Abstract The application of error separation techniques to roundness measuring instruments is investigated experimentally, using digital computers. The accuracy of such techniques is substantiated by comparative measurements with two independent multi-orientation systems. Results obtained with these and other systems confirm that the errors of conventional roundness measuring instruments can be reduced by a factor of ten or more and meaningful polar graphs obtained at radial magnifications of up to one million. These advances in accuracy can be achieved in relatively poor working environments and with little extra skill on the part of the instrument operator.
1 Introduction
Advances in the design and manufacture of precision bearings are making increasing demands on the accuracy with which departures from roundness need to be measured. In the case of certain bearing components, notably those used in precision gyroscopes, accuracies are now being demanded which are of the same order as, or even less than, the rotational accuracy of a roundness measuring instrument's reference axis of rotation. A typical figure for the radial error? of a top class instrument spindle is 0.025 pm (1 pin). It is doubtful whether this figure can be improved significantly without considerable development and a large increase in manufacturing cost.A most attractive and cost effective solution to improving instrument accuracy is to identify and remove the systematicerrors of rotation of the instrument spindle. Whitehouse (1 976)has shown theoretically how multi-orientation and multiprobe techniques may be used to remove both systematic and random spindle errors. In this paper, practical systems based on multiorientation techniques are examined with the aim of extending the current limits of roundness measurement.
2 Limitations of conventional instruments
Most high accuracy roundness measuring instruments are limited in radial magnification to x 10 000 or x 20 000. This upper limit is chosen on the basis that at these magnifications, errors in the profile graph due to spindle error are barely perceptible and do not have significant effect on the profile. Much higher magnifications can be used but the resultant profile graph represents a combination of both spindle and component errors and needs very careful interpretation in order to be meaningful. To illustrate this point, it is interesting to examine the effect of measuring a precision component, in this case an optically polished glass hemisphere as used for testing roundness instruments, with a radial magnification of x 106. Operation at such a high magnification is greatly facilitated by operating the instrument on-line to a digital computer, using techniques similar to those described by Chetwynd and Kinsey (1973). In this particular case, a Talyrond 73 instrument was used on-line to a Hewlett Packard 2116C computer, with sampling of the transducer signal initiated by a radial grating mounted on the instrument spindle. The component was centred initially under manual controi such that its magnified profile could be contained within the limits of the polar chart at a magnification of x 20 000. Eccentricity terms were then calculated and subtracted from the transducer signal using the limacon approximation (Whitehouse 1973) as criterion for best fit. Remaining data were magnified by the computer and then displayed on the polar chart at a magnification of x 106. This process is essentially the same as physically centring the component and remeasuring it. However, the latter operation is exceedingly difficult to perform at magnifications in excess of 5 x 10*since the manual centring controls do not possess the required sensitivity. Using the computer, centred polar graphs can be obtained at very high magnification with an absolute minimum of setup time. Figure 1 shows some results obtained with this system and illustrates the variation of both graph shape and roundness
parameter values with relative orientation between component and spindle. All graphs are shown with the chart centre coincident with the least squares centre of the profile and the well known peak-to-valley (P+V), mean-line-average (MLA) and root-mean-square (RMS) parameters are listed. The variation of these parameters with orientation, plotted in graphical form, indicates a cyclical variation with a period of approximately 180" which suggests that the spindle and component errors are predominantly of second harmonic order. This is confirmed by the graphs of the individual spindle and component errors, shown for comparison purposes together withcorresponding parameter values. These errors were extracted from the combined error profiles using the reversal technique described subsequently.
Examination of the values listed in figure 1 soon reveals that any attempt to compensate for spindle error by subtracting a singleparameter value from the combined error value can give, at best, only a marginal improvement in the estimate of component error and, at worst, a completely misleading estimate. To increase the accuracy of a roundness measuring instrument, it is therefore not sufficient to merely increase its gain without in some way accurately compensating for its spindle error.
3 Multi-orientation techniques
To separate the spindle and component errors requires more information than can be obtained from a single roundness profile. Sufficientadditional information can be obtained either by multiprobe techniques, in which more than one transducer is used simultaneously or by multi-orientation methods, in which several measurements are made with differing relative orientations between component and spindle. A detailed
analysis of the possibilities of these techniques is given by
Whitehouse (1976); discussion here is confined to a brief
outline of the most suitable methods for high accuracy
roundness measurement.
Multiprobe techniques are particularly suited to in situ
measurement but are less attractive at very high accuracies
since very careful electrical and mechanical matching of the
transducers is necessary. A further difficulty is that of ensuring
coincidence of the plane of measurement for all the transducers concerned. After some consideration, it was decided to
restrict the investigation to multi-orientation methods in which
only one transducer is used.
All multi-orientation methods are dependent on both the
spindle and component errors exhibiting good short term
repeatability during the measurement cycle. Under controlled
environmental conditions, this requirement does not present
too much difficulty for the component but it does require that
the spindle errors exhibit only a very small amplitude of
random fluctuations. In practice, some random noise, whether
specific to the spindle or not, will be introduced into the
measurement system. However, providing this is not excessive,
it may be effectively removed by averaging the profile over
several revolutions and cancelling out random errors by integration. The effect of averaging can be seen from figure 1 in
which the combined error graphs are obtained from the
operation of a single stage 0-20 umt filter over one revolution
whereas the individual error graphs are produced after
averaging over 40 revolutions.
Two multi-orientation methods, differing in both technique
and analysis, were selected for investigation and comparison.
The first method, which we shall term the 'multistep technique'
(Reason 1966, Spragg and Whitehouse 1968) entails taking a
whole series of roundness profiles in each of which the component is stepped through equal angles relative to the spindle.
It is possible, in principle, to separate the errors from just two