula π T N P= 60 Sample Problems iii) If T = 10Nm, N = 1000 rpm what is P? (1.05kW) iv) If P=kW, N = 1450 rpm what is T? (13.Nm) v) If P = 4 Hp, T = 10 Nm, what is N? (850rpm) 1 of 1

2 3. Losses and Efficiency MOTOR Input P electrical P loss Losses are Mainly Heat plus some Wind T Speed N Output P mechanical Important Formula Important Formula Input = Output+ Losses P electrical P η = P = P mechanical Efficiency= η = mechanical electrical + P 100% loss Output Input 100% Sample Questions vi) An electric motor is delivering 1kW of mechanical power and consuming 100W of electrical power. What are the losses? What is the efficiency? (83.3%) vii) An electric motor operating at 85% efficiency is delivering kw of mechanical power. What is the electrical input power? What are the losses?(353w) of 1

3 4. Motor Sizing Motor sizing refers to the process of picking the correct motor for a given load. It sis important to size a motor correctly because: a. If a motor is too small for an application it may not have sufficient torque to start the load and run it up to the correct speed. Even if it does get the load up to speed the motor will overheat and burnout if it is too small for the application. b. If a motor is too large for an application then money has been wasted in purchasing such a large motor. Also motors typically operate inefficiently when they are run well below rated load. So money is also wasted in running costs. Excellent web Reference: A very good reference on motor sizing can be found on the web at: Read this and in particular pay attention to the definitions of Starting torque, Pull up torque, Breakdown torque and Full load torque. Warning You will also come across the term pullout torque for induction motors. Please note that pull out torque is the peak point of the troque versus speed curve and is not the same as pull up torque. Warning Because this is an American website it uses horsepower for Power and Foot-Pounds for torque. 3 of 1

4 Important Concept: Ratings Every Motor will have a rated values of voltage, current, speed and power (and frequency for an ac motor). Normally these are visible on the motors nameplate but in any case they will be given in the documentation. In general rated values represent the maximum values that the motor should be subjected to in normal use however there are some slight differences in the meaning of the different ratings: 1. Rated Voltage should never be exceeded. There is a risk of damaging the machine or exposing the user to an electric shock hazard.. Rated Current Should not be exceeded for any prolonged time. The rated current may be exceeded temporarily during transient events (eg starting the motor). There is a risk of overheating and burning out the motor windings. 3. Rated Speed should generally not be exceeded however induction motors are designed to run slightly faster than rated speed (up to a speed called synchronous speed) when they are lightly loaded. For example an induction motor with rated speed of 1450rpm may have a synchronous speed of 1500rpm and would be safe up to this speed. There is a risk of mechanical failure due to centrifugal force on the rotating components. 4. Rated Power should generally not be exceeded. However some motors have a service factor which allows the motor to be used at more than the rated power for short periods. This can be useful for dealing with variable loads that may exceed the rated power requirement for short times during the operating cycle. Exceeding rated power risks overheating and in extreme cases may also risk mechanical failure. 5. Rated Often this is not given on the nameplate but it I sa very important parameter for appropriately sizing the motor. In both DC motors and AC induction motors operating current is proportional to so exceeding rated torque is likely to lead to overheating and burnout of the motor windings. Exceeding rated torque also risks mechanical damage to couplings and drive shaft. Rated torque can be calculated from rated power and rated speed. Important Formula 60 P Rated = π N rated rated 4 of 1

6 Motor Load Operating Speed Speed This motor will start the load and get it up to speed correctly. Motor Load Operating Speed Speed This motor will never even start 6 of 1

7 Motor Load Stall Point Operating Speed Speed This motor will start the load but it will get stuck at the stall point. How long will the system take to get up to operating speed? It is beyond the scope of this course to calculate this but it is worth noting that the time it takes the motor to get up to full speed can be calculated from the area between the motor torque speed curve and the load torque speed curve. The bigger this area the quicker the system will get up to speed. 7 of 1

8 What if the load varies? Some loads do not present a constant torque even after they have got up to full speed. This presents a variable power to the motor and complicates the sizing problem. In general we should ensure that 1. Peak load torque (or power) < Rated Motor torque (or power) x (1+Service factor/100%). The root mean square load torque (power) requirement must be less than 100% of the rated motor torque (power) and ideally greater than 75% of rated motor torque (power). 3. Check that the Motor can start the load and get it up to speed. First Example: Constant speed operation at rated speed but with variable torque eg Induction motor running at constant speed. Since the load is running at rated motor speed we do not need to calculate torques but can work in power instead. Root Mean Square Power is calculated as follows: For a load which requires power P 1 for time t 1 followed by P for time t followed by P 3 for time t 3 and so on up to P n for time t n in a cycle which repeats: Important Formula RMS power = P t Pt t + t 1 + P3 t Pnt + t t 3 n n 8 of 1

9 Example The following load torque profile was measured for a constant speed load. Choose an appropriately sized motor to drive this load assuming a service factor of 0%. You do not need to consider starting performance. Load Power 6kW 4kW Cycle Repeats kw 5s 10s 0s Time Sizing the motor 1. Peak Load Power requirement = 6kW. Peak load power must be less than Rated Motor Power x Service Factor => 6kW < P motor x 1. => P motor >6/1. = 5kW. The RMS load power should ideally be between 75% and 100% of Rated Motor Power. RMSLoadpower = P t Pt t + t 1 + P3 t Pnt + t t 3 n n = = 4.16kW If we choose P motor =5kW then RMS load power = 4.16/5*100% = 83% of P motor which is acceptable. NB Important If RMS load power turned out to be less than 75% of 5kW we soul dstill need to choose a 5kW motor in order to be able to supply the peak power 9 of 1

10 requirement. However if RMS load power was great than 100% of rated motor power we would need to choose a bigger motor to meet this requirement. 3. Starting Performance Not a requirement in this case: Answer: Choose a 5kW motor. Second Example: Contant Speed variable torque at a speed below rated speed (Example a DC motor running at less than rated speed). This is very similar to the first example but in this case In this case we must work in torque rather than power. Work out load torque requirements (peak and rms and compare with rated motor torque). Third Example: Variable Speed load. (EG variable speed induction motor drive). In this case we must work with torque rather than power. Also we must take accelerating torque into account. This depends on the desired speed versus time profile and the moment of inertia of the motor and load. 10 of 1

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