# Patent

## Title
Plasma insensitive height sensing

## Abstract

A method for determining a distance between a first piece and a second piece includes measuring, at the first or second piece, a first signal at a first frequency, and measuring, at the first or second piece, a second signal at a second frequency. The second frequency is different from the first frequency. The distance is determined based on the measured first and second signals.

## Background
FIELD OF THE INVENTION
The present technology relates generally to a method and apparatus for determining a distance between a first piece and a second piece that is insensitive to the presence of a plasma or other electrically conductive substance between the two pieces.
BACKGROUND
Thermal processing systems, such as laser and plasma arc systems, are widely used in the cutting, welding, heat treating, and processing of metallic materials. A laser-based apparatus generally includes a nozzle through which a gas stream and laser beam pass to interact with a workpiece. Both the beam and the gas stream exit the nozzle through an orifice and impinge on a target area of the workpiece. The laser beam heats the workpiece. The resulting heating of the workpiece, combined with any chemical reaction between the gas and workpiece material, serves to heat, liquefy and/or vaporize a selected area of workpiece, depending on the focal point and energy level of the beam. This action allows the operator to cut or otherwise modify the workpiece.
In general, a thermal processing system can include a laser-based or plasma-based torch, an associated power supply, a gas console, a positioning apparatus, a cutting table, a torch height control, and an associated computerized numeric controller (CNC).
In operation, a user places a workpiece on the cutting table and mounts the torch on the positioning apparatus, which provides relative motion between the tip of the torch and the workpiece to direct the laser beam or the plasma arc along a processing path. The CNC accurately directs motion of the torch and/or the cutting table to enable the workpiece to be cut to a desired pattern. Position information is returned from the positioning apparatus to the CNC to allow the CNC to operate interactively with the positioning apparatus to obtain an accurate cut path.
A torch height control module sets the height of the torch relative to the workpiece. A lifter, which is controlled by the torch height control module through a motor, moves the torch in a vertical direction relative to the workpiece to maintain a desired processing quality during cutting for a particular application. Typically, capacitive height sensing (CHS) is used to measure the distance between the torch and the workpiece during machining. In a typical implementation of CHS, a single sinusoidal electrical signal is applied to the torch and the capacitive impedance between the torch and the workpiece is measured to derive the distance. CHS models the electrical circuit between the torch and the workpiece as a single capacitor. As a result, CHS does not provide for accurate distance measurements in situations where a plasma or other electrically conductive substance forms or is present between the torch and the workpiece.
SUMMARY OF THE INVENTION
What is needed is a distance measurement that is insensitive to the presence of a plasma between a first and a second piece. One approach to determining a distance between a first piece and a second piece is to perform measurements at two different frequencies. In one aspect, there is a method for determining a distance between a first piece and a second piece. The method involves measuring, at the first or second piece, a first signal at a first frequency. A second signal at a second frequency is measured at the first or second piece. The second frequency is different from the first frequency. The distance is determined based on the measured first and second signals.
In another aspect, there is a system capable of determining a distance between a first piece and a second piece. The system comprises a measuring device adapted to measure, at one or both of the first and second piece, a first signal and a second signal. The first signal has a first frequency and the second signal has a second frequency different from the first frequency. The system further comprises a signal processing device adapted to determine the distance based on the measured first and second signals. In some embodiments, the system can further include a first band-pass filter adapted to pass the first signal and attenuate the second signal. The system can further include a second band-pass filter adapted to pass the second signal and attenuate the first signal. The system can further include a first source adapted to apply, at the first or second piece, a first source signal at the first frequency. The system can further include a second source adapted to apply, at the first or second piece, a second source signal at the second frequency. The first source and the second source can be adapted to combine the first source signal and the second source signal before applying the first and second source signals. The measuring device can be adapted to measure the first signal at a first position after a first known electrical element. The first known electrical element can be located between the first position and the first source.
In another aspect, there is a system capable of determining a distance between a first piece and a second piece. The system comprises measuring means for measuring, at the first or second piece, a first signal and a second signal. The first signal has a first frequency and the second signal has a second frequency different from the first frequency. The system further comprises signal processing means for determining the distance based on the measured first and second signals. In some embodiments, the system can further include first filtering means for passing the first signal and attenuating the second signal. The system can further include second filtering means for passing the second signal and attenuating the first signal. The system can further include first source means for applying, at the first or second piece, a first source signal at the first frequency. The system can further include second source means for applying, at the first or second piece, a second source signal at the second frequency. The first source means and the second source means can be adapted to combine the first source signal and the second source signal before applying the first and second source signals.
In other examples, any of the aspects above can include one or more of the following features. In some embodiments, the first piece can include a torch component and the second piece can include a workpiece. The torch component can include a laser nozzle. Determining the distance can include calculating a gap capacitance between the first piece and the second piece based on the measured first and second signals, and determining the distance based on the gap capacitance. Determining the gap capacitance can be based on: the first frequency, the second frequency, a magnitude of the first signal, a magnitude of the second signal, or any combination thereof. Determining the distance can include using a calibration data set to determine the distance. The calibration data set can include data values associated with: the first signal, the second signal, a magnitude of the first signal, a magnitude of the second signal, or any combination thereof. The second frequency can be essentially zero. At least one of the first signal or the second signal can include: a current signal, a voltage signal, or any combination thereof. Measuring the first signal at the first frequency can include passing the first signal through a first band-pass filter. The first band-pass filter can attenuate the second signal. Measuring the second signal at the second frequency can include passing the second signal through a second band-pass filter. The second band-pass filter can attenuate the first signal. The first band-pass filter can be a high-pass filter and the second band-pass filter can be a low-pass filter. The first signal and the second signal can be measurements of a combined signal. The method can further include determining a plasma resistance between the first piece and the second piece based on the measured first and second signals. The method can further include applying, at the first or second piece, a first source signal at the first frequency. The method can further include applying, at the first or second piece, a second source signal at the second frequency. At least one of the first source signal or the second source signal can include: a current source signal, a voltage source signal, or any combination thereof. The first source signal and the second source signal can be a combined source. The step of determining the distance can include using a calibration data set to determine the distance. The calibration data set can include data values associated with: the first signal, the second signal, a magnitude of the first signal, a magnitude of the second signal, a magnitude of the first source signal, a magnitude of the second source signal, or any combination thereof. Measuring the first signal can include measuring the first signal at a first position after a first known electrical element. The first known electrical element can be located between the first position and a first source of the first source signal. Measuring the second signal can include measuring the second signal at a second position after a second known electrical element. The second known electrical element can be located between the second position and a second source of the second source signal. The first known electrical element and the second known electrical element can be the same.
Any of the above implementations can realize one or more of the following advantages. Performing measurements at two different frequencies allows for distance measurements independent of the presence of a plasma. In addition, the insensitivity of the distance measurement to plasma or other conductive elements allows for accurate height determination of a component in real time. Moreover, the insensitivity of the distance measurement to plasma or other conductive elements allows for height determination of a component while an operation is being carried out using the component (e.g., thermal processing).
Other aspects, examples, and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating the principles of the invention by way of example only.



BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing and other features and advantages of the present invention, as well as the invention itself, will be more fully understood from the following description of various embodiments, when read together with the accompanying drawings.
FIG. 1 is a schematic diagram of a thermal processing system.
FIG. 2 is a model diagram illustrating the electrical circuit between a torch component and a workpiece.
FIG. 3 is a block diagram of a measurement device.
FIG. 4 is a normalized DC shift plot showing the relationship between the resistance ratio Rref/Rp and the normalized DC shift.
FIG. 5 is a normalized AC shift plot showing the relationship between the normalized correction term Δcorrection and the normalized DC shift.
FIG. 6 is a plot showing an example of measured signal magnitudes over time.
FIG. 7 is a plot showing an example relationship between the normalized correction term Δcorrection and the normalized DC shift.
FIG. 8 is a plot showing an example of measured signal magnitudes over time overlaid with a distance calibration curve.



DETAILED DESCRIPTION
Capacitive height sensing (CHS) can be used to determine the distance between two pieces that exhibit measurable capacitance between them, due to the dependence that capacitance has on the distance. In one embodiment, the distance can be calculated based on a value of capacitance (e.g., based on first principles, such as distance=area permittivity/capacitance for the simplified case of a parallel plate capacitor). In another embodiment, the distance can be correlated with a value of capacitance (e.g., using a calibrated table for more complicated geometries). In a thermal processing system 100, as illustrated in FIG. 1, the two pieces can be a torch component 110 and a workpiece 120. CHS distance measurements in such a system can provide feedback during the operation. Therefore, the distance between the torch and the workpiece can be accurately set depending on the particular application. In general, however, CHS measurements can be used to determine the distance between any two pieces that exhibit capacitance between them.
FIG. 2 is a model diagram 200 illustrating the electrical circuit between a torch component 210 and a workpiece 220. The torch component 210 can be, for example, a torch head or a nozzle of a laser-based or plasma-based torch. The torch component 210 is separated from the workpiece 220 by a distance 230. In applications where a plasma or other electrically conductive substance (e.g., metal vapor such as when cutting galvanized metal) forms or is present between the torch component 210 and the workpiece 220, the electrical impedance between the torch component 210 and the workpiece 220 can be modeled as a gap impedance Zg 240, which is the combination of a gap capacitance Cg 242 in parallel with a plasma resistance Rp 244. The gap capacitance Cg 242 can be due to the geometrical properties of the torch component 210 and the workpiece 220, and the capacitive properties of the material between them, which can be a non-conductive gas. The plasma resistance Rp 244 can be due to the presence of a plasma and/or other electrically-conductive substance between the torch component 210 and the workpiece 220. The gap impedance Zg 240 can be given by:




  
    
      
        
          
            Z
            g
          
          =
          
            
              
                C
                g
              
              //
              
                R
                p
              
            
            =
            
              
                R
                p
              
              
                1
                +
                
                  jω
                  ⁢
                  
                    
                  
                  ⁢
                  
                    C
                    g
                  
                  ⁢
                  
                    R
                    p
                  
                
              
            
          
        
        ,
      
    
    
      
        (
        1
        )
      
    
  




where j=√{square root over (−1)} and ω=2πf is the radian frequency at which the gap impedance Zg 240 is measured. A sinusoidal source (not pictured) can be used to supply a source signal Us 250 to the torch component 210. The source signal Us 250 can be provided, for example, by a voltage source or a current source. The source signal Us 250 can be generated by, for example, one or more oscillators operating at one or more different frequencies. A known reference resistance Rref 252 can be included between the sinusoidal source of Us 250 and the torch component 210.

A signal Um 260 can be measured at the torch component 210. Using the voltage divider rule, the measured signal Um 260 can be represented as:




  
    
      
        
          U
          m
        
        =
        
          
            
              U
              s
            
            ⁡
            
              (
              
                
                  Z
                  g
                
                
                  
                    Z
                    g
                  
                  +
                  
                    R
                    ref
                  
                
              
              )
            
          
          =
          
            
              
                U
                s
              
              ⁡
              
                (
                
                  1
                  
                    1
                    +
                    
                      
                        R
                        ref
                      
                      /
                      
                        R
                        p
                      
                    
                    +
                    
                      jω
                      ⁢
                      
                        
                      
                      ⁢
                      
                        C
                        g
                      
                      ⁢
                      
                        R
                        ref
                      
                    
                  
                
                )
              
            
            .
          
        
      
    
    
      
        (
        2
        )
      
    
  




From equation (2), the magnitude of the measured signal Um 260 can be represented as:





  
    
      
        
          
          
            U
            m
          
          
        
        =
        
          
            
              
              
                U
                s
              
              
            
            
              
                
                  
                    (
                    
                      1
                      +
                      
                        
                          R
                          ref
                        
                        /
                        
                          R
                          p
                        
                      
                    
                    )
                  
                  2
                
                +
                
                  
                    (
                    
                      ω
                      ⁢
                      
                        
                      
                      ⁢
                      
                        C
                        g
                      
                      ⁢
                      
                        R
                        ref
                      
                    
                    )
                  
                  2
                
              
            
          
          .
        
      
    
    
      
        (
        3
        )
      
    
  




The magnitude of the measured signal Um 260 can be determined using, for example, a true-RMS meter, an application-specific integrated circuit (ASIC), a peak-detection circuit, or other signal measurement device. The magnitude of the measured signal Um 260 can be a peak amplitude, a peak-to-peak amplitude, an RMS amplitude, or another amplitude of the measured signal Um 260.

Equation (3) includes two unknowns: the gap capacitance Cg 242 and the plasma resistance Rp 244. By measuring the magnitude of the measured signal Um 260 at two different frequencies, the gap capacitance Cg 242 and/or the plasma resistance Rp 244 can be solved for from the two resulting equations:




  
    
      
        
          
            
              
                
                
                  U
                  
                    s
                    ,
                    
                      ω
                      1
                    
                  
                
                
              
              2
            
            
              
                
                
                  U
                  
                    m
                    ,
                    
                      ω
                      2
                    
                  
                
                
              
              2
            
          
          =
          
            
              
                (
                
                  1
                  +
                  
                    
                      R
                      ref
                    
                    
                      R
                      p
                    
                  
                
                )
              
              2
            
            +
            
              
                (
                
                  
                    ω
                    1
                  
                  ⁢
                  
                    C
                    g
                  
                  ⁢
                  
                    R
                    ref
                  
                
                )
              
              2
            
          
        
        ,
      
    
    
      
        (
        4
        )
      
    
  
  
    
      
        
          
            
              
              
                U
                
                  s
                  ,
                  
                    ω
                    2
                  
                
              
              
            
            2
          
          
            
              
              
                U
                
                  m
                  ,
                  
                    ω
                    2
                  
                
              
              
            
            2
          
        
        =
        
          
            
              (
              
                1
                +
                
                  
                    R
                    ref
                  
                  
                    R
                    p
                  
                
              
              )
            
            2
          
          +
          
            
              
                (
                
                  
                    ω
                    2
                  
                  ⁢
                  
                    C
                    g
                  
                  ⁢
                  
                    R
                    ref
                  
                
                )
              
              2
            
            .
          
        
      
    
    
      
        (
        5
        )
      
    
  




Subtracting equation (5) from equation (4) yields:





  
    
      
        
          
            
              
                
                  
                  
                    U
                    
                      s
                      ,
                      
                        ω
                        1
                      
                    
                  
                  
                
                2
              
              
                
                  
                  
                    U
                    
                      m
                      ,
                      
                        ω
                        1
                      
                    
                  
                  
                
                2
              
            
            -
            
              
                
                  
                  
                    U
                    
                      s
                      ,
                      
                        ω
                        2
                      
                    
                  
                  
                
                2
              
              
                
                  
                  
                    U
                    
                      m
                      ,
                      
                        ω
                        2
                      
                    
                  
                  
                
                2
              
            
          
          =
          
            
              (
              
                
                  ω
                  1
                  2
                
                -
                
                  ω
                  2
                  2
                
              
              )
            
            ⁢
            
              
                (
                
                  
                    C
                    g
                  
                  ⁢
                  
                    R
                    ref
                  
                
                )
              
              2
            
          
        
        ,
      
    
    
      
        (
        6
        )
      
    
  




which is independent of the plasma resistance Rp 244. From equation (6), the gap capacitance Cg 242 can be found to be a function of the known frequencies (ω1,ω2), the magnitudes of the measured signals 260 (|Um,107 1|,|Um,ω2|), the magnitudes of the source signals 250 (|Us,107 1|,|Us,ω2|), and the known reference resistance 252 Rref:





  
    
      
        
          C
          g
        
        =
        
          
            1
            
              R
              ref
            
          
          ⁢
          
            
              
                
                  1
                  
                    (
                    
                      
                        ω
                        1
                        2
                      
                      -
                      
                        ω
                        2
                        2
                      
                    
                    )
                  
                
                ⁢
                
                  (
                  
                    
                      
                        
                          
                          
                            U
                            
                              s
                              ,
                              
                                ω
                                1
                              
                            
                          
                          
                        
                        2
                      
                      
                        
                          
                          
                            U
                            
                              m
                              ,
                              
                                ω
                                1
                              
                            
                          
                          
                        
                        2
                      
                    
                    -
                    
                      
                        
                          
                          
                            U
                            
                              s
                              ,
                              
                                ω
                                2
                              
                            
                          
                          
                        
                        2
                      
                      
                        
                          
                          
                            U
                            
                              m
                              ,
                              
                                ω
                                2
                              
                            
                          
                          
                        
                        2
                      
                    
                  
                  )
                
              
            
            .
          
        
      
    
    
      
        (
        7
        )
      
    
  




Equation (7) can be simplified in cases where ω2<<ω1 (e.g., where ω2=0) as:




  
    
      
        
          C
          g
        
        =
        
          
            1
            
              
                ω
                1
              
              ⁢
              
                R
                ref
              
            
          
          ⁢
          
            
              
                (
                
                  
                    
                      
                        
                        
                          U
                          
                            s
                            ,
                            
                              ω
                              1
                            
                          
                        
                        
                      
                      2
                    
                    
                      
                        
                        
                          U
                          
                            m
                            ,
                            
                              ω
                              1
                            
                          
                        
                        
                      
                      2
                    
                  
                  -
                  
                    
                      
                        
                        
                          U
                          
                            s
                            ,
                            
                              ω
                              2
                            
                          
                        
                        
                      
                      2
                    
                    
                      
                        
                        
                          U
                          
                            m
                            ,
                            
                              ω
                              2
                            
                          
                        
                        
                      
                      2
                    
                  
                
                )
              
            
            .
          
        
      
    
    
      
        (
        8
        )
      
    
  




In the DC case (where ω2=0), the source signal Us 250 can be a sinusoid with a DC offset, wherein the measured signal will also be a sinusoid with a DC offset. The plasma resistance Rp 244 can be solved for in a similar fashion using equations (4) and (5). In an alternative embodiment, in DC situations or where one of the source signals 250 (Us,ω1,Us,ω2) is DC, the plasma resistance Rp 244 can be solved for directly. From equation (2), where ω=0, the plasma resistance Rp 244 can be solved as:





  
    
      
        
          R
          p
        
        =
        
          
            R
            ref
          
          ⁢
          
            
              
                U
                
                  m
                  ,
                  
                    ω
                    =
                    0
                  
                
              
              
                
                  U
                  
                    s
                    ,
                    
                      ω
                      =
                      0
                    
                  
                
                -
                
                  U
                  
                    m
                    ,
                    
                      ω
                      =
                      0
                    
                  
                
              
            
            .
          
        
      
    
    
      
        (
        9
        )
      
    
  




From equation (9), the unknown plasma resistance Rp 244 can be determined in terms of the source and measured DC signal levels.

The source signal Us 250 and the measured signal Um 260 can each be measured with respect to the workpiece 220 (e.g., the workpiece 220 can operate as the electrical “ground”). Furthermore, equations (1) and (2) include phasor representations (i.e., frequency-domain representations) of the signals 250 and 260. From a time-domain perspective, the source signal Us 250 can be represented by a combined signal:

Us(t)=A1 sin(ω1t+φ1)+A2 sin(ω2t+φ2),  (10)

where A1 and A2 are arbitrary amplitudes, and φ1 and φ2 are arbitrary phases. As described above, the source signal Us 250 can be generated by two oscillators and summed via a non-inverting adder circuit before being applied to the torch component 210 through the reference resistor Rref 252. In an alternative embodiment, the source signal Us 250 can comprise a single signal at frequency ω1 while a separate source signal (not pictured) applied to the torch component 210 can comprise a single signal at frequency ω2≠ω1. In another alternative embodiment, the source signal Us 250 can periodically vary between supplying a signal at a single frequency ω1 and a signal at a single frequency ω2≠ω1.

In the model diagram 200, the source signal Us 250 is supplied to the torch component 210, but other configurations can also be used. For example, in an alternative or supplemental embodiment, the source signal Us 250 can be supplied to the workpiece 220. In yet a further alternative or supplemental embodiment, the reference resistance 252 can more generally be any known reference impedance Zref (i.e., the reference impedance can include a resistor, capacitor, inductor, or any combination thereof).
FIG. 3 is a block diagram 300 of a measurement device 310. In the block diagram 300, the measurement device 310 receives and/or senses the measured signal Um 260 as a combined signal of measurements at two different frequencies, but other configurations can also be used. For example, in an alternative or supplemental embodiment, the measurement device 310 can receive two separate measured signals corresponding to two different frequencies. The measurement device 310 includes a first band-pass filter 320 and a second band-pass filter 330. The band-pass filters 320 and 330 can filter the measured signal Um 260 at specified frequencies (e.g., ω1 and ω2) to determine, respectively, the measurements Um,ω1 321 and Um,ω1 331 to be used in equations (1)-(9). The second band-pass filter 330 can be a low-pass filter and the first band-pass filter 320 can be a high-pass filter. In a supplemental or alternative embodiment, the first and/or the second band-pass filters 320 and 330 can be a notch filter, which can filter additional noise and/or spurious frequency signals.
Using equation (8), the gap capacitance Cg 242 between the torch component 210 and the workpiece 220 can be determined based on, in part, the measurements Um,ω1 321 and Um,ω2 331 at two different frequencies. As described above, in one embodiment, the distance 230 can be related to the gap capacitance Cg 242 using a calibrated correlation data set. The calibrated correlated data set can be derived, for example, by measuring the distance 230 between the torch component 210 and the workpiece 220 in the absence of a plasma (i.e., the plasma resistance Rp 244=∞). In this case, equation (3) simplifies to:




  
    
      
        
          
            
              
              
                U
                
                  m
                  ,
                  ω
                
              
              
            
            ⁢
            
              
                ❘
              
              open
            
          
          =
          
            
              
              
                U
                
                  s
                  ,
                  ω
                
              
              
            
            
              
                1
                +
                
                  
                    (
                    
                      ω
                      ⁢
                      
                        
                      
                      ⁢
                      
                        C
                        g
                      
                      ⁢
                      
                        R
                        ref
                      
                    
                    )
                  
                  2
                
              
            
          
        
        ,
      
    
    
      
        (
        11
        )
      
    
  




where “open” indicates the absence of a plasma. In the DC case, equation (11) simplifies further to yield:

Um,DC|open=Us,DC.  (12)

In an alternative or supplemental embodiment, the magnitude of the measured signal Um 250 in the absence of a plasma can be directly related to the distance 230 using a calibrated correlation data set, eliminating the need to directly determine the gap capacitance Cg 242. Specifically, a magnitude of an AC measurement (e.g., Um,ω∥open) can be used to correlate and/or determine the distance 230. When a plasma forms, however, simply using the magnitude of the measured signal |Um,ω| would yield an inaccurate distance. To correct for this, a correction term can be determined and added to the magnitude of the measured signal |Um,ω| as illustrated in equation (13) below:

|Um,ω|+Δcorrection=“effective”|Um,ω∥open,  (13)

where the effective |Um,ω∥open can then be used in relation to the calibration data set to determine the distance 230. The use of the correction term Δcorrection advantageously eliminates the need to perform additional processing to calculate the unknown gap capacitance Cg 242.

In one embodiment, the correction term Δcorrection can be determined from the perspective of a Taylor series representation of equation (3) where the variable is the inverse of the plasma resistance Rp 244:




  
    
      
        
          
            
            
              U
              
                m
                ,
                ω
              
            
            
          
          ⁢
          
            (
            
              1
              
                R
                p
              
            
            )
          
        
        =
        
          
            
              
                
                
                  U
                  
                    m
                    ,
                    ω
                  
                
                
              
              ⁢
              
                (
                
                  
                    1
                    
                      R
                      p
                    
                  
                  =
                  0
                
                )
              
            
            +
            
              
                1
                
                  R
                  p
                
              
              ⁢
              
                d
                
                  d
                  
                    1
                    
                      R
                      p
                    
                  
                
              
              ⁢
              
                (
                
                  
                    
                    
                      U
                      
                        m
                        ,
                        ω
                      
                    
                    
                  
                  ⁢
                  
                    (
                    
                      1
                      
                        R
                        p
                      
                    
                    )
                  
                
                )
              
            
          
          ⁢
          
            |
            
              
                1
                
                  R
                  p
                
              
              =
              0
            
          
          ⁢
          
            
          
          ⁢
          
            
              +
              
                
              
              ⁢
              higher
            
            ⁢
            
              
            
            ⁢
            order
            ⁢
            
              
            
            ⁢
            
              terms
              .
            
          
        
      
    
    
      
        (
        14
        )
      
    
  




From equations (13) and (14), the correction term Δcorrection can be determined to be:





  
    
      
        
          Δ
          correction
        
        =
        
          
            
              -
              
                1
                
                  R
                  p
                
              
            
            ⁢
            
              d
              
                d
                
                  1
                  
                    R
                    p
                  
                
              
            
            ⁢
            
              (
              
                
                  
                  
                    U
                    
                      m
                      ,
                      ω
                    
                  
                  
                
                ⁢
                
                  (
                  
                    1
                    
                      R
                      p
                    
                  
                  )
                
              
              )
            
          
          ⁢
          
            |
            
              
                1
                
                  R
                  p
                
              
              =
              0
            
          
          ⁢
          
            
              -
              
                
              
              ⁢
              higher
            
            ⁢
            
              
            
            ⁢
            order
            ⁢
            
              
            
            ⁢
            
              terms
              .
            
          
        
      
    
    
      
        (
        15
        )
      
    
  




Assuming that the higher order terms are negligible (i.e., where Rp>>Rref), and using equation (3), the correction term Δcorrection to first order is:





  
    
      
        
          Δ
          correction
        
        =
        
          
            
              R
              ref
            
            
              R
              p
            
          
          ⁢
          
            
              
                
                
                  U
                  
                    s
                    ,
                    ω
                  
                
                
              
              
                
                  (
                  
                    1
                    +
                    
                      
                        ω
                        2
                      
                      ⁢
                      
                        C
                        g
                        2
                      
                      ⁢
                      
                        R
                        ref
                        2
                      
                    
                  
                  )
                
                
                  3
                  /
                  2
                
              
            
            .
          
        
      
    
    
      
        (
        16
        )
      
    
  




One skilled in the art will appreciate that higher orders can be included as necessary for greater accuracy. Assuming that ω2Cg2Rref2<<1, then the correction term Δcorrection can be approximated as being independent of the gap capacitance 242:





  
    
      
        
          Δ
          correction
        
        =
        
          
            
            
              U
              
                s
                ,
                ω
              
            
            
          
          ⁢
          
            
              
                R
                ref
              
              
                R
                p
              
            
            .
          
        
      
    
    
      
        (
        17
        )
      
    
  




The plasma resistance Rp 244 can be determined using the DC measurements as illustrated in equation (9), where Um/s,DC≡Um/s,ω=0, resulting in:





  
    
      
        
          Δ
          correction
        
        =
        
          
            
            
              U
              
                s
                ,
                ω
              
            
            
          
          ⁢
          
            
              (
              
                
                  
                    U
                    
                      s
                      ,
                      DC
                    
                  
                  
                    U
                    
                      m
                      ,
                      DC
                    
                  
                
                -
                1
              
              )
            
            .
          
        
      
    
    
      
        (
        18
        )
      
    
  




From equations (13) and (18), the effective |Um,ω∥open, which can be used in relation to the calibration data set to determine the distance 230, is:




  
    
      
        
          
            
              
                “
                effective
                ”
              
              ⁢
              
                
                
                  U
                  
                    m
                    ,
                    ω
                  
                
                
              
            
            ⁢
            
              |
              open
            
          
          =
          
            
              
              
                U
                
                  m
                  ,
                  ω
                
              
              
            
            +
            
              
                
                
                  U
                  
                    s
                    ,
                    ω
                  
                
                
              
              ⁢
              
                (
                
                  
                    
                      U
                      
                        s
                        ,
                        DC
                      
                    
                    
                      U
                      
                        m
                        ,
                        DC
                      
                    
                  
                  -
                  1
                
                )
              
            
          
        
        ,
      
    
    
      
        (
        19
        )
      
    
  




which is a function of the magnitudes of: the measured AC signal Um,ω, the measured DC signal Um,DC, and the AC and DC source signals Us,ω and Us,DC.

In an alternative or supplemental embodiment, the correction term Δcorrection can be determined using different approximations from that illustrated above. From equations (3), (11), and (13), the correction term Δcorrection normalized to the AC source magnitude can be represented as:




  
    
      
        
          
            
              Δ
              correction
            
            
              
              
                U
                
                  s
                  ,
                  ω
                
              
              
            
          
          =
          
            
              1
              
                
                  1
                  +
                  
                    
                      (
                      
                        ω
                        ⁢
                        
                          
                        
                        ⁢
                        
                          C
                          g
                        
                        ⁢
                        
                          R
                          ref
                        
                      
                      )
                    
                    2
                  
                
              
            
            -
            
              1
              
                
                  
                    (
                    
                      1
                      +
                      
                        
                          R
                          ref
                        
                        
                          R
                          p
                        
                      
                    
                    )
                  
                  +
                  
                    
                      (
                      
                        ω
                        ⁢
                        
                          
                        
                        ⁢
                        
                          C
                          g
                        
                        ⁢
                        
                          R
                          ref
                        
                      
                      )
                    
                    2
                  
                
              
            
          
        
        ,
      
    
    
      
        (
        20
        )
      
    
  




which can be thought of as a “normalized shift in the AC measurement” caused by the presence of a plasma. In general, it is not possible to explicitly separate the influence of the two unknowns in equation (20): the gap capacitance Cg 242 and the plasma resistance Rp 244. However, in certain special cases, such as, for example, when Rref/Rp and/or ωCgRref are small compared to 1, the correction term Δcorrection can become a strong function of Rref/Rp and only weakly dependent upon ωCgRref, which can therefore be ignored. The correction to be applied to the measured signal magnitude |Um,ω| can, in this case, be determined solely in terms of the quantity Rref/Rp, or alternatively, in terms of the source and measured DC signal levels from equation (9). Furthermore, the correction term Δcorrection can generally be represented as a polynomial function of the source and measured DC signal magnitudes. A polynomial representation of first or second order can be sufficiently accurate, though higher order functions can also be used.

The DC voltage drop across the reference resistor Rref 252 is Ur,DC=Us,DC−Um,DC, and a “normalized shift in the DC measurement” caused by the plasma can be represented as:




  
    
      
        
          
            U
            
              r
              ,
              DC
            
          
          
            U
            
              s
              ,
              DC
            
          
        
        =
        
          1
          -
          
            
              
                U
                
                  m
                  ,
                  DC
                
              
              
                U
                
                  s
                  ,
                  DC
                
              
            
            .
          
        
      
    
    
      
        (
        21
        )
      
    
  




Note that in the absence of a plasma (i.e., Rp=∞), Um,DC|open=Us,DC, so there is no DC shift. From equation (9), where, the normalized shift in the DC measurement can be related to Rref/Rp:





  
    
      
        
          1
          +
          
            
              R
              ref
            
            
              R
              p
            
          
        
        =
        
          
            
              U
              
                s
                ,
                DC
              
            
            
              U
              
                m
                ,
                DC
              
            
          
          =
          
            
              1
              
                1
                -
                
                  
                    U
                    
                      r
                      ,
                      DC
                    
                  
                  /
                  
                    U
                    
                      s
                      ,
                      DC
                    
                  
                
              
            
            .
          
        
      
    
    
      
        (
        22
        )
      
    
  




Using equation (22), the correction term Δcorrection equation (20) becomes:





  
    
      
        
          
            
              Δ
              correction
            
            
              
              
                U
                
                  s
                  ,
                  ω
                
              
              
            
          
          =
          
            
              1
              
                
                  1
                  +
                  
                    
                      (
                      
                        ω
                        ⁢
                        
                          
                        
                        ⁢
                        
                          C
                          g
                        
                        ⁢
                        
                          R
                          ref
                        
                      
                      )
                    
                    2
                  
                
              
            
            -
            
              1
              
                
                  
                    (
                    
                      1
                      
                        1
                        -
                        
                          
                            U
                            
                              r
                              ,
                              DC
                            
                          
                          /
                          
                            U
                            
                              s
                              ,
                              DC
                            
                          
                        
                      
                    
                    )
                  
                  +
                  
                    
                      (
                      
                        ω
                        ⁢
                        
                          
                        
                        ⁢
                        
                          C
                          g
                        
                        ⁢
                        
                          R
                          ref
                        
                      
                      )
                    
                    2
                  
                
              
            
          
        
        ,
      
    
    
      
        (
        23
        )
      
    
  




FIG. 4 illustrates a normalized DC shift plot 400 showing the relationship between the resistance ratio Rref/Rp and the normalized DC shift of equation (21). The plot 400 is a one-to-one mapping from the values (0−∞) for Rref/Rp, to (0−1) for the normalized DC shift. FIG. 5 illustrates a normalized AC shift plot 500 showing the relationship between the normalized correction term Δcorrection and the normalized DC shift of equation (21) for different values of ωCgRref. The plot 500 illustrates that the exact AC correction term Δcorrection can be determined over the entire range of Ur,DC/Us,DC (i.e., Rref/Rp), not just for situations where Rref/Rp<<1. However, an assumption can be made regarding the value of ωCgRref, which is unknown. If ωCgRref<0.3 (e.g., by choosing appropriate values for the frequency and/or the reference resistor Rref 252), such that (ωCgRref)2<0.1, plot 500 shows that minimal error can occur if the top four curves of plot 500 are replaced by a single straight line, i.e., Δcorrection/|Us,AC|=m·Ur,DC/Us,DC, where m can be an adjustable slope. The slope m is 1 for ωCgRref=0 and can decrease for larger values of ωCgRref. Corrections can be made for even larger values of ωCgRref by decreasing m and optionally adding a quadratic term to the correction.
In the case where the plasma correction is represented by a first order polynomial function of the measured DC shift, a general-purpose operational-amplifier can be used as a gain element and an adder circuit can then add the appropriate correction to the magnitude measurement at the higher frequency. The DC shift itself can be measured by utilizing an instrumentation amplifier, or a difference amplifier. More complex functions can also be used, as described above, which can be implemented, for example, in either an analog form and/or digital form.
FIG. 6 is a plot 600 showing an example of measured signal magnitudes over time utilizing the above-described techniques. In this example, the nozzle of a torch component was maintained at a constant distance of about 6 mm from the workpiece. A plasma was formed between approximately −1.8 seconds and 0.5 seconds. Disturbances in both Um,DC and |Um,AC| can be seen to result due to the presence of the plasma. The disturbances are similar, as confirmed in FIG. 7, which is a plot 700 showing the time-traced relationship between the normalized correction term Δcorrection and the normalized DC shift in this example (electronic noise in the data acquisition system as well as minor variations in the gap cause the data points to not completely follow the same trace). The data plotted in 700 shows a substantially linear correlation, with a slope of  ̃0.57. Therefore, using m=0.57 in the calculation of the AC correction, the corrected AC measurement can be obtained, which is illustrated as the effective |Um,AC| in plot 600. The effective |Um,AC| is substantially constant in plot 600, which confirms that the distance between the nozzle and the workpiece is constant in this example, independent of the presence of the plasma. In this example, ω2=236 kHz and Rref=67 kΩ. Generally, AC frequencies can range from between about 100 kHz to about 700 kHz, but other frequencies below or above this range can also be used. In addition, the reference resistance Rref can range from between about 25 kΩ to about 75 kΩ, but other values below or above this range can also be used. Furthermore, in this example, the capacitance at this distance is about 0.08 pF and the minimum plasma resistance Rp was about 400 kΩ.
FIG. 8 is a plot 800 showing the measured signal magnitudes of plot 600 overlaid with a distance calibration curve. Plot 800 illustrates the error in distance that can occur by using an uncorrected AC measurement of |Um,AC|. At about −0.5 secs, |Um,AC| reaches about 2.5 V, which corresponds to a distance of about 0.5 mm. However, using the corrected |Um,AC|, the distance is 6 mm.
In a supplemental or alternative embodiment, the above described techniques can be extended to cases where the plasma cannot be considered to be a purely ohmic resistance. For example, the physical effects between the interface of a plasma region with a non-plasma region can be characterized by the presence of a Debye sheath, which can act primarily as a capacitance. Therefore, the gap impedance Zg 240 can be modeled more accurately as a gap capacitance Cg 242 in parallel with a plasma impedance Zp, where the plasma impedance Zp, in turn, can be modeled as a plasma resistance Rp in series with a plasma capacitance Cp. One skilled in the art will appreciate that the three unknowns (Cg, Rp, Cp) in this model require measurements at three different frequencies (i.e., to obtain three equations) in order to solve for the three unknowns.
The above-described techniques can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. The implementation can be as a computer program product, i.e., a computer program tangibly embodied in an information carrier, e.g., in a machine-readable storage device or in a propagated signal, for execution by, or to control the operation of, data processing apparatus, e.g., a programmable processor, a computer, or multiple computers. A computer program can be written in any form of programming language, including compiled or interpreted languages, and the computer program can be deployed in any form, including as a stand-alone program or as a subroutine, element, or other unit suitable for use in a computing environment. A computer program can be deployed to be executed on one computer or on multiple computers at one site.
Method steps can be performed by one or more programmable processors executing a computer program to perform functions of the invention by operating on input data and generating output. Method steps can also be performed by, and an apparatus can be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit). Subroutines can refer to portions of the computer program and/or the processor/special circuitry that implements that functionality.
Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor receives instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memory devices for storing instructions and data. Generally, a computer also includes, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. Data transmission and instructions can also occur over a communications network. Information carriers suitable for embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD, DVD, and HD-DVD disks. The processor and the memory can be supplemented by, or incorporated in special purpose logic circuitry.
To provide for interaction with a user, the above described techniques can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer (e.g., interact with a user interface element). Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input.
The above described techniques can be implemented in a distributed computing system that includes a back-end component, e.g., as a data server, and/or a middleware component, e.g., an application server, and/or a front-end component, e.g., a client computer having a graphical user interface and/or a Web browser through which a user can interact with an example implementation, or any combination of such back-end, middleware, or front-end components.
The computing system can include clients and servers. A client and a server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
One skilled in the art will realize the invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The foregoing embodiments are therefore to be considered in all respects illustrative rather than limiting of the invention described herein. Scope of the invention is thus indicated by the appended claims, rather than by the foregoing description, and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

## Claims

1. A method for determining a distance between pieces of a thermal processing system using a processor or an electronic circuit, the method comprising:
directing a laser beam or a plasma arc on to a first or a second piece;
applying, using the processor or electronic circuit, at the first or second piece, a source AC signal different from a source signal of the laser beam or the plasma arc, the source AC signal including a source DC offset;
measuring, using the processor or electronic circuit, at the first or second piece, an AC signal generated by the source AC signal that is different from the source signal of the laser beam or the plasma arc, the AC signal including a DC offset; and
determining, using the processor or electronic circuit, the distance using a calibration data set that includes data values associated with the measured AC signal and the source AC signal that is different from the source signal of the laser beam or the plasma arc, deriving the distance by calculating a gap capacitance between the first piece and the second piece, the derived gap capacitance is a function of at least the measured AC signal and the source AC signal, wherein the calibration data set further includes the gap capacitance.

2. The method of claim 1, wherein the first piece comprises a torch component and the second piece comprises a workpiece.

3. The method of claim 2, wherein the torch component comprises a nozzle or a torch head.

4. The method of claim 1, wherein determining the gap capacitance is derived from: a frequency of the AC signal, a magnitude of the AC signal, a magnitude of the DC offset, a magnitude of the source AC signal, a magnitude of the source DC offset, or any combination thereof.

5. The method of claim 1, wherein the AC signal comprises:
a current signal or a voltage signal.

6. The method of claim 1, wherein measuring the AC signal comprises passing the AC signal through a high band-pass filter, the high band-pass filter attenuating the DC offset.

7. The method of claim 6, wherein measuring the AC signal comprises measuring the DC offset by passing the AC signal through a low band-pass filter.

8. The method of claim 1 further comprising determining a plasma resistance between the first piece and the second piece based on the measured AC signal and the source AC signal.

9. The method of claim 1, wherein the source AC signal comprises: a current source signal or a voltage source signal.

10. The method of claim 1, wherein the calibration data set comprises data values associated with: a frequency of the AC signal, a magnitude of the AC signal, a magnitude of the DC offset, a magnitude of the source AC signal, a magnitude of the source DC offset, or any combination thereof.

11. The method of claim 1, wherein measuring the AC signal comprises measuring the AC signal at a position after a known electrical element, the known electrical element being located between the position and a source of the source AC signal.

12. A system for determining a distance between pieces of a thermal processing system, the system comprising:
a source adapted to apply, at a first or a second piece, a source AC signal different from a source signal of a laser beam or a plasma arc directed on the first or the second piece, the source AC signal including a source DC offset;
a measuring device adapted to measure, at one or both of the first and second piece, an AC signal generated by the source AC signal different from the source signal of the laser beam or the plasma arc, the AC signal including a DC offset; and
a signal processing device adapted to determine the distance using a calibration data set that includes data values associated with the measured AC signal and the source AC signal different from the source signal of the laser beam or the plasma arc, deriving the distance by calculating a gap capacitance between the first piece and the second piece, the derived gap capacitance is a function of at least the measured AC signal and the source AC signal, wherein the calibration data set further includes the gap capacitance.

13. The system of claim 12, wherein the first piece comprises a torch component and the second piece comprises a workpiece.

14. The system of claim 12 further comprising:
a high band-pass filter adapted to attenuate the DC offset; and
a low band-pass filter adapted to pass the DC offset.

15. The system of claim 12, wherein the measuring device is further adapted to measure the AC signal at a position after a known electrical element, the known electrical element being located between the position and the source.

16. A system for performing a capacitive distance measurement between pieces of a thermal processing system, the system comprising:
source means for applying, at a first or a second piece, a source AC signal different from a source signal of a laser beam or a plasma arc directed on the first or the second piece, the source AC signal including a source DC offset;
measuring means for measuring, at the first or second piece, an AC signal generated by the source AC signal different from the source signal of the laser beam or the plasma arc, the AC signal including a DC offset; and
signal processing means for determining the distance using a calibration data set that includes data values associated with the measured AC signal and the source AC signal different from the source signal of the laser beam or the plasma arc, deriving the distance by calculating a gap capacitance between the first piece and the second piece, the derived gap capacitance is a function of at least the measured AC signal and the source AC signal, wherein the calibration data set further includes the gap capacitance.

17. The system of claim 16, wherein the first piece comprises a torch component and the second piece comprises a workpiece.

18. The system of claim 16 further comprising:
high-pass filtering means for attenuating the DC offset; and
low-pass filtering means for passing the DC offset.

19. An apparatus for determining a distance between a first piece and a second piece, the apparatus adapted to utilize the method of claim 1.

20. The method of claim 3, wherein the nozzle comprises a laser nozzle.