Application of sampling length and evaluation length in roughness measurement

Surface roughness values ​​are usually measured using light-section microscopes, interference microscopes and profilometers (meters). The reasonable selection of sampling length and evaluation length plays an important role in the evaluation of roughness values. However, in the use of instruments, the selection of sampling length and evaluation length is often not implemented according to the standard, which affects the accuracy of the measurement results. Therefore, it is particularly necessary to seek a correct implementation method for sampling length and evaluation length in instrument measurement.

1 Selection of sampling length and evaluation length

GB1031-83 "Surface roughness parameters and their values" gives the sampling length values ​​(Table 1), with a common ratio of 10½. The standard stipulates that the sampling length value should be selected from this series of values.

The purpose of specifying and selecting the sampling length is to limit and reduce the influence of surface waviness on the surface roughness measurement results, so that the obtained roughness value correctly reflects the roughness characteristics of the surface. In general, it can be selected according to the surface processing method and the size of the roughness parameter value. Appendix B of GB1031-83 stipulates the recommended sampling length value (Table 2).

Table 1 Sampling length values ​​(mm)

0.08

0.25

0.8

2.5

8

25

Table 2 Selected values ​​of sampling length l and evaluation length ln of Ra, Rz and Ry

Ra(µm)	Rz,Ry(µm)	l(mm)	ln=5l(mm)
≥0.008～0.02 ＞0.02～0.1 ＞0.1～2.0 ＞2.0～10.0 ＞10.0～80.0	≥0.025～0.10 ＞0.10～0.50 ＞0.50～10.0 ＞10.0～50.0 ＞50.0～320	0.08 0.25 0.8 2.5 8.0	0.4 1.25 4.0 12.5 40.0

The standard stipulates that when evaluating the roughness, a minimum length that can reflect the roughness characteristics of the machined surface must be taken, which includes one or several sampling lengths, and the sum of these sampling lengths is called the evaluation length.

The evaluation length value is selected according to the surface processing method and the corresponding sampling length according to Appendix B of GB1031-83. Generally, the evaluation length selected for the machined surface is 5 consecutive sampling lengths (Table 2). For surfaces with good processing uniformity, an evaluation length of less than 5 sampling lengths can be selected; for surfaces with poor uniformity, an evaluation length of more than 5 sampling lengths can be selected. If the evaluation length value has been indicated on the drawing or in the technical document, it should be implemented according to the provisions of the drawing or technical document.

The so-called "uniformity of the machined surface" refers to the degree of consistency of the roughness values ​​of various parts of the surface after processing. If the roughness values ​​obtained by continuously measuring several sections of the sampling length on a machined surface are the same, it means that the machined surface is uniform; on the contrary, if the roughness values ​​are different, sometimes even very different, it means that the machined surface is uneven.

The roughness of any surface is composed of a series of peaks and valleys of different heights and spacings, which reflect the microscopic geometric characteristics of the machined surface. From the appearance or feel, this characteristic usually always carries the characteristics of the processing method used in the surface processing process.
The surfaces processed by turning, milling and planing often have uniform spacing and clear tool mark directions, and their textures have obvious regularity. It forms a typical periodic profile (sometimes superimposed with different degrees of random components) with obvious cycles. This cycle reflects that the feed amount is uniform and equal, and the surface uniformity is good.

Although the grinding surface has general directionality, the spacing is usually irregular and the texture has no obvious regularity. The grinding surface is a surface produced by the reciprocating action of the abrasive, and often has no directionality. Grinding and lapping use grinding wheels and abrasives for cutting and polishing to make the surface smooth and flat. However, due to the irregular size of the grinding wheel grains, the size and shape of the abrasive grains, and the different cutting forces, the machined surface forms a random profile. Although there are periodic components, the random components are the main ones, and the surface uniformity is poor.

Therefore, the roughness of the machined surface is the result of the combined effect of multiple factors (machine tool-tool-workpiece system, machining method, cutting amount, cooling lubricant) during the machining process. The process of these factors is quite complex and constantly changing. Therefore, the roughness values ​​of different surfaces and different parts of the same batch of parts cut by different machining methods or under the same machining method and cutting conditions are not exactly the same. According to the unique surface characteristics of each machining method, Table 3 lists the empirical values ​​of sampling length and evaluation length selected by various typical methods.

Table 3 Experience values ​​of sampling length and evaluation length for common processing methods (mm)

Characteristics of surface profile	Sampling length l	Evaluation length ln
		GB1031 recommended value	Experience Value	American Standard ASA B46.1	British Standard BS1134
Relatively regular and uniform (such as turning, milling, planing)	2.5	(1～3)l	2l	(5～20)l	＞5l
Not very regular and uniform (such as fine turning, grinding, end milling)	0.8	(2～6)l	(3～4)l (3～6)l
Very irregular and uniform (such as finishing, grinding, polishing)	0.25	(6～17)l	(6～7)l
Extremely irregular and uniform (such as fine grinding, fine polishing)	0.08	—	(8～10)l (10～12)l
Note: For surfaces with good uniformity, the evaluation length can be a smaller value in the range listed in the table, otherwise a larger value can be selected. When the processed surface is uneven, it should be measured at least 3 different positions on the surface, and the roughness of an evaluation length (including several sampling lengths) should be measured at each position. The American National Standard ASAB46.1 "Surface Roughness, Waviness and Processing Texture" was first established in 1940. It was revised three times in 1947, 1955 and 1962 to ASA B46.1.1962, and the 1962 standard was reaffirmed in 1971. The American standard given in the table is ASA B46.1.1962, which was revised in 1978 to the current ANSI B46.1.1978 "Surface Structure Surface Roughness, Waviness and Processing Texture". The first national standard in the UK was BS1134:1950 "Evaluation of surface texture" published in 1950. The table shows the British standard BS1134:1961 "Evaluation of surface texture", which was revised in 1978 to BS1134:1972 "Methods of evaluation of surface texture". The sampling length series regulations of various countries are basically the same. All countries use 6 levels of 0.08, 0.25, 0.8, 2.5, 8 and 25mm. The British and American standards stipulate that 0.8mm is the preferred sampling length. For the control of the assessment length, the British and American standards stipulate the corresponding values ​​between the cut-off value and the stroke length.

2 Implementation of sampling length and evaluation length in measuring instruments

The profiler (meter) uses filters to suppress the influence of waviness to achieve the selection of sampling length. Usually, the filter characteristics change sharply at the cutoff wavelength. After the profile spectrum is filtered, the roughness with a spacing less than the cutoff wavelength passes without change, while the roughness with a spacing greater than the cutoff wavelength is completely suppressed.

The cutoff wavelength is the wavelength of a sine wave in the profile spectrum that is numerically equal to the sampling length. It is also customarily called the cutoff length, usually called the cutoff value. Therefore, the cutoff value of the instrument is equivalent to the sampling length during measurement.

The difference between the cutoff value and the sampling length is that the cutoff value is a means by which the obtained profile waveform can be limited to the sampling length for evaluation. The sampling length is a baseline length used to identify the surface roughness characteristics. It can distinguish the surface roughness parameter value from the unevenness with waviness and wave spacing greater than its value. [page]

When the recorder records the surface profile curve, the cutoff value does not need to be considered. When measuring with an average value scale, the cutoff value must be considered. The cut-off value knob is placed on the electrical box. There are usually three cut-off pitch values ​​(for TALY-SURF-4 profiler, the three levels are J, K, and L), which correspond to 0.25, 0.8, and 2.5 mm sampling length values ​​respectively.

To select the cut-off value, you should first understand the processing method of the test piece and make a preliminary judgment on the surface roughness value, and then determine it according to Table 4.

Table 4 Cut-off values ​​of profilometers

Cut-off value Switch position	Cut-off value (mm)	Selection range
		Processing methods	Ra(µm)	Rz,Ry(µm)
J	0.25	Precision and ultra-precision surface machining	＞0.02～0.1	＞0.1～0.5
K	0.8	General finishing surface	＞0.1～2	＞0.5～10
L	2.5	Ordinary turning, milling and planing surface	>2～10	＞10～50

The evaluation length is a necessary length for evaluating the surface roughness of the profile, which includes one or several sampling lengths. The evaluation length of the profiler (meter) is characterized by the instrument measurement stroke length. The measurement stroke length of the profiler (meter) is a trimmed profile length used to measure the surface roughness, that is, the stylus movement trajectory synchronized with the sensor generated by the filter during measurement. The measurement stroke length includes one or several sampling lengths.

The difference between the measurement stroke length and the evaluation length is that the "length" based on which the surface roughness parameter value is evaluated is different. The former is a trimmed profile length obtained by the profiler (meter) in actual measurement, while the latter is a theoretically defined length necessary for evaluating the surface roughness. It can be said that the stroke length is the specific embodiment of the evaluation length in actual measurement, which enables the profiler (meter) to realize the measurement of surface roughness parameters. The same thing

about the measurement stroke length and the evaluation length is that they both include one or several sampling lengths. Generally, the stroke length takes 5 cutoff values ​​(equivalent to 5 sampling lengths), which is consistent with the general selection of the evaluation length as 5 times the sampling length.

The stroke length knob is placed on the drive box and marked with three gears: J, K, and L. The position of the stroke length knob is determined by the position of the cutoff value knob, and the two must correspond one to one. The

stroke lengths of various profilers (meters) are not the same. The stroke lengths corresponding to the cutoff values ​​of 0.25, 0.8, and 2.5 mm for the J, K, and L gears of the TALYSURF-4 profiler are 0.25×8≈1.9mm, 0.5×8≈3.8mm, and 2.5×3≈7.6mm. When measuring, the stroke length knob is adjusted to a position consistent with the cutoff value knob. For example, if the TALYSURF-4 type measurement stroke length knob is in gear K, the roughness value measured by the instrument is the average value of a measurement stroke length of 3.8mm.

It must be pointed out that the currently used stylus profiler can directly measure the roughness (Ra) value. Generally, the result cannot be directly measured according to the definition of roughness Rz and Ry, but it can be calculated by recording the contour graph. At this time, it should be noted that the direction of the recorded graph should be on the horizontal line as much as possible, and the cutoff value should be measured on the overall direction of the contour. As long as the vertical magnification of the recorded graph is reliable and the horizontal magnification of the intercepted cutoff value is accurate, reliable Rz and Ry values ​​can be obtained.

Attention should be paid to the change of horizontal magnification. This change is obtained by changing the speed selection knob on the drive box to change the sensor movement speed, so it is important to correctly select the gear position of the speed knob. Table 5 gives the reference value of the speed selection knob.

Table 5 Profiler (meter) speed selection knob reference value

Speed ​​ Knob	Horizontal magnification Enlarge the magnification	use	Measured surface roughness value (µm)
			Ra	RZ, RY
N	—	The installation and adjustment of the measured part during manual measurement is equipped with a 500X transmission device for high-precision surface profile graphic recording.	0.01～0.02	0.05～0.1
AV	4	For average value meter readings and recording waviness graphs	—	—
20X	20	Record the surface contour graph of turning, milling, planing and hobbing processing; Record the waviness graph	＞1.25～10	＞6.3～40
100X	100	Record general surface roughness profile graphs	＞0.02～1.25	＞0.1～6.3

The general principle for selecting the speed knob is to make the distance between the peaks in the contour graph not too dense but to open them up. When the cutoff value is 0.8mm and the horizontal magnification is 20X, 0.8×20=16mm should be measured in the general direction of the contour graph.

The multi-parameter profiler can directly display the roughness RZ and RY values, but the roughness RY value displayed by the instrument is different from the roughness RY defined in the standard. Generally, it is the result given within the stroke length or the maximum value of the microscopic roughness height (adjacent peaks and valleys).

Light cutting microscopes and interference microscopes are usually used to measure the roughness RZ and RY parameter values. When measuring, the sampling length and evaluation length should be determined according to regulations. For roughness RZ, within the sampling length in the instrument field, the values ​​of the 5 highest points and the 5 lowest points are measured to calculate the roughness RZ value, and the roughness RZ values ​​on several continuous sampling lengths are measured within the evaluation length, and the average value is taken as the measurement result. If the diameter of the instrument's field of view is less than one sampling length or one evaluation length, and it is not possible to calculate according to the defined points when measuring arc surfaces (Table 6), in this case, the workbench must be moved during one measurement so that the measured parts are moved into the field of view in sequence. It is recommended to use the following method for calculation: divide the selected sampling length l into 5 equal components l'1, l'2, ... l'5, measure a maximum peak-to-valley height on each sampling length component (see figure) to obtain h1, h2, ... h5, and calculate

Table 6 Field diameter of light-section microscope

Objective lens nominal magnification	Measuring range RZ (µm)	Field of view diameter (mm)	Sampling length (mm)
7 14 30 60	25～100 6.3～25 1.6～6.3 0.8～1.6	2.5 1.3 0.6 0.3	2.5 0.8 2.5 0.25 0.8 0.25

It should be pointed out that each sampling length component must be continuous. In order to ensure l′1=l′2=…=l′5, the workbench should be moved evenly so that the workbench movement is equal. At the same time, pay attention to the movement of the measured surface profile from the eyepiece field of view to avoid repeated measurement of the same length profile curve. For roughness RY, if the instrument field of view diameter is less than a specified sampling length, the field of view diameter can be taken as the sampling length, the maximum peak-to-valley value can be taken within the observation range, and then a maximum profile height can be measured in the adjacent field of view. The larger of the two readings is taken as the measurement value of a sampling length. Strictly speaking, the roughness RZ and RY values ​​obtained by the above method are approximate values.