JPH0435005B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Application Field] The present invention moves four or more distance sensors arranged at equal intervals along the surface of an object to be measured such as a rolling roll, and the distance sensors move by the distance of the arrangement. The present invention relates to a method for measuring the surface profile of an object to be measured based on respective distance measurements, and to a device used for carrying out the method. [Prior art] As wear progresses on the surface (circumferential surface) of a rolling roll, its surface profile deteriorates and the quality of the rolled material deteriorates. Therefore, the surface profile of the rolling roll is periodically measured to check for wear. If it has progressed, it will need to be ground and taken care of. Conventionally, as a method for measuring the surface profile of this type of roll, three distance sensors 131, 1 are used in the axial direction of the roll 11, as shown in FIG.
32, 133 arranged in parallel at equal intervals is moved in parallel in the axial length direction of the rolling roll 11, and the measuring unit 13 is connected to the distance sensors 131, 13
A method called the so-called sequential three-point method is known in which the distance measurement values of the distance sensors 131, 132, and 133 are sequentially detected each time the distance sensors 131, 132, and 133 move by an arrangement interval of 2,133. This method will be explained in detail below. A pair of rails 12, 12 are arranged parallel to the axial direction of the roll 11 at positions spaced apart from the surface of the roll 11 by an appropriate length in the radial direction. A sensor mounting base 13a of a rectangular parallelepiped measuring unit 13 is mounted on the rails 12,12.
The mounting base 13a is screwed into a screw rod 14 horizontally installed in the center between the rails 12, 12 and parallel to the rails. The screw rod 14 is connected to the output shaft of an electric motor 15, and when the electric motor 15 is driven, the sensor mounting base 13
a, that is, the measuring unit 13 is connected to the rails 12, 12
The thread will be threaded in the direction shown by the white arrow in the figure. A rotary encoder 16 is connected to the electric motor 15, and the number of rotations of the screw rod 14 that rotates integrally with the output shaft of the electric motor 15 is determined by the number of rotations, or in other words, the number of rotations corresponds to the amount of movement of the measuring unit 13 that is threaded. A pulse is generated and this pulse is given to the arithmetic unit 20. Three distance sensors 13 are mounted on the sensor mounting base 13a at a distance of L in the extending direction of the rail 12.
1, 132, and 133 are arranged in parallel. Contacts 131a, 132a, 133a are located on the rolling roll 11 side of each distance sensor 131, 132, 133, respectively. Each contact 131a, 132a, 1
The height position of 33a is determined to be the same as the height position of the axis of the rolling roll 11. Even if there are irregularities on the surface of the rolling roll 11, the contact 1
Distance sensors 131, 1 are fixed to the sensor mounting base 13a such that the tips of 31a, 132a, 133a are always in sliding contact with the surface with a predetermined contact pressure.
32, 133 respective sensor bodies 131b, 132
b, 133b, each contactor 131a, 132a, 1
33a is held. Note that the distance sensor is not limited to such a contact type, but may be a non-contact type that uses light, electrostatic capacity, or eddy current. The distance sensors 131, 132, 133 are connected to the surface of the rolling roll 11 to the respective distance sensor bodies 131b, 13.
The separation distance between 2b and 133b is measured, and the measurement result is input to the calculation device 20. The calculation device 20 calculates the measurement unit 1 by counting the number of pulses from the rotary encoder 16.
3 has moved by the distance L between distance sensor arrangements, each distance sensor 13
1,132,133 outputs y ^m _i,j are sequentially read and accumulated. Here, the subscripts i and j are both natural numbers, i is a number indicating the measurement position or the reading position of the distance sensor output value, that is, the number indicating the occupied position of the measurement unit 13 at the time of measurement, and j is Each distance sensor 13
1, 132, and 133 are serial numbers of points whose distances are sequentially measured. The surface position of the rolling roll 11 corresponding to this j is indicated by ... in the drawing. For example, when the measurement unit 13 is at the measurement start position (i=1 position), the position directly facing the distance sensor 131 located at the rearmost side in the moving direction of the measurement unit 13 becomes the measurement point j=1, and the following The positions deviated by L in the moving direction are the second measurement points, respectively.
The third measurement point... Next, based on this accumulated data, the following calculations are executed to detect the measurement unit 13 that occurs due to the drive mechanism of the measurement unit 13 itself.
vibration during movement of the rails 12,1
As a result of the measuring unit 13 not directly facing the rolling roll 11 due to the bending of the rolling roll 1, etc.
The amount of deviation of the measurement unit 13 moving in and out in the radial direction of the sensor 1 (specifically, the amount of deviation of the distance sensor 132 located in the middle) and the distance it rotates in a horizontal plane using the distance sensor 132 located in the middle as a fulcrum. Sensor 13
1,133 respective deviation amounts (distance sensor 132 to distance sensor 131 in the radial direction of the rolling roll 11
or 133 distance, hereinafter referred to as the swing amount. )
By correcting the above, the unevenness (surface profile value) at each measurement point of the rolling roll 11 is measured. Next, the content of this calculation will be explained based on FIG. 10. FIG. 10 is an explanatory diagram showing the measurement position on the surface of the rolling roll 11, the distance measurement values of the distance sensors 131, 132, and 133, the amount of deviation, and the amount of head vibration. The arithmetic device 20 calculates each distance sensor 13 when the measurement unit 13 is at the measurement start position (i=1).
1,132,133 output (distance measurement value) y ^m _1,1 ,
Read and accumulate y ^m _1,2 and y ^m _1,3 . By the way, in this case, as mentioned above, rail 1
2 and 12, the measuring unit 13 or the distance sensor 132 is deviated from the reference line C in the radial direction of the rolling roll 11 by _d1 as shown in FIG. ±k ₁
Suppose that it is deviated by . Here, the reference line C is the center line of the rails 12, 12, and the sign of the deviation amount _d1 is the distance sensor 132 from the reference line C to the rolling roll 11.
The sign of the oscillation amount _k1 is negative when the distance sensor 131 approaches the rolling roll 11, and negative when the distance sensor 131 moves away from the roll 11. Correct. Now, the true surface profile value (distance between the surface of the rolling roll 11 and the reference line C) at each measurement point is y _j
When (j=1, 2...), the following relationship holds true between these values and the sensor output in the illustrated case. y ^m _1,1 =y ₁ −d ₁ +k ₁ +ε _1,1 y ^m _1,2 =y ₂ −d ₁ +ε _1,2 y ^m _1,3 =y ₃ −d ₁ −k ₁ +ε _1,3 ...(1) However, ε _i,j is the distance sensor 131, 132, 13
3 This is a measurement error that it itself has, and the reason why k ₁ does not exist in the term y ^m _1,2 in equation (1) is because the distance sensor 132 is regarded as the fulcrum of the swing as described above. . Next, when it is detected by the output of the rotary encoder 16 that the measurement unit 13 has moved by L, that is, when it moves to the measurement position of i=2, the sensor outputs at that time y ^m _2,2 , y ^m _2,3 , y Load ^m _2,4 . In this case as well, the following relationship holds true. y ^m _2,2 =y ₂ −d ₂ +k ₂ +ε _2,2 y ^m _2,3 =y ₃ −d ₂ +ε _2,3 y ^m _2,4 =y ₄ −d ₂ −k ₂ +ε _2,4 ...(2) Next, the calculation shown in the following equation (3) is executed to obtain the difference b between the distance measurement values of the distance sensors 132 and 133 at the third measurement point. b=y ^m _2,3 −y ^m _1,3 (3) Here, b is the distance sensor 132 at the center of the measuring unit 13 located at the temporary reference line C' [first measurement position (i=
Three distance sensors 131, 13 in 1)
2,133] is a value that should be zero when moving while on the straight line connecting 2,133. In the illustrated example, the difference d 2 -d 1 between the deviation amount d ₁ of the distance sensor 132 at the first measurement position of the measurement unit 13 and the deviation amount d ₂ at the second measurement position is calculated from the difference d ₂ -d ₁ of the distance sensor 132 at the first measurement position. This corresponds to the value obtained by subtracting the head vibration amount k ₁ of 133. In addition, a is the amount of head vibration at the first measurement position
Difference between k ₁ and the amount of head vibration k ₂ at the second measurement position k ₂ - k ₁
This corresponds to , and a is calculated using the following equation (4). a=y ^m _2,2 −y ^m _1,2 −b (4) Next, by executing the calculation shown in the following equation (5) based on a and b, the fourth measurement of the distance sensor 133 is performed. Find the correction value y ^c _2,4 for the distance measurement value y ^m _2,4 at the point. y ^c _2,4 = y ^m _2,4 + a-b = y ^m _2,4 + (y ^m _2,2 − ^{y m} _1,2 ) −2 (y ^m _2,3 − ^{y m} _1,3 ) = y ₄ −d ₁ −2k ₁ + (−ε _1,2 +2ε _1,3 −2ε _2,3 +ε _2,2 +ε _2,4 ) …(5) This correction value y ^c _2,4 is the first measurement position A straight line connecting the three distance sensors 131, 132, 133 at (i=1) is defined as a temporary reference line C', and this value represents the distance between this temporary reference line C' and the measurement point. In other words, this correction value is the distance measurement value at point _j after correcting the deviation amount ( ^di ) and head vibration amount (ki) of the measurement unit 13 from the distance measurement value y m i,j. It is. Next, the measuring unit 13 moves to the third measuring position (i
= 3), the sensor outputs y ^m _3,3 , y ^m _3,4 , y ^m _3,5 at that time are read to obtain the following relationship. y ^m _3,3 =y ₃ −d ₃ +k ₃ +ε _3,3 y ^m _3,4 =y ₄ −d ₃ +ε _3,4 y ^m _3,5 =y ₅ −d ₃ −k ₃ +ε _3,5 ...(6) Then, by similarly executing the calculation shown in equation (7) below, the correction value y ^c _3,5 at the fifth measurement position is obtained. y ^c _3,5 =y ^m _3,5 +a−b=… =y ₅ −d ₁ −3k ₁ +(−2ε _1,2 +3ε _1,3 +2ε _2,2 −4ε _2,3 +2ε _2,3 +ε _3,3 −2ε _3,4 +ε _3,5 ) …(7) However, b＝y ^m _3,4 − ^c _2,4 a＝y ^m _3,3 −y ^m _1,3 −b …(8) Now, the problem with the surface profile is the relative unevenness at each measurement position, and it is not necessarily necessary to determine the absolute amount of distance from a certain reference line to the surface at each measurement position. Therefore, it is not necessary to find the distances y ₄ , y ₅ ... from the original reference line C, but rather the distance from the temporary reference line C'.
You may also find and use y ^c _2,4 , y ^c _3,5 , etc. Note that the distance y _j from the reference line C and the distance y ^c _i,j from the temporary reference line C'
As seen in equations (5) and (7), is expressed as y ^c _i,j = y _j (±) d ₁ (±) (j-2) k ₁ + (measurement error component), and the right-hand side The second and third terms are a linear equation representing the temporary reference value C'. [Problems to be Solved by the Invention] However, in the case of the above-mentioned sequential three-point method, the measurement error ε _i,j component included in the surface profile value increases significantly as the measurement position progresses,
As a result, there was a problem that accurate measurements could not be performed. That is, as is clear from equations (5) and (7) above, y ^c _2,4 ,
y ^c _{3 and 5} include measurement error components as shown in the fourth term on the right side of equations (5) and (7), respectively. Similarly, y ^c _4,6 , y ^c _5,7 , y ^c _6,8 are calculated as follows: y ^c _4,6 = y ₆ −d ₁ −4k ₁ + (−3ε _1,2 +4ε _1,3 +3ε _2,2 −6ε _2,3 +3ε _2,4 +2ε _3,3 −4ε _3,4 +2ε _3,5 +ε _4,4 −2ε _4,5 +ε _4,6 ) …(9) y ^c _5,7 = y ₇ −d ₁ −5k ₁ +(−4ε _1,2 +5ε _1,3 +4ε _2,2 −8ε _2,3 +4ε _2,4 +3ε _3,3 −6ε _3,4 +3ε _3,5 +2ε _4,4 − 4ε _4,5 +2ε _4,6 +ε _5,5 −2ε _5,6 +ε _5,7 ) …(10) y ^c _6,8 =y ₈ −d ₁ −6k ₁ +(−5ε _1,2 +6ε _{1, 3} +5ε _2,2 −10ε _2,3 +5ε _2,4 +4ε _3,3 −8ε _3,4 +4ε _3,5 +3ε _4,4 −6ε _4,5 +3ε _4,6 +2ε _5,5 −4ε _5,6 +2ε _5,7 +ε _6,6 −2ε _6,7 +ε _6,8 ) ...(11) Each of the fourth terms includes a measurement error component. The influence of each of the above measurement error components on measurement accuracy should be strictly evaluated.
The concrete calculation of the square root of the sum of products (hereinafter referred to as the accumulation of measurement errors) is as follows. For y ^c _2,4 , √(-1) ² +2 ² +1 ² +(-2) ² +1 ² =√11≒3.32…(
12) For y ^c _3,5 , √(-2) ² +3 ² +2 ² +(-4) ² +2 ² +1 ² +(-2) ²
+1 ² =√43≒6.56…(13) y ^c For _4,6 , √(-3) ² +4 ² +3 ² +(-6) ² +3 ² +2 ² +(-4) ²
+2 ² +1 ² +(-2) ² +1 ² =√109≒10.44...(14) √(-4) for y ^c _5,7 2 +5 ^{2 +4 2} +(-8) ² +4 ² +3 ² +( -6) ²
+3 ² +2 ² +(-4) ² +2 ² +1 ² +(-2) ² +1 ² =√221≒14.87...(15) For y ^c _6,8 , √(-5) ² +6 ² +5 ² +( -10) ² +5 ² +4 ² +(-8) ²
+4 ² +3 ² +(-6) ² +3 ² +2 ² +(-4) ^{2 +2} 2 +1 ² +(-2) ² +1 ² =√391≒19.77...(16) From formulas (12) to (16) As is clear, in the sequential three-point method as described above, the accumulation of measurement errors increases dramatically as the measurement position progresses, and as a result of the cumulative effect of this measurement error, the In this case, the correction value includes a large error component, making it impossible to measure the surface profile with high accuracy. Incidentally, Table 1 shows the accumulation at each measurement point.

[Means for solving problems]

The present invention has been made in view of the above circumstances, and includes moving four or more distance sensors arranged at equal intervals in a direction along the surface of the object to be measured, and each time the distance sensors move by the distance of the arrangement, Obtain the distance measurement value of each distance sensor at that time, and for each distance measurement value, measure the deviation amount, head vibration amount, and the object to be measured of each distance sensor, which are derived from the relationship between these distance measurement values. The surface profile of the object to be measured is obtained by obtaining a simultaneous linear equation in which the unknown is the surface profile value at a point based on a temporary reference line as described later, and solving this using the method of least squares. It is an object of the present invention to provide a surface profile measuring method that can significantly reduce the accumulation of measurement errors that each distance sensor itself has and, as a result, can perform highly accurate measurements, and an apparatus used for carrying out the method. In the surface profile measuring method according to the present invention, r (r≧4) distance sensors arranged at equal intervals in the moving direction are moved along the surface of the object to be measured. A method of obtaining a distance measurement value each time the object is moved by an interval and measuring the surface profile of the object based on the distance measurement value, the method comprising: approaching the surface of the object to be measured by any one of r distance sensors; , the offset position in the direction of separation, the amount of swing of each of the other r-1 distance sensors in the direction with respect to the distance sensor, the amount of these deviations, and the true distance when there is no amount of swing, as unknowns. Then, a number of simultaneous linear equations expressing the relationship between these and the distance measurement value are obtained, and then, in this simultaneous linear equation,
Should be used as a reference line for surface profile identification.
By solving the simultaneous linear equations using the method of least squares, setting any two values of the unknowns to 0, so that a straight line having a certain slope with respect to the surface of the object to be measured is uniquely determined, It is characterized by determining the surface profile of the object to be measured. [Example] The present invention will be described in detail below based on drawings showing an example in which r=5. FIG. 1 is a schematic plan view showing an implementation state of the surface profile measuring method according to the present invention, and FIG. 2 is a left sectional view of FIG. 1. A pair of rails 2 are installed parallel to the axial direction of the roll 1 at a position radially apart from the surface of the roll 1 which has been removed from the rolling mill and supported by a support member (not shown). , 2 are installed in parallel. A rectangular parallelepiped sensor mounting base 3a of a measurement unit 3 is provided between the rails 2, 2. A prismatic threaded body 3b having a longitudinal dimension narrower than the sensor mount 3a and approximately the same length is fixed to the center of the lower surface of the sensor mount 3a. A screw hole 3c is drilled in the center of the screw body 3b in the longitudinal direction,
A screw rod 4, which is horizontally suspended between the rails 2 and 2, is screwed into the screw hole 3c. One end of the screw rod 4 is connected to the output shaft of an electric motor 5, and is rotated by the drive of the electric motor 5. When the screw rod 4 rotates, the screw assembly 3b screwed thereon, that is, the measurement unit 3, is threaded in the measurement direction shown by the white arrow in the figure. A rotary encoder 6 is connected to the electric motor 5, and the number of rotations of the screw rod 4 that rotates integrally with the output shaft of the electric motor 5 is determined by the number of rotations, or in other words, the number of rotations corresponds to the amount of movement of the measuring unit 3 that is threaded. A pulse is emitted and this pulse is sent to the calculation device 1.
Give to 0. Five distance sensors 3 are mounted on the sensor mounting base 3a at a distance of L in the extending direction of the rails 2, 2.
1, 32, 33, 34, and 35 are arranged in parallel. Note that the number of distance sensors is not limited to five,
It is sufficient if the number is 4 or more. Each distance sensor 31, 3
Contactors 31a, 32a, 33a, 34a, 35 are provided on the rolling roll 1 side of 2, 33, 34, 35, respectively.
a is located. Each contact 31a, 32a, 3
The height positions of 3a, 34a, and 35a are those of rolling roll 1.
The height position of the axis is the same as that of the Even if there are irregularities on the surface of the rolling roll 1, the contacts 31a, 32a, 33a, 34a, 3
Distance sensors 31, 32, 33, 34, fixed on the sensor mounting base 3a such that the tips of each of the sensors 5a are always in sliding contact with the roll surface with a predetermined contact pressure.
35 respective sensor bodies 31b, 32b, 33b,
34b and 35b. Distance sensor 3
1, 32, 33, 34, 35 are the surface of the rolling roll 1~sensor body 31b, 32b, 33b, 34
b, 35b, and input the measurement results to the arithmetic unit 10. By counting pulses from the rotary encoder 6, the arithmetic unit 10 detects that the measuring unit 3 has moved by the distance L between the distance sensor arrangements, and each time it detects that the measuring unit 3 has moved by the distance L between the distance sensor arrangements, it activates each distance sensor 31 in the same manner as described in the conventional method described above. , 32, 33, 34, 35 outputs y ^m _i,j are sequentially read and accumulated. Based on this accumulated data, each distance sensor 31, 32, 33,
34 and 35 during movement, the amount of deflection, the amount of head vibration, and the surface profile value are determined. Next, the content of calculations performed by the calculation device 10 will be explained. Now, the measuring unit 3 is at the first measuring position (i=
1) to the n-th measurement position (i=n), each distance sensor 31, 32, 33, 34, 35
Assuming that the output is read, the arithmetic unit 10 calculates n distance measurements for each distance sensor 31, 32, 33, 34, 35, a total of 5n distance measurements y ^m _i,j (i=1, 2...
n, j=1, 2...n+4). Arithmetic device 10
For each of these 5n distance measurement values y ^m _i,j , the relationship as explained in the conventional method described above is created. Then, we obtain 5n simultaneous linear equations shown in equation (17) below.

[Table] However, y _j , d _i , k _i are the same as those explained in the conventional method above, and since five distance sensors are used in the present invention, the distance sensors are The amount of vibration of the distance sensors 32 and 34 is k _i , and the amount of vibration of the distance sensors 31 and 35 is 2k _i . Furthermore, since the measurement error ε _i,j will be described later, it will be ignored here. Now, equation (17) can be converted to the following equation (18) using matrix product.
It is shown by the formula. Ax→=b→ …(18) However, A is the unknown numbers y _i , d _i , k _i in equation (17)
x→ is a (3n+4,1) matrix of unknowns y _i , d _i , k _i , b→ is a (5n, 1) matrix of distance measurements y ^m _i,j It is. The details of equation (18) are shown in equation (19) below.

【table】

[Table] However, all blank parts of matrix A are 0. Now, as mentioned above, the surface profile can be obtained by simply determining the relative unevenness at each measurement point, and there is no need to determine the absolute amount of distance from a certain reference line to the surface at each measurement point. Therefore, as shown in Fig. 4, n+4 measurement points [,..., n+1, n+2, n+3
, n+4 ], any two measurement points,
The straight line connecting the true surface profile values y _l = 0, y _n at (1≦l<m≦n+4) is the aforementioned reference line C.
Instead, the temporary reference line C'' is selected, and the distance between this temporary reference line C'' and each measurement point is the true surface profile value [the surface profile is the unevenness from the line connecting , on the surface of the rolling roll 1]. . Then, in the simultaneous linear equations shown in equation (17) above, y _l =0, y _n =0, and the simultaneous linear equations based on the temporary reference line C″, that is, the values of y _j , d _i , k _i It is changed to a system of linear equations whose values are based on C″. As a result, the matrix A becomes a (5n, 3n + 2) matrix A ₁ with the l and mth columns deleted, and the vector x → becomes a (3n + 2, 1) matrix x → ₁ with y _l and y _n deleted. . Therefore, equation (18) is changed to equation (20), and equation (19) is changed to equation (21). A ₁ x→ ₁ = b→ …(20)

【table】

[Table] However, all blank parts of matrix _A1 are 0. The temporary reference line C'' is determined by determining the surface profile value at two different measurement points as described above.
It is not limited to combinations that connect y _l and y _n , that is, make y _l and y _n 0 at the same time, but also unknown numbers y _j ,
The following combinations of d _i and k _i may be used. That is, it is a combination of y _j and d, and it is a combination of y j and d, and
The surface profile value at any one measurement point, e.g. y ₃ , as shown in , and the other measurement point m+
It is also possible to set the deviation amount d _n at 2 to 0, that is, the straight line C'' connecting both points. In this case, it is obvious that the straight line passing through the two points is uniquely determined, and the above equation (17) If we solve this by setting y ₃ =0 and d _n =0, we will obtain a surface profile based on the straight line C''. Also, for the combination of y _j and k _i , y ₃ =0, k _n =0 as shown in Figure 5b, that is, the slope is the same as the slope of the measuring unit 3 at the measuring point m+2. Then, y ₃ may be set to 0, that is, it may be a straight line C'' passing through the measurement point.It is obvious that the straight line C'' is uniquely defined in this case as well, and in the above equation (17), y ₃ = 0, k _n = 0 and solve this problem, a surface profile based on the straight line C'' will be obtained. Also, for the combination of two d _j , as shown in Figure 5c, for example, At the measurement point, m+2
It is also possible to set d ₂ and d _n to 0, that is, a straight line `` that connects both points. In this case as well, the straight line C '' is uniquely defined, and in the above equation (17), d ₂ = 0, d _n = 0, and solving this will yield a surface profile based on the straight line C''. Also, as shown in Figure 5d, for example, the combination of d _i and k _i , the measurement point k _n at measurement point m+2 passing through the point where both d ₂ are 0
is 0, that is, the slope is the same as the slope of the measuring unit 3 at the measuring point m+2, and d ₂ =0.
It may also be a straight line C″. In this case, the straight line
C″ is uniquely defined, and in the above equation (17), d ₂
= 0, k _n = 0, and by solving this, a surface profile based on the straight line C'' will be obtained. There are six combinations of the two unknowns y _j , d _i , k _i However, in the case of a combination of two k _i ,
Even if two slopes are given, a straight line cannot be identified, so
In this case, the temporary reference line C'' does not exist.
Even in the combination shown in FIG. 5a, if the combination is y ₃ =0, d ₁ =0, as shown in FIG. It cannot serve as a reference line, and such combinations are excluded. Therefore, in the above equation (17), the unknowns y _j , d _i ,
Among the combinations that make any two values of k _i 0 at the same time, combinations excluding _k If the combination yields a straight line with a certain inclination to
C'' exists. Now, returning to equation (20) above, matrix A is not a square matrix and its inverse matrix A ^-1 does not exist, so it cannot be solved as is. However, (20)
There are more equations than the number of unknowns (3n+2). Therefore, equation (20) can be solved by using the least squares method. The steps for this solution will be explained below. First, both sides of equation (20) are multiplied by the transposed matrix A ^t ₁ of the matrix A ₁ from the left. A ^t ₁ ×A ₁ ×x→ ₁ =A ^t ₁ ×b→ (22) However, the details of A ^t ₁ are shown in the following equation (23).

[Table] Then, A ^t ₁ ×A ₁ becomes a square matrix of (3n+2, 3n+2), and its inverse matrix (A ^t ₁ ×A ₁ ) ^-1 exists, so equation (22) above can be solved. . That is, (A ^t ₁ ×A ₁ ) ^-1 ×A ^t ₁ ×A ₁ ×x→ ₁ = (A ^t ₁ ×A ₁ ) ^-1 ×A ^t ₁ ×b→ …(24), and b→ ₁ =(A ^t ₁ ×A ₁ ) ^-1 ×A ^t ₁ ×b→ …(25). Therefore, by performing the calculation shown in equation (25), the surface profile values y ₁ , y ₂ ...y _l-1 , y _l+1 ...y _n-1 , y _n+1 …y _o ,
y _o+1 , y _o+2 , y _o+3 , y _o+4 deviation amounts d ₁ , d ₂ ...d _o and head swing amounts k ₁ , k ₂ ...k _o can be calculated at once. can. According to the method of the present invention, even if the measurement unit 3 is deflected or oscillated, the surface profile value can be determined while minimizing the accumulation of measurement errors, as will be described later. Note that when the temporary reference line C'' is selected using the other combinations mentioned above, the number of unknowns is 3n+2, so y _j , d _i , and k _i can be found in the same way. We will explain the measurement error when using the invented method.Now, (A ^t ₁ ×A ₁ ) in the above equation (25)
^-1 ×A ^t Each element of ₁ is a _p,q (p=1,2...3n+1,3n
+2, q=1,2...5n-1,5n), then x→ ₁
y _j of each element is shown by the following equation (26).

[Table] Then, the measurement error ε i _,j included in each distance measurement value y ^m i _,j is also

〔effect〕

Next, the effects of the present invention will be explained based on an example in which surface profile values were measured using the simulated surface profile shown in FIG. In this example, seven points were selected as measurement points, so the number of measurements n was n=3, and a straight line passing through the measurement points at both ends was selected as the temporary reference line, and r= 5, so a total of 15 pieces of data can be obtained. Note that the shape of the simulated surface profile is the first,
The 3rd, 6th, 7th measurement points, etc. have the same unevenness, whereas the 2nd measurement point has 1 mm,
In addition, the fourth and fifth measurement points are shaped to protrude by 2 mm. First, the accumulation of measurement errors in such an embodiment will be explained. The matrices A15 and A13 according to this embodiment are expressed as follows.

[Table] However, all blank parts of matrix A are 0. And matrix A ₁ 15,11 is matrix A15,1
3 with the first and seventh columns deleted, and is expressed as follows.

[Table] Then, the transposed matrix A ^t ₁ of matrix A ₁ , square matrix
The inverse matrices of A ^t ₁ ×A ₁ 11 and 11 (A ^t ₁ ×A ₁ ) ⁻¹ are as follows, respectively. Further, (A ^t ₁ ×A ₁ ) ⁻¹ ×A ^t ₁ is expressed by the following equation (33).

【table】

【table】

[Table] And the measurement error ε _i,j when using the method of the present invention
The accumulation is the square root of the sum of squares of the elements in each row in equation (33) above. In addition, in equation (33), the measurement point and the reference point are removed, so the first and seventh rows are removed.
In other words, the accumulation is 0, and the square root of the sum of squares of each element in the second row corresponds to the accumulation of the measurement points, and the third to sixth rows correspond to the measurement points, respectively. The calculation results are shown in Table 2 below.

[Table] The accumulation of measurement errors in this case, the accumulation of measurement errors in the case of the conventional sequential three-point method shown in Table 1 above, and the improved sequential three-point method (similarly shown in Table 3 below) Figure 7 shows the cumulative measurement error in the case where , is used as the reference point). 7th
The figure is a graph showing measurement points on the horizontal axis and cumulative magnification of measurement error on the vertical axis.

[Table] As is clear from the graph, in the conventional sequential three-point method, the accumulation increases dramatically as the measurement points progress, but in the case of the method of the present invention, the accumulation increases dramatically as the measurement points progress. The value is substantially constant regardless of the value, and the value itself is significantly smaller, and is also sufficiently smaller than when using the improved sequential three-point method. Therefore, when using the method of the present invention, the influence of measurement errors on the profile measurement value is extremely small, and as a result, the surface profile can be measured with high accuracy. Note that in the above explanation, measurement points at both ends of the reference point were selected, but if high measurement accuracy is required at the center, for example, measurement points,
By selecting , it is possible to reduce the measurement error in the central part. In addition, in the above explanation, five distance sensors 31,
Although the central distance sensor 33 among the sensors 32, 33, 34, and 35 has been described as the fulcrum for the swing of the measuring unit 3, even if other distance sensors are assumed to be the fulcrum for the swing, the surface profile values will have exactly the same accuracy. Therefore, among the five distance sensors, measurement unit 3
Any one point can be assumed as the fulcrum of the swing. For example, if the distance sensor 31 located at the rearmost side in the moving direction is considered as the fulcrum, the above equation (17) is revised to the following equation (34), and the distance sensor 32
If we consider this as a fulcrum, we can change it to the following equation (35).

【table】

[Table] If similar calculations are performed in this case, the surface profile value finally determined will be the same as in the above case. Next, Table 4 shows the actual measured values of the distance sensor when the method of the present invention is performed using the simulated surface profile shown in FIG. The measurement results by the sequential two-point method are shown in Table 5 with specific numerical values, and
The respective errors are shown in comparison in FIG. Note that the blank spaces in the sequential two-point method and sequential three-point method tables in Table 5 correspond to data corresponding to y ^m _4,5 in the sequential two-point method and y ^m _4,6 and later in the sequential three-point method. This is because, in the sequential five-point method of this embodiment, the data to be collected has not been collected until three or two steps earlier. However, the true value (y _j ) here is the value using the aforementioned temporary reference line C'' as the reference line, and in both the conventional sequential three-point method and sequential two-point method, the true value (y _j ), The fixed value (y ^m _j ) has a slope, but this is due to the measurement unit shaking its head at first, which is essential for recognizing irregularities in the profile shape. This is not a failure. In addition, in Figure 8, the horizontal axis shows the measurement points and the vertical axis shows the measurement error (mm).

【table】

【table】

【table】

[Table] As is clear from the graph shown in FIG. 8, the measurement accuracy of the method of the present invention is significantly improved compared to the conventional three-point sequential method and two-point sequential method. Note that the reason why some of the measurement errors due to the sequential two-point method are omitted in the graph is that the values have become significantly large. The reason for this is that, as mentioned above, an unreasonable assumption was made that there was no head swing. When the surface profile is measured by the method of the present invention as described above, the accumulation of measurement errors, which was a problem in the conventional three-point sequential method, can be significantly reduced, and as a result, the surface profile can be measured with high accuracy.

[Brief explanation of drawings]

Fig. 1 is a schematic plan view showing the implementation state of the method of the present invention, Fig. 2 is a left sectional view of Fig. 1, Fig. 3 is a schematic diagram showing the amount of deviation and swing amount, and Fig. 4 is a tentative diagram. reference line
A schematic diagram to explain C'', Figure 5 is a temporary reference line
Schematic diagram showing combinations of unknowns for C″ selection,
Fig. 6 is a schematic diagram showing the simulated surface profile, Fig. 7 is a graph showing the magnification of the cumulative measurement error, and Fig. 8 is a graph showing the magnification of the cumulative measurement error.
The figure is a graph comparing the measurement errors of the method of the present invention, the conventional sequential three-point method, and the sequential two-point method.
Figure 0 is a schematic diagram for explaining measurement points, deviation amounts, and oscillation amounts. 1... Rolling roll, 3... Measuring unit, 10
... Arithmetic device, 31, 32, 33, 34, 35...
...Distance sensor.

Claims (1)

[Claims] 1. R (r≧4) distance sensors arranged at equal intervals in the movement direction are moved along the surface of the object to be measured, and the distance sensors are moved by the distance of the arrangement. A method for measuring the surface profile of an object to be measured by obtaining a distance measurement value each time the distance sensor is used, and measuring the surface profile of the object to be measured based on the measured distance value, the method comprising the amount of deviation in the direction, the amount of swing of each of the other r-1 distance sensors in the direction with respect to the distance sensor, and the amount of these deviations,
The true distance when there is no amount of head vibration is taken as an unknown quantity, and a number of simultaneous linear equations expressing the relationship between these and the measured distance values are obtained. Next, in these simultaneous linear equations, a reference line and a reference line for specifying the surface profile are calculated. Solving simultaneous linear equations using the method of least squares, setting any two values of the unknown quantities to 0, so that a straight line having a certain slope with respect to the surface of the object to be measured is uniquely determined. A surface profile measuring method characterized in that the surface profile of the object to be measured is determined by: 2. A measuring unit which is movable in the direction along the surface of the object to be measured and has r (r≧4) distance sensors arranged at equal intervals in the direction of movement; and each of the distance sensors. a means for reading and accumulating distance measurement values each time the sensor moves by the distance of the distance sensor; deviation amount and any one of the above
means for calculating the amount of oscillation in the direction of the other r-1 distance sensors relative to the distance sensor; means for obtaining a large number of simultaneous linear equations with distance as an unknown; and means for solving simultaneous linear equations using the method of least squares, setting any two values of the unknown quantities to 0, as determined by .