MethodToEstimateRA031705-1

# MethodToEstimateRA031705-1 - i Method To Estimate RA...

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Method To Estimate RA Contents M. D. Fox 3/20/05 Estimating R A ................................................................................................................. 1 Abstract ............................................................................................................... 1 Introduction ........................................................................................................ 1 Theory .................................................................................................................. 2 General ........................................................................................................... 2 Determine R A from experimental data ........................................................... 2 Methods .............................................................................................................. 3 Results ................................................................................................................. 4 Result 1 .......................................................................................................... 4 Framework for taking raw data. ............................................................... 4 Framework for assigning data to the variable d1. ......................................... 4 Framework for fitting and plotting data. ..................................................... 5 Determination of Ra. ................................................................................ 6 Testing the Result ........................................................................................... 7 Plot experimental points and theory line in one step ...................................... 8 Discussion and Conclusions ..................................................................... 9 i ©1988-200 5 FOX Research All rights reserved.

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Estimating R A Martin Fox 3/16/05 Abstract The armature resistance R A must be deduced to be able to calculate the droop in speed with increasing torque in DC motors, and to estimate electrical losses and separate them from mechanical losses. The basic equation for a DC motor is f = V A ÅÅÅÅÅÅÅÅÅ C - i A R A ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ C which relates the output frequency of the rotary pulse encoder [RPE] to the measured armature voltage and current. To deduce the unknown constants C and R A from a set of measurements of f versus V A and I A it is necessary to do a multivariate regression. Performing such a regres- sion using Mathematica indicated that for the particular DC motor studied in this experiment, the armature resistance was estimated to be 15.1219 Ohm. Introduction For a DC motor, we know that the speed varies linearly with the internal or generator voltage E A . For no-load conditions, we can usually get a straight line relationship between the applied external voltage V A and the motor speed, since current draw is small. Such a relationship will exhibit an offset from the origin that can be used to deduce the armature resistance if the current draw of the motor is known. In this note we will provide an example of how to do this calculation using the multvariate regression function in Mathematica . By providing the constants that give the best fit for a number of experimental points, this provides an approach to estimation of the effective armature resistance under dynamic conditions.
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