Roundness measuring

• US 5,926,781 A
• Filed: 05/28/1997
• Issued: 07/20/1999
• Est. Priority Date: 10/18/1994
• Status: Expired due to Term

• Current Assignee: Taylor Hobson Limited (Ametek Incorporated)
• Original Assignee: Taylor Hobson Limited (Ametek Incorporated)
• Inventors: Scott, Paul James
• Primary Examiner(s): Barlow, John
• Assistant Examiner(s): VO, HIEN XUAN
• Application Number:
  US08/817,491
• Time in Patent Office: 783 Days
• Field of Search: 702/150, 702/167, 702/168, 702/169, 702/151, 702/157, 364/474.37, 364/474.35, 33/503, 33/504, 33/505, 33/554, 33/569, 33/644, 33/548, 33/645
• US Class Current: 702/151
• CPC Class Codes: G01B 21/20 for measuring contours or curvatures, e.g. determining profile

Abstract

A roundness measuring machine is described which measures the position of the surface of an object as the object is rotated on a turntable. The machine determines the circle which is the best fit to the measured points and converts the measurements to distances from the best fit circle. An improved algorithm for determining the best fit circle is used in place of the limacon fit. Calculated differences between the measured surface position and the best fit circle are corrected for the effect of measuring the difference in the direction towards the center of rotation of the turntable instead of in the direction towards the center of the circle. Data values are calculated representing points at equal angles around the center of the best fit circle rather than equal angles around the center of rotation of the turntable. The improved accuracy of correction allows the machine to tolerate greater eccentricity of the workplace relative to the turntable, reducing the necessity for accurate centering of the workpiece.

Claims

1. An instrument for measuring the roundness of a workpiece cross-section, said workpiece cross-section having a center and a perimeter defining a shape, said instrument comprising:

a turntable for mounting a workpiece, said turntable being rotatable about an axis of rotation;

a holder for holding a measuring probe, the measuring probe being operable to provide a signal representative of the shape of the workpiece cross-section as the turntable rotates about the axis of rotation; and

a processor for receiving and processing data derived from said signal, said data representing a plurality workpiece surface points which are located on the perimeter of said workpiece cross-section at respective different ones of a plurality of known angles around the axis of rotation determined in relation to a reference line radiating from the axis of rotation;

wherein said processor is operable to process said data to;

(i) estimate a position of the center of the workpiece cross-section relative to the axis of rotation; and

(ii) calculate, from said data and said estimated position, a measure of the distance between the centre of the workpiece cross-section and the perimeter of the workpiece cross-section at a plurality of known angles around the centre of the workpiece cross-section.

2. An instrument according to claim 1, wherein said processor is arranged to calculate each of said measures by applying a box filter having a variable integration interval to said data representing the plurality of workpiece surface points, wherein said variable integration interval of the box filter is arranged to vary for each of said measures dependent upon the estimated position of the center of the workpiece.

8. An instrument according to any of claims 1 to 7, wherein the instrument further comprises a centering unit and a leveling unit to enable approximate manual alignment of the workpiece.

9. An instrument according to any of claims 1 to 8, wherein the instrument further comprises means for mounting a jig adapted to hold the workpiece.

3. An instrument for measuring the roundness of a workpiece cross-section, said workpiece cross-section having a center and a perimeter defining a shape, said instrument comprising:

a turntable for mounting a workpiece, said turntable being rotatable about an axis of rotation;

a holder for holding a measuring probe, the measuring probe being operable to provide a signal representative of the shape of the workpiece cross-section as the turntable rotates about the axis of rotation; and

a processor for receiving and processing data derived from said signal, said data comprising a set of distances, each of said distances being representative of the distance between a point on the perimeter of the workpiece cross-section and a circle centered on the axis of rotation along a respective different one of a plurality of lines radiating from the axis of rotation, each of said plurality of lines being at a respective different one of a plurality of known angles determined in relation to a reference line radiating from the axis of rotation,

wherein said processor is operable to process said data to;

(i) estimate a position of the center of the workpiece cross-section relative to the axis of rotation by fitting a reference shape to said data;

(ii) calculate a measure of the distance between the perimeter of the workpiece cross-section and said reference shape along each of said plurality of lines; and

(iii) adjust, using the estimated position, each of said measures to at least partially compensate for the difference in measuring said measure in a direction towards the axis of rotation as compared with measuring said measure in a direction towards the centre of the workpiece cross-section.

4. An instrument according to claim 3, wherein said processor is arranged to divide each of said measures by a respective value, said respective value being cos(θ

-α

), where

α

is the angle between the respective one of said plurality of lines and the reference line, and

θ

is the angle between a line radiating from the estimated position of the center of the workpiece cross-section parallel to the reference line and a line radiating from the estimated position of the center of the workpiece cross-section to a point on the reference shape at which said respective one of said plurality of lines intersects said reference shape.

5. An instrument according to claim 3, wherein the reference shape is defined by a function having the form c+a cos (α

)+b sin (α

i), where

α

is the angle between a respective one of said plurality of lines and the reference line,

a is a first constant corresponding to the component of the estimated position of the centre of workpiece cross-section relative to the axis of rotation in the direction corresponding to α

=0°

,

b is a second constant corresponding to the component of the estimated position of the center of the workpiece cross-section relative to the axis of rotation in the direction corresponding to α

=90°

, and

c is a third constant.

6. An instrument for measuring the roundness of a workpiece cross-section, said workpiece cross-section having a center and a perimeter defining a shape, said instrument comprising:

a turntable for mounting a workpiece, said turntable being rotatable about an axis of rotation;

a holder for holding a measuring probe, the measuring probe being operable to provide a signal representative of the shape of the workpiece cross-section as the turntable rotates about the axis of rotation; and

a processor for receiving and processing data derived from said signal, said data comprising a set of first distances, each of said first distances being representative of the distance between a point on the perimeter of the workpiece cross-section and a circle centered on the axis of rotation along a respective different one of a plurality of lines radiating from the axis of rotation, each of said plurality of lines being at a respective different one of a plurality of known angles determined in relation to a reference line radiating from the axis of rotation,

wherein said processor is operable to process said data to;

(i) estimate an eccentricity of the workpiece relative to the axis of rotation by fitting a first function having the form c+a cos (α

)+b sin (α

) to said set of first distances, where

α

is the angle between a respective one of said plurality of lines and the reference line,

a is a first constant corresponding to an estimate of the component of the eccentricity in the direction corresponding to α

=0°

,

b is a second constant corresponding to an estimate of the component of the eccentricity in the direction corresponding to α

=90°

, and

c is a third constant;

(ii) calculate a set of second distances by subtracting a fourth constant from each of said set of first distances, said fourth constant being such that a sum of the set of second distances around the axis of rotation equals zero; and

(iii) subtract from each value of the set of second distances a second function, said second function integrating to zero over α

=0°

to α

=360° and

differing from a cos (α

)+b sin (α

) by a first correction term and a second correction term, where

the first correction term has a magnitude which varies with α and

represents at least approximately the difference between said first function and an equation for an eccentric circle, and

the second correction term has a magnitude which does not vary with α and

represents at least approximately the magnitude of the integral of the first correction term over α

=0°

to α

=360°

.

7. An instrument for measuring the roundness of a workpiece cross-section, said workpiece cross-section having a center and a perimeter defining a shape, said instrument comprising;

a turntable for mounting a workpiece, said turntable being rotatable about an axis of rotation;

a holder for holding a measuring probe, the measuring probe being operable to provide a signal representative of a shape of the workpiece cross-section as the turntable rotates about the axis of rotation; and

a processor for receiving and processing data derived from said signal, said data comprising a set of first distances, each of said first distances being representative of the distance between a point on the perimeter of the workpiece cross-section and a circle centered on the axis of rotation along a respective different one of a plurality of lines radiating from the axis of rotation, each of said plurality of lines being at a respective different one of a plurality of known angles determined in relation to a reference line radiating from the axis of rotation,

wherein said processor is operable to process said data to;

(i) estimate a position of the center of the workpiece cross-section relative to the axis of rotation, thereby providing an estimate of an eccentricity of the workpiece cross-section, by fitting a first function having the form c+a cos (α

)+b sin (α

) to said set of first distances, where

α

is the angle between a respective one of said plurality of lines and the reference line,

a is a first constant corresponding to an estimate of the component of the eccentricity in the direction corresponding to α

=0°

,

b is a second constant corresponding to an estimate of the component of the eccentricity in the direction corresponding to α

=90°

, and

c is a third constant;

(ii) calculate a set of second distances by subtracting a fourth constant from each of the set of first distances, said fourth constant being such that a sum of the set of second distances around the axis of rotation equals zero;

(iii) calculate a set of third distances by subtracting from each of the set of second distances a second function, said second function integrating to zero over α

=0°

to α

=360° and

differing from a cos (α

)+b sin (α

) by a first correction term and a second correction term, where

the first correction term has a magnitude which varies with α and

represents at least approximately the difference between said first function and an equation for an eccentric circle, and

the second correction term has a magnitude which does not vary with α and

represents at least approximately the magnitude of the integral of the first correction term over α

=0°

to α

=360°

;

(iv) adjust each of the set of third distances to at least partially compensate for the difference in measuring said set of third distances in a direction towards the axis of rotation and measuring said set of third distances in a direction towards the center of the workpiece cross-section; and

(v) use said set of third distances and the estimated position of the center of the workpiece cross-section to obtain a measure of the distance between the center of the workpiece cross-section and the perimeter of the workpiece cross-section at a plurality of known angles around the center of the workpiece cross-section.

10. A computer useable medium having computer readable instructions stored therein for causing the computer to process data derived from a signal received from a measuring probe as the measuring probe follows a perimeter of a workpiece cross-section as a turntable on which a workpiece is mounted rotates about an axis of rotation, the instructions comprising instructions for causing the computer to process said data to:

(i) estimate a position of the center of the workpiece cross-section relative to the axis of rotation; and

(ii) calculate, from said data and said estimated position, a measure of the distance between the centre of the workpiece cross-section and the perimeter of the workpiece cross-section at a plurality of known angles around the centre of the workpiece cross-section.

11. A computer useable medium having computer readable instructions stored therein for causing the computer to process data derived from a signal received from a measuring probe as the measuring probe follows a perimeter of a workpiece cross-section as a turntable on which a workpiece is mounted rotates about an axis of rotation, said data being a set of distances with each of said distances being representative of the distance between a point on the perimeter of the workpiece cross-section and a circle centered on the axis of rotation along a respective different one of a plurality of lines radiating from the axis of rotation, each of said plurality of lines being at a respective different one of a plurality of known angles determined in relation to a reference line radiating from the axis of rotation,

the instructions comprising instructions for causing the computer to process said data to:

(i) estimate a position of the center of the workpiece cross-section relative to the axis of rotation by fitting a reference shape to said data;

(ii) calculate a measure of the distance between the perimeter of the workpiece cross-section and said reference shape along each of said plurality of lines; and

(iii) adjust, using the estimated position, each of said measures to at least partially compensate for the difference in measuring said measure in a direction towards the axis of rotation as compared with measuring said measure in a direction towards the centre of the workpiece cross-section.

12. A computer useable medium having computer readable instructions stored therein for causing the computer to process data derived from a signal received from a measuring probe as the measuring probe follows a perimeter of a workpiece cross-section as a turntable on which a workpiece is mounted rotates about an axis of rotation, said data comprising a set of first distances with each of said first distances being representative of the distance between a point on the perimeter of the workpiece cross-section and a circle centered on the axis of rotation along a respective different one of a plurality of lines radiating from the axis of rotation, each of said plurality of lines being at a respective plurality of known angles determined in relation to a reference line radiating from the axis of rotation,

the instructions comprising instructions for causing the computer to process said data to:

(i) estimate an eccentricity of the workpiece relative to the axis of rotation by fitting a first function having the form c+a cos (α

)+b sin (α

) to said set of first distances, where

α

is the angle between a respective one of said plurality of lines and the reference line,

a is a first constant corresponding to an estimate of the component of the eccentricity in the direction corresponding to α

=0°

,

b is a second constant corresponding to an estimate of the component of the eccentricity in the direction corresponding to α

=90°

, and

c is a third constant;

(ii) calculate a set of second distances by subtracting a fourth constant from each of said set of first distances, said fourth constant being such that a sum of the set of second distances around the axis of rotation equals zero; and

(iii) subtract from each value of the set of second distances a second function, said second function integrating to zero over α

=0°

to α

=360° and

differing from a cos (α

)+b sin (α

) by a first correction term and a second correction term, where

the first correction term has a magnitude which varies with α and

represents at least approximately the difference between said first function and an equation for an eccentric circle, and

the second correction term has a magnitude which does not vary with α and

represents at least approximately the magnitude of the integral of the first correction term over α

=°

to α

=360°

.

13. A computer useable medium having computer readable instructions stored therein for causing the computer to process data derived from a signal received from a measuring probe as the measuring probe follows a perimeter of a workpiece cross-section as a turntable on which a workpiece is mounted rotates about an axis of rotation, said data comprising a set of first distances with each of said first distances being representative of the distance between a point on the perimeter of the workpiece cross-section and a circle centered on the axis of rotation along a respective different one of a plurality of lines radiating from the axis of rotation, each of said plurality of lines being at a respective different one of a plurality of known angles in relation to a reference line radiating from the axis of rotation,

the instructions comprising instructions for causing the computer to process said data to:

(i) estimate a position of the center of the workpiece cross-section relative to the axis of rotation, thereby providing an estimate of an eccentricity of the workpiece cross-section, by fitting a first function having the form c+a cos (α

)+b sin (α

) to said set of first distances, where

α

is the angle between a respective one of said plurality of lines and the reference line,

a is a first constant corresponding to an estimate of the component of the eccentricity in the direction corresponding to α

=0°

,

b is a second constant corresponding to an estimate of the component of the eccentricity in the direction corresponding to α

=90°

, and

c is a third constant;

(ii) calculate a set of second distances by subtracting a fourth constant from each of the set of first distances, said fourth constant being such that a sum of the set of second distances around the axis of rotation equals zero;

(iii) calculate a set of third distances by subtracting from each of the set of second distances a second function, said second function integrating to zero over α

=0°

to α

=360° and

differing from a cos (α

)+b sin (α

) by a first correction term and a second correction term, where

the first correction term has a magnitude which varies with α and

represents at least approximately the difference between said first function and an equation for an eccentric circle, and

the second correction term has a magnitude which does not vary with α and

represents at least approximately the magnitude of the integral of the first correction term over α

=0°

to α

=360°

;

(iv) adjust each of the set of third distances to at least partially compensate for the difference in measuring said set of third distances in a direction towards the axis of rotation and measuring said set of third distances in a direction towards the center of the workpiece cross-section; and

(v) use said set of third distances and the estimated position of the center of the workpiece cross-section to obtain a measure of the distance between the centre of the workpiece cross-section and the perimeter of the workpiece defining the shape of the workpiece cross-section at a plurality of known angles around the center of the workpiece cross-section.