Machine capability verification and diagnostics (CAP/DIA) system, method and computer program product

• US 6,721,675 B1
• Filed: 03/10/2003
• Issued: 04/13/2004
• Est. Priority Date: 01/31/2003
• Status: Expired due to Fees

• Current Assignee: The Boeing Co.
• Original Assignee: The Boeing Co.
• Inventors: Chawla, Mohinder Paul
• Primary Examiner(s): Bui, Bryan
• Application Number:
  US10/385,342
• Time in Patent Office: 400 Days
• Field of Search: 702/33, 702/34, 702/35, 702/36, 702/94, 702/95, 702/105, 702/168, 702/182, 702/183, 700/108, 700/109, 700/110, 700/159, 73/10.1, 73/17.9, 73/18.1, 331/14, 335/02
• US Class Current: 702/105
• CPC Class Codes: G01B 21/042 Calibration or calibration artifacts G01B3/30, G01B9/02072 take precedence

Abstract

A method for verifying the accuracy of a CNC machine or a CMM. The methodology segregates the measured error into an assignable cause portion and a common cause (or random error) portion. The methodology may be employed to affect the calibration of the machine tool to factor out the mean value of the assignable cause portion. Inherent in this methodology is the ability to diagnose mechanical problems with the CNC machine or CMM that affects the repeatability and accuracy of such machine tools; identify degradation in the performance of such machine tools that is indicative of mechanical failure; and improve the accuracy and repeatability of such machine tools in certain situations.

Claims

1. A method for calibrating a machine having a base, a movable element, which is movable relative to the base in reference to an axis, and a control system for numerically controlling movement of the movable element in reference to the axis along a predetermined distance, the method comprising:

identifying a plurality (N+1) of predetermined spaced-apart positions (i) along the predetermined distance, each of the positions (i) being associated with a desired position (DP_r,i) and spaced apart by a distance of L, the desired position (DP_r,i) being representative of a desired location of the movable element in the predetermined distance;

moving the movable element to each of the predetermined positions (i) in a first direction and calculating an error (E_r,i) between the desired position (DP_r,i) and an actual position (AP_r,i) of the movable element relative to the base and in reference to the axis at each of the predetermined positions (i);

translating the structure to each of the predetermined positions (i) in a second direction opposite the first direction and calculating error (E_r+1,i) between the desired position (DP_r+1,i) and an actual position (AP_r+1,i) of the movable element relative to the base and in reference to the axis at each of the predetermined positions (i);

repeating the above two steps a predetermined number (R/2) of times; and

determining an average cumulative positioning error per unit length (m) based upon an average of the differentials (E_r,i) and (E_r+1,i) at each of the predetermined positions (i) and an amount by which the movable element is moved relative to the base.

2. The method of claim 1, further comprising the step of determining an average reversal error ({overscore (E)}_REV) based on an average of the differentials (E_r,i) and (E_r+1,i) at each of the predetermined positions (i) and an amount by which the movable element is moved relative to the base.

3. The method of claim 2, wherein the average reversal error ({overscore (E)}_REV) is calculated as follows:

${\stackrel{\_}{E}}_{\mathrm{REV}}=\frac{\underset{i=0}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left[\frac{\left(E_{2,i}+E_{4,i}+\mathrm{\dots <br><br>}+E_{R,i}\right)}{\left(R/2\right)}-\frac{\left(E_{1,i}+E_{3,i}+\mathrm{\dots <br><br>}+E_{\left(R-1\right),i}\right)}{\left(R/2\right)}\right]}{\left(N+1\right)}.$

4. The method of claim 3, further comprising calculating a repeat capability index (Repeat C_pk).

5. The method of claim 4, wherein the repeat capability index (Repeat C_pk) is calculated as follows:

$\mathrm{Repeat}<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{pk}}=\frac{{\mathrm{Spec}}_{\mathrm{REP}}-<br><br>{\stackrel{\_}{X}}_{\mathrm{REP}}<br><br>}{3\times <br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{REP}}}$

where;

Spec_REP is a predetermined constant, $\begin{array}{c}{\stackrel{\_}{X}}_{\mathrm{REP}}=\frac{\underset{i=0}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left[\frac{\underset{r=2}{\overset{R}{\sum <br><br>}}<br><br><br><br>E_{r,i}-E_{\left(r-1\right),i}<br><br>}{\left(R-1\right)}\right]}{\left(N+1\right)}\\ s_{\mathrm{REP}}=\sqrt{\frac{\underset{i-0}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\left[\underset{r=1}{\overset{R}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{<br><br>E_{r,i}-E_{\left(r-1\right),i}<br><br>}{\left(R-1\right)}-{\stackrel{\_}{X}}_{\mathrm{REP}}\right]}^2}{N}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ {\mathrm{\sigma <br><br>}}_{\mathrm{REP}}=S_{\mathrm{REP}}\times <br><br>\sqrt{\left(1+\frac{1}{N+1}\right)}<br><br>\text{\hspace{1em}<br><br>}.\end{array}$

6. The method of claim 5, further comprising calculating a safe tolerance for repeatability error (ST_REP) as follows:

7. The method of claim 2, wherein the average cumulative positioning error per unit length (m) is calculated as follows:

$m=\frac{2\times <br><br>\left[\underset{i=0}{\overset{N}{\sum <br><br>}}<br><br>\frac{\begin{array}{c}\{\left[E_{1,i}+E_{3,i}+\mathrm{\dots <br><br>}+E_{\left(R-1\right),i}\right]+[\left(E_{2,i}-{\stackrel{\_}{E}}_{\mathrm{REV}}\right)+\\ \left(E_{4,i}-{\stackrel{\_}{E}}_{\mathrm{REV}}\right)+\mathrm{\dots <br><br>}+\left(E_{R,i}-{\stackrel{\_}{E}}_{\mathrm{REV}}\right)]\}\end{array}}{\left(R\right)}\right]}{\left(L\times <br><br>N\right)}.$

8. The method of claim 7, wherein an adjusted error value (AE_r,i) is substituted for each error value (E_r,i) when the average cumulative positioning error per unit length (m) is calculated, the adjusted error values (AE_r,i) being calculated as follows:

9. The method of claim 2, further comprising calculating a cumulative capability index (Cumulative C_pk).

10. The method of claim 9, wherein the cumulative capability index (Cumulative C_pk) is calculated as follows:

$\mathrm{Cumulative}<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{pk}}=\frac{{\mathrm{Spec}}_{\mathrm{CUM}}-<br><br>{\stackrel{\_}{X}}_{\mathrm{CUM}}<br><br>}{3\times <br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{CUM}}}$

where;

Spec_CUM is a predetermined constant, $\begin{array}{c}{\stackrel{\_}{X}}_{\mathrm{CUM}}=\frac{\underset{i=0}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left[\frac{\underset{r=1}{\overset{R}{\sum <br><br>}}<br><br>E_{r,i}}{R}\right]}{\left(N+1\right)}\\ s_{\mathrm{CUM}}=\sqrt{\frac{\underset{i-0}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\left[\underset{r=1}{\overset{R}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{E_{r,i}}{R}-{\stackrel{\_}{X}}_{\mathrm{CUM}}\right]}^2}{N}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ {\mathrm{\sigma <br><br>}}_{\mathrm{CUM}}=S_{\mathrm{CUM}}\times <br><br>\sqrt{\left(1+\frac{1}{N+1}\right)}<br><br>\text{\hspace{1em}<br><br>}.\end{array}$

11. The method of claim 10, further comprising calculating a safe tolerance for cumulative error (ST_CUM) as follows:

12. The method of claim 2, wherein the average cumulative positioning error per unit length (m) is calculated as follows:

$m=\frac{2\times <br><br>\left[\underset{i=0}{\overset{N}{\sum <br><br>}}<br><br>\frac{\begin{array}{c}\{\left[E_{1,i}+E_{3,i}+\mathrm{\dots <br><br>}+E_{\left(R-1\right),i}\right]+[\left(E_{2,i}-{\stackrel{\_}{E}}_{\mathrm{REV}}\right)+\\ \left(E_{4,i}-{\stackrel{\_}{E}}_{\mathrm{REV}}\right)+\mathrm{\dots <br><br>}+\left(E_{R,i}-{\stackrel{\_}{E}}_{\mathrm{REV}}\right)]\}\end{array}}{\left(R\right)}\right]}{\left(L\times <br><br>N\right)}.$

13. The method of claim 2, further comprising the step of calculating a home error (E_H).

14. The method of claim 13, wherein the home error (E_H) is calculated as follows:

$E_H=\frac{\begin{array}{c}\{\left[E_{1,0}+E_{3,0}+\mathrm{\dots <br><br>}+E_{\left(R-1\right),0}\right]+[\text{\hspace{1em}<br><br>}<br><br>\left(E_{2,0}-{\stackrel{\_}{E}}_{\mathrm{REV}}\right)+\\ \left[\left(E_{4,0}-{\stackrel{\_}{E}}_{\mathrm{REV}}\right)+\mathrm{\dots <br><br>}+\left(E_{R,0}-{\stackrel{\_}{E}}_{\mathrm{REV}}\right)\right]\}\end{array}}{\left(R\right)}.$

15. The method of claim 14, wherein an adjusted error value (AE_r,i) is substituted for each error value (E_r,i) when the home error (E_H) is calculated, the adjusted error values (AE_r,i) being calculated as follows:

16. The method of claim 13, further comprising calculating a position capability index (Position C_pk).

17. The method of claim 16, wherein the position capability index (Position C_pk) is calculated as follows:

$\mathrm{Position}<br><br>\text{\hspace{1em}<br><br>}<br><br>C_{\mathrm{pk}}=\frac{{\mathrm{Spec}}_{\mathrm{POS}}-<br><br>{\stackrel{\_}{X}}_{\mathrm{POS}}<br><br>}{3\times <br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{POS}}}$

where;

Spec_POS is a predetermined constant, $\begin{array}{c}{\stackrel{\_}{X}}_{\mathrm{POS}}=\underset{i=0}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left[\frac{\underset{r=1}{\overset{R}{\sum <br><br>}}<br><br>\frac{E_{r,i}+E_{\left(r+1\right),i}}{2}}{\left(N+1\right)}\right]\\ S_{\mathrm{POS}}=\sqrt{\frac{\underset{i=0}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\left[\underset{r=1}{\overset{R}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{E_{r,i}+E_{\left(r+1\right),i}}{2}-{\stackrel{\_}{X}}_{\mathrm{POS}}\right]}^2}{N}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ {\mathrm{\sigma <br><br>}}_{\mathrm{POS}}=S_{\mathrm{POS}}\times <br><br>\sqrt{\left(1+\frac{1}{N+1}\right)}.\end{array}$

18. The method of claim 17, further comprising calculating a safe tolerance for position error (ST_POS) as follows:

19. The method of claim 2, wherein the controller includes a first register and a plurality of second registers, the first register being operable for compensating for reversal error, each of the second registers being associated with a predetermined point (x) in the predetermined distance and being operable for correcting for error at the predetermined point (x) in the predetermined distance, wherein the methodology employs the average reversal error ({overscore (E)}_REV) in calculating a value for use in the first register and wherein the methodology employs the average cumulative positioning error per unit length (m) in calculating a value for each of the second registers.