DC Motor-Examples. Dr. Kurtuluş Erinç Akdoğan.

Transcription

1 DC Motor-Examples Dr. Kurtuluş Erinç Akdoğan

2 Example 1 Motor 1624T009S is to be operated with 9 volts applied to the motor terminals. The torque load is 1.41mNm(0.2 oz-in). Find the resulting motor speed, motor current, efficiency, and mechanical power output. From the motor datasheet, it can be seen that the no-load speed of the motor is 11,700 rpm (Note: Ignore that it is given in datasheet a close but different value).

3 A part of Datasheet of Motor 1624T009S You can find complete datasheet from course webpage.

4 Example 1 What will be the winding temperature of DC motor, if it operates at a 22 C room temparature? Thermal resistances of DC motor are given in its datasheet as Rth1=8 C/watt and Rth2=39 C/watt. Solution: Check the uploaded the document titled as DC motor calculations. Note: In these document calculations use oz-in units rather than Nm. Don t forget to convert units.

5 Example 1 How much torque the motor can safely provide without overheating, if the maximum allowable winding temperature is 100 C? Solution: Check the uploaded the document titled as DC motor calculations. Note: There is a mistake in the solution at the end of DC motor calculations. Torque constant must be oz-in instead of oz-in. Recalculate this solution with the true torque constant.

6 Example 2: How to select a DC Motor? This example is given in the course notes of Actuators and revisited again to clarify some parts of the solutions

7 Selecting a DC Motor Constant current operation of a DC motor produces constant output torque regardless of speed. Given a constant load (torque requirement) the motor speed is determined solely by the applied voltage. Power is the product of speed and torque. Maximum power is produced at an operating point that is defined by half the no-load speed and half the stall torque. A motor will seldom be operated at maximum output due to thermal considerations. As a rule of thumb, DC motors are typically operated at 70% to 90% of the no-load speed and from 10% to 30% of the stall torque. This is the region of maximum efficiency. For DC motors operated at a constant voltage, the higher the torque output, the lower the speed will be. Other factors to consider are size, environmental factors, weight and required life

8 Motor for a CPAP Pump The torque required is 3.5mNm at a speed of 5000rpm A 20V supply is available Select a dc motor satisfying these requirements.

9 Output Power The conversion factor for rotational speed from rpm (n) to rad/s (), 2/60 = The output power is P o = P o n W The motor rating should be 1.5 to 2 times the desired output power Therefore P mot = 2.7 to 3.6 W

10 Possible Maxon Motor Referring to the Maxon catalog the smallest motor to achieve this power rating is the RE 16 series (16 mm diameter 40 mm long). The 24 V version has the closest operating voltage to the 20 V available. No load 24V n o (rpm) 7250 No load current I o (ma) 3.11 Terminal resistance R () 42.8 Torque constant K m (mnm/a) 31.4 Speed Constant K s (rpm/v) 304 Output power P o (W) 3.2 Maximum winding temperature, T max (C) 85 Thermal resistance: housing ambient, R th1 (C/W) 30 Thermal resistance: winding housing, R th2 (C/W) 8.5

11 Three constans have relationship below k T = k E =1/k s Torque constant K m (mnm/a) 31.4 Speed Constant K s (rpm/v) 304 Using the conversion factor for rotational speed from rpm (n) to rad/s (), 2/60 = /(304x0.1047)=31.4mNm/A

12 No-load Speed at 20V As a first approximation, the no-load speed can be found by taking the specified value and scaling it by the ratio of the voltages n no rpm Since the desired speed is 5000 rpm, this represents 82% of the no-load speed, which falls well within the 70% to 90% range, and so the motor will operate at optimum efficiency.

13 Approximation of relationship between V and no load speed a typical DC motor circuit. For DC motors, the torque and electrical constants, k T and k E, are equal, so the angular velocity equation can be simplified to: No load speed of a DC motor is directly proportional to voltage source since T=0 at no load speed by neglecting no load current. However, I=T/k T + I 0. f

14 w Actual relationship between V and no load speed At no load speed, I 0, I=3.11mA (no load current) V IR K e s K e IR ( V IR) K ( ) rpm is 5rpm more that given 7250 given in datasheet. If no load current is neglected, this result is found as 7296rpm V IR w K e ( V IR) K ( ) 304 s If no load current is neglected, this result is found as 6080rpm w V 7255rpm 6039rpm

15 Torque Speed Relationship No load speed decreases from 7255rpm to 6039rpm in proportion to decrasing voltage supply from 24V. mot s s n mot s s n

16 Motor Current The current through the motor is the sum of the no-load current and the load current The no-load current is neglected as it is very small. Therefore I K m ma 31.4 If no load current is not neglected I ma

17 Actual Motor Speed The volt drop across the motor windings is the product of the motor current and the terminal resistance V = IR. The reduction in motor speed is equal to the product of this volt drop and the speed constant Therefore the motor speed is n n 20 IRK s rpm This is close enough to 5000rpm that the motor would probably be ok 3

18 Motor speed calculation formula w V IR K e If no load current is neglected. If no load current is not neglected w ( ( ) rpm n n 20 IRK s rpm ) K s