Principles and sources of systematic error in the roundness measurement system using a coordinate measuring machine

Thread Content

Roundness falls under shape errors in geometric tolerances. Besides the roundness gauge, there are various other methods for measuring roundness, such as the two-point method, the V-block method, and the dial indicator method. However, these methods yield less accurate results due to the small number of points taken for measurement, and data processing is also complicated. Even with a roundness gauge, larger workpieces cannot be measured. Edward’s 3D coordinate measuring machine is convenient for data collection, offers high measurement efficiency, and can measure large workpieces; therefore, it is necessary to explore methods for using 3D coordinate measuring machines to measure roundness. 1. Single-point measurement: Since a single-point touch measurement yields discrete points, least squares method is used for calculation and evaluation. When using least squares method for calculation, the sampling points are generally even in number and evenly distributed. When using the single-point method for roundness measurement, the number of sampling points should not be too low, as this will prevent an accurate representation of the roundness. Generally, 16 points or more are sufficient to reflect the basic contour shape of the circle being measured; if a more precise depiction of the shape is desired, the number of measurement points can be increased, such as to 24 or 32. Automatic measurement is generally used during sampling, as manual sampling makes it difficult to control the vector direction. The single-point touch measurement method is characterized by high measurement efficiency and minimal wear on the measuring ball. 2. Scan measurement: To obtain the complete shape, a scanning method can be used. With this method, a complete contour is obtained, which is then evaluated using the minimum enclosing region technique. The scanning method is characterized by slightly lower efficiency, but it allows for a detailed analysis of the part’s contour. Both methods can provide accurate measurements of roundness, and the choice can be made based on actual requirements. 3. Influence of surface roughness on roundness error: Surface roughness has a significant impact on roundness error. Based on the characteristics of roundness, surface roughness and waviness should be removed from the roundness measurement, and this is achieved through filtering. Roundness meters are equipped with specialized electronic filters, featuring cutoff frequencies such as 1–15, 1–45, and 15–450 cycles per revolution, which indicate the number of sine waves per rotation. Edward coordinate measuring machines also provide corresponding digital filters (commands) to perform the same function, with the frequency expressed in terms of the number of measurement points. The purpose of selecting a cutoff frequency is to suppress higher harmonic components (surface roughness and waviness). The cutoff frequency is determined primarily based on the process requirements, that is, whether surface roughness and waviness have a significant impact on the parts. In most cases, a value of 15 is used; however, when it is necessary to analyze the roughness components, a higher cutoff frequency is chosen, such as 50, 150, 500, etc. Principle of systematic error: The difference between the average result of numerous repeated measurements of the same quantity to be measured and the true value of that quantity. Generally speaking, imperfections in the measurement steps can lead to errors in the measurement results, some of which stem from systematic errors and others from random errors. Random error is assumed to arise from unpredictable sources of variation or random temporal and spatial variations in the effects. Some systematic errors can be eliminated or usually reduced if the system arises from identifiable effects of the influencing quantities on the measurement results. Sources of systematic error: Instrument error: Caused by defects in the instrument itself or by using it under conditions that are not specified. Errors that arise from an inaccurate zero point of the instrument, improper calibration of the instrument, and the influence of the external environment (light, temperature, humidity, electromagnetic fields, etc.) on the measuring instrument. Theoretical error (methodological error): refers to the errors that arise from the approximations in the theoretical formulas on which measurements are based, or from experimental conditions that do not meet the requirements specified by those formulas, or from imperfections in the experimental methods themselves. For example, in thermal experiments, the heat loss caused by heat dissipation is not taken into account, and when measuring resistance using the volt-ampere method, the effect of the internal resistance of the meter on the experimental results is not considered. Operational error: refers to the errors that arise from differences in the responses of an observer’s sensory organs and motor skills, as well as from individual differences; it varies from person to person and is related to the observer’s mental state at the time. Reagent error refers to the deviation between the measured result and the actual value, caused by impurities in the distilled water used or by the impurity in the reagents employed. Some systematic errors are constant, such as an inaccurate zero point of the instrument, while others are cumulative; for example, when using a steel ruler that expands due to heat for measurement, the reading will be lower than its actual length. It should be noted that systematic errors always cause the measurement results to deviate in one direction, either being too high or too low; therefore, taking an average of multiple measurements does not eliminate systematic errors. Computers can also make errors when processing data; for example, when dealing with numeric fields, the results obtained can be inaccurate due to differences in the number of bits used for processing, which is similar to the results produced by using the rounding method in our calculations.