# Brush DC Motor Basics. by Simon Pata Business Unit Manager, Brushless DC

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1 thinkmotion Brush DC Motor Basics by Simon Pata Business Unit Manager, Brushless DC

2 Ironless DC Motor Basics Technical Note Brushed DC ironless motors are found in a large variety of products and applications such as medical, robotics, factory automation, security and access, civil aviation and aerospace products. The ironless technology surpasses by far the performance of conventional ironcore brushed DC motors. The main advantages of this unique concept are: absence of iron losses, low friction and a good thermal dissipation resulting in a very efficient motor meaning a perfect choice for battery operated equipment. The design of the low inertia rotor enables very high acceleration and fast reaction time. Finally the linear torque-speed characteristics make the motor very easy to drive. This article is a brief technical introduction on ironless DC motors. It is intended to help engineers to better understand the brushed DC ironless motors basics and to help them to select the best motor for their application. 1. The basics equations of the brush DC ironless motors: A motor with ironless rotor can be represented by the following simplified diagram. R I U O = RI + U 1 U O U 0 = power supply voltage, V I = current, A V i = voltage (EMF inducted in the rotor, V R = winding resistance, Ohms U i The voltage induced in the rotor is proportional to the angular velocity of the rotor U i = k * ω k: torque constant ω: angular velocity So the resulting equation is: U = R * I + k * ω (V (Ώ (A (Nm/a (rd/s (1

3 The particularity of the ironless DC motor is such as the speed and torque function are linear. The speed being proportional to the voltage and the torque being proportional to the current (2 T = k * ( I I O (Nm (Nm/A (A (A I: armature current I O : no load current 2. How to determine the mechanical power, the electrical power and the efficiency? The mechanical power developed by the motor is equal to the sum electrical power given to the motor and the power dissipated (heat: P elect = P mech + P J Input Losses P elect = U * I (3 P J = R * I 2 + k * I O * ω (4 Output P mech = T * ω (5 The efficiency is defined by the ratio of the mechanical power and the electrical power η = P mech / P (6 elect The efficiency of a brushed DC coreless motor may reach up to 90% To remember: the highest efficiency is obtained at high speed 3. Understand the equations - 4 things to remember: η : efficiency n: speed P: power I: current η : efficiency n: speed P: power I: current #1: the current in the motor is proportional to the motor torque #2: the speed of the motor is proportional to supply voltage #3: the maximum efficiency is obtained at high speed #4: the maximum mechanical power reaches its maximum when the load torque is equal to half the stall torque

4 4. How to determine the rotor temperature and the rotor resistance at this temperature (Brushed DC coreless motor maximum coil temperature is usually rated to 155 C R 22 * I 2 * (R th1 + R th2 * (1-22 α + T a T r = 1 - α * R 22 * I 2 * (R th1 + R th2 R = R 22 * (1 + α * Δ Temp (7 (8 T r : temperature of the rotor ( C R 22 : motor resistance at 22 C (Ohms - catalog value I: current (A R th1 : thermal resistance rotor/body ( C/W -catalog value R th2 : thermal resistance body/ambient ( C/W -catalog value α: thermal coefficient of the resistance of copper (0.0039/ C T a : ambient temperature ( C R: resistance (Ohms Δ Temp = Tr How to determine the time constant of the system and the starting time of a brushed DC ironless motor (voltage driven τ = τ M * ( 1 + J L / J M t = τ * ln (ω 1 / (ω 1 -ω τ: time constant of the motor + load (ms τ M : time constant of the motor alone (ms catalog value J L : inertia of the load (kgm2 J M : inertia of the motor (kgm2 catalog value t: starting time (ms ω 1 : angular velocity obtain after an infinite time (rd/s ω: angular velocity (rd/s after a time = t

5 6. The Portescap Brushed DC Ironless technology in one glance Long-life patented commutator system virtuall eliminated brush Models available from 8mm to 35mm diameter Select either sleeve or ball bearings Ironless rotor coil enables high acceleration Optional gearboxes and magnetic or optical encoders can easily be added High efficiency design is ideal for battery-fed applications Concept Detail Motor Characteristics Advantages for the Applications Low moment of inertia High acceleration, Ideal for incremental motion Linear speed-torque function, Insensitive to shocks Ironless Rotor No hysteresis and eddy current losses High efficiency, low losses from friction only Ideal for battery operation No magnetic saturation High peak torques without the risk of demagnetization Central Stator Magnet High power per size and per weight Ideal for portable or small equipment or requiring small dimenions Small Sized Bearings Precious Metal Commutation System Ratafente Series Copper- Graphic Commutation Low viscous damping Low starting voltage Low friction, little electrical noise High current densities may be commutated Rated motor temperature up to 155 C Very compact commutation system High torque to inertia ratio High peak speeds, very low speed dependent losses Low losses and wear, low electromagnetic interference High continuous and peak torques without the risk of demagnetizing the motor. Very long life. Ideal for chopper drives Continuous torque is exceptionally high for motr size, reducing the weight, dimensions, and the cooling system Excellent resistance to shocks and vibration High acceleration, short mechanical time constant 2009 Portescap, A Danaher Motion Company. ALL RIGHTS RESERVED.

6 7. How to select the appropriate Brush DC motor? Let s take a look using a miniature air pump application as an example. A 6 volts, 0.6 A battery operated miniature air pump needs to have a flow range of cc/min which is equivalent to T = 3mNm of torque at rpm (ω = rd/s. The requested mechanical power is; Pmech = T * ω = * = 2.82 W Portescap 16G brushed DC motor series is rated for 5W maximum output power. Let consider the 16G88-220E 1 (6v rated winding

7 First step is to calculate the current which is supplied to the motor under the conditions described above. T = k * ( I I O I = T / k + I O = / = A Second step is to determine the supply voltage to get the requested speed rpm (942.5 rd/s U = R * I + k * ω = 1.6 * * = 5.93 V < 6 V Thus the motor will reaches the desired speed under the specified torque within the limitations of the battery. Now we can determine the motor efficiency Pelect = U x I = 5.93 * = 3.45 W Efficiency = P mech / P elect = 2.82 / 3.45 = 81% The motor efficiency is above 80% which will contribute to very long battery life. Achieving such efficiency is only possible thanks to the Portescap state-of-the-art brushed DC ironless motor technology. Let consider this pump needs to reach at least 5000 rpm m in less than 15ms. Load inertia: 1 x 10-7 kg.m2 Rotor inertia: 0.91 x 10-7 kg.m2 τ = τm * ( 1 + J L / J M t = τ * ln (ω 1 / (ω 1 -ω τ = 5.3 * (1+1/0.91 = 11.12ms t = * ln (9000 / ( = 9ms < 15ms The speed of the pumps will be 5000rpm after 9ms. This excellent dynamic characteristic is due to the ironless rotor concept. The low moment of inertia of the rotor enables very high acceleration.

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