Error’s analysis

Usually, inaccuracies are inevitably during measurements of any kind. The reason for the development of measurement errors are very manifoldy, thus it is necessary to analyse the process of obtaining mea

(3.) the applied measuring method,

(4.) the personal characteristics and skills of the people performing the measurement and (5.) environmental conditions.

It is normally the case that for the development of a measurement error not only one single reason is responsible, but it is the result of a combination of many different error parts with different kinds of causales. Reducing the measurement error requires a quantitative description of error sources, a sufficient metrological experiences and the knowledge about the random or systematically character of errors. Three different kinds can be distinguished:

1. rough errors, 2. random errors, 3. systematic errors

ough er gs or

in either direction) in the easured data due to the precision limitations of the measurement device. The influence on e measurement result can be reduced by means of multiple repeated measurements and averag trast, are reproducible inaccuracies that are consistently

ecific regularity, they are in principle controllable,

allo cting for systematic error takes a lot

of esearches measurement errors

com lculations. Concerning the above presented laboratory

test calc

d.) Measurement of iron- and copper losses

R rors can occur because of inadvertence, wrong handling, incorrect readin damaged measuring devices. Generally, rough errors are avoidable and easy to identify.

During the laboratory tests of the three SRM prototypes, rough measuring errors can be excluded since all measurement devices have been checked and certificated; all measurements have been multiple repeated and then averaged.

Random errors can appear for a number of different reasons. They lead to a statistical distribution of the results, indifferent the source of errors can be described physically. But even if a measured value is reproducible, it can differ considerably from the true value.

Random errors occur due to the influence of many different stochastic events. They can not be corrected or ‘switched off’. They lead to statistical fluctuations (

m th

ing. Systematic errors, by con

in the same direction. Systematic errors are often due to a problem which persists throughout the entire experiment. The main casuals for such systematically errors are:

• The devices used for the measurement are calibrated wrongly.

• Problems during the applied method of measurement.

Since systematic errors occur with a sp

cateable and correctable. However, spotting and corre care. In the following, a structural error’s analyses r

pared to analytical and numerical ca

results for the three SRM prototypes, reasons for the variation measurement results from ulations will be pointed out for

a.) Dynamic inductance measurement

b.) Measurement of characteristics torque vs. angle c.) Measurement of characteristics speed vs. torque

a) Dynamic inductance measurement

The difference between measuring inductance by means of 50Hz-method and dynamic inductance was described in Chapter 6.1.1 and 6.1.2. It was found that measuring dynamic ind thod is preferable since it considers saturation effects of the iron and the non-sinusoidal current feeding. The difference between both methods for inductance

h calculation,

The me ristics are the same for

bot S nt errors are assumed. In the

rious simplifications with respect to d end-winding effects.

• ifier is not totally smooth in spite of a

oscillations of the torque during a hich presses on the digital weight is slightly t).

and averaging the measurement results minimizes that error.

uctance by di/dt-me

values in the aligned position is in the range of 10-20%. Compared to calculation results, the error of dynamic inductance is less than 6% (aligned position) for both FEM and analytical calculation. The maximum errors in unaligned position are 16% and 10% for analytical and numerical calculation, respectively (see also Table 6.1). The main reasons for those errors are

• simplification of analytical magnetic flux pat

• end-winding effects which are not considered by FEM and only rough considered in analytical inductance calculation,

• bouncing of the mechanical switch for turning on- and off the phase current,

• inaccuracies during reading the graphics on the oscilloscope (reading error) and

• fluctuations and small break-in of the dc-link voltage at the instant of current switch-on.

In order to minimize the measuring errors, all measurements have been multiple repeated and averaged. Thus, measurement- and calculation results match very well and the maximum error does not increase 16% for both SRM I and II, which is a quiet good result!

b) Measurement of characteristics torque vs. angle

asurement procedure for determining torque vs. angle characte h RM I and II, thus the same reasons for measureme

presented laboratory test results, a maximal error of 12% occurs compared to analytical calculations, and 7% compared to FEM. Reasons for that differences are very manifoldy; the most important ones can be summarized as follows:

• Calculation of torque vs. angle characteristics bases on inductance calculation and therefore includes the same systematically error as described above since the mathematical inductance model involves va

determining flux paths, saturation- an

The dc supply voltage provided by the 2-pulse rect large dc-link capacitor, leading to high-frequency fixed rotor position angle (the lever arm w

‘buzzing’ especially at high curren

• The rotor position sensor RENISHAW RE36 has a resolution of 360deg/(255steps)≈1,41deg/step. The digital display only shows full steps with integer number. Therefore the rotor position angle can not be exactly determined since rounding errors occur. Note, the same is true for the inductance measurement. However, repeating

Comparing measurement and calculation results shows: the measurement error is quiet small, the analytical and numerical SRM models provide very accurate and reliable results. The analytical calculation error is in the range of 10% and slightly increases for very high current level when the iron is strongly saturated. That is true for SRM I, II and III. The major error

so c the torque measuring shaft

si e

comp racteristics. An accurate calibration of the entire

m

c)

calculation rror occurs since the simulation model uses static torque- and inductance characteristics as a cs were determined by means of static

d)

Loss since

leadi with different frequencies

in i

commutation and high frequency harm investigation and the determ

must be recognized when measurement results are analysed and compared to calculations:

•

•

nce. Therefore measured ur e of torque measurement for SRM III is the resolution of

nc the torque values to measure are very small. Mechanical friction and vibrations quiet licates determination of T(i,Θ) cha

easurement system is absolutely essential.

Measurement of characteristics speed vs. torque

For SRM I and II speed vs. torque characteristics have been measured as a function of the current switching angles and a comparison to simulation results obtained with the program SIMPLORER^® 4.2 was shown. The results match very well, however a principle

e

function of angle and current. Those characteristi

analytical calculations respectively magnetostatic FEM computations and it is problematic to transfer these static calculations on dynamic measurements when the motor runs with high speed where among others mutual couplings play an important role. Nevertheless, the calculation error is less than 10% showing the high accuracy of the developed SRM models.

Measurement of iron- and copper losses

calculation- and measurement is one of the most difficult tasks during researching SRMs saturation effects occur and the motor is supplied by non-sinusoidal current waveforms, ng among others to non-sinusoidal magnetic flux-waveforms

d fferent parts of the magnetic circuit. Further, overlapping of phase currents during onics of the current waveform complicate the ination of iron and copper losses. The following error sources

Reading error from the oscilloscope for calculating the r.m.s. current from the real current waveform referring to (3.184) to determine the copper losses with (3.185).

The SKIN-effect occurring at high current frequencies is not considered in analytical calculations of copper losses and increases the phase resista

copper losses rise stronger with the motor speed then predicted.

• Calculation of core losses bases on analytical inductance calculation with all the simplifications mentioned above and also described in Chapter 3 (e.g. end winding effects, saturation, etc.), leading to a systematic error.

• The flux waveform in the different machine parts can differ from the idealized waveform shown in Chapter 3.5.2 due to overlapping of phase currents or high frequency harmonic oscillations of the phase current.

• Thermal effects are not considered in numerical and analytical calculations. However, operating temperature of the prototype all measurements have been performed with

SRMs. The phase resistance is of course also calculated assuming a warm winding. A further warming of SRM II during high speed where friction in the bearings produced unexpected much heat is not considered in calculations.

In spite of these error sources, the measurement results are quiet accurate and match well with the predicted values showing once again that the developed hybrid design- and calculation procedure proposed in this thesis gives reliable results, how simple it may be. The calculation error of copper losses of SRM II is in the range of 5-7% for the researched torque-speed range. The core losses have an error of 10-17% compared to the analytical calculation results.

These are very accurate results and allow a realistic determination of motor efficiency.