TA priori evaluation of error in measurements of deviation from rectilinearity

Abstract

Analysis of the state of metrological methods for measuring deviation from rectilinearity and planarity of surfaces indicates that at the present time in industry hundreds of thousands of measurement devices (MD) are in use, the range of which comprises dozens of types. Both specialized and universal instruments are widely used in various branches of industry (machinetool building, heavy energy and transport machine building, ship building, aircraft building, etc.) to measure deviation from rectilinearity. The variety of engineering problems the solution of which requires measurements of deviation from rectilinearity and the corresponding variety of conditions in which these measurements are carried out, as well as the high requirements on their reliability, make the problem of evaluating error in measurement devices an entirely timely one. Error in working measurements is evaluated, as a rule, from the nominal metrologicaI characteristics of the measurement devices established in accordance with technical documentation and monitored through test procedures. In specific cases corrections are introduced to take influence functions into account. It is evident that the nominal metrological characteristics established by designers for certain definite conditions of use of MD do not take into account and, it is clear, cannot take into account the significant deviations possible in practice of the real conditions of use of MD from those for which the nominal metrological characteristics and influence functions were established. Thus, in measurements of deviation from rectilinearity of surfaces, the error in the result depends significantly on the characteristics of roughness and ripple of the surface. When optical instruments with open channels are used, random fluctuations in the index of refraction of the air in the line of measurement depending on local temperature and pressure gradients make a significant contribution to the error of the measurement. These and other sources of error in measurements under real conditions are in practice impossible to take into account in establishing the nominal metrological characteristics and influence functions without unjustified "hardening" of the MD. On the other hand, in these measurements information on the actual values of the measurement error, which with mathematical processing can be used to construct reliable a posteriori evaluations of the precision of the results, is preserved. In direct working measurements the result is obtained, as a rule, on the basis of a single measurement of the object, and the error is determined from known metrological characteristics of the MD. Experimental evaluation of the random component of the error is not used in the majority of practical instances, with the exception, perhaps, of measurements performed during research work. A basic factor limiting the use of a posteriori evaluation of error is the cost of performing and processing multiple observations. General introduction of measurement devices based on microcomputers and microprocessors is significantly reducing this limitation but is not removing it completely. The problem is that the time spent on a series of observations is determined not only by the speed of the recording apparatus but also by the spectral properties of the error: the frequency of readings taken should not significantly exceed the width of the error spectrum, i.e. the series of observations should not be performed over a too short time interval, since this leads to shifting (lowering) of the error evaluation. Moreover, for reliable evaluation of the error, the series should be sufficiently long, and so it is necessary in practice to perform ten to twenty times more observations than in error evaluation carried out using the predetermined metrological characteristics of the MD.