TWI534410B - Linear shape measurement method and linear shape measuring device - Google Patents

Description

Linear shape measuring method and linear shape measuring device

The present invention relates to a method and a measuring device for measuring a linear shape of a surface of an object to be measured.

A technique of measuring the straightness of the surface of an object to be measured by a three-point method is known (Patent Document 1). In the successive three-point method, the heights of three points are simultaneously measured by three sensors arranged at equal intervals, and the degree of local curvature (curvature) of the plane is obtained from the measurement results. The linear shape of the plane is obtained by second-order numerical integration of the obtained curvature by the distance between the sensors.

Patent Document 2 discloses a method of obtaining a straightness by adding a fourth sensor to three sensors used in the three-point method. The three sensors are equally spaced, and the fourth sensor is disposed on the inner side of the sensor at the end of the three sensors, spaced apart by a smaller pitch δ P . In the method disclosed in Patent Document 2, the height of the surface of the object to be measured is measured while moving the sensor unit including the four sensors at a pitch δ P .

(previous technical literature) (Patent Literature)

Patent Document 1: Japanese Laid-Open Patent Publication No. 2003-232625

Patent Document 2: Japanese Laid-Open Patent Publication No. 2007-333556

It is clarified that the reproducibility of the measurement results of the machined surface having the surface roughness of the non-mirror of the conventional three-point method is low. For example, if the linear shape of the surface of the same object is measured over a length of 1 m, a deviation occurs in the range of several μm per measurement. Therefore, the conventional three-point method cannot be applied to the evaluation of the processed surface of the linear shape with an accuracy of about 1 μm or less.

An object of the present invention is to provide a linear shape measuring method and a linear shape measuring device capable of measuring a linear shape of a surface of an object to be measured with good reproducibility.

According to one aspect of the invention, there is provided a method for measuring a linear shape, comprising: arranging three sensors arranged at equal intervals in a first direction against a surface of a workpiece, and the first object along the first object a process of collecting the height data of the surface of the object to be measured at a sampling interval of 1 mm or less with respect to the relative movement; and sampling points distributed on the surface of the object to be measured at the sampling interval along the first direction according to the height data The process of curvature; and The process of determining the linear shape of the surface of the object to be measured is based on the aforementioned curvature.

According to another aspect of the present invention, a linear shape measuring apparatus includes: three sensors arranged at equal intervals along a first direction; and a moving mechanism that supports the sensor opposite to a surface of the object to be measured, And moving the object to be measured relative to the first direction in the first direction; and the processing device controls the moving mechanism to move the sensor in the first direction, and collects height data measured by the sensor, In the processing apparatus, the sensor is configured to collect the height data at a sampling pitch of 1 mm or less while moving in the first direction, and to obtain the sample to be measured at the sampling pitch along the first direction based on the height data. The curvature of the sampling point on the surface is obtained by determining the linear shape of the surface of the object to be measured based on the curvature.

By calculating the linear shape using the height data of the sampling points sampled at a pitch of 1 mm or less, it is possible to reduce the deviation of the measurement results of the linear shape of the surface including the surface roughness as compared with the conventional three-point method.

10‧‧‧ movable workbench

11‧‧‧Workbench guidance mechanism

12‧‧‧guide track

13‧‧‧Wheel head

14‧‧‧ grinding wheel

15‧‧‧Processing device

16‧‧‧ Input device

17‧‧‧Output device

20‧‧‧Measured objects

30‧‧‧Sensor unit

31i, 31j, 31k‧‧‧ sensors

A, B, C‧‧‧ measured points

P‧‧‧sensor spacing

△p‧‧‧Sampling spacing

Fig. 1A is a perspective view of a linear shape measuring device based on an embodiment Fig. 1B is a schematic view of a sensor and an object to be measured attached to the lower end of the grinding wheel head.

Fig. 2 is a graph showing the result of measuring the linear shape of the object to be measured by a conventional three-point method.

3A and 3B are schematic views of the surface of the object to be measured and the sensor unit.

Fig. 4 is a flow chart based on the linear shape measuring method of the embodiment.

FIGS. 5A and 5B are schematic diagrams showing time courses of the positional relationship between the object to be measured and the sensor unit when the linear shape is measured by the method according to the embodiment.

Fig. 6 is a line diagram showing the positional relationship between the origin of the sensor and the point to be measured.

Fig. 7 is a graph showing an example of the curvature ρ calculated using actual measurement data.

Fig. 8 is a line diagram showing the relationship between the origin of the sensor and the position of the measured point.

Fig. 9 is a graph showing the results of five straight line shape measurements along the same straight line on the surface of the object to be measured by the method according to the embodiment.

Fig. 10 is a line diagram for explaining the principle of a method of calculating a straight line shape by a method based on other embodiments.

A perspective view of a linear shape measuring device according to an embodiment is shown in Fig. 1A. This linear shape measuring device is mounted on a surface grinding device. Start work The stage 10 is supported by the table guiding mechanism (moving mechanism) 11 so as to be movable in one direction. The xyz rectangular coordinate system that defines the moving direction of the movable table 10 as the x-axis and the vertical lower side as the y-axis is defined.

The guide rail 12 supports the grinding wheel head 13 above the movable table 10. The grinding wheel head 13 is movable along the guide rail 12 in the z-axis direction. Further, the grinding wheel head 13 can be raised and lowered in the y direction with respect to the movable table 10. A grinding wheel 14 is attached to the lower end of the grinding wheel head 13. The grinding wheel 14 has a cylindrical outer shape, and its central axis is attached to the grinding wheel head 13 in a posture parallel to the z-axis.

The object to be measured (ground material) 20 is held on the movable table 10. When the grinding wheel 14 is brought into contact with the surface of the object to be measured 20, the movable table 10 is moved in the x direction while rotating the grinding wheel 14, whereby the surface of the object 20 can be ground.

Various command values required to measure a straight line shape are input from the input device 16 to the processing device 15. The command value includes a moving speed of the movable table 10 when measuring a straight line shape, a spatial frequency of the surface roughness, a measurement start signal, and the like. The processing device 15 calculates a straight line shape based on the measurement result, and outputs the result to the output device 17.

As shown in FIG. 1B, the sensor unit 30 is attached to the lower end of the grinding wheel head 13. Three sensors 31i, 31j, and 31k are mounted in the sensor unit 30. The sensors 31i, 31j, and 31k are opposed to the surface of the object 20 to be measured. As the sensors 31i, 31j, and 31k, for example, a high-resolution laser displacement meter having a degree of amplitude capable of detecting surface roughness, for example, a displacement of ultra-fine level or lower is used. The sensors 31i, 31j, 31k are capable of measuring the distance from the origin of each of the sensors 31i, 31j, 31k to the surface of the object 20 to be measured from. The calibration is performed such that the heights of the origins of the sensors 31i, 31j, 31k when the zx plane is the reference are equal.

The three sensors 31i, 31j, and 31k are arranged at equal intervals in the x direction. The pitch of the origins of the sensors 31i and 31j adjacent to each other and the pitch of the origins of the sensors 31j and 31k are referred to as sensor pitches. The sensor spacing is denoted by p. The measured points of the three sensors 31i, 31j, 31k are also arranged on the surface of the object 20 in the x direction at the sensor pitch p. The sensor pitch p is, for example, 100 mm. The grinding wheel head 13 is measured while moving relative to the object 20 in the x direction, whereby the linear shape of the surface of the object 20 in the x direction can be measured. Further, actually, by moving the movable table 10 in the x direction, the object to be measured 20 is relatively moved in the x direction with respect to the grinding wheel head 13. Measurement data is input from the sensors 31i, 31j, and 31k to the processing device 15 (Fig. 1A).

Referring to Fig. 2, a problem in the case of measuring the linear shape of the object to be measured by a conventional three-point method will be described. In the conventional three-point method, the sensor unit 30 (Fig. 1B) is moved in the x direction at a sampling pitch equal to the sensor pitch p, and is measured by the sensors 31i, 31j, 31k. Measure the height of the surface of the object. The curvature of the measured point (sampling point) is obtained from the measurement result. The linear shape of the surface of the object to be measured is obtained by performing second-order integration on the obtained curvature at the sampling pitch. In order to evaluate the measurement results based on the conventional three-point method, five measurements were made along the same line on the surface of the object to be measured.

The results of the five measurements are shown in Fig. 2. The horizontal axis represents the distance from the reference point on the measured line in units of "mm", and the vertical axis is in units of "μm". Indicates the displacement from the reference height of the surface of the object being measured. The symbols of the star, the quadrangle, the triangle, the hexagon, and the circle in Fig. 2 indicate the first to fifth measurement results, respectively. As shown in Fig. 2, it can be seen that there is a large variation between the five measurement results.

For example, in the fifth measurement result (circular mark), the surface is lowered by about 2 μm from a measurement distance of 400 mm toward a position of 600 mm, but in the second measurement result (quadruple mark), the surface is measured from a distance of 400 mm to a position of 600 mm. It rises by about 5 μm. Thus, since the measurement results are inconsistent, the linear shape cannot be measured with high accuracy.

Refer to Fig. 3A and Fig. 3B for explaining the cause of the deviation of the measurement results. A schematic view of the surface of the object 20 and the sensor unit 30 is shown in FIG. The surface of the object 20 to be measured has a shape that overlaps the surface roughness of a shorter period on the fluctuation of a longer period. In Fig. 3A, the surface on which only the fluctuation is considered is indicated by a broken line, and the actual surface in consideration of the surface roughness is indicated by a solid line. For example, the surface roughness of the surface subjected to precision grinding is about several tens of cycles/mm, and the difference in surface roughness is in the range of 0.1 μm to several μm.

Therefore, even if the sensor unit 30 is shifted by only several μm in the x direction, the heights of the measured points A, B, and C measured by the three sensors 31i, 31j, and 31k largely fluctuate. As a result, the curvature calculated from the measured height data also largely changes, and the linear shape obtained by second-order integration of the curvature at each measurement is also inconsistent. Also, it is assumed that the positions of the measured points A, B, and C are the same at each measurement, but the measured height data does not reflect the data of the wave shape itself, but is reflected in the wave shape. A material with a surface roughness shape. The amplitude of the surface roughness is equal to or higher than the wave height value of the fluctuation, and therefore the curvature based on the linear shape cannot be accurately obtained from the measured height data.

For example, in FIG. 3A, the measured point A based on the sensor 31i is located substantially in the middle of the peak of the surface roughness and the trough, and in FIG. 3B, the measured point A is located at the vertex of the peak of the surface roughness. If the heights of the points to be measured A, B, and C measured by the three sensors 31i, 31j, and 31k do not match, the curvature calculated based on the height is also inconsistent. As a result, the measurement result of the linear shape obtained by the curvature also varies. This deviation can be reduced in the embodiment described below.

The linear shape measuring device and the linear shape measuring method according to the embodiment will be described with reference to FIGS. 4 to 7 . A flowchart of the linear shape measuring method based on the embodiment is shown in FIG.

In step S1, the collection condition of the height data is input to the linear shape measuring device. This input is performed by the input device 16 (Fig. 1). The collection conditions of the height data include the scanning speed V, the maximum spatial frequency Fmax of the surface roughness of the object 20 to be measured, and the sensor pitch p. In addition, the sensor pitch p may be stored in advance in the processing device 15.

In step S2, the sampling frequency Fs is determined. The determination of the sampling frequency Fs can be performed by the processing device 15 (Fig. 1), or the sampling frequency Fs can be determined by the operator. When the operator determines the sampling frequency Fs, the determined sampling frequency Fs is input from the input device 16 (Fig. 1).

Sampling frequency Fs to satisfy the inequality Fs The mode of 2 × V × Fmax is determined. Hereinafter, the physical meaning of the inequality will be described. The above inequality can be rewritten as V/Fs 1/(2×Fmax). The V/Fs on the left is equal to the sampling pitch in the x direction of the collected height data (hereinafter, referred to as the sampling pitch Δp). The 1/(2 × Fmax) on the right side is equal to 1/2 of the minimum period Pmin of the surface roughness. That is, the above inequality indicates that the sampling pitch Δp is 1/2 or less of the minimum period Pmin of the surface roughness.

In step S3, the sensors 31i, 31j, and 31k are relatively moved with respect to the object 20 in the x direction at the scanning speed V, and the height data is collected at the sampling frequency Fs. Further, actually, as shown in FIG. 1A and FIG. 1B, the sensors 31i, 31j, and 31k are stationary, and the object 20 is moved in the x direction.

The time course of the positional relationship between the object 20 to be measured and the sensor unit 30 when the height data is measured in step S3 is shown in FIGS. 5A and 5B. In the state shown in Fig. 5A, the height data a, b, and c are collected by the sensors 31i, 31j, and 31k, respectively. Here, the height data a, b, and c indicate the distances from the origin of the sensors 31i, 31j, and 31k to the measured points A, B, and C of the object 20, respectively.

As shown in FIG. 5B, the height data a, b, and c are collected when the sensor unit 30 moves only the sampling pitch Δp in the x direction with respect to the object 20 to be measured. The sampling pitch Δp corresponding to the sampling frequency Fs determined in step S2 (Fig. 4) is 1/2 or less of the minimum period Pmin of the surface roughness. The height data of the plurality of measured points A, B, and C arranged at the sampling pitch Δp in the x direction are collected by collecting the height data a, b, and c at the sampling frequency Fs. By setting the sampling pitch Δp to 1/2 or less of the minimum period Pmin of the surface roughness, the aliasing phenomenon accompanying sampling can be avoided.

In step S4 (Fig. 4), low-pass filtering processing for removing the waveform components having a wavelength smaller than twice the sensor pitch P for the collected height data a, b, c is performed. This low pass filtering process is executed by the processing device 15 (Fig. 1A).

In step S5, the curvature ρ of the sampling point distributed at the sampling pitch Δp in the x direction on the surface of the object 20 is calculated based on the height data a, b, and c after the low pass filtering process.

Referring to Fig. 6, a method of obtaining the curvature ρ will be described. Fig. 6 shows the positional relationship of the origins D, E, and F of the sensors 31i, 31j, and 31k and the points to be measured A, B, and C. The length of the line segment DA corresponds to the height data a, the length of the line segment EB corresponds to the height data b, and the length of the line segment FC corresponds to the height data c. The length of the line segment DE and the length of the line segment EF correspond to the sensor pitch p. The radius of the circumference passing through the three measured points A, B, and C is represented by r, and the center of the circumference is represented by O.

The intersection of the line segment EB and the line segment AC is indicated by G, and the intersection of the line segment BO and the line segment AC is indicated by H. The length g of the line segment BG is expressed as follows.

g=b-(a+c)/2...(1)

The length g indicates the degree of bending of the surface from the measured point A of the object 20 to be measured to the point C to be measured. The length g may also be referred to as height data indicating the height of the surface of the object 20 to be measured.

The angle between the line segment EB and the line segment BO is very small. Therefore, the length of the line segment GB can be made equal to the length of the line segment HB, and the line segment GC can be made The length is equal to or approximate to the length of the line segment HC. Therefore, the length of the line segment HB can be approximated by g, and the length of the line segment HC is approximated to p. The length of the line segment OH is similar to r-g. If the Pythagorean theorem is applied in a right triangle OHC, the following formula is established.

r ² =(rg) ² +p ² (2)

The curvature ρ is defined as ρ = 1 / r, so the following formula is obtained from the definition formula and the formula (2).

ρ=1/r=2g/(g ² +p ² )...(3)

If g on the right side of the formula (3) is substituted into the formula (1), the curvature ρ of the measured point B can be calculated. p is about 100 mm, so g is on the order of microns. Since it can be assumed that the p-fill is larger than g(p>>g), the formula (3) can be approximated by the following formula.

ρ=2g/p ² ...(4)

The positive curvature ρ represents the curvature that protrudes downward, and the negative curvature ρ represents the curvature that protrudes upward. The curvature ρ is obtained for each of a plurality of sampling points arranged at a sampling pitch Δp on the measurement line. Thereby, the distribution ρ(x) of the curvature ρ in the x direction is calculated.

An example of the curvature ρ calculated using the actual measurement data is shown in Fig. 7. The horizontal axis represents the position of the object 20 in the x direction in units of "mm", and the vertical axis represents the curvature in units of "mm ^-1 ". The thinner solid line in Fig. 7 indicates the curvature ρ calculated from the height data a, b, and c before the low-pass filter processing of step S4, and the thicker solid line indicates the height data a according to the low-pass filter processing. b, c calculate the curvature ρ.

It can be seen that the curvature ρ calculated using the height data a, b, and c before the low-pass filter processing is affected by the surface roughness is large. By performing the low-pass filter processing, the influence of the surface roughness can be excluded, and the curvature based on the surface fluctuation can be obtained. In addition, the height data g can be calculated according to the measured height data a, b, c, and the calculated height data g is subjected to low-pass filtering processing instead of performing low on the measured height data a, b, c The filter is processed and the height data g is calculated from the formula (1).

In step S6 (Fig. 4), the sampling pitch Δp is used as the integral pitch of the numerical integration, and the distribution of the curvature ρ(x) is second-order integrated for the sampling interval, thereby obtaining the linear shape. Hereinafter, a specific method of obtaining a linear shape based on second-order integral will be described with reference to FIG.

Fig. 8 shows the positional relationship of the origins D, E, F of the sensors 31i, 31j, 31k and the points to be measured A, B, C. The inclination dy ₁ /dx ₁ of the line segment AB and the inclination dy ₂ /dx _{2 of the} line segment BC are respectively expressed by the following formula.

The second derivative d ² y/dx ^{2 of the} point B to be measured is expressed by the following formula.

The second derivative is equal to the curvature ρ obtained from equation (4). Therefore, it can be seen that the linear shape y(x) can be obtained by performing second-order integration on the distribution ρ(x) of the curvature.

Next, a method of performing second-order numerical integration on the curvature ρ(x) will be described. When the serial number i starting from 1 is marked at the sampling point, the following recurrence formula can be obtained.

The second derivative d ² y/dx ² (i-1) and d ² y/dx ² (i) are the same as the curvatures ρ(i-1) and ρ(i) obtained from the formula (4). Therefore, the straight line shape y(i) can be obtained from the above recursion formula.

In step S7 (Fig. 4), the inclination correction of the linear shape is performed. As can be seen from the above recursive formula, if dy/dx when i=1, that is, the initial value of the inclination is set to an arbitrary value, for example, “0”, and according to the recursion When the calculation is performed, the average inclination of the straight line shape y(i) is sometimes generated. In step S7, the inclination correction is performed so that, for example, the average inclination of the straight line shape y(i) becomes "0".

Fig. 9 shows the results of 5 measurements along the same line on the surface of the object to be measured by the method according to the embodiment. The horizontal axis represents the distance from the reference point on the measured straight line in units of "mm", and the vertical axis represents the displacement from the reference height of the surface of the object to be measured in units of "μm". The results of the five measurements overlap roughly. Comparing Fig. 2 with Fig. 9, it can be seen that the deviation of the measurement results is remarkably reduced by applying the linear shape measuring method based on the embodiment. As described above, by applying the straightness measurement method based on the embodiment, it is possible to perform measurement with high reproducibility and high accuracy.

In the above embodiment, the low-pass filter processing is executed in step S4 (fourth diagram), but the low-pass filter processing may be omitted. The integral operation has the property of attenuating the high frequency components of the original waveform. Therefore, even if the curvature of the second-order integral object as the step S6 (Fig. 4) is sharply changed in a short period as in the waveform before the low-pass filter processing of Fig. 7, by performing the second-order integration, the high-frequency component is also attenuation. Therefore, even if the low-pass filter processing is omitted, it is possible to actually obtain the same straight line shape as that of the second-order integration of the curvature of the height data after the low-pass filter processing.

Further, in the above embodiment, the curvature ρ(x) is second-order integrated in step S6 (Fig. 4), but the moving average value may be obtained for the curvature ρ(x), and the moving average value may be second-ordered. integral. For example, when the sampling pitch Δp is 1 mm, the moving average value of the curvature ρ(x) can be obtained by the length 10 mm, and the moving average value can be second-order integrated. The second order In the integration, the integration pitch is set to 10 times Δp, that is, 10 mm.

In the above embodiment, in step S2, the sampling pitch Δp is set to 1/2 or less of the minimum period Pmin of the surface roughness, but the sampling pitch Δp is set to 1 mm or less, and the sampling pitch Δp is sensed. Compared with the conventional three-point method in which the detector pitch p is equal, it is possible to perform a measurement with higher accuracy.

Next, other embodiments will be described. In the embodiment described below, the complex vector method is applied.

As shown in FIG. 10, the linear shape of the surface of the object 20 can be represented by the connection of the micro unit vector x(i). Where i is an integer of 0 or more. The angle represented by the vector x(i-1) and x(i) is represented by Δθ(i-1). The radius of curvature of the position of the vector x(i-1) is represented by r(i-1). The length Δs(i-1) of the arc having the radius r(i-1) and the central angle Δθ(i-1) can be calculated by the following formula.

△s(i-1)=r(i-1)×△θ(i-1)...(8)

The angle Δθ(i-1) represented by the vector x(i-1) and the vector x(i) is small, so the following approximation formula holds.

△s(i-1)=|x(i)|...(9)

Where |x(i)| represents the length of the vector x(i). The length of the micro unit vector x(i) (i = 0, 1, 2, 3, ...) is constant.

The following formula is obtained from the formula (8) and the formula (9).

Δθ(i-1)=|x(i)|/r(i-1)...(10)

The length of the vector x(i) can be approximated to be equal to the sampling pitch Δp. The radius of curvature r(i-1) can be calculated from the above formula (3). Therefore, the angle Δθ(i-1) represented by the vectors x(i-1) and x(i) can be obtained.

The vector x(i) is equal to the vector that causes the vector x(i-1) to rotate only by the angle Δθ(i-1). Therefore, the vector x(i) can be expressed by the following formula.

The end point coordinates of the nth minute unit vector x(n) can be obtained by finding the vector sum of the small unit vectors x(i) from i=0 to i=n. The linear shape can be determined by finding the end point coordinates of each of the minute vectors x(i).

The present invention has been described based on the above embodiments, but the present invention is not limited thereto. For example, various changes, modifications, combinations, and the like can be made, as will be apparent to those skilled in the art.

20‧‧‧Measured objects

30‧‧‧Sensor unit

31i, 31j, 31k‧‧‧ sensors

A, B, C‧‧‧ measured points

Pmin‧‧‧ Minimum period of surface roughness

△p‧‧‧Sampling spacing

Claims (4)

A method for measuring a linear shape, wherein three sensors arranged at equal intervals in the first direction face the surface of the object to be measured, and the object to be measured is relatively moved in the first direction by 1 mm or less. The sampling interval is used to collect the height data of the surface of the object to be measured; and according to the height data, the process of determining the curvature of the sampling point distributed on the surface of the object to be measured along the first direction by the sampling interval; and according to the foregoing The curvature is obtained by determining the linear shape of the surface of the object to be measured, and the linear shape of the surface of the object to be measured is obtained by second-order integration of the curvature or the moving average of the curvature. The linear shape measuring method according to claim 1, wherein the sampling pitch is equal to or less than 1/2 of a period of a maximum spatial frequency corresponding to a surface roughness of the surface of the object to be measured. A linear shape measuring device having: three sensors arranged at equal intervals along a first direction; a moving mechanism supporting the aforementioned sensor opposite to a surface of the object to be measured and causing the aforementioned object to be measured The first direction is relatively moved; and the processing device controls the moving mechanism to move the sensor in the first direction, and collects height data measured by the sensor, In the processing apparatus, the sensor is configured to collect the height data at a sampling pitch of 1 mm or less while moving in the first direction, and to obtain the measurement in the first direction along the first sampling direction based on the height data. The curvature of the sampling point on the surface of the object is determined according to the curvature, and the linear shape of the surface of the object to be measured is obtained. The processing device obtains the surface of the object to be measured by second-order integration of the curvature or the moving average of the curvature. Straight line shape. The linear shape measuring apparatus according to claim 3, wherein the sampling pitch is equal to or less than 1/2 of a period of a maximum spatial frequency corresponding to a surface roughness of the surface of the object to be measured.