Modeling an abrasive process to achieve controlled material removal

• US 7,089,081 B2
• Filed: 01/31/2003
• Issued: 08/08/2006
• Est. Priority Date: 01/31/2003
• Status: Expired due to Fees

• Current Assignee: 3M Innovative Properties Company (3M Company)
• Original Assignee: 3M Innovative Properties Company (3M Company)
• Inventors: Palmgren, Gary M.
• Primary Examiner(s): Picard, Leo
• Assistant Examiner(s): Masinick, Michael D.
• Application Number:
  US10/355,659
• Publication Number:
  US 20040153197A1
• Time in Patent Office: 1,285 Days
• Field of Search: 700/175, 700/172, 700/164, 451/21, 451/22, 451/6
• US Class Current: 700/175
• CPC Class Codes: B24B 37/042 operating processes therefor
• CPC Class Codes: B24B 49/16 taking regard of the load
• CPC Class Codes: B24B 51/00 Arrangements for automatic control of a series of individual steps in grinding a workpiece if applicable to other machine tools, G05B takes precedence

Abstract

In general, techniques are described that allow an abrasive manufacturing process to achieve a controlled performance parameter, e.g., an amount of material removal, without requiring the use of feedback controls within the abrasive manufacturing process. For example, a system includes a machine to abrade a workpiece with an abrasive article, and a controller to control the application of the abrasive article to the workpiece by the machine to achieve a substantially constant cut rate for the abrasive article. The controller controls one or more process variables in accordance with an open-loop mathematical model that relates the cut rate of the abrasive article to an application force of the abrasive article to achieve controlled material removal. For example, a constant rate of cut can be achieved or a fixed amount of material can be removed while abrading one or more workpiece in accordance with the model.

Claims

1. A method for controlling an abrasive process comprising:

generating an open-loop model of a cut rate of an abrasive article type when applied to workpiece type over an abrading period, wherein generating the model comprises computing the cut rate R of the abrasive article as a function of a length of time that the abrasive article has been applied to the workpiece at a substantially constant force in accordance with a first equation as follows;

R=R₁×

e<sup>−

t/T1</sup>+R₂×

e<sup>−

t/T2</sup>,

where R₁ and R₂ are constants set according to an initial cut rate for the abrasive article,

t equals a length of time that the abrasive article has been applied to the workpiece, and

T₁ and T₂ are time constants; and

abrading a workpiece of the workpiece type with an abrasive article of the abrasive article type in accordance with the model to achieve a substantially constant cut rate.

2. The method of claim 1, wherein abrading the workpiece further comprises:

obtaining a feedback signal representing a state of the workpiece; and

applying the abrasive article to the workpiece in accordance with the open-loop model and the feedback signal.

3. The method of claim 1, wherein abrading a workpiece comprises:

applying the abrasive article against the workpiece in accordance with one or more process control variables; and

adjusting at least one of the process control variables over the abrading period accordance with the model to achievc the substantially constant cut rate.

4. The method of claim 3, wherein adjusting at least one of the process control variables comprises adjusting at least one of an application force of the abrasive article against the workpiece in accordance with the model, an application velocity of the abrasive article relative to the workpiece in accordance with the model, a duration for the abrading period, and a coolant flow.

5. The method of claim 1, wherein abrading a workpiece comprises:

selecting a target cut rate;

computing values for a process control variable over the abrading period in accordance with the model using the target cut rate as an input to the model; and

controlling the process control variable over the abrading period based on the computed values.

6. The method of claim 5, wherein computing values comprises computing application force values, and controlling the process control variable comprises controlling an application force at which the abrasive article is applied against the workpiece over the abrading period based on the computed values.

7. The method of claim 5, further comprising:

selecting the abrasive article from a plurality of abrasive articles; and

updating the computed values for the process control variable based on selected article.

8. The method of claim 7, wherein updating the computed values comprises:

reading a performance index from the selected abrasive article; and

computing the values for the process control variable using the performance index as an input to the model.

9. The method of claim 5, further comprising:

storing the computed values within a grinding machine; and

abrading the workpiece with the abrasive article using the grinding machine over the abrading period in accordance with the computed values for the process control variable.

10. The method of claim 1, further comprising:

abrading a test workpiece with the abrasive article during at test abrading period;

measuring an amount of material removed from the test workpiece at intervals during the test abrading period;

generating cut rate data that represents a cut rate per unit time based on the measure amount of material; and

fitting the first equation to the cut rate data to compute cut rate as a function of time.

11. The method of claim 10, generating cut rate data comprises computing an average cut rate for each interval based on the measured amount of material removed during at least two intervals.

12. The method of claim 10, further comprising:

computing a residual error based on the first equation and the cut rate data; and

adjusting T₁ and T₂ based on the computed residual error.

13. The method of claim 1, wherein generating the model comprises generating the model to compute an application force of the abrasive article to the workpiece as a function of a target constant cut rate and a length of time that the abrasive article has been applied to the workpiece.

14. The method of claim 13, wherein generating model comprises generating the model to express the application force (F) in accordance with a second equation as follows:

$F<br><br>\left(t\right)=\left[\frac{R_c-I}{R_1<br><br>{\mathrm{e<br><br>}}^{-t/T_1}+R_2<br><br>{\mathrm{e<br><br>}}^{-t/T_2}-I}\right]\times <br><br>F_c,$

where R_C represents the target constant cut rate during the abrading period,

where R₁ and R₂ are constants set according to an initial cut rate for the abrasive article,

F_C represents the substantially constant force used to determine the first equation, and

I represents an intercept value from the first equation at an initial time T₀.

15. The method of claim 1, wherein abrading the workpiece comprises abrading the workpiece with the abrasive article at achieve the substantially constant cut rate for an abrading period that exceeds at least 500 seconds.

16. The method of claim 1, wherein abrading the workpiece comprises abrading the workpiece with the abrasive article at achieve the substantially constant cut rate for an abrading period that exceeds at least one hour.

17. A system comprising:

a machine to abrade a workpiece with an abrasive article; and

a controller to control the application of the abrasive article to the workpiece by the machine in accordance with an open-loop model to achieve a substantially constant cut rate for the abrasive article;

wherein the open-loop model comprises computing the cut rate R of the abrasive article as a function of a length of time that the abrasive article has been applied to the workpiece at a substantially constant force in accordance with a first equation as follows;

R=R₁×

e<sup>−

t/T1</sup>+R₂×

e<sup>−

t/T2</sup>,

where R₁ and R₂ are constants set according to an initial cut rate for the abrasive article,

t equals a length of time that the abrasive article has been applied to the workpiece, and

T₁ and T₂ are time constants.

18. The system of claim 17, wherein the controller obtains a feedback signal representing a state of the workpiece, and controls the machine to apply the abrasive article to the workpiece in accordance with the open-loop model and the feedback signal.

19. The system of claim 17, wherein the controller controls the machine in accordance with one or more process control variables, and adjusts at least one of the process control variables over an abrading period to achieve the substantially constant cut-rate.

20. The system of claim 18, wherein the controller adjusts at least one of an application force of the abrasive article against the workpiece, an application velocity of the abrasive article relative to the workpiece, a duration of the abrading period, and a coolant flow.

21. The system of claim 17, wherein the controller comprises a computer-readable medium to store a set of values for a process control variable for use in controlling the machine during the abrading period.

22. The system of claim 21, wherein the set of values represent application forces and associated time intervals within the abrading period, and the controller directs the machine to apply the abrasive article against the workpiece during the abrading period in accordance with the values to achieve the substantially constant rate of cut.

23. The system of claim 21, wherein the controller updates the values for the process control variable based on a performance index associated with the abrasive article.

24. The system of claim 21, wherein the controller receives data indicating an actual cut rate of the abrasive article during the abrading period, and re-computes the values for the process control variable in real-time based on the data.

25. The system of claim 17, further comprising a computer-readable medium to store the first equation.

26. The system of claim 25, wherein the controller invokes the model for real-time computation of values for a process control variable for use by the machine when abrading the workpiece to achieve the substantially constant rate of cut.

27. The system of claim 25, further comprising a computer to generate the model and store the model on the computer-readable medium contained within the computer, wherein computer calculates values for a process control variable in accordance with the model, and communicates the values to the machine for use when abrading the workpiece to achieve the substantially constant rate of cut.

28. The system of claim 27, further comprising a user interface presented by the computer to receive a target cut rate, wherein the computer calculates the values in accordance with the model using the target cut rate as an input to the model.

29. The system of claim 27, comprising a user interface presented by the computer to receive input data indicating an amount of material removed from a test workpiece at respecting intervals during a test abrading period, wherein the computer generates the model based on the input data.

30. The system of claim 29, wherein the computer generates the model by calculating cut rate data indicating a cut rate per unit time based on the input data, and fits the first equation to the cut rate data to compute cut rate for the abrasive article as a function of time.

31. The system of claim 30, wherein the computer calculates the cut rate data by computing an average cut rate for each interval based on the measured amount of material removed during at least two intervals.

32. The system of claim 30, wherein the computer computes a residual error based on the first equation and the cut rate data;

and adjusts T₁ and T₂ based on the computed residual error.

33. The system of claim 27, wherein the model represents an application force of the abrasive article to the workpiece as a function of a target constant cut rate and a length of time that the abrasive article has been applied to the workpiece.

34. The system of claim 33, wherein the model represents the application force (F) in accordance with a second equation as follows:

$F<br><br>\left(t\right)=\left[\frac{R_c-I}{R_1<br><br>{\mathrm{e<br><br>}}^{-t/T_1}+R_2<br><br>{\mathrm{e<br><br>}}^{-t/T_2}-I}\right]\times <br><br>F_c,$

where R_C represents the target constant cut rate during the abrading period,

where R₁ and R₂ are constants set according to an initial cut rate for the abrasive article,

F_C represents the substantially constant force used to determine the first equation, and

I represents an intercept value from the first equation at an initial time T₀.

35. The system of claim 17, wherein the machine abrades the workpiece with the abrasive article at the substantially constant cut rate for an abrading period that exceeds at least 500 seconds.

36. The system of claim 17, wherein the machine abrades the workpiece with the abrasive article at the substantially constant cut rate for an abrading period that exceeds at least one hour.

37. A computer-readable medium comprising instructions to cause a programmable controller to direct a machine to abrade a workpiece with an abrasive article in accordance with an open-loop model to achieve a substantially constant cut rate for the abrasive article over an abrading period;

wherein the open-loop model comprises computing the cut rate R of the abrasive article as a function of a length of time that the abrasive article has been applied to the workpiece at a substantially constant force in accordance with a first equation as follows;

R=R₁×

e<sup>−

t/T1</sup>+R₂×

e<sup>−

t/T2</sup>,

where R₁ and R₂ are constants set according to an initial cut rate for the abrasive article,

t equals a length of time that the abrasive article has been applied to the workpiece, and

T₁ and T₂ are time constants.

38. The computer-readable medium of claim 37, wherein the instructions cause the controller to apply the abrasive article against the workpiece in accordance with one or more process control variables, and adjusts at least one of the process control variables over the abrading period to achieve the substantially constant cut-rate.

39. The computer-readable medium of claim 37, wherein the instructions cause the controller to direct the machine during the abrading period in accordance with a set of values for a process control variable calculated using the first equation.

40. The computer-readable medium of claim 37, wherein the set of values represent application forces and associated time intervals within the abrading period, and the instructions cause the controller to direct the machine to apply the abrasive article against the workpiece during the abrading period in accordance with the values to achieve the substantially constant rate of cut.

41. The computer-readable medium of claim 39, wherein the instructions cause the controller to receive the values from a computing device that executes the model.

42. The computer-readable medium of claim 39, wherein the instructions cause the controller to invoke the model for real-time computation of the values.

43. A computer-readable medium comprising data representing an open-loop model for use by a machine to abrade a workpiece with an abrasive article to achieve a substantially constant cut rate for the abrasive article over an abrading period;

wherein the open-loop model comprises computing the cut rate R of the abrasive article as a function of a length of time that the abrasive article has been applied to the workpiece at a substantially constant force in accordance with a first equation as follows;

R=R₁×

e<sup>−

t/T1</sup>+R₂×

e<sup>−

t/T2</sup>,

where R₁ and R₂ are constants set according to an initial cut rate for the abrasive article,

t equals a length of time that the abrasive article has been applied to the workpiece, and

T₁ and T₂ are time constants.

44. The computer-readable medium of claim 43, wherein the model represents an application force of the abrasive article to the workpiece as a function of a target constant cut rate and a length of time that the abrasive article has been applied to the workpiece.

45. The computer-readable medium of claim 44, wherein the model represents the application force (F) in accordance with a second equation as follows:

$F<br><br>\left(t\right)=\left[\frac{R_c-I}{R_1<br><br>{\mathrm{e<br><br>}}^{-t/T_1}+R_2<br><br>{\mathrm{e<br><br>}}^{-t/T_2}-I}\right]\times <br><br>F_c,$

where R_C represents the target constant cut rate during the abrading period,

where R₁ and R₂ are constants set according to an initial cut rate for the abrasive article,

F_C represents the substantially constant force used to determine the first equation, and

I represents an intercept value from the first equation at an initial time T₀.

46. A method for controlling an abrasive process comprising:

generating an open-loop model of a cut rate of an abrasive article type when applied to a workpiece type over an abrading period, wherein generating the model comprises computing the cut rate R of the abrasive article as a function of a length of time that the abrasive article has been applied to the workpiece at a substantially constant force in accordance with a first equation as follows;

R=R₁×

e<sup>−

t/T1</sup>+R₂×

e<sup>−

t/T2</sup>,

where R₁ and R₂ are constants set according to an initial cut rate for the abrasive article,

t equals a length of time that the abrasive article has been applied to the workpiece, and

T₁ and T₂ are time constants; and

abrading a workpiece of the workpiece type with an abrasive article of the abrasive article type in accordance with the model to achieve a controlled amount of material removed from the workpiece during the abrading period.

47. The method of claim 46, wherein abrading the workpiece comprises abrading the workpiece in accordance with the model to achieve a substantially constant rate of cut during the abrading period.

48. The method of claim 46, wherein abrading the workpiece comprises abrading the workpiece in accordance with the model to remove a target amount of material from the workpiece during the abrading period.

49. A method for controlling an abrasive process comprising:

generating an open-loop model of a performance parameter of a type abrasive article type when applied to a type of semiconductor conditioning pad, wherein generating the model comprises computing the cut rate R of the abrasive article as a function of a length of time that the abrasive article has been applied to the workpiece at a substantially constant force in accordance with a first equation as follows;

R=R₁×

e<sup>−

t/T1</sup>+R₂×

e<sup>−

t/T2</sup>,

where R₁ and R₂ are constants set according to an initial cut rate for the abrasive article,

t equals a length of time that the abrasive article has been applied to the workpiece, and

T₁ and T₂ are time constants;

polishing a plurality of semiconductor wafers with a conditioning pad of the conditioning pad type; and

repeatedly abrading the conditioning pad with an abrasive article of the abrasive article type in accordance with the model to remove a substantially equal amount of material from the pad during each of the abradings.

50. The method of claim 49, wherein repeatedly abrading the conditioning pad comprises varying a time period for each of the abradings in accordance with the model.

51. The method of claim 49, wherein repeatedly abrading the conditioning pad comprises varying an application force of the abrasive article during the abradings in accordance with the model.