Fundamentals of test metrology
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Fundamentals of test metrology. Measurement technology is an advanced science with its own specialized framework, encompassing multiple disciplines, and characterized by both strong theoretical and practical aspects. Having a solid understanding of the basic knowledge in measurement techniques is the foundation for mastering measurement skills and independently carrying out the measurement of geometric parameters of mechanical products. 1.1 Definition of measurement: To determine whether a finished product meets the geometric accuracy requirements specified in the design, several methods are commonly used. Measurement: It is all the operations carried out with the aim of determining the value of the object being measured. In this process, the object under test is compared with a standard quantity of the reproduction measurement unit, and the measurement result is expressed as the ratio of the measured value to the unit quantity along with its accuracy. For example, measuring the diameter of a shaft using a vernier caliper involves comparing the object in question (the shaft’s diameter) to a unit of length (millimeters) through a specific measurement method (measuring with a vernier caliper). If the ratio is 30.52 and the accuracy is ±0.03 mm, then the measurement result can be expressed as (30.52±0.03) mm. Any measurement process consists of four elements: the object being measured, the unit of measurement, the measurement method, and measurement error. Test: refers to a measurement of experimental nature. It can also be understood as the entire process of testing and measurement. Testing: It is the process of determining whether the physical quantity being measured is within acceptable limits; in general, it involves checking whether a product meets the design requirements, that is, it is a process of assessing the product’s compliance, and it is not always necessary to determine the exact value. Therefore, testing can also be understood as a measurement that does not require knowing the specific values. Measurement: To achieve uniformity in measurement units and accurate and reliable values. 1.2 Measurement Standards A measurement standard is a measuring instrument that reproduces and preserves measurement units and possesses the characteristics specified for those units. In the field of geometric dimension measurement, measurement references can be divided into length references and angle references. Length standard: At its 17th General Conference on Weights and Measures in 1983, based on the report of the International Committee for Weights and Measures, the conference approved a new definition of the meter: “One meter is the distance that light travels in a vacuum in a time interval of 1/299,792,458 seconds.” Figure 1-1: Simplified table of length measurement verification systems. Length. The **primary, secondary, and working references established based on the definition of the meter generally cannot be used directly in production to measure parts. To ensure the rationality and consistency of measurement values, it is necessary to transfer the **benchmarks** with the highest metrological characteristics step by step in accordance with the provisions of the **Metrological Verification System**, all the way to various measuring instruments used for product testing. Figure 1-1 is a simplified table of the length (end dimension) measurement verification system. Angle reference: Angle measurements are different from length measurements. Since the commonly used unit of angle (degree) is defined by an inscribed angle, namely an inscribed angle equals 360°, and there are definite conversion relationships between radians and degrees, minutes, and seconds, it is not necessary to establish a natural basis for angles. 1.3 Gauge blocks: Gauge blocks are a type of measuring tool for parallel flat surfaces, also known as block gauges. It is an important and commonly used physical measuring tool to ensure consistency in length measurements. In addition to serving as a working standard, gauge blocks can also be used to adjust instruments, machine tools, or to directly measure parts. General characteristics: A gauge block is a physical standard whose length is determined by the distance between its two end surfaces; it is a single-value measuring tool. Its material and heat treatment process must meet the requirements for dimensional stability, high hardness, and good wear resistance. They are usually made of chrome-manganese steel, chromium steel, and bearing steel. Its linear expansion coefficient is the same as that of ordinary steel, namely (11.5±1)×10‑6 /℃, and its dimensional stability ensures that the annual variation does not exceed ±0.5～1μm/m. Structure: The vast majority of the blocks are made into right rectangular prisms, as shown in Figure 1-2 ； Cylinders with a diameter of φ20 are also available. Each gauge block has two parallel planes with extremely smooth surfaces and high flatness accuracy, which are known as the measuring surfaces (or working surfaces) of the gauge block. The length (dimension) of a gauge block refers to the distance between a point on one of its measuring surfaces and the surface of an auxiliary body (made of the same material as the gauge block) that is in contact with it (also known as the auxiliary surface). To eliminate the influence of the flatness error of the measuring surface of the gauge block and the parallelism error between the two measuring surfaces on the length of the gauge block, the working dimension of the gauge block is defined as its central length, that is, the length between the center points of the two measuring surfaces. Accuracy: Gauge blocks are classified into five “grades” based on their manufacturing accuracy: Grades 00, 0, 1, 2, and 3. Grade 00 has the highest precision, while grade 3 has the lowest. The grading is based on the limit deviation of the gauge block length and the allowable value of length variation. Most gauge block manufacturers sell these blocks to the market in terms of \"grades.\" As a result, users can only use the blocks according to their nominal dimensions, which inevitably leads to the influence of actual deviations in the center length of the blocks, thereby introducing manufacturing errors into the measurement results. In the work of value transfer, in order to eliminate the impact of manufacturing errors in gauge blocks on measurements, their actual dimensions as determined after calibration are often used. Calibration methods with varying precisions can produce gauge blocks with different measurement uncertainties, and the grade of these gauge blocks is determined accordingly, as shown in Figure 1-1. After calibration, the gauge blocks can have their actual deviations from the nominal center length determined. Obviously, when a set of gauge blocks is used in a \"balanced\" manner, higher measurement accuracy (lower measurement uncertainty) can be achieved. However, since using them on an “equal” basis is cumbersome and the inspection costs are high, they are still used on a “grade” basis in the production site. Usage: Using a single gauge block is very inconvenient; therefore, gauge blocks of various nominal sizes are usually provided in sets. When in use, several appropriate gauge blocks are selected as needed and combined for use. Generally, the total number of gauge blocks required to achieve the desired size should not exceed four. For example, to achieve a dimension of 89.765 mm, four gauge blocks with dimensions of 1.005 mm, 1.26 mm, 7.5 mm, and 80 mm can be selected from a set of such blocks. That is: 89.765 – 1.005 = 88.76; 88.76 – 1.26 = 87.50; 87.50 – 7.5 = 80.00. Precautions: When using gauge blocks, the following points should be taken into account: ① The gauge blocks must be within their valid usage period; otherwise, they should be sent to a professional facility for calibration promptly. ②The selected gauge blocks should first be cleaned in aviation gasoline and dried with a clean silk cloth; they can be used only after their temperature matches that of the surrounding environment. ③It is used in a favorable environment, which prevents various corrosive substances from damaging the gauge blocks and prevents dust on the working surface from causing scratches that could affect their ability to perform grinding tasks. ④Handle and place the blocks gently to prevent any collisions or drops. ⑤Do not touch the gauge blocks directly with your hands, to prevent sweat from corroding them and to avoid affecting the accuracy of measurements due to hand temperature. ⑥After use, the gauge blocks should first be cleaned with aviation gasoline, dried, coated with rust preventive grease, and then stored properly in a dedicated box. 1.4 Classification of measurement methods: Based on the different ways in which measurement results are obtained, they can be divided into direct measurement and indirect measurement: Direct measurement refers to obtaining the value of the quantity being measured directly from the reading device of the measuring instrument, or the deviation from a standard value. Such as measuring the shaft diameter using a vernier caliper or an outside diameter micrometer. Measurement in which the quantity to be measured is determined by measuring a quantity that has a certain functional relationship with it, based on the known functional relationship, is called indirect measurement. The actual value of the arc radius can be obtained by measuring the chord length and the arc height corresponding to the arc. Absolute measurement and relative measurement: A measurement in which the reading indicated by the measuring instrument directly reflects the value of the quantity being measured is an absolute measurement. Measuring the shaft diameter with a vernier caliper and an outer diameter micrometer is not only an absolute measurement but also an absolute measurement. A measurement in which the quantity to be measured is compared with a standard value to obtain the difference between the two is called a relative measurement. Measuring the hole diameter with an inner-diameter dial indicator is a relative measurement. Contact measurement and non-contact measurement: Measurement in which the probe of the measuring instrument makes contact with the surface of the part being measured, and mechanical force is applied, is known as contact measurement. Measuring surface roughness using a light-sectioning microscope is an example of non-contact measurement. Individual measurement and comprehensive measurement: The measurement of a single, individual parameter that is not related to other parameters is called an individual measurement. It involves measuring multiple parameters of a single part as well as their combined effects. Measuring the pitch diameter, half-angle, and pitch of a thread using measuring instruments is considered a single measurement task ； Testing threads with the go end of a thread gauge constitutes comprehensive measurement. Passive measurement and active measurement: Measurement after product processing is complete is considered passive measurement ； Measurements taken during the processing stage are active measurements. Passive measurement can only detect and identify defective items. Active measurement, through the feedback of its measured values, can control the processing process of equipment to prevent and eliminate the generation of defective products.
1.5 Measurement error: The measurement error arising from imperfections in the measurement process leads to uncertainty in the dispersion of the measured values. Therefore, during the measurement process, it is very important to correctly analyze the nature of measurement errors and their causes, to perform necessary data processing on the measured values, and to obtain measurement results that meet a certain required confidence level. Definition of measurement error: It is the difference between the measured value x of the quantity being measured and its true value x0, that is, △ = x – x0. Since the true value cannot be determined with exactness, this definition of measurement error is also an ideal concept. In practical work, a value with higher credibility (precision) than the measured value is often taken as the \"true value\" of that current measurement. Sources of error: Measurement errors are primarily caused by factors such as measuring instruments, measurement methods, measurement environment, and the personnel performing the measurements. ①Measuring instruments: Principle errors present in the design of measuring instruments, such as lever mechanisms and Abbe error. Errors in the manufacturing and assembly processes can also cause errors in its indicated value. Examples include manufacturing errors of ruled scales, errors in the production and calibration of gauge blocks, eccentricity in the marking and assembly of dials, errors in the magnification factor of optical systems, and gear indexing errors. The most important among these is the error of reference standards, such as the errors of scale rulers and gauge blocks, which are the main source of error in measuring instruments. ②Measurement method: In the indirect measurement method, errors arise from the use of approximate functional relationships, as well as from the accumulation of errors resulting from calculations on multiple data sets. ③Measurement environment: The measurement environment mainly includes factors such as temperature, air pressure, humidity, vibration, and air quality. In general measurement processes, temperature is the most important factor. Measuring errors can arise from the deviation of the measured temperature from the standard temperature (+20°C), temperature changes during measurement, as well as the temperature difference between the measuring instrument and the object being measured. ④Surveyor: The errors caused by the surveyor are mainly due to parallax, estimation errors, adjustment errors, etc., and their magnitude depends on the surveyor’s technical skills and other subjective factors. Error classification: Measurement errors can be classified into systematic errors, random errors, and gross errors, based on their causes, patterns of occurrence, and their impact on the measurement results. ①Systematic error: An error whose absolute value and sign remain constant or change according to a definite pattern under specified conditions is called a systematic error. Systematic errors whose absolute value and sign remain unchanged are constant systematic errors, while those that change according to a certain pattern are variable systematic errors. Such as the error of gauge blocks, the error of ruled scales, and the error of dial eccentricity. Most systematic errors can be eliminated by using correction values or by identifying their patterns of variation. ②Random error: Under specified conditions, an error whose absolute value and sign change in an unpredictable manner is called random error. For a single measurement, the occurrence of random error follows no pattern, and therefore cannot be eliminated. However, if multiple repetitions of equal precision are conducted, it exhibits the fundamental characteristic of having statistical patterns, just like other random events; by analysis, it is possible to estimate the range of random error values. Random errors are primarily caused by various random factors such as temperature fluctuations, changes in the measuring force, instability in the transmission mechanisms of measuring instruments, and parallax. Although they cannot be eliminated, their impact on the measurement results can be reduced by carefully analyzing the causes behind them. ③Large error: An error that significantly exceeds what is expected under specified conditions is called a large error. Large errors are caused by some abnormal factor. Such as incorrect readings, sudden large fluctuations in temperature, recording errors, etc. This error can be eliminated according to error theory, following certain rules. 1.6 Processing of measurement data: After correcting the known systematic errors and removing the significant errors, the measured values still contain random errors as well as some systematic errors. It is necessary to estimate the magnitude of these measurement errors and assess the uncertainty of the measured values. Only by knowing the measured values and their range of variation (confidence level) can a complete set of measurement results be obtained. Evaluation of measurement uncertainty: The uncertainty of measurement results, expressed in terms of standard deviation, is known as the standard uncertainty. Depending on the evaluation method used, it can be divided into two categories: The method that involves statistical analysis of a series of repeated measurements to calculate the standard uncertainty is referred to as Category A evaluation ； Evaluating the standard uncertainty using methods other than statistical analysis is referred to as Category B evaluation. Class A evaluation: According to statistical theory, the best estimate of the expected value of a random variable is the arithmetic mean x of n measured values*. x = ∑ *∕n. The estimated standard deviation S of the values in this set is given by S＝√∑（*－x）2∕（n－1）=√∑ui2∕（n－1). If the arithmetic mean is used as the result, the standard uncertainty is S_X = S∕√n. The measurement result can be expressed as x = x ±S_X. Category B assessment: In most practical measurement tasks, it is not possible or unnecessary to conduct multiple repeated measurements; in such cases, the uncertainty can only be determined using non-statistical analysis methods for Category B assessment. A Class B assessment requires a scientific judgment based on relevant information. The sources of this information include previous measurement data, product manuals for measuring instruments, calibration certificates, technical manuals, etc. If the uncertainty of a measuring instrument is found to be 6 μm according to the product manual, and a confidence level of 3 standard deviations corresponding to a normal distribution (99.73%) is desired, then the standard uncertainty under Category B assessment should be u = 6/3 = 2 μm. Estimation of the combined standard uncertainty: In the measurement process, there are usually multiple independent error sources that collectively affect the uncertainty of the measurement, and depending on the measurement method, the impact of each error source varies. The combination of the standard uncertainties of various error sources can be divided into the following two categories depending on the measurement method: ① Combined standard uncertainty for direct measurements: It is the square root of the sum of the squares of the standard uncertainties of each independent error source, that is, u=√∑ui2 + ∑uj2. ② Combined standard uncertainty for indirect measurements: In the case of indirect measurements, the measurement result is obtained by calculating it using the various indirect measurement values according to a pre-determined functional relationship. Since the standard uncertainties of various indirect measurement values have different impacts on the measurement result, when estimating the uncertainty of the measurement result, it is necessary to first compute the partial derivatives of each measurement value in the function to determine their uncertainty propagation coefficients. The standard uncertainty of each measurement value is multiplied by the corresponding propagation factor, and the square root of the sum of squares is taken to obtain the uncertainty of the measurement result. 1.7 Basic measurement principles In actual measurements, multiple methods can often be employed to measure the same quantity. To reduce measurement uncertainty, the following basic measurement principles should be followed as much as possible: The Abbe principle: which requires that the length being measured and the reference length be placed on the same straight line during the measurement process. If the length to be measured is placed side by side with the reference length, manufacturing errors and deviations in the direction of movement lead to an angle forming between the two lengths, resulting in significant measurement errors. The magnitude of the error depends not only on the angle between the two lengths but also on the distance between them; the greater the distance, the larger the error. Principle of unified reference: The measurement reference should be consistent with the machining reference and the usage reference. That is, process measurements should use the process criteria as the basis for measurement, while final inspection measurements should use the design criteria as the basis for measurement. Principle of shortest chain: In indirect measurement, other quantities that have a functional relationship with the quantity being measured form a measurement chain with that quantity. The more links in the measurement chain, the greater the uncertainty of the quantity being measured. Therefore, the number of links in the measurement chain should be reduced as much as possible to ensure measurement accuracy, a principle known as the shortest chain principle. Of course, according to this principle, it is best to use direct measurement rather than indirect measurement. Therefore, indirect measurement is used only when direct measurement is not possible, or when the accuracy of direct measurement cannot be guaranteed. A set of gauge blocks that forms the desired dimension using the smallest possible number of blocks is a practical application of the shortest chain principle. Principle of minimum deformation: Both the measuring instrument and the part being measured undergo deformation due to actual temperatures deviating from the standard temperature as well as forces applied (gravity and measuring forces), which results in measurement errors. During the measurement process, controlling the measurement temperature and its variations, ensuring that there is sufficient equilibration time between the measuring instruments and the parts being measured, selecting measuring instruments with a linear expansion coefficient similar to that of the parts being measured, choosing an appropriate measurement force and maintaining its stability, and selecting suitable support points are all effective measures to achieve the principle of minimal deformation.
1.8 Main technical performance indicators of measuring instruments: The nominal value of a measuring instrument is the value indicated on it to specify its characteristics or guide its use. Such as the dimensions marked on gauge blocks, the dimensions marked on graduated scales, etc. Scale: A combination of linear markings on a measuring instrument that indicate different values is called a scale. Scale spacing: The distance between the centers of two adjacent scale marks, measured along the length of the scale, is known as the scale spacing, or also referred to as the ruler spacing. Division value: The difference between the values represented by two adjacent markings is called the division value of the instrument. It is the smallest unit of value that an instrument can read. Generally speaking, the smaller the division value, the higher the precision of the measuring instrument. Digital measuring instruments do not have scales or dials; instead, resolution is used to represent them. Resolution is the measured value represented by the interval between the last digits displayed by the instrument. Range of indication: The range from the lowest value to the highest value displayed or indicated by a measuring instrument is called the range of indication. Measurement range: The range from the lower limit to the upper limit of the quantity being measured that an measuring instrument can determine, within the allowable uncertainty. The difference between the measurement range and the indicated value range is that the measurement range includes not only the indicated value range as shown in Figure 1-3, the comparison diagram of measurements, but also the adjustment range of certain components of the instrument. For example, if the measurement range of an outside diameter micrometer is 0–25 mm, 25–50 mm, 50–75 mm, etc., its indication range is always 25 mm. The measurement range of the comparator is 180 mm, while its indication range is ±0.1 mm (as shown in Figure 1-3). The indication range is related to the scale, while the measurement range depends on the structure. Range: The difference between the upper and lower limits of the measurement range is called the range. Instruments with a large measurement range are more convenient to use, but their linear error increases as a result, reducing the accuracy of the instrument. Sensitivity: The ability of a measuring instrument to respond to changes in the value being measured is called sensitivity. For ordinary length measuring instruments, the sensitivity is equal to the ratio of the scale spacing a to the division value I; it is also known as the magnification ratio or the number of digits of magnification K, that is, K = a / I. Measuring force: When measurement is carried out using the contact method, it refers to the force of contact between the sensor of the measuring instrument and the surface of the part being measured. The measuring force and its variations can affect the accuracy of the measurement results. Therefore, the vast majority of measuring instruments that use contact measurement methods are equipped with a measuring force stabilization mechanism. Indication error: The difference between the indication of the measuring instrument and the true value of the quantity being measured. For example, if the diameter of a shaft is measured with a micrometer and the reading obtained is 31.675 mm, while the true value is 31.678 mm, then the indicated error of the micrometer is equal to 31.675 – 31.678 = –0.003 mm. Clearly, the indicated errors of measuring instruments vary at different readings. Currently, the accuracy of measuring instruments is mostly expressed using the limit of indication error, which serves as the boundary value for the indication error of such instruments. Return error: It refers to the absolute difference between the two readings, under the same conditions with an unchanged measured value, when the direction of movement of the measuring instrument is different. This error is caused by factors such as gaps, deformation, and friction in the measurement system of the measuring instrument. When it is required that the displayed measurement value changes continuously back and forth (with continuous positive and negative value variations), a measuring instrument with a smaller backtracking error should be selected. Measurement uncertainty: Measurement uncertainty is a parameter that expresses the dispersion of the measured value in the measurement result. Due to imperfections in the measurement process, the measured values always deviate from the true value, and this deviation is uncertain. The parameter that expresses this degree of uncertainty is known as uncertainty. Correction value: A specific value indicated on the calibration certificate to correct the indication error of a measuring instrument. Its magnitude is equal to the absolute value of the indication error, with the opposite sign. Adding the appropriate correction values to the measurement results can improve the accuracy of the measurements. 1.9 Selection of measuring instruments In the past, most factories chose measuring instruments based on experience. Typically, the maximum allowable measurement error of the measuring instrument is chosen to be 1/3 to 1/5, or 1/3 to 1/10 of the tolerance of the workpiece. For some high-precision workpieces, a value of 1/2 is even used. In short, there is no unified standard; it often varies from person to person and from factory to factory. Not only that, but in most factories, when using measuring instruments to inspect workpieces, the acceptance limits are set based on the extreme dimensions specified in the drawings. This method of aligning the acceptance limit with the ultimate dimensions of the workpiece often leads to \"incorrect acceptance\" and \"incorrect rejection\" due to inherent errors in the measuring instruments and measurement conditions, resulting in numerous quality issues and unnecessary losses. The so-called “wrong acceptance” refers to the situation where substandard products are mistakenly deemed to be qualified and thus accepted ； The so-called \"wrong rejection\" refers to the situation where a product that is actually qualified is mistakenly judged as unqualified and thus rejected. Selection principle: Choosing measuring instruments appropriately is of great significance for ensuring product quality, improving measurement efficiency, and reducing costs. Generally speaking, the choice of equipment depends primarily on the precision requirements of the workpiece to be inspected. While ensuring these precision requirements are met, factors such as size, structural shape, material, and the position of the surface to be inspected also need to be considered. Additionally, factors like the batch size of the workpieces, the production method, and production costs must also be taken into account. For large batches of workpieces, specialized measuring instruments are commonly used, while for small batches of individual pieces, general-purpose measuring instruments are more frequently employed. Selection method: First, based on the tolerance value of the workpiece under inspection, determine the safety margin A and the allowable uncertainty value U1 for the measuring instrument from Table 1-4. Then, refer to Tables 1-5 through 1-7 to select a measuring instrument such that its uncertainty value U1 is ≤ U1. Finally, calculate the acceptance limit. For example: If the workpiece is marked with certain values on the drawing, what measuring instrument should be used to take measurements and determine the acceptance limits? Solution: (1) Determine the safety margin A and the allowable uncertainty value U1 for the measuring instrument. Using the tolerance value of 0.46 mm, Table 1-4 shows that A = 0.032 mm and U1 = 0.029 mm. (2) Select the measuring instrument. Since the workpiece dimension is 250 mm, it falls within the range of 200 mm to 500 mm as indicated in Table 1-5; accordingly, the uncertainty value for a vernier caliper with a division value of 0.02 mm is U1/ = 0.02 mm