JPH0556443B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Application Field] The present invention moves r (r≦3) or more distance sensors arranged at equal intervals along the surface of an object to be measured such as a rolling roll, and This invention relates to an improvement in a measurement method that can be called a sequential r-point method, in which the surface profile of an object to be measured is measured based on distance measurements each time the object is moved by an arrangement interval. [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, as shown in FIG. 12, three distance sensors 131,
The measuring unit 13 in which distance sensors 132 and 133 are arranged side by side at equal intervals is moved in parallel in the axial length direction of the rolling roll 11, and the measuring unit 113 is connected to the distance sensors 131 and 133.
A method called the so-called sequential three-point method is known in which the distance measurement values of the respective distance sensors 131, 132, 133 are sequentially detected each time the distance sensors 132, 133 are moved by the distance between the distance sensors 132, 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, capacitance, 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 (position i = 1), the position directly facing the distance sensor 131 located last in the movement direction of the measurement unit 13 becomes the measurement point j = 1, and from then on The positions shifted by L in the direction become the second measurement point, the third measurement point, etc., respectively. 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 measurement 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. 13. FIG. 13 is an explanatory diagram showing measurement positions on the surface of the rolling roll 11, distance measurement values of the distance sensors 131, 132, and 133, deviation amounts, and head vibration amounts. 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 deviates 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 are distance sensors 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 are 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 ₂ ' between the distance measurement values of the distance sensors 132 and 133 regarding the third measurement point. b ₂ ′=y ^m _2,3 −y ^m _1,3 ……(3) Here, b ₂ ′ is the distance sensor 132 at the center of the measuring unit 13 located at the temporary reference line C′ [first measurement position (i
= 1), three distance sensors 131, 13
2,133] is a value that should be zero when moving while on the straight line connecting 2,133. Note that only one temporary reference line C' is determined for a certain measurement object, and does not change as the sensor unit moves. In the illustrated example, the deviation amount d ₁ of the distance sensor 132 at the first measurement position of the measurement unit 13 and the second
The first difference from the deviation d ₂ at the measurement position is d ₂ −d ₁ .
This corresponds to the value obtained by subtracting the amount of swing k ₁ of the distance sensor 133 at the measurement position. Further, a corresponds to the difference k ₂ −k ₁ between the amount of head vibration k ₁ at the first measurement position and the amount k ₂ of head vibration at the second measurement position, and a ₂ ′ is obtained using the following equation (4). a ₂ ′=y ^m _2,2 −y ^m _1,2 −b ₂ ′ ……(4) Next, based on this a ₂ ′ and b ₂ ′, perform the operation shown in the following equation (5). Therefore, the correction value y ^c _2,4 of the distance measurement value y ^m _2,4 at the fourth measurement point of the distance sensor 133 is
seek. y ^c _2,4 = y ^m _2,4 + a ₂ ′−b ₂ ′ = 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 calculated using the temporary reference line C', which is the straight line connecting the three distance sensors 131, 132, 133 at the first measurement position (i=1). This value represents the distance between the measurement point 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, the correction value y ^c _3,5 at the fifth measurement position is obtained by similarly executing the calculation shown in equation (7) below. y ^c _3,5 =y ^m _3,5 +a ₃ ′−b ₃ ′=…=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 ₃ ′=y ^m _3,4 −y ^c _2,4 a ₃ ′=y ^m _3,3 −y ^m _1,3 −b ₃ ′ ...(8) Now, the surface profile The relative unevenness at each measurement position becomes a problem, 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 necessarily 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 _i 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), y ^c _i,j = y _j (±) d ₁ (±) (j-2) k ₁ + (measurement error component of the distance sensor itself). The second and third terms on the right side are linear expressions representing the provisional reference value C'. Here, a' and b' are values determined when the measuring unit 13 is located at a certain measuring point, and as a function of the measuring point i, a _i '=y ^m _i,i −y ^m _1,i −b _i ′ b It is expressed as _i ′=y ^m _i,i+1 −y ^c _i-1,i+1 (i=2,..., ny ^c _1,3 =y ^m _1,3 ). [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 −6
ε _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 −8
ε _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 −10
ε _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 which includes a measurement error component in the fourth term. 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) For y ^c _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≒1
4.87
...(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) As is clear from equations (12) to (16), in the sequential three-point method as described above, the As a result, the accumulation of measurement errors increases dramatically, and due to the cumulative effect of measurement errors, the correction value includes a large error component at the latter half of the measurement position.
Accurate surface profile measurements cannot be performed. Incidentally, Table 1 shows the accumulation at each measurement point.

[Means for solving problems]

The present invention has been made in view of such circumstances, and the amount of deviation of the zero point existing in each distance sensor is determined as described below, and the amount of deviation of the zero point caused by the amount of deviation of the zero point is determined from the surface profile of the measured object. The true surface profile is determined by subtracting the measurement error component, and the deviation of the zero point is corrected from the distance measurement value of the distance sensor, and the true surface profile is determined based on the corrected distance measurement value. An object of the present invention is to provide a surface profile measurement method that can perform surface profile measurement with high accuracy. The surface profile measuring method according to the first invention includes:
Distance sensors r (r≧4) at equal intervals in the direction of movement
The individually arranged measuring units are moved along the surface of the object to be measured, and each time the measuring unit moves by the distance sensor arrangement interval, a distance measurement value is obtained, and an arbitrary one of r pieces is obtained. The amount of deviation of the distance sensor caused by the movement of the measuring unit in the direction toward and away from the surface of the object to be measured is not in a straight line, and the amount of deviation of the other r-1 distance sensors based on the distance sensor. The amount of swing in each of the above directions, the amount of deviation thereof, and the true distance determined for each measurement point when there is no amount of swing are taken as unknowns, and a large number of variables representing the relationship between these and the distance measurement value are calculated. A first simultaneous linear equation is obtained, and then, in the first simultaneous linear equation, a straight line having a certain slope with respect to the surface of the object to be measured is uniquely determined as a reference line for specifying the surface profile. In this method, the surface profile of the object to be measured is determined by solving the first simultaneous linear equations, with any two values of the unknown quantities set to 0, The amount of deviation of the zero point of each distance sensor corresponding to the amount of positional deviation from the measurement reference position (zero point) is calculated from the zero point of the remaining r-2 distance sensors using the straight line connecting the zero points of any two distance sensors as a reference. In order to solve for the amount of deviation as an unknown quantity and to obtain the measurement error component included in the surface profile due to the amount of deviation at the zero point, the distance sensor is connected to a reference line connecting any two points on the surface thereof. A second simultaneous linear equation similar to the first simultaneous linear equation and/or the amount of deviation of any one distance sensor in the direction toward or away from the surface of the reference object; The amount of swing in the direction, the offset position of these, and the true distance determined for each measurement point when there is no amount of swing are taken as unknowns, and these, the arbitrary one, and the r
- Obtain one or more third simultaneous linear equations indicating a relationship between the distance measurements of two or less distance sensors, and apply the second simultaneous linear equations and/or the third simultaneous linear equations to the surface profile identification. By selecting and solving the reference line on the surface of the reference measurement object as the reference line, the true distance at the point where the distance in the distance measurement direction is known is determined, and the measurement error component is calculated as the difference between these distances. Then, the deviation amount, the head vibration amount, and the coefficient of each distance measurement value when finding the true distance obtained in the process of solving the second simultaneous linear equations and/or the third simultaneous linear equations, respectively. r-2 values that are determined as the sum of certain elements in certain rows of the matrix and that determine the quantitative relationship between the value that affects the measurement error component, the measurement error component, and the undifferentiated number; By obtaining the fourth simultaneous linear equations and solving the fourth simultaneous linear equations, r-
Obtain solutions to the two unknowns, use these solutions to find the measurement error component included in the surface profile of the object to be measured, and subtract this measurement error component from the surface profile to find the true surface profile. Features. In the second invention, a measurement unit in which r (r≧4) distance sensors are arranged at equal intervals in the movement direction is moved along the surface of the object to be measured, and the measurement unit Obtain a distance measurement value each time the distance is moved, and calculate the amount of deviation of any one of the r distance sensors in the direction toward or away from the surface of the object to be measured, using the distance sensor as a reference. The amount of swing of each of the other r-1 distance sensors in the above direction, the amount of deviation thereof, and the true distance determined for each measurement point when there is no amount of swing are taken as unknowns, and these and the distance A number of first simultaneous linear equations expressing the relationship with measured values are obtained, and then, in the first simultaneous linear equations, a certain value is calculated for the surface of the object to be measured, which is to be used as a reference line for specifying the surface profile. A method for determining the surface profile of the object to be measured by solving the first simultaneous linear equations by setting any two values of the unknowns to 0 so that a straight line having an inclination is uniquely determined, the method comprising: Calculate the amount of deviation of each zero point of each distance sensor corresponding to the amount of positional deviation from the measurement reference position (zero point) in the distance measurement direction, which exists in the sensor, with the remaining r -2
In order to solve the amount of deviation of the zero point of the distance sensor as an unknown quantity, and to find the measurement error component included in the surface profile due to the amount of deviation of the zero point, the distance sensor is 2
A second simultaneous linear equation similar to the first Simultaneous linear equations and/or the amount of deviation of any one distance sensor in the direction toward or away from the surface of the reference measurement object, r-2 or less of the other r-1 with respect to the distance sensor Let the amount of swing of each distance sensor in the above direction, their offset position, and the true distance when there is no amount of swing be unknowns, and these, the arbitrary one, and the r-2 or less distance sensors. One or more third simultaneous linear equations indicating the relationship with the distance measurement value are obtained, and the second simultaneous linear equations and/or the third simultaneous linear equations are used as the reference line for specifying the surface profile of the reference measurement object. By selecting and solving the reference line on the surface of A certain row of a matrix created by the coefficients of the deviation amount, head vibration amount, and each distance measurement value when determining the true distance obtained in the process of solving the equation and/or the third simultaneous linear equations, respectively. obtain r-2 fourth simultaneous linear equations that determine a quantitative relationship between a value that is determined as a sum of elements and that affects the measurement error component, the measurement error component, and the undifferentiated number. , by solving the fourth simultaneous linear equations to obtain solutions for r-2 unknowns, and correcting to eliminate the influence of this solution from the distance measurement value obtained when measuring the surface profile of the object to be measured, The method is characterized in that a fifth simultaneous linear equation similar to the first simultaneous linear equation is obtained for the corrected distance measurement value, and the true surface profile is obtained by solving the fifth simultaneous linear equation in the same manner. In the third invention, a measurement unit having three distance sensors arranged at equal intervals in the movement direction is moved along the surface of the object to be measured, and the measurement unit is moved by the distance between the distance sensors. Obtain a distance measurement value each time, and determine the amount of deviation of any one of the three distance sensors in the direction toward or away from the surface of the object to be measured, and the amount of deviation of the other two distance sensors based on the distance sensor. The amount of swing of each distance sensor in the above-mentioned direction, the amount of deviation thereof, and the true distance when there is no amount of swing are taken as unknowns, and a large number of first simultaneous linear equations expressing the relationship between these and the distance measurement value are set as unknowns. get the equation, then this first
In the simultaneous linear equations, any two values of the unknowns are set to 0 so that a straight line having a certain slope with respect to the surface of the object to be measured, which should be the reference line for specifying the surface profile, is uniquely determined. As,
A method of determining the surface profile of the object to be measured by solving the first simultaneous linear equations, the distance corresponding to the amount of positional deviation from the measurement reference position (zero point) in the distance measurement direction, which exists in the distance sensor. In order to solve the amount of deviation of the zero point of each sensor with respect to the straight line connecting the zero points of any two distance sensors, the amount of deviation of the zero point of the remaining one distance sensor as an unknown quantity, and also to solve the amount of deviation of the zero point of the remaining distance sensor, In order to find the measurement error component included in the surface profile, the distance in the distance measurement direction between the reference line connecting the distance sensor between two arbitrary points on the surface and another arbitrary point is determined. A sixth simultaneous linear equation similar to the first simultaneous linear equation is obtained by moving it along the surface of a known reference measurement object, and the sixth simultaneous linear equation is used as a reference line for specifying the surface profile. By selecting and solving the reference line on the surface of the reference measurement object, the true distance at the point where the distance in the distance measurement direction is known is determined, the measurement error component is determined as the difference between these distances, and then , the sum of a certain element in a certain row of a matrix made of the coefficients of the deviation amount, the head vibration amount, and each distance measurement value when determining the true distance, obtained in the process of solving the sixth simultaneous linear equations. is required as,
Obtain a linear equation that determines the quantitative relationship between the value that affects the measurement error component, the measurement error component, and the unknown, obtain a solution to the unknown by solving the linear equation, and use this solution to The present invention is characterized in that the measurement error component included in the surface profile of the object to be measured is determined, and the true surface profile is determined by subtracting this measurement error component from the surface profile. In the fourth invention, a measurement unit having three distance sensors arranged at equal intervals in the movement direction is moved along the surface of the object to be measured, and the measurement unit is moved by the distance at which the distance sensors are arranged. Obtain a distance measurement value each time, and determine the amount of deviation of any one of the three distance sensors in the direction toward or away from the surface of the object to be measured, and the amount of deviation of the other two distance sensors based on the distance sensor. The amount of swing of each distance sensor in the above-mentioned direction, the amount of deviation thereof, and the true distance when there is no amount of swing are taken as unknowns, and a large number of first simultaneous linear equations expressing the relationship between these and the distance measurement value are set as unknowns. get the equation, then this first
In the simultaneous linear equations, any two values of the unknowns are set to 0 so that a straight line having a certain slope with respect to the surface of the object to be measured, which should be the reference line for specifying the surface profile, is uniquely determined. As,
A method of determining the surface profile of the object to be measured by solving the first simultaneous linear equations, the distance corresponding to the amount of positional deviation from the measurement reference position (zero point) in the distance measurement direction, which exists in the distance sensor. In order to solve the amount of deviation of the zero point of each sensor with respect to the straight line connecting the zero points of any two distance sensors, the amount of deviation of the zero point of the remaining one distance sensor as an unknown quantity, and also to solve the amount of deviation of the zero point of the remaining distance sensor, In order to find the measurement error component included in the surface profile, the distance in the distance measurement direction between the reference line connecting the distance sensor between two arbitrary points on the surface and another arbitrary point is determined. A sixth simultaneous linear equation similar to the first simultaneous linear equation is obtained by moving it along the surface of a known reference measurement object, and the sixth simultaneous linear equation is used as a reference line for specifying the surface profile. By selecting and solving the reference line on the surface of the reference measurement object, the true distance at the point where the distance in the distance measurement direction is known is determined, the measurement error component is determined as the difference between these distances, and then , as the sum of a certain element in a certain row of a matrix created by the coefficients of the deviation amount, the head vibration amount, and the distance measurement value when finding the true distance, obtained in the process of solving the sixth simultaneous linear equations. obtain a linear equation that determines a quantitative relationship between a value that is calculated and influences the measurement error component, the measurement error component, and the unknown, obtain a solution to the unknown by solving the linear equation, Correcting the distance measurement value obtained when measuring the surface profile of the object to be measured to eliminate the influence of this solution, and obtaining a fifth simultaneous linear equation similar to the first simultaneous linear equation for the corrected distance measurement value, The present invention is characterized in that the true surface profile is obtained by similarly solving the fifth simultaneous linear equations. Further, when r=3, since the number of unknowns is one, a solution to this unknown is obtained based on the second simultaneous linear equations. [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. Each distance sensor 31, 32, 33, 34, 35 has a contactor 31a, 32a, 3 on the rolling roll 1 side.
3a, 34a, and 35a are located. The height position of each contactor 31a, 32a, 33a, 34a, 35a is determined to be the same as the height position of the axis of the rolling roll 1. Even if there are irregularities on the surface of the rolling roll 1, the contacts 31a, 32a,
Distance sensors 31 fixed on the sensor mount 3a such that the tips of each of 33a, 34a, 35a are always in sliding contact with the roll surface with a predetermined contact pressure.
32, 33, 34, 35 each sensor body 31
b, 32b, 33b, 34b, and 35b. Distance sensor 31, 32, 33, 34, 3
5 is the surface of the rolling roll 1 to the sensor body 31b, 3
The separation distance between each of 2b, 33b, 34b, and 35b is measured, and the measurement results are input to the calculation device 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 nth 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 , and 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. Note that equation (17) corresponds to the first simultaneous linear equations in the claims. Now, equation (17) can be expressed as equation (18) below using matrix multiplication. Ax→=b→ ...(18) However, A is a (5n, 3n+4) matrix created by the coefficients of unknowns y _j , d _i , k _i in equation (17), and x→ is an unknown.
A (3n+4,1) matrix of y _j , d _i , k _i and b→ is a (5n,1) matrix of distance measurements y ^m _i,j . The details of equation (18) are shown in equation (19) below.

[Table] However, all blank parts of matrix A are 0. Now, as mentioned above, the surface profile can be obtained by 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 l, m
Replace the straight line connecting the true surface profile values y _l and y _n at (1≦l<n+4) with the reference line C mentioned above,
A temporary reference line C'' is selected, and the distance between this temporary reference line C'' and each measurement point is defined as the true surface profile value (the surface profile is the unevenness from the line connecting the surface of the rolling roll 1). Note that the temporary reference line C'' mentioned above is the same as the temporary reference line C'. Then, in the simultaneous linear equations shown in equation (17) above, y _l = 0, y _n = 0, and the temporary reference line The simultaneous linear equations based on C″, that is, the values of y _j , d _i , and k _i are
The matrix A 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 vectors x→ are y _l , y The (3n+2, 1) matrix x→ ₁ with _n eliminated. Therefore, equation (18) is changed to equation (20), and equation (19) is changed to equation (21). A ₁ x→ ₁ =b→ ……(20)

[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 _i , and the surface profile value y ₃ at any one measurement point, for example, as shown in FIG.
It is also possible to set the deviation amount d _n to 0, that is, the straight line C'' connecting the two points. In this case, it is obvious that the straight line passing through the two points is uniquely determined, and the above
If we solve Equation (17) with y ₃ = 0 and d _n = 0, we will obtain a surface profile with the straight line C'' as the reference. Also, for the combination of y _i and k _i , As shown in Figure 5b, y ₃ =0, k _n =0, that is, the slope is the same as the slope of the measuring unit 3 at measuring point m+2, and y ₃ is 0, that is, passing through the measuring point. It may be a straight line C″. It is clear that the straight line C″ is uniquely determined in this case as well, and the above
In equation (17), if we solve this by setting y ₃ = 0 and k _n = 0, we will obtain a surface profile based on the straight line C''. Also, if d _j is a combination of two As shown in Figure c, 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 C'' connecting both points. In this case, the straight line C'' is also uniquely defined, and in the above equation (17), d ₂ = 0, d _n = As 0,
Solving this will yield a surface profile based on the straight line C''. Also, as shown in Figure 5d, the combination of d _i and k _i , for example, the deviation at the measurement point. k _n at measurement point m+2 passing through the point where the quantity d ₂ is 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,
If k _n = 0 and solve this problem, a surface profile based on the straight line C'' will be obtained. Note that there are six combinations of the two unknowns y _j , d _i , and k _i . , k _i , a straight line cannot be specified even if two slopes are given, so in this case, the temporary reference line C'' does not exist. Furthermore, even in the combination shown in FIG. 5a, if y ₃ =0 and d ₁ =0 as shown in FIG. 5e, the straight line is perpendicular to the surface of the rolling roll 1. It cannot be used as a temporary reference line, and such combinations are excluded. Therefore, in the above equation (17), among the combinations that simultaneously make any two values of the unknowns y _j , d _i , k _i 0, k _i
If it is a combination excluding each other, and a straight line connecting the points that make these two values 0 at the same time has a certain slope with respect to the surface of the rolling roll 1, A temporary reference line 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 method of least squares. 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 x→ 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 , based on the temporary reference line C'' are obtained. 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 swing amounts k ₁ , k ₂ ... k _o can be calculated at once. can. The description of the present invention up to this point has been made in the above-mentioned patent application filed in 1983.
The content is the same as the explanation of the sequential r-point method proposed in No. 281287, and when solving the above equation (20) using the least squares method, as explained in detail in the previous application, the conventional sequential three-point method is Unlike the method, the accumulation of measurement errors ε _i,j can be significantly reduced, so in the case of the present invention, there is no need to consider the accumulation of measurement errors. Now, as explained in the [Problems to be Solved by the Invention] section, if the distance sensor has a zero point deviation, this zero point deviation will be present in the distance measurement value y ^m _i,j . It will be included. If the amount of deviation of this zero point is y _z , the measured value y ^m _i,j is expressed by the following equation (26). y ^m _i,j =y _j −d _i +(i−j+1)k _i +1 _z(j−i+
1) (Sequential three-point method) y ^m _i,j =y _j −d _i +(i−j+1)k _i +1 _z(j−i+
1) (Sequential three-point method) y ^m _i,j =y _j −d _i +(i-j+2)k _i +y _z(j-i+1) (Sequential five-point method)...(26) And the above According to the present invention, ε _i,j
can be ignored, so y and _z will be explained below.
Now distance sensors 31, 32, 33, 34, 35
If the amount of deviation of each zero point is y _z1 , y _z2 , y _z3 , y _z4 , y _z5 , y _z1 is the distance measurement value y ^m _1,1 , y ^m _2,2 ...y ^m _o,o , y _z2
is the distance measurement value y ^m _1,2 , y ^m _2,3 …y ^m _o,o+1 , and y _z3 is the distance measurement value y ^m _1,3 , y ^m _2,4 …y ^m _o,o+2 , y _z4 is the distance measurement y ^m _1,4 , y
^m _2,5
…y ^m _o,o+3 and y _z5 are distance measurements y ^m _1,5 , y ^m _2,6 …
They will be included in y ^m _{o and o+4,} respectively. Therefore, when calculating the surface profile value y _j , deviation amount d _i , and head vibration amount k _i using the above equation (25), y _z1 , y _z2 , y _z3 , y _z4 , y _z5 that appear in these The influence of
For example, looking at the pth of these unknowns, that is, the element in the pth row of the vector x→ ₁ , it is expressed by the following equation (27). (E _p,1 +E _p,6 +…+E _p,5o-4 )×y _z1 (E _p,2 +E _p,7 +…+E _p,5o-3 )×y _z2 (E _p,3 +E _{p, 8} +…+E _p,5o-2 )×y _z3 (E _p,4 +E _p,9 +…+E _p,5o-1 )×y _z4 (E _p,5 +E _p,10 +…+E _p,5o ) ×y _z5 ...(27) Here E _p,q (p=1, 2...l-1, l+1, m
−1, m+1...n+4, q=1...5n) are each element of the matrix (A ^t ₁ ×A ₁ ) ⁻¹ ×A ^t ₁ in the above equation (25). Now, let's say that the number of measurements n is 17, that is, 21 measurement points (∵n+4=17), and the measurement data
Assuming that 85 pieces (∵17×5=85) are obtained as y ^m _i,j , the above equation (27) is expressed by the following equation (28). (E _p,1 +E _p,6 +…+E _p,81 )y _z1 (E _p,2 +E _p,7 +…+E _p,82 )y _z2 (E _p,3 +E _p,8 +…+E _{p, 83} )y _z3 (E _p,4 +E _p,9 +…+E _p,84 )y _z4 (E _p,5 +E _p,10 +…+E _p,85 )y _z5 …(28) And the measurement point, is the reference point, i.e. y ₁ =
By solving the above equation (20) with 0, y ₂₁ = 0,
When calculating y _j , d _i , k _i , the influence of y _z1 , y _z2 , y _z3 , y _z4 , y _z5 at each measurement point, that is, the value in parentheses in equation (28) above (hereinafter the zero point The influence factor of the amount of deviation) is calculated as shown in Table 2 below. The results are shown in FIG. FIG. 6 is a graph in which the vertical axis shows the influence magnification of the amount of deviation of the zero point, and the horizontal axis shows each measurement point. Note that the influence multiplier for y _z4 is symmetrical with the influence multiplier for y _z2 around the center measurement point, and similarly, the influence multiplier for y _z5 is symmetrical with the influence multiplier for y _z1 . There is. As is clear from FIG. 6, each distance sensor 31,
The influence magnification of the amount of deviation of the zero points 32, 33, 34, and 35 appears as a bow-shaped curve that becomes maximum at the measurement point. Since this influence magnification is included in the profile value y _j obtained by solving equation (25) above, the error in the surface profile value y _j will similarly be a curved shape where the value at the central measurement point is maximum. It appears as a shaped curve.
Hereinafter, this bow-shaped error occurrence amount will be referred to as the bow occurrence amount. Note that the amount of bowing corresponds to the measurement error component in the claims. Therefore, now, suppose each distance sensor 31, 32, 3
Assuming that the deviation of the zero points of 3, 34, and 35 is 1 μm,
The amount of arching at the center measurement point is amplified to about 7 to 14 μm, and as mentioned above, it is difficult to manufacture a zero point reference board to calibrate this amount of zero point deviation, so if it is left as is, it will not be possible to obtain a high accuracy. Surface profile measurements will not be possible. However, each such distance sensor 31, 32, 33,
Since it is possible to quantitatively grasp the negative effect of the amount of deviation in the zero points of distance sensors 34 and 35 on measurement accuracy, the amount of deviation in the zero points of each distance sensor 31, 32, 33, 34, and 35 can be determined, and furthermore, the error caused by this can be determined. Find the ingredients,
If this error component value is excluded from the surface profile value y _j , each distance sensor 31, 3
The surface profile can be measured accurately without calibration of the zero points of 2, 33, 34, 35. This procedure will be explained below. The relationship expressed by the following equation (29) holds between the amount of arching at each measurement point and the amount of zero point deviation of each distance sensor 31, 32, 33, 34, 35. ΔC _j =F _1,5 y _z1 +F _2,5 y _z2 +F _3,5 1 _z3 +F _4,5 1 _z4 +F _5,5 y _z
Five
...(29) However, ΔC _j is the amount of bow occurrence at the j-th measurement point, and F _1,5 , F _2,5 , F _3,5 , F _4,5 , F _5,5 are the above ( 27) Each coefficient of y _z1 , 1 _z2 , y _z3 , y _z4 , and y _z5 in the formula, and is expressed by the following formula (30). In addition, F _1,5 ,
F _2,5 , F _3,5 , F _4,5 , and F _5,5 correspond to values that affect the measurement error component referred to in the claims. F _1,5 =E _p,1 +E _p,6 +…+E _p,5o-4 F _2,5 =E _p,2 +E _p,7 +…+E _p,5o-3 F _3,5 =E _{p, 3} +E _p,8 +…+E _p,5o-2 F _4,5 =E _p,4 +E _p,9 +…+E _p,5o-1 F _5,5 =E _p,5 +E _p,10 +…+E _p,5o ...(30) By the way, the five distance sensors 31, 32, 33,
34, 35 zero point deviation y _z1 , y _z2 , y _z3 , y _z4 ,
When calculating y _z5 , it is not necessary to use each distance sensor 31, 32, 33, 34, 35 from the specific reference line.
It is not necessary to find the absolute amount of deviation of each zero point, but for the reason shown below, the deviation of the zero points of any two sensors out of the five sensors is set to 0, that is, the straight line connecting the zero points of both sensors is As a temporary reference line, the amount of deviation of the zero points of the remaining three distance sensors from this temporary reference line may be determined. That is, for example, as shown in FIG. 7, assuming that there is no deviation in the zero points of each distance sensor 31, 32, 33, 34, and 35, let V be the straight line (specific reference line) connecting these zero points. , and the distance sensor 3 when the measurement unit 3 is located at an arbitrary measurement point.
Assuming that the straight line V' connecting the zero points of 2 and 34 is a temporary reference line, each distance sensor 31, 32, 33, 34, 35
The zero point deviations y _z1 , y _z2 , y _z3 , y _z4 , y _z5 are y′ _z1 , y′ _z2 , y′ _z3 , y′ _z4 , y′ respectively for the temporary reference line V′.
It becomes _z5 . However, regarding the sign of these values, the direction away from the specific reference line V is positive, and the opposite direction is negative. Then, y _z1 and y′ _z1 , y _z2 and y′ _z2 , y _z3 and y′ _z3 ,
Between y _z4 and y' _z4 and between y _z5 and y' _z5 , the relationship shown in the following equation (31) is established due to the geometrical relationship shown in FIG.

[Table] The proof is as follows. Straight lines V, V',
Line segments y _z1 , y _z2 , y _z3 , y _z4 , y _z5 and their intersections with extensions are H, I, J, K, L, M, N, O,
Let them be P and Q. Further, draw an auxiliary line U parallel to the straight line V passing through point K, and let R be the point of intersection with this auxiliary line, and S be the point of intersection with the extension of the line segment. y _z1 is expressed by the following formula (32). y _z1 =+y′ _z1 ...(32) However, the sign of y′ _z1 is opposite to that of y _z1 . is the sum of (=y _z2 ), and is △
From the relationship RIK∽△KOS, it is equal to 1/2. Here it is equal to y _z2 −y _z4 . Then, is expressed by the following equation (33). =y _z2 +1/2 (y _z2 −y _z4 )=3/2y _z2 −1/2y _z4 ...(33) Therefore, by substituting equation (33) into equation (32), y _z1 = y ′ _z1 +3/2y _z2 −1/2y _z4 ...(34) The proof of y _z2 =y′ _z2 +y _z2 =y _z2 is clear from FIG. Next, y _z3 will be explained. y _z3 is expressed by the following equation (35). y _z3 = y' _z3 + ... (35) is also expressed by the following equation (36) from =1/2. =1/2(+)=1/2y _z4 +1/2y _z2
...(36) Therefore, by substituting equation (36) into equation (35), y _z3 = y′ _z3 +1/2y _z2 +1/2y _z4 ...(37). The proof of y _z4 =y′ _z4 +y _z4 =y _z4 is clear from FIG. Next, y _z5 will be explained. y _z5 is below (38)
It is shown by the formula. y _z5 =+y' _z5 (38) In FIG. 7, draw an auxiliary line W passing through O and parallel to the straight line V, and an auxiliary line X passing through Q and parallel to the straight line V. The intersection with the auxiliary line W is defined as Y, and the intersection with the auxiliary line X is defined as Z. Then,
It is expressed as PQ=(=y _z4 )−, and △YKO
From ∽△ZOQ, it is expressed as =1/2=1/2(y _z2 −y _z4 ) ...(39), so =y _z4 −1/2(y _z2 −y _z4 )=−1/ 2y _z2 +3/2y _z4
...(40) becomes. Therefore, y _z5 can be calculated by substituting equation (40) into equation (38), y _z5 = y′ _z5 −1/2y _z2 + 3/2y _z4 ...(41) Now, returning to equation (29) above, For example, if you select y _z1 , y _z2 , y _z3 , y _z4 , and y _z5 as the measurement points and multiply them by the magnification of the amount of deviation shown in Table 2 above to find the sum of these, the following is obtained. It is expressed by equation (42). −2.98y _z1 +1.97y _z2 +2.46y _z3 +1.09y _z4 −2.54y _z5
...(42) Expanding equation (42), we get equation (43) below. −2.98(y′ _z1 +3/2y _z2 −1/2y _z4 )+1.97y _z2 +2.
46(y′ _z3 +1/2y _z2 +1/2y _z4 )+1.09y _z4 −2.54(y′ _z5 −1/2y _z2 +3/2y _z4 )=−2.98y′
_z1 +2.46y′ _z3 −2.54y′ _z5 ...(43) Now, in equation (43), distance sensors 31, 33,
Only the term related to the amount of deviation of the zero point from the temporary reference line V' of distance sensor 35 remains, and the term related to the zero point of distance sensors 32 and 34 is deleted. In other words, when determining the amount of deviation of the zero point of each of the five distance sensors, two of the five
You can set a straight line connecting the zero points of two distance sensors as a temporary reference line, and find the amount of deviation of the zero points of the remaining three distance sensors as the amount of deviation from this temporary reference line. The amount of bowing included ΔC _j can be found, and therefore,
It is mathematically proven that the above assumption is correct. In the above explanation, the straight line connecting the zero points of the distance sensors 32 and 34 was selected as the temporary reference line V', but it is also possible to set the straight line connecting the zero points of any two distance sensors among the five as the temporary reference line. Of course, this is a good thing. The same applies to all distance measurement points. Furthermore, in the above explanation, a measurement method that could be called a sequential five-point method using five distance sensors 31, 32, 33, 34, and 35 was described, but the two distance measurements y ^m _i,j
is determined by the relationship between each distance measurement value,
In order to obtain simultaneous linear equations with y _j , d _i , and k _i as unknowns, it is necessary to It is sufficient that the distance sensors are in contact with each other. In other words, the number of distance sensors may be three or more. Also, from this, even if the measuring unit 3 is equipped with five distance sensors, the total distance sensor 3 is
It is not necessary to read all the distance measurement values 1, 32, 33, 34, and 35;
Measured value of one or two distance sensors y ^m _i,j
It is also possible to exclude the reading of . That is, the method shown in FIG. 8a is a measurement method that excludes the reading of the distance measurement value y ^m _i,j of the distance sensor 35, which can be called a sequential four-point method, and the method shown in FIG. 8b
What is shown is the distance measurement value of distance sensors 34 and 35.
This is a measurement method that can be called a sequential three-point method that excludes the reading of y ^m _{i,j, and} the method ^shown in FIG.
This is a measurement method that excludes the reading of data, so to speak, and can be called a sequential three-point method. Now, the simultaneous linear equations corresponding to the above equation (17) when using the sequential four-point method, sequential three-point method, and one-step sequential three-point method are expressed by the following equations (44), (45), and (46), respectively. be done.

【table】

【table】

〔effect〕

Next, the effects of the present invention will be explained based on specific examples. Measurement object 40 used in this example
(also serves as a zero adjustment reference board) is a flat surface with good flatness, where 21 measurement points were measured as shown in Figure 10, and the thickness was 60μ at the 5th, 9th, and 14th measurement points.
M films 42, 42, 42 are attached to form irregularities. In addition, measurement points were selected as reference points for identifying the temporary reference line C''. Table 3 below shows the distance measurement values y ^m _i,j at each measurement point measured by the sequential five-point method. Table 4 shows the magnification of the deviation amount of the zero point in this case, and Table 5 below shows the calculation results of the surface profile value y _j.In addition, the calculation results using the sequential four-point method, sequential three-point method, and skip-one three-point method are shown in Table 5 below. y _z1 at the central measurement point in case,
Influence factor of y _z2 , y _z5 F′ _1,4 , F′ _3,4 , F″ _1,3 , F″ _3,3 ,
F
The results of calculating _1,3 , F _3,3 and F _5,3 [see formula (59)] are shown in Table 6 below.

[Table] In addition, the amount of arching ΔC ₁₁ ′, C ₁₁ ″, and C ₁₁ at the center measurement point when using the sequential four-point method, sequential three-point method, and one-stop sequential three-point method were as follows. ΔC ₁₁ ′=−0.233 ΔC ₁₁ ″=−0.440 ΔC ₁₁ =−0.106 (61) Then, the above equation (59) can be expressed as the following equation (62). −0.233=616y _z1 +16y _z3 −0.440=−32y _z1 +32y _z3 −0.106=−8y _z1 +16y _z3 −8y _z5 ...(62) Calculating y _z1 , y _z3 , and y _z5 from equation (62) is shown below. Becomes a value. y _z1 =0.014mm y _z3 =−0.0004 y _z5 =−0.0017 (63) However, y _z2 =y _z4 =0. Then, calculate ΔC _j from the influence magnification at each measurement point shown in Table 4 and the above formula (29), and use the following formula (64).
The true surface profile value y ^c _j at each measurement point is determined by executing the calculation shown in the formula. y ^c _j =y _j −ΔC _j (64) Now, as a calculation example, how to obtain the true surface profile value y ^c ₁ at the first measurement point will be described. y ^c ₁ =0.072−(5.40y _z1 −5.13y _z3 +4.89y _z5 )=0
.072−{5.40×0.014 −5.13×(−0.0004)+4.89×(−0.0017)=
0.001mm……(65) Then, by performing the same calculation as the above equation (65), the true surface profile value at each measurement point is calculated.
Find y ^c _j . Table 7 below shows the results of this calculation.

【table】

[Table] FIG. 11 shows a comparison between the error when using the surface profile value y _j including the amount of arching and the difference when using the true surface profile value y ^c _j . As is clear from FIG. 11, according to the method of the present invention, it is possible to eliminate the influence of the error component due to the deviation amount _yz of the zero point of each distance sensor, so that highly accurate surface profile measurement can be performed. Furthermore, as mentioned above, the zero adjustment reference board used in the method of the present invention only needs to have a known distance between the straight lines connecting the surface of at least one measurement point to the surface of any two other measurement points, and the distance between the entire measurement plane There is no need to process the material into a high-precision flat surface, and therefore, it is easy to manufacture and does not cause any inconvenience in implementing the method of the present invention. In the above embodiment, the amount of deviation y and _z of the zero points of each distance sensor is determined, and then the amount of arching, which is the product of this amount of deviation and the influence magnification at each measurement point of the object to be measured, is determined, and the surface profile value is calculated. We decided to find the true surface profile value y ^c _j by subtracting the amount of bowing _from , but the procedure is not limited to this. By correcting the distance measurement value y ^m _i,j that includes these values, a distance measurement value y′ ^m _i,j that is not affected by the amount of deviation of the zero point is obtained, and the distance measurement value y′ ^m _i
,j
As described above, simultaneous linear equations (corresponding to the fifth simultaneous linear equations in the claims) may be obtained and the true surface profile value y ^c _j may be determined by solving them using the least squares method.

【table】

【table】

【table】

Claims (1)

[Claims] 1 Distance sensors r (r≧
4) Move the individually arranged measurement units along the surface of the object to be measured, obtain a distance measurement value each time the measurement unit moves by the distance sensor arrangement interval, and measure any one of the r pieces. The amount of deviation due to the fact that the movement of the measurement unit in the direction of approaching and away from the surface of the object to be measured of one distance sensor is not in a straight line, and the amount of deviation of other r-1 distance sensors based on the distance sensor The amount of swing of each distance sensor in the above direction, the amount of deviation thereof, and the true distance determined for each measurement point when there is no amount of swing are taken as unknowns, and the relationship between these and the distance measurement value is expressed. A number of first simultaneous linear equations are obtained, and in the first simultaneous linear equations, a straight line having a certain slope with respect to the surface of the object to be measured is uniquely determined as a reference line for specifying the surface profile. A method for determining the surface profile of the object to be measured by solving the first simultaneous linear equations with any two values of the unknown quantities set to 0, The amount of deviation of the zero point of each distance sensor corresponding to the amount of positional deviation from the measurement reference position (zero point) in the direction is calculated from the remaining r-2 distance sensors using the straight line connecting the zero points of any two distance sensors as a reference. Connecting the distance sensor between any two points on the surface in order to solve for the amount of deviation at the zero point as an unknown quantity and to obtain a measurement error component included in the surface profile due to the amount of deviation at the zero point. A second simultaneous linear equation similar to the first simultaneous linear equation and /or the amount of deviation of any one distance sensor in the direction toward or away from the surface of the reference measurement object, and each of r-2 or less distance sensors among other r-1 distance sensors with respect to the distance sensor; The amount of swing in the direction, the offset position of these, and the true distance determined for each measurement point when there is no amount of swing are taken as unknowns, and these, the arbitrary one, and the r-2 or less points One or more third simultaneous linear equations representing the relationship with the distance measurement value of the distance sensor are obtained, and the second simultaneous linear equations and/or the third simultaneous linear equations are used as the reference line for specifying the surface profile. By selecting and solving the reference line on the surface of the reference object, the true distance at the point where the distance in the distance measurement direction is known is determined, the measurement error component is determined as the difference between these distances, and then the measurement error component is determined as the difference between these distances. One of the matrices created by the coefficients of each distance measurement value when determining the deviation amount, head vibration amount, and true distance obtained in the process of solving the two simultaneous linear equations and/or the third simultaneous linear equations, respectively. r-2 fourth simultaneous linear equations that determine a quantitative relationship between a value that is determined as a sum of certain elements in a row and that affects the measurement error component, the measurement error component, and the unknown quantity; Then, by solving the fourth simultaneous linear equations, solutions for r-2 unknowns are obtained. From these solutions, the measurement error component included in the surface profile of the object to be measured is determined, and this measurement error component is A surface profile measuring method characterized by obtaining a true surface profile by subtracting from the profile. 2 Distance sensors r (r≧
4) Move the individually arranged measurement units along the surface of the object to be measured, obtain a distance measurement value each time the measurement unit moves by the distance sensor arrangement interval, and measure any one of the r pieces. the amount of deviation of one distance sensor in the direction toward or away from the surface of the object to be measured, the amount of swing of each of the other r-1 distance sensors in the direction with respect to the distance sensor, and Using the true distance determined for each measurement point when there is no deviation or head vibration as an unknown, a number of first simultaneous linear equations expressing the relationship between these and the distance measurement values are obtained, and then, In this first simultaneous linear equation, any two of the unknowns are determined so that a straight line having a certain slope with respect to the surface of the object to be measured, which is to be the reference line for specifying the surface profile, is uniquely determined. A method of determining the surface profile of the object to be measured by solving the first simultaneous linear equations with a value of 0, the method comprising: determining the positional deviation of the distance sensor from the measurement reference position (zero point) in the distance measurement direction; In order to solve the amount of deviation of the zero points of each distance sensor corresponding to the amount, using the straight line connecting the zero points of any two distance sensors as a reference, and the amount of deviation of the zero points of the remaining r-2 distance sensors as unknowns, In order to find the measurement error component included in the surface profile due to the amount of deviation of the zero point, the distance sensor is measured between a reference line connecting arbitrary two points on the surface and another arbitrary point. A second simultaneous linear equation similar to the first simultaneous linear equation and/or the reference of any one distance sensor is moved along the surface of the reference object whose distance is known. The amount of deviation in the direction approaching or moving away from the surface of the object to be measured, the amount of swing of each of r-2 or less distance sensors among the other r-1 distance sensors in the direction with respect to the distance sensor, and these deviations. Let the true distance in the case where there is no position or amount of head vibration be unknown, and these, the arbitrary one, and the r-
Obtain one or more third simultaneous linear equations indicating the relationship between the distance measurement values of two or less distance sensors, and
The distance in the distance measurement direction is known by solving the simultaneous linear equations and/or the third simultaneous linear equations by selecting a reference line related to the surface of the reference measurement object as a reference line for specifying the surface profile. Find the true distance at the point, find the measurement error component as the difference between these distances, and then calculate the deviation amount, neck, obtained in the process of solving the second simultaneous linear equations and/or the third simultaneous linear equations, respectively. It is determined as the sum of a certain element in a certain row of a matrix created by the coefficient of each distance measurement value when determining the amount of vibration and the true distance, and the value that affects the measurement error component and the measurement error component. , by obtaining r-2 fourth simultaneous linear equations that determine the quantitative relationship between the undifferentiated numbers, and solving the fourth simultaneous linear equations, r-
Obtaining solutions for the two unknowns, correcting the distance measurement value obtained when measuring the surface profile of the object to be measured to eliminate the influence of this solution, and calculating the first simultaneous linear equations for the corrected distance measurement value. A surface profile measuring method characterized in that a true surface profile is obtained by obtaining a similar fifth simultaneous linear equation and solving the fifth simultaneous linear equation in the same manner. 3. A measurement unit with three distance sensors arranged at equal intervals in the movement direction is moved along the surface of the object to be measured, and the distance measurement value is obtained each time the measurement unit moves by the distance sensor arrangement interval. obtained, 3
The amount of deviation of any one of the distance sensors in the direction toward or away from the surface of the object to be measured, and the amount of deviation of each of the other two distance sensors in the direction with respect to the distance sensor. The amount of head vibration, the amount of deviation thereof, and the true distance in the absence of the amount of head vibration are taken as unknown quantities, and a number of first simultaneous linear equations expressing the relationship between these and the distance measurement value are obtained, and then this first In the simultaneous linear equations, any two values of the unknowns are set to 0 so that a straight line having a certain slope with respect to the surface of the object to be measured, which should be the reference line for specifying the surface profile, is uniquely determined. A method of determining the surface profile of the object to be measured by solving the first simultaneous linear equations, which corresponds to the amount of positional deviation of the distance sensor from the measurement reference position (zero point) in the distance measurement direction. In order to solve the amount of deviation of the zero point of each distance sensor, using the straight line connecting the zero points of any two distance sensors as a reference, and the amount of deviation of the zero point of the remaining distance sensor as an unknown,
In addition, in order to obtain a measurement error component included in the surface profile due to the amount of deviation of the zero point,
The distance sensor is moved along the surface of the reference object for which the distance in the distance measurement direction between a reference line connecting arbitrary two points on the surface and one other arbitrary point is known. , obtain a sixth simultaneous linear equation similar to the first simultaneous linear equation, and solve the sixth simultaneous linear equation by selecting a reference line related to the surface of the reference measurement object as a reference line for specifying the surface profile. By this, the true distance at the point where the distance in the distance measurement direction is known is found, the measurement error component is found as the difference between these distances, and then the sixth simultaneous linear equations are solved.
A value that is determined as the sum of a certain element in a certain row of a matrix made of the coefficients of the deviation amount, head vibration amount, and each distance measurement value when determining the true distance, and that affects the measurement error component. and obtain a linear equation that defines a quantitative relationship between the measurement error component and the unknown quantity,
Obtain the solution to the unknown by solving the linear equation,
A surface profile measuring method characterized in that the measurement error component included in the surface profile of the object to be measured is determined from this solution, and the true surface profile is determined by subtracting this measurement error component from the surface profile. 4. A measurement unit with three distance sensors arranged at equal intervals in the movement direction is moved along the surface of the object to be measured, and the distance measurement value is obtained each time the measurement unit moves by the distance sensor arrangement interval. obtained, 3
The amount of deviation of any one of the distance sensors in the direction toward or away from the surface of the object to be measured, and the amount of deviation of each of the other two distance sensors in the direction with respect to the distance sensor. The amount of head vibration, the amount of deviation thereof, and the true distance in the absence of the amount of head vibration are taken as unknown quantities, and a number of first simultaneous linear equations expressing the relationship between these and the distance measurement value are obtained, and then this first In the simultaneous linear equations, any two values of the unknowns are set to 0 so that a straight line having a certain slope with respect to the surface of the object to be measured, which should be the reference line for specifying the surface profile, is uniquely determined. A method for determining the surface profile of the object to be measured by solving the first simultaneous linear equations, the method comprising: calculating the surface profile of the object to be measured by solving the first simultaneous linear equations; In order to solve the amount of deviation of the zero point of each distance sensor, using the straight line connecting the zero points of any two distance sensors as a reference, and the amount of deviation of the zero point of the remaining one distance sensor as an unknown, we also calculate the amount of deviation of the zero point. In order to find the measurement error component included in the surface profile due to The first object is moved along the surface of the reference object whose distance is known.
Obtain the sixth simultaneous linear equation similar to the simultaneous linear equation,
By solving the sixth simultaneous linear equations by selecting a reference line related to the surface of the reference object as a reference line for specifying the surface profile, the true distance at the point where the distance in the distance measurement direction is known is determined. , the measurement error component is determined as the difference between these distances, and then the distance measurement value when determining the deviation amount, head vibration amount, and true distance obtained in the process of solving the sixth simultaneous linear equations a linear equation that is determined as the sum of a certain element in a certain row of a matrix made of coefficients and determines a quantitative relationship between a value that affects the measurement error component, the measurement error component, and the unknown quantity; obtain a solution to the unknown by solving the linear equation, correct the distance measurement value obtained when measuring the surface profile of the object to be measured to remove the influence of this solution, and obtain the corrected distance measurement value. A method for measuring a surface profile, characterized in that a fifth simultaneous linear equation similar to the first simultaneous linear equation is obtained for , and the true surface profile is obtained by solving the fifth simultaneous linear equation in the same manner.