System and method for controlling a wire electrical discharge machine

Abstract

An embodiment of the present disclosure provides a wire electrical discharge machine (EDM), the wire EDM including a transport system for transporting the wire electrode and the workpiece toward one or a combination of the wire electrode and the workpiece and the transport system for generating an electrical discharge between the wire electrode and the workpiece. The wire EDM includes a light source for illuminating the wire electrode with a coded illumination pattern and a camera for acquiring a set of images of the wire electrode illuminated with the coded illumination pattern. The wire EDM includes a processor for reconstructing positions of segments of the wire electrode at a reconstruction rate higher than the acquisition rate of the camera by utilizing compressed sensing with sparse reconstruction techniques, and a controller for controlling the transport system and the energy based on the reconstructed positions.

Description

[Technical Field]

[0001] The present invention relates generally to wire electrical discharge machines (EDMs), and more particularly to a method for controlling a wire EDM for machining a workpiece. [Background technology]

[0002] Electrical discharge machining (EDM) is a metal manufacturing process that uses electrical discharges (or sparks) to obtain a desired shape in a metal workpiece. Material is removed from the metal workpiece by a series of rapidly repetitive electrical discharges between two energized electrodes separated by a dielectric liquid. One of the electrodes is the tool electrode, or tool, and the other is the workpiece electrode, or workpiece. The manufacturing process relies on the tool and workpiece not being in physical contact.

[0003] A wire electrical discharge machine (wire EDM) is a precision cutting device that utilizes the EDM manufacturing process to machine a workpiece. The tool electrode in wire EDM is a wire, and the workpiece acts as the second electrode. When a high voltage is applied between the wire and the workpiece, the electric field strength in the space between the wire and the workpiece increases, causing breakdown of the dielectric liquid and the creation of an arc. This results in the removal of material from the electrode, i.e., the wire, and the workpiece.

[0004] Typically, to avoid wire wear that could lead to wire breakage, the wire is wound between two spools so that the effective length of the wire is constantly changing. However, the occurrence of discharges and the relatively small diameter of the wire cause the wire to vibrate, which is damped on the two supports that limit the length of the wire's vibration.

[0005] Generally, wire EDM is configured for one or two types of machining or cutting, such as rough cutting and skim cutting. Rough cutting involves roughly and quickly machining the workpiece, while skim cutting involves an additional operation in which the wire returns along the same path after the rough cutting is completed. Therefore, compared to rough cutting, skim cutting requires greater precision to achieve finer and more accurate cuts with surface integrity. Notably, although the respective purposes of rough cutting and skim cutting are different, the accuracy of both cuts depends on the vibration of the wire.

[0006] Traditionally, estimating such vibrations with the desired accuracy is difficult due to the disturbances and various forces acting during wire EDM. Additionally, one or more conventional methods use an optical system to focus reflected light onto a one-dimensional sensor, which then detects the unidirectional vibration of the wire as a change in the position of the sensor's image point. While such a configuration can detect small vibrations in the wire, the resulting vibration estimates are inaccurate enough to control wire EDM for precision machining processes.

[0007] Therefore, to address the above problems, a method is needed to estimate the vibration of the wire with an accuracy suitable to maintain the accuracy of wire EDM during the roughing and skimming steps. Summary of the Invention

[0008] The present disclosure provides a wire electrical discharge machine (EDM) and a method for controlling the wire EDM for machining a workpiece.

[0009] Some embodiments are based on the understanding that the vibration of the wire electrode can be reconstructed in the frequency domain by detecting the positional change of the image point of the camera's one-dimensional sensor. However, for such reconstruction, several assumptions must be made. For example, one assumption is that the frequency of the timing of the linear positional change indicates the vibration of the entire wire electrode. However, in the case of wire EDM, such an assumption may be incorrect because small waves in the electrolyte caused by the discharge and machining of the workpiece disturb the wire electrode at multiple unknown frequency harmonics.

[0010] Therefore, controlling the machining of a workpiece based solely on linear vibration feedback may provide insufficient information for control. A wire electrode is a soft, continuous material that deforms significantly during machining. This deformation is transmitted to the machined surface of the workpiece, reducing workability. Because wire electrodes are affected by a complex interplay of physical phenomena, including explosions caused by electrical discharges and hydraulic pressure from processing fluids, predicting their behavior is difficult. Therefore, it is necessary to estimate the physical behavior of the wire electrode to improve the control accuracy of wire EDM.

[0011] Some embodiments are based on the recognition that the physical behavior of a wire electrode can be represented by its position and / or shape at different times. Such a representation indicates both the displacement of the wire and the frequency and amplitude of vibration, which is advantageous for precision of control. Therefore, an objective of some embodiments is to estimate different positions and / or shapes of at least segments of the wire electrode at different times. Additionally or alternatively, an objective of some embodiments is to estimate the frequency and amplitude of vibration of different segments of the wire.

[0012] Some embodiments further recognize that the position of the wire electrode at different times can be reconstructed using a camera that observes the wire electrode over at least a two-dimensional (2D) field of view (FoV). However, such a solution has several problems. For example, the vibration frequency of the wire electrode in wire EDM is typically in the range of approximately 1 kilohertz (kHz). Therefore, a camera with an acquisition rate of at least 2000 frames per second (fps) would be required to accurately identify the position of the wire electrode. Such a high-speed camera can significantly increase the cost of wire EDM equipment. In addition, discharges create wide, blurry white areas that interfere with the acquisition of 2D images. Furthermore, bubbles or other transient objects can also create shadows that interfere with the acquisition of 2D images. Therefore, an objective of some embodiments is to utilize compressed sensing with sparse reconstruction techniques to reduce the cost of using wire EDM by eliminating the need for high-fps high-speed cameras, which can be expensive.

[0013] To that end, some embodiments are based on the implementation of a wire EDM for machining a workpiece. The wire EDM includes a transport system, such as a pulley, for contacting one or a combination of a wire electrode and a workpiece and feeding the wire electrode and the workpiece toward each other. The wire EDM further includes an energy source configured to generate an electrical discharge between the wire electrode and the workpiece. The EDM further includes a wire electrode position measurement system, the wire electrode position measurement system including a camera having a light source configured to illuminate the wire electrode with a coded illumination pattern and an image sensor positioned to acquire a set of images showing the wire electrode at different positions illuminated with the coded illumination pattern. The wire EDM further includes a processor configured to reconstruct positions of at least segments of the wire electrode at a reconstruction rate higher than the acquisition rate of the camera by utilizing compressed sensing with sparse reconstruction techniques. The wire EDM further includes a controller configured to control at least one of the transport system and the energy source based on the positions of at least segments of the wire electrode reconstructed at the reconstruction rate.

[0014] Some embodiments are based on the recognition that the energy source is further configured to generate a waveform consisting of a sequence of on-time voltage pulses and off-time voltage pulses. The processing energy is reduced by shortening the duration of the on-time voltage pulses or lengthening the duration of the off-time processing energy, and is increased by lengthening the duration of the on-time voltage pulses or shortening the duration of the off-time voltage pulses. While keeping the processing energy constant, voltage feedback control is applied to control the processing speed of the workpiece. By controlling the processing speed of the workpiece, machining accuracy of the workpiece can be achieved.

[0015] Some embodiments are based on the recognition that the coded illumination pattern of the light source is configured to generate a pseudo-random sequence of on and off light pulses. The duration of each pulse in the pseudo-random sequence of on and off light pulses is less than or equal to the Nyquist sampling rate of the frequency of the vibration of the wire electrode. The total duration of the pseudo-random sequence of on and off light pulses is less than or equal to the duration of a frame exposure of the camera. By having the duration of each pulse in the sequence of on and off light pulses be less than or equal to the Nyquist sampling rate of the frequency of the vibration of the wire electrode, the cost of the camera can be reduced.

[0016] Some embodiments are based on the recognition that the light source and camera of the wire electrode position measurement unit are positioned on either side of the wire electrode. The image sensor of the camera is configured to acquire a set of images of the sum of the shadows of the wire electrode encoded by the illumination pattern as the wire electrode moves across the image sensor of the camera. By acquiring the set of images of the sum of the shadows, movement or vibration of the wire electrode can be determined.

[0017] Some embodiments are based on the recognition that compressed sensing using a sparse restoration technique includes buffering a set of images acquired from a camera. The compressed sensing using a sparse restoration technique further includes generating a set of bubble-free images of the wire electrode encoded with the encoded illumination pattern by removing a bubble shadow from a shadow of the wire electrode moving across the image sensor captured in the set of images acquired from the camera. By generating the bubble-free images, spectral contamination of the purely vibrating wire electrode can be removed from the set of images. The compressed sensing using a sparse restoration technique further includes compressing the pixel dimensions of the set of bubble-free images by multiplying the pixel dimensions by a Gaussian random matrix to be equal to the number of images in the set of images, and outputting a set of compressed images. The compressed sensing using a sparse restoration technique further includes calculating a spectral matrix of the wire electrode from the set of compressed images by solving a group 1-norm sparse recovery problem. The wire electrode vibrates while moving across the image sensor. The compressed sensing using sparse reconstruction techniques further includes identifying a reduced set of frequency bins corresponding to the location of a row of the spectral matrix having the largest Euclidean norm. The compressed sensing using sparse reconstruction techniques further includes reconstructing a high-temporal resolution set of images of the wire electrode movement with a spatial resolution equal to the spatial resolution of the camera's image sensor by solving a least-squares reconstruction problem using the reduced set of frequency bins. The compressed sensing using sparse reconstruction techniques further includes outputting positions of at least segments of the wire electrode from the reconstructed high-temporal resolution set of images of the wire electrode movement. By utilizing compressed sensing using sparse reconstruction techniques, a high-temporal resolution set of images can be reconstructed without requiring an expensive, high-fps camera.

[0018] Some embodiments are based on the recognition that removing bubble shadows from a set of images acquired from a camera to generate a set of bubble-free images is performed by solving a robust principal component analysis problem. The robust principal component analysis problem includes modeling the set of images as consisting of low-rank matrix elements and sparse matrix elements. The low-rank matrix elements correspond to the vibrating wire electrode without bubbles, and the sparse elements correspond to bubbles. The robust principal component analysis problem further includes outputting the low-rank matrix elements as the set of bubble-free images.

[0019] Some embodiments are based on the recognition that solving the group 1-norm sparse retrieval problem includes minimizing the difference between a set of compressed images and a composite set of compressed images formed by the product of a spectral matrix of the vibrating wire electrode and a Fourier transform applied in the upsampled time domain. Solving the group 1-norm sparse retrieval problem further includes regularizing the minimization of the difference by a sum of Euclidean norms of the rows of the spectral matrix of the vibrating wire electrode, and outputting a spectral matrix in the upsampled time domain that is sparse in frequency bins by having a small number of non-zero row norms.

[0020] Some embodiments are based on the recognition that the controller is further configured to determine at least a frequency of vibration of the wire electrode by converting the reduced set of frequency bins into physical frequency values. The controller is further configured to determine at least an amplitude of vibration of the wire electrode by converting positions of segments of the wire electrode on the sensor array into physical positions of the wire electrode according to the geometry of components of the wire electrode position measurement unit. The determined frequency of vibration of the wire electrode and amplitude of vibration of the wire electrode are utilized to control the wire EDM for precision machining of the workpiece.

[0021] Some embodiments are based on the recognition that the controller is configured to reduce the likelihood of the wire electrode breaking during rough machining by performing control actions based on an analysis of the determined significant changes in the frequency and amplitude of vibration of the wire electrode, reducing the process energy input to the wire electrode based on the detection of the one or more significant changes, and reducing the process speed of the workpiece and the transport system based on the detection of the one or more significant changes. The reduced process energy input and reduced process speed of the workpiece and the transport system enable safe operation of the wire EDM.

[0022] Some embodiments are based on the recognition that the controller is further configured to control the amount of straightness and size error of the cut during skimming by performing control actions based on: analyzing the amplitude of the vibration of the wire and detecting that the amplitude is greater than a threshold; reducing the processing speed of the workpiece and the transport system to reduce the amplitude of the vibration of the wire electrode if the shape of the wire electrode is estimated to be convex; increasing the processing speed of the workpiece and the transport system to increase the amplitude of the vibration of the wire electrode if the shape of the wire electrode is estimated to be concave; and increasing the machining energy when the wire electrode is farther from the workpiece and decreasing the machining energy when the wire electrode is closer to the workpiece. Such control can increase the accuracy of the skimming.

[0023] Some embodiments are based on the recognition that the controller is further configured to control streaks of cut during skimming by performing control actions based on: analyzing the amplitude of vibration of the wire electrode to detect vibration fluctuations; reducing the processing speed of the workpiece and the transport system to reduce the amplitude of vibration of the wire electrode when the wire electrode shape is estimated to be convex; increasing the processing speed of the workpiece and the transport system to increase the amplitude of vibration of the wire electrode when the wire electrode shape is estimated to be concave; and increasing machining energy when the wire electrode is farther from the workpiece and decreasing machining energy when the wire electrode is closer to the workpiece. Such control of streaks of cut during skimming can improve the accuracy of skimming.

[0024] Accordingly, some embodiments disclose a method for machining a workpiece. The method includes transporting a wire electrode near the workpiece. The method further includes generating an electric discharge between the wire electrode and the workpiece. The method further includes illuminating the wire electrode with a coded illumination pattern. The method further includes acquiring a set of images showing the wire electrode illuminated with the coded illumination pattern at different positions. The method further includes utilizing compressed sensing with sparse reconstruction techniques to reconstruct positions of at least segments of the wire electrode at a reconstruction rate higher than an acquisition rate of a camera acquiring the set of images. The method further includes controlling at least one of a transport system that transports the wire electrode near the workpiece and an energy source that generates the electric discharge based on the positions of at least segments of the wire electrode reconstructed at the reconstruction rate.

[0025] Accordingly, some embodiments disclose a non-transitory computer-readable medium storing computer-executable instructions for machining a workpiece. The computer-executable instructions are configured to transport a wire electrode near the workpiece. The computer-executable instructions are further configured to generate an electrical discharge between the wire electrode and the workpiece. The computer-executable instructions are further configured to illuminate the wire electrode with a coded illumination pattern. The computer-executable instructions are further configured to acquire a set of images showing the wire electrode illuminated with the coded illumination pattern at different positions. The computer-executable instructions are further configured to reconstruct positions of at least a segment of the wire electrode at a reconstruction rate higher than an acquisition rate of a camera that acquires the set of images by utilizing compressed sensing with sparse reconstruction techniques. The computer-executable instructions are further configured to control at least one of a transport system that transports the wire electrode near the workpiece and an energy source that generates the electrical discharge based on the positions of at least a segment of the wire electrode reconstructed at the reconstruction rate.

[0026] The present disclosure is further described in the following detailed description with reference to several drawings, in which like reference numerals represent like parts in the several views, shown as non-limiting examples of exemplary embodiments of the present disclosure. The drawings shown are not necessarily to scale, rather emphasis is generally placed upon illustrating the principles of embodiments of the present disclosure. [Brief explanation of the drawings]

[0027] [Figure 1A] 1 shows a schematic diagram of basic components of a wire electrical discharge machine (EDM), according to some embodiments of the present disclosure. [Figure 1B] FIG. 1 shows a schematic diagram of a wire EDM for machining a workpiece, according to some embodiments of the present disclosure. [Figure 2]1A-1C illustrate inaccuracies that affect the quality of a cut on a workpiece in conventional wire EDM, according to some embodiments of the present disclosure. [Figure 3A] 1A-1C show schematic diagrams illustrating exemplary positions of various components of a wire electrode position measurement unit relative to a wire electrode immersed in a working fluid, according to some embodiments of the present disclosure. [Figure 3B] 1 shows a schematic diagram of an image from a set of images acquired by a camera of a wire electrode position measuring unit, according to some embodiments of the present disclosure. [Figure 4A] FIG. 1 illustrates a block diagram for controlling a camera to determine trigger timing and a light source to generate a lighting pattern according to some embodiments of the present disclosure. [Figure 4B] 1A and 1B show diagrams illustrating constant illumination patterns produced by a light source, according to some embodiments of the present disclosure. [Figure 4C] FIG. 1 shows a diagram illustrating a pseudo-random sequence of on and off light pulses generated by a light source, according to some embodiments of the present disclosure. [Figure 5] 1A-1C illustrate pictorial representations of the position of a section of a wire electrode as it changes over time and the corresponding sensor measurements observed by a camera, according to some embodiments of the present disclosure. [Figure 6A] FIG. 1 shows a diagram illustrating a measurement operator “A” corresponding to an illumination pattern having a pseudo-random sequence of on and off light pulses beginning at the same time as the start of the camera exposure, according to some embodiments of the present disclosure. [Figure 6B] FIG. 10 shows a diagram illustrating a measurement operator “A” corresponding to an illumination pattern having a pseudo-random sequence of on and off light pulses beginning at random times within the duration of a camera exposure, according to some embodiments of the present disclosure. [Figure 7] 1A-1C show diagrams illustrating a set of images of a moving wire electrode captured by a camera, according to some embodiments of the present disclosure. [Figure 8]1 shows a diagram illustrating the continuous movement of a wire electrode versus a set of sequential images captured by a camera, according to some embodiments of the present disclosure. [Figure 9] FIG. 1 shows an exemplary block diagram of steps used in compressed sensing with sparse reconstruction techniques to reconstruct the positions of at least segments of wire electrodes, according to some embodiments of the present disclosure. [Figure 10] 1A-1C show diagrams illustrating the presence of bubbles in machining fluid around a wire electrode in wire EDM, according to some embodiments of the present disclosure. [Figure 11] 1 shows a diagram illustrating generating a set of bubble-free images from a set of images acquired from a camera, according to some embodiments of the present disclosure. [Figure 12] FIG. 1 shows an exemplary block diagram for determining at least the frequency and amplitude of vibration of a wire electrode according to some embodiments of the present disclosure. [Figure 13] FIG. 1 shows an exemplary block diagram for reducing the likelihood of wire electrode breakage during rough machining in accordance with some embodiments of the present disclosure. [Figure 14] FIG. 1 shows an exemplary block diagram for controlling the amount of cut straightness and size error during skimming, according to some embodiments of the present disclosure. [Figure 15] FIG. 1 shows an exemplary block diagram for controlling streaks of cut during skim machining in accordance with an embodiment of the present disclosure. [Figure 16] FIG. 1 illustrates a waveform generated by an energy source according to some embodiments of the present disclosure. [Figure 17] FIG. 1 is a flowchart illustrating a method for machining a workpiece, according to some embodiments of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0028] (Detailed explanation) In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be apparent to those skilled in the art that the present disclosure may be practiced without these specific details. In other instances, devices and methods are shown in block diagram form solely to avoid obscuring the disclosure. It is intended that various changes may be made in the function and arrangement of elements without departing from the spirit and scope of the disclosed subject matter, as set forth in the appended claims.

[0029] As used in this specification and claims, the terms "for example," "for instance," and "such as," as well as the verbs "comprising," "having," "including," and other forms of these verbs, when used in conjunction with a list of one or more components or other items, should each be construed as open-ended, meaning that the list should not be considered to exclude further components or items. The term "based on" means based at least in part on. Furthermore, it should be understood that the style and terminology used herein are for purposes of description and should not be considered limiting. Any headings used herein are for convenience only and are not to be considered legal or limiting.

[0030] Specific details are provided in the following description for a thorough understanding of the embodiments. However, those skilled in the art will understand that the embodiments may be practiced without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form in order to avoid obscuring the embodiments with unnecessary detail. In other instances, well-known processes, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments. Furthermore, like reference numbers and names in the various drawings indicate like elements. (System Overview)

[0031] 1A illustrates a schematic diagram 100A of a portion of a wire electrical discharge machine (EDM) according to some embodiments of the present disclosure. The schematic diagram 100A includes a workpiece 102, a wire electrode 104, a wire guide 106, and an energy source 108. The schematic diagram 100A further illustrates a direction of movement 110 of the workpiece 102 and a direction of movement 112 of the wire electrode 104. In different implementations, the EDM is configured to move either the workpiece or the wire electrode itself, or a combination thereof. Thus, in some embodiments, the machining speed is the relative speed of the wire and the workpiece. The schematic diagram 100A also illustrates an electrical discharge 114.

[0032] The workpiece 102 may be a piece of metal that needs to be manufactured into a desired shape. The wire electrode 104 may be a length of wire that can be utilized to manufacture the workpiece 102. Wire EDM utilizes electrical discharges 114 or sparks to remove material from the workpiece 102 to obtain the desired shape of the workpiece 102. The wire electrode 104 acts as a first electrode, and the workpiece 102 acts as a second electrode. The wire electrode 104 and the workpiece 102 are separated by a dielectric liquid, and application of a voltage from an energy source 108 creates a series of rapidly recurring electrical current discharges or discharges 114 between the two electrodes, such as the wire electrode 104 and the workpiece 102, to remove material from the workpiece 102.

[0033] An energy source 108, such as a voltage source, is used to apply a voltage between the two electrodes. During machining of the workpiece 102, the workpiece 102 moves in a motion direction 110, and the speed of the workpiece 102 movement is the processing rate. The wire electrode 104 moves in a motion direction 112 to machine the workpiece 102, and the speed of the wire electrode 104 movement is the wire electrode 104 feed rate. The movement of the wire electrode 104 may be controlled via a wire guide 106. Additionally, the generation of the discharge 114 and the relatively small diameter of the wire electrode 104 cause the wire electrode 104 to vibrate, while the vibration of the wire is damped on two supports that limit the length of the wire vibration. Further details of the wire EDM and its associated components of the present disclosure are provided, for example, in FIG. 1B.

[0034] FIG. 1B shows a schematic block diagram 100B of a wire EDM 116 for machining a workpiece 102 according to some embodiments of the present disclosure. The wire EDM 116 can include a wire electrode 104, an energy source 108, a transport system 118, a machining fluid 120, and a wire electrode position measurement system 122. In some implementations, the transport system 118 is a wire bobbin configured to control the feed of the wire. Additionally or alternatively, in some embodiments, the wire feed speed is controlled from the wire bobbin, but the position of the wire itself is also controlled by a workpiece motor 132. The wire electrode position measurement system 122 further includes a light source 124 and a camera 126 having an image sensor, such as a line sensor and / or a two-dimensional (2D) sensor. The line sensor can reconstruct the vibration of a point on the wire. In some implementations, the image sensor is 2D, reconstructing a section of the wire including multiple points. This implementation provides more accurate results. The wire EDM 116 may further include a processor 128 and a controller 130. In some embodiments, the processor 128 and the controller 130 may be part of a control unit. The wire EDM 116 may further include a workpiece motor 132, a set of electrode supports 134, a set of power supply pieces 136, and a waste box 138.

[0035] The transport system 118 may include pulleys, also referred to as wire bobbins, that contact the wire electrode 104 and / or the workpiece 102 to transport the wire electrode 104 and the workpiece 102 close to one another. The transport system 118 is configured to transport the wire electrode 104 near the workpiece 102. The transport system 118 may include a roll of the wire electrode 104 so that a portion of the wire electrode 104 can be fed from the roll near the workpiece 102 as needed. The wire electrode 104 and the workpiece 102 may be immersed in a machining fluid 120. In some embodiments, the machining fluid 120 may be comprised of either water or oil.

[0036] The energy source 108 is configured to generate an electrical discharge 114 between the wire electrode 104 and the workpiece 102. As the voltage between the two electrodes (i.e., the wire electrode 104 and the workpiece 102) increases, the electric field strength in the space between these electrodes increases, causing a breakdown of the dielectric liquid (e.g., the working liquid 120) and generating an arc or discharge 114. This results in material being removed from the electrode. When the current is stopped, new liquid dielectric is pumped into the space between the electrodes, carrying away solid particles (or debris) and allowing the insulating properties of the dielectric liquid to be restored. Further, new liquid dielectric is added to the space between the electrodes, a process known as flushing. After the current is passed, the voltage between the electrodes is restored to the same level as before the breakdown, causing a new liquid breakdown, and the cycle repeats.

[0037] The wire electrode position measurement system 122 includes a light source 124 configured to illuminate the wire electrode 104 with a coded illumination pattern. In some embodiments, the light source 124 is a light-emitting diode (LED). In one or more embodiments, the wire electrode position measurement system 122 may further include a lens 124A positioned in the line of sight of the light source 124 to focus light from the light source 124 toward the wire electrode 104. The wire electrode position measurement system 122 may further include a camera 126 having an image sensor. The camera 126 may be positioned to acquire a set of images showing the wire electrode 104 illuminated with the coded illumination pattern at different positions. For example, the camera 126 may be positioned on opposite sides of the direction of the light source 124 to capture the set of images such that a segment of the wire electrode 104 falls between the light source 124 and the image sensor of the camera 126. In some embodiments, the discharge 114 may produce a white blur. The effect of this white fuzzy area in the set of images acquired may be reduced by generating a coded illumination pattern that is opposite to the white fuzzy area.

[0038] The processor 128 is configured to utilize compressed sensing with sparse reconstruction to reconstruct the positions of at least segments of the wire electrode 104 at a reconstruction rate higher than the acquisition rate of the camera 126. The reconstruction rate may be defined as the rate at which the positions of at least segments of the wire electrode 104 are reconstructed by the processor 128. Additionally, the acquisition rate may be defined as the rate at which the camera 126 acquires a set of images. Compressed sensing with sparse reconstruction processes the acquired set of images using a computational technique that may enable the precise position of the wire electrode 104 to be identified by temporal upsampling of the positions of the wire electrode 104 at a temporal sampling rate (or reconstruction rate) that matches or exceeds the Nyquist rate. The Nyquist rate may be related to a sampling rate that may be equal to or twice the bandwidth of a frame (e.g., a set of images) acquired by the camera 126. In this manner, the set of images may be acquired at a slower rate, i.e., slower than the Nyquist rate. Acquiring a set of images at such a low rate may reduce the cost of the camera 126 by eliminating the requirement for a high-frame-rate camera, which can be expensive. Furthermore, compressed sensing with sparse recovery models the video of the vibrating wire electrode 104 as a frequency-sparse signal. The controller 130 may be configured to formulate a joint sparse recovery problem to recover the high-frame-rate video as well as determine the frequency of the vibration of the wire electrode 104. Such a solution can address disturbances caused by bubbles and / or small waves in the working fluid 120 that have frequencies that do not match the sparsity of the vibration of the wire electrode 104. Further details of compressed sensing with sparse recovery are provided, for example, in FIG. 10 .

[0039] 1B , the controller 130 is configured to control at least one of the transport system 118 and the energy source 108 based on the position of at least a segment of the wire electrode 104 restored at the restoration rate. The controller 130 may ensure a clean or smooth cut of the workpiece 102 by determining the processing speed of the workpiece 102 and the amount of electrical potential (or voltage) that may be applied during processing. The controller 130 may receive information regarding the position of the wire electrode 104 from the wire position measurement system 122. However, certain inaccuracies in the overall operation of the wire EDM 116 may compromise the quality of the cut of the workpiece 102.

[0040] 2 illustrates the imprecision that affects the quality of the cut of the workpiece 102 in the wire EDM 116. The wire EDM 116 may be configured to perform two cutting techniques: a roughing technique and a skimming technique. A roughing technique may include roughly machining the workpiece 102. A skimming technique may include an additional operation in which the wire electrode 104 can return following the same path after the roughing is completed. As such, skimming requires more precision than roughing to achieve a finer and more accurate cut along with surface integrity.

[0041] However, the quality of the cut on the workpiece 102 can be affected by various factors, such as numerous vibrations in the wire electrode 104 of the wire EDM 112. For example, the straightness 202 of the cut on the workpiece 102 can be affected, resulting in inconsistent cuts. Furthermore, vibrations in the wire electrode 104 can cause streaks 204 to form on the workpiece 102. Furthermore, size errors 206 in the wire electrode 104 due to vibrations can result in an undesirable finished size of the workpiece 102. Additionally, wear and tear on the wire electrode 104 due to vibrations can result in breaks 208 being observed in the wire electrode 104. The wire EDM 116 of the present disclosure overcomes the above-listed inaccuracies by minimizing vibrations in the wire electrode 104 using a wire position measurement system 122. Further details of the wire EDM 116 that can control the vibration of the wire electrode 104 are provided, for example, in FIGS. 3A-17 .

[0042] FIG. 3A shows a schematic diagram 300A illustrating exemplary positions of various components of a wire electrode position measurement system 122 relative to a wire electrode 104 submerged in a working fluid 120, according to some embodiments of the present disclosure. The light source 124 and camera 126 of the wire electrode position measurement system 122 are positioned on either side of the wire electrode 104. The image sensor 126A of the camera 126 is configured to acquire a set of images of the sum of the shadows of the wire electrode 104 encoded by the illumination pattern as the wire electrode 104 moves across the image sensor 126A of the camera 126. Illumination from the light source 124 can be focused using a lens 124A positioned within the field of view of the light source 124. The light source 124 can be positioned such that sections of the wire electrode 104 cut off the illumination. The locations where the sections of the wire electrode 104 cut off the illumination can be obtained as the sum of the shadows of the wire electrode 104 encoded by the illumination pattern.

[0043] 3B shows a schematic diagram 300B of an image 302 from a set of images acquired by the camera 126 of the wire electrode position measurement system 122, according to some embodiments of the present disclosure. The camera 126 records a shadow 304 of the wire electrode 104 on a sensor plane (such as the Y-axis shown). The shadow 304 may be formed by an illumination pattern incident on the wire electrode 104. Similarly, a sum of shadows, such as shadow 304, is acquired corresponding to a set of images, such as image 302.

[0044] 4A shows a block diagram 400A for controlling a camera 126 to determine trigger timing and controlling a light source 124 to generate a coded lighting pattern according to some embodiments of the present disclosure. A controller 130 may be coupled to the light source 124. In some embodiments, the controller 130 may be coupled to the light source 124 via an LED control unit 402. The controller 130 may be configured to trigger the coded lighting pattern of the light source 124. The controller 130 may be in communication with the LED control unit 402 to trigger the coded lighting pattern of the light source 124.

[0045] The controller 130 may be connected to the camera 126. The controller 130 may determine the timing of the trigger of the camera 126. The timing of the trigger of the camera 126 may initiate the exposure of the camera 126 and the triggering of the lighting pattern of the light source 124 to coincide with the duration of the exposure of the camera 126. The LED control unit 402 may be programmed to generate a fixed coded lighting pattern or a pseudo-random sequence of on and off light pulses.

[0046] 4B shows a diagram 400B illustrating a constant coded illumination pattern 404 generated by a light source 124, according to some embodiments of the present disclosure. The constant coded illumination pattern 404 may be generated during a period when the camera 126 is triggered, i.e., during the exposure time of the camera 126. For example, the constant illumination pattern 404 may include an OFF light pulse of 0-0.5 millisecond duration and an ON light pulse of 0.5-1 millisecond duration.

[0047] Additionally, diagram 400B shows a graph 406 illustrating the exposure time of camera 126. In one embodiment, the exposure time may be one millisecond (1 msec). Light source 124 may be triggered based on a trigger of camera 126.

[0048] 4C shows a diagram illustrating a pseudo-random sequence of on and off light pulses 408 generated by light source 124, according to some embodiments of the present disclosure. In some embodiments, the coded illumination pattern of light source 124 is configured to generate the pseudo-random sequence 408 of on and off light pulses.

[0049] FIG. 400C includes a graph 406 illustrating the exposure time of the camera 126. A pseudo-random sequence 408 of on and off light pulses may be generated during the period in which the camera 126 is triggered, i.e., during the exposure time of the camera 126. The duration of each pulse in the sequence of on and off light pulses is less than or equal to the Nyquist sampling rate of the frequency of vibration of the wire electrode 104. In an example, the duration of each off light pulse may be 0.1 milliseconds, and the duration of each on light pulse may be 0.1 milliseconds. Furthermore, the total duration of the pseudo-random sequence of on and off light pulses 408 is less than or equal to the duration of a frame exposure or exposure time of the camera 126. The frame exposure or exposure time of the camera 126 may be, for example, 1 millisecond. The total duration of the pseudo-random sequence of on and off light pulses 408 may be less than 1 millisecond.

[0050] FIG. 5 shows a diagram 500 of the position 502 of a section of the wire electrode 104 as it changes over time and corresponding sensor measurements 504 observed by the camera 126, according to some embodiments of the present disclosure. The position 502 of the section of the wire electrode 104 changes over time due to vibration of the wire electrode 104. The observed sensor measurements 504 may represent multiple frames or a set of images acquired by the camera 126. The set of images shows the shadow of the section of the wire electrode 104 as it moves within the field of view of the image sensor of the camera 126. For example, a first image 504A shows the position of the section of the wire electrode 104 at a first time point, a second image 504B shows the position of the section of the wire electrode 104 at a second time point, a third image 504C shows the position of the section of the wire electrode 104 at a third time point, and so on. Examples of illumination patterns generated based on the sensor measurements 504 observed by the camera 126 are further shown, for example, in FIGS. 6A and 6B.

[0051]

number

[0052] Diagram 600A further includes the duration 604 of the exposure of camera 126. Measurement operator 602 represents the sampling process performed by the combination of the illumination pattern of light source 124 and the exposure duration 604 of the image sensor of camera 126. The number of rows in measurement operator A 602 may indicate the number of images in the acquired set. An illumination pattern having a pseudo-random sequence of on and off light pulses is generated at the same time as the duration 604 of the exposure of camera 126.

[0053] FIG. 6B shows a diagram 600B illustrating a measurement operator "A" corresponding to an illumination pattern having a pseudo-random sequence of on and off light pulses beginning at a random time within the duration of the exposure 604 of the camera 126, according to some embodiments of the present disclosure. An example of the measurement operator "A" is shown as measurement operator 606 in FIG. 6B . The measurement operator 606 represents a sampling process performed by a combination of the illumination pattern of the light source 124 and the exposure time 604 of the image sensor of the camera 126. The number of rows in the measurement operator 606 may indicate the number of images in the acquired set. The illumination pattern having the pseudo-random sequence of on and off light pulses begins at a random time within the exposure duration 604 of the camera 126.

[0054] Generating such illumination patterns, such as those of Figures 6A and 6B, is necessary to determine the vibration of the wire electrode 104. Knowledge of the exact position and shape of the wire electrode 104, or cutting wire, is important to determine the vibration or tension of the wire electrode 104 and the quality of the cut. Typically, the frequency of the vibration of the wire electrode 104 is in the range of approximately 1 kilohertz (KHz), so a camera with an acquisition rate of at least 2000 fps is required to accurately determine the location of the wire electrode 104. Because such a high-speed camera would significantly increase the cost of the equipment, the wire EDM 116 utilizes a camera 126 with a standard frame rate along with time-coded illumination or aperture and computation to recover the vibration frequency and exact location of the wire electrode 104.

[0055] The position of the vibrating wire electrode 104 may be estimated as a super-temporal resolution problem from a low frame rate video or from a set of images acquired by the camera 126. <t f Encoded illumination pattern a for i∈{1 … m}, occupying a time segment of i ∈{0,1} n may be adopted.

[0056] The duration of the coded illumination pattern may correspond to the exposure or acquisition interval of a low-rate camera, such as camera 126, for which the coded illumination pattern may be active. Typically, the exposure or acquisition interval is effectively 1 / 2 second for each frame t, since camera 126 may need some time to reset and transmit data. f The duration of the

[0057]

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[0058]

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[0059]

number

[0060] 6A and 6B show two examples of measurement operator A, corresponding to the acquisition of a set of five video frames or images, with m=5, c=5, and n=100. In FIG. 6A, the white lines in the illumination pattern may indicate when strobe illumination is on. In such an example, every frame can be observed through a different pseudo-random illumination pattern. In FIG. 6B, illumination pattern a i is shown as a white line. In such an example, all exposures of the camera 126 are divided into five segments, with the first segment containing the illumination pattern. The remaining four segments may correspond to dead times in the camera exposure. Additionally, the effect of the measurement operator A on the oscillating series of wire electrodes 104 can be seen from FIGS. 7 and 8.

[0061] FIG. 7 shows a diagram 700 illustrating a set of images 702 of a moving wire electrode 104 acquired by a camera 126, according to some embodiments of the present disclosure. For example, the set of images 702 or frames of video of the moving wire electrode 104 are acquired using measurement operator A shown in FIG. 6A . The set of images 702 shows the blurred areas formed by each image of the wire electrode 104 as it moves through space while illuminated using a time-coded illumination pattern. The set of images 702 may include a first image 702A, a second image 702B, a third image 702C, a fourth image 702D, and a fifth image 702E. In some embodiments, the set of images 702 may be identical to the sensor measurements 504 of the camera 126.

[0062] A set of images 702, such as a first image 702A, a second image 702B, a third image 702C, a fourth image 702D, and a fifth image 702E, are acquired from the vibrating wire electrode 104, with measurements corresponding to m=5, c=5, and n=100. Every frame, or one image in the set of images 702, may consist of 10x151 pixels. The set of images 702 shows the blurring effect that results from observing the true vibrating wire electrode 104 through measurement operator A. The diagram 700 further includes a graph 704 showing the average of the five observed frames, such as the set of images 702.

[0063] FIG. 8 illustrates a diagram 800 depicting the continuous motion of a wire electrode 104 versus a set of sequential images 702 acquired by a camera, according to some embodiments of the present disclosure. The diagram 800 includes a vibration sequence U 802 (captured as a high frame rate video) of the wire electrode 104 compared to a measurement sequence Y 804 observed through measurement operator A. The last row 806 of measurement sequence Y 804 may correspond to an average of the five observed video frames illustrated by graph 704. An example set of five video frames captured through operator A of vibration sequence U is shown. When the wire electrode 104 is moving, measurement operator A introduces blurring artifacts. The average of the observed video frames may be added to the measurements as part of measurement operator A to aid in speeding up the reconstruction of the direct current (DC) component of the acquired vibration video.

[0064] As can be seen from equation (1), the measurement operator A can operate in the same way on all pixels of a video, such as the vibration sequence U. Note that the problem in equation (1) can be a very unique problem, since there may be infinitely many solutions for the vibration sequence U for the system. However, because the wire electrode 104 is moving or vibrating within a narrow frequency band, an accurate reconstruction of the true matrix of the vibration sequence U can be obtained by exploiting sparsity in the frequency domain.

[0065]

number

[0066] Since intensity fluctuations in the acquired image set or video are driven by vibrations of the wire electrodes 104, the locations of significant non-zero coefficients in the columns of matrix X are likely to be in the same frequency bin. As a result, a joint sparsity structure can be exploited in matrix X, which may enable the exploitation of multiple measurement vectors, such as columns of the measurement sequence Y contributed by different pixels in the observed video, to recover the support of the row norm of matrix X.

[0067]

number

[0068]

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[0069] 9 shows an exemplary block diagram 900 of steps used in compressed sensing using sparse reconstruction techniques to recover the positions of at least segments of a wire electrode 104, according to an embodiment of the present disclosure. Block diagram 900 includes steps 902-916.

[0070] In step 902, a set of images or video may be buffered in matrix Y by collecting the images or video together as shown in measurement sequence Y 804. The set of images 702 may be acquired from camera 126.

[0071] In step 904, outliers caused by bubbles in the working fluid 120 may be removed. In one embodiment, the bubble shadow is removed from the shadow of the wire electrode 104 moving across the image sensor, as captured in the set of images 702 acquired from the camera 126. This may generate a set of bubble-free images of the wire electrode 104 encoded with the coded illumination pattern. Details of generating the set of bubble-free images are provided, for example, in FIGS. 10 and 11 .

[0072] In step 906, the pixel dimensions of the set of bubble-free images obtained in step 904 may be compressed to equal the number of images in the set of images 702 by multiplying the pixel dimensions by a Gaussian random matrix, outputting a set of compressed images. For example, the dimensionality of the problem in equation (2) may be compressed.

[0073]

number

[0074] In step 908, a group 1-norm sparse retrieval problem may be solved to calculate the spectral matrix of the wire electrode 104 from the set of compressed images. For example, a group 1-norm sparse retrieval problem or a sparse least squares problem may be solved to calculate the compressed spectral matrix. The wire electrode 104 may vibrate while moving across the image sensor of the camera 126.

[0075]

number

[0076] Further details regarding solving the group 1-norm sparse recovery problem are provided, for example, in FIG.

[0077]

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[0078]

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[0079]

number

[0080] In step 912, a reduced set of frequency bins corresponding to the location of the row of the spectral matrix containing the largest Euclidean norm is identified. The compressed spectral matrix may be used to identify the support of the joint sparse signal X.

[0081]

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[0082]

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[0083]

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[0084]

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[0085] At step 916, positions of at least segments of the wire electrode 104 may be output from the high temporal resolution set 702 of reconstructed wire electrode 104 motion images. The output positions, such as positions 918 of at least segments of the wire electrode 104, indicate vibrations of the wire electrode 104 over time.

[0086] FIG. 10 illustrates the presence of bubbles in the machining fluid 120 around the wire electrode 104 of a wire EDM 116, according to an embodiment of the present disclosure. In a practical wire EDM 116 scenario, the wire electrode 104 may vibrate within the machining fluid 120, which may help lubricate and cool the mechanical components. The presence of the machining fluid 120 and the vibration of the wire often results in the generation of bubbles 1002, such as gas bubbles, moving within the machining fluid 120. Such bubbles 1002 may be captured by a video camera, such as camera 126, where their movement introduces spectral components that contaminate the spectrum of a purely vibrating wire electrode 104. Fortunately, the movement of the bubbles 1002 is not periodic, and their appearance in the captured video is generally transient.

[0087]

number

[0088] FIG. 11 shows a diagram 1100 illustrating the generation of a set of bubble-free images 1102 from a set of images 702 acquired from a camera 126 according to an embodiment of the present disclosure.

[0089] In one embodiment, generating the set of bubble-free images 1102 by removing the shadows of the bubbles 1002 from the set of images 702 acquired from the camera 126 is performed by solving a robust principal component analysis (PCA) problem. The robust PCA problem may further include modeling the set of images 702 as consisting of low-rank matrix elements and sparse matrix elements 1104. The low-rank matrix elements correspond to the vibrating wire electrode 104 without bubbles 1002 (such as the set of bubble-free images 1102), and the sparse matrix elements 1104 correspond to bubbles. The low-rank matrix elements may be output as the set of bubble-free images 1102.

[0090]

number

[0091] In the PCA approach, a robust PCA problem may be first solved to calculate the low-rank matrix L. Furthermore, a support estimation may be performed and a video restoration step may be performed after replacing the matrix Y with the low-rank matrix L.

[0092]

number

[0093] In some embodiments, solving a group 1-norm sparse recovery problem may be required to calculate the spectral matrix X of the wire electrode 104 from a set of compressed images. For example, the difference between the set of compressed images and a composite set of compressed images formed by the product of the spectral matrix of the vibrating wire electrode 104 and a Fourier transform applied in the upsampled time domain may be minimized. This minimization may be described by the use of equation (4), described in step 908 of FIG. 9 .

[0094] Furthermore, the difference minimization may be regularized by summing the Euclidean norms of the rows of the spectral matrix of the vibrating wire electrode 104. Details of the difference minimization are further provided in Algorithm 1, e.g., in step 910 of Figure 9.

[0095] Furthermore, a spectral matrix in the upsampled time domain, which may be sparse in frequency bins by having a small number of non-zero row norms, may be output. Details of the output of the spectral matrix are further provided in Algorithm 1, e.g., in step 910 of FIG. 9.

[0096] 12 shows an exemplary block diagram 1200 for determining at least the frequency and amplitude of vibration of the wire electrode 104, according to an embodiment of the present disclosure. The design of the illumination pattern and corresponding sensing matrix A plays an important role in determining the reconstruction quality of the super-resolution video captured by the camera 126. In particular, the instantiation and length of the encoded illumination pattern within the duration of the exposure of a video frame can affect the ability to determine accurate signal support.

[0097] Encoded lighting pattern a i If A is triggered at equal intervals, the measurement operator A will exhibit a sparse spectrum in the frequency domain and may be indistinguishable from the support of the recovered signal U. Alternatively, the strobe sequence may be allowed to occupy random starting positions in the frame exposure interval. Such an approach may help to destroy the periodicity of the sampling operator, resulting in a relatively flat spectrum that may not exhibit high-value coefficients at harmonic frequencies.

[0098] In some embodiments, the controller 130 may be further configured to determine a frequency 1202 of vibration of the wire electrode 104 by converting the reduced set of frequency bins into physical frequency values. The controller 130 may receive as input the position 918 of at least the segment of the wire electrode 104. The controller 130 may divide the segment of the wire electrode 104 into one or more time blocks 1204. The frequency 1202 of vibration of the wire electrode 104 may be determined based on the number of oscillations or peaks 1206 of the wire electrode 104 in each time block of the one or more time blocks 1204. For example, the determined frequency may be equal to the number of oscillations of the wire electrode 104.

[0099] The controller 130 may further be configured to determine an amplitude 1208 of the vibration of the wire electrode 104 by converting the position of the segments of the wire electrode 104 on the sensor array into a physical position of the wire electrode 104 according to the geometry of the components of the wire electrode position measurement system 122. The amplitude 1208 may be determined based on a calculation of the length 1210 of the segments of the wire electrode 104.

[0100] In one embodiment, the controller 130 may be further configured to determine a curvature 1212 of the vibration of the wire electrode 104. The curvature 1212 may be determined based on the position of the peaks 1206 of the wire electrode 104 in each time block of the one or more time blocks 1204. To control the quality of the cut, the exact frequency 1202, amplitude 1208, and curvature 1212 of the wire electrode 104 are determined from the reconstructed high-temporal resolution video of the wire electrode 104.

[0101] 13 illustrates an exemplary block diagram 1300 for reducing the likelihood of wire electrode 104 breaking during rough machining, according to an embodiment of the present disclosure. Wire breakage is the most common problem in rough machining techniques. If the amplitude of wire vibration increases or the frequency of vibration varies significantly during processing, the process may become unstable and the likelihood of wire breakage may increase.

[0102] In some embodiments, the controller 130 may be further configured to reduce the likelihood of the wire electrode breaking during rough machining by performing control actions.

[0103] In step 1302, the controller 130 may estimate the stability of the wire electrode 104. Control action may be based on an analysis of the determined frequency 1202 and amplitude 1208 of the vibration of the wire electrode 104 for significant changes.

[0104] In step 1304, a control action may be based on detecting one or more significant changes, or may be based on reducing the processing energy input to the wire electrode 104, for example, based on the determined frequency 1202 and amplitude 1208 of vibration of the wire electrode 104. In step 1306, the reduced processing energy is output by the controller 130.

[0105] In step 1308, a control action may be based on detecting one or more significant changes, or may be based on reducing the processing speed of the workpiece 102 and transport system 118, for example, based on the determined frequency 1202 and amplitude 1208 of the vibration of the wire electrode 104. In step 1310, the reduced processing speed of the workpiece 102 and transport system 118 may be output by the controller 130. Additionally, the machining energy is controlled by controlling the machining current and dwell time.

[0106] 14 shows an exemplary block diagram 1400 for controlling the amount of straightness and size error of the cut during skimming, according to an embodiment of the present disclosure. In some embodiments, the controller 130 may be further configured to control the amount of straightness and size error of the cut during skimming by performing a control action.

[0107] Skimming requires less processing energy than roughing, so there is less chance of wire breakage, but there may be concerns about deterioration of straightness, streaks, and size errors. The controller 130 may use the frequency 1202, curvature 1212, and amplitude 1208 to control the processing power and processing speed.

[0108] It should be noted that the straightness refers to the vertical straightness of the machined surface of the workpiece 102, and the streaks refer to the streaks that occur on the machined surface. Since the shape of the amplitude 1208 of the wire vibration is transmitted to the workpiece 102, the straightness may be predicted by the amplitude 1208 of the wire vibration. When the amplitude 1208 of the wire vibration is small, the straightness improves, and when the vibration is large, the straightness deteriorates. Because the straightness is caused by such a physical phenomenon, it may be further controlled by the processing speed and electrical conditions.

[0109] In step 1402, a control action may be performed based on an analysis of the amplitude 1208 of the wire vibration to detect that the amplitude 1208 is greater than a threshold. For example, the threshold may be determined based on an acceptable limit for vibration of the wire electrode 104. An amplitude 1208 determined to be greater than the threshold may determine that the vibration of the wire electrode 104 is high and may result in an inaccurate cut. In one embodiment, the controller 130 may receive the frequency 1202, the curvature 1212, and the amplitude 1208 as inputs to control the amount of straightness and size error of the cut during skimming.

[0110] In step 1406, the control action may be based on controlling the processing power. In one embodiment, the control action may be based on increasing the machining energy when the wire electrode 104 moves farther from the workpiece 102 and decreasing the machining energy when the wire electrode 104 moves closer to the workpiece 102. The accuracy of the size error may be improved by controlling the machining energy. In step 1406, the controlled processing power may be output from the controller 130.

[0111] In step 1408, the control action may be based on controlling the processing speed of the workpiece 102 and the transport system 118. In one embodiment, the action may be based on slowing down the processing speed of the workpiece 102 and the transport system 118 to reduce the amplitude 1208 of the vibration of the wire electrode 104 when the shape of the wire electrode 104 is estimated to be convex. When the processing speed is slowed, the explosive force of the discharge weakens due to a lower discharge frequency, and the electrostatic attraction between the wire electrode 104 and the workpiece 102 becomes dominant, causing the wire electrode 104 to bend toward the workpiece 102, resulting in a concave straightness of the machined surface. In another embodiment, the action may be based on increasing the processing speed of the workpiece 102 and the transport system 118 to increase the amplitude 1208 of the vibration of the wire electrode 104 when the shape of the wire electrode 104 is estimated to be concave. When the processing speed is increased, the discharge frequency becomes higher, and the explosive force caused by the discharge acts more strongly on the wire electrode 104, causing the wire electrode 104 to bend in a direction away from the workpiece 102, and the machined surface has a convex straightness accuracy. In step 1410, the controlled processing speed may be output by the controller 130.

[0112] Therefore, by controlling the processing speed and electrical conditions according to the mode of wire vibration, it is possible to improve straightness accuracy. The same machining control as for straightness can be used to improve dimensional error accuracy. Furthermore, with regard to dimensional error, it may be possible to change the machining trajectory itself based on the measured wire position so that it matches the desired shape.

[0113] 15 shows an exemplary block diagram 1500 for controlling streaks of cut during skimming, according to an embodiment of the present disclosure. In some embodiments, the controller 130 may be further configured to control streaks of cut during skimming by performing a control action.

[0114] In step 1502, control action may be based on analyzing the amplitude 1208 of the vibration of the wire electrode 104 to detect vibration fluctuations. To control streaks, it may be necessary to suppress the vibration component of the wire electrode 104. To suppress the vibration component of the wire electrode 104, machining controls such as suppressing process speed fluctuations or increasing wire tension may be considered, as described in later steps. In one embodiment, the controller 130 may receive the frequency 1202, curvature 1212, and amplitude 1208 as inputs for controlling streaks.

[0115] In step 1504, the control action may be based on controlling the machining energy. In one embodiment, the control action may be based on increasing the machining energy when the wire electrode 104 moves farther from the workpiece 102 and decreasing the machining energy when the wire electrode 104 moves closer to the workpiece 102. In step 1506, the controlled machining energy may be output by the controller 130.

[0116] In step 1508, the control action may be based on controlling the process speed of the workpiece 102 and the transport system 118. In one embodiment, the control action may be based on, for example, reducing the process speed of the workpiece 102 and the transport system 118 to reduce the amplitude 1208 of the vibration of the wire electrode 104 when the shape of the wire electrode 104 is estimated to be convex. In another embodiment, the control action may be based on increasing the process speed of the workpiece 102 and the transport system 118 to increase the amplitude 1208 of the vibration of the wire electrode 104 when the shape of the wire electrode 104 is estimated to be concave.

[0117] Further, control by the controller 130 of the energy source 108 based on the position of at least a segment of the wire electrode 104 restored at a restoration rate is provided, for example, in FIG.

[0118] 16 illustrates a waveform 1600 generated by the energy source 108, according to some embodiments of the present disclosure. The energy source 108 is further configured to generate the waveform 1600 consisting of a sequence of on-time voltage pulses and off-time voltage pulses. The generated waveform 1600 may show voltage on the x-axis and time on the y-axis. The sequence of on-time and off-time voltage pulses includes alternating on-time voltage pulses 1602 and off-time voltage pulses 1604.

[0119] The process energy can be reduced by shortening the duration of the on-time voltage pulse or lengthening the duration of the off-time voltage pulse. A longer rest time or a shorter on-time voltage pulse results in a shorter on-time per unit time, which can lead to a reduction in process energy.

[0120] The processing energy can be increased by extending the duration of the on-time voltage pulse or shortening the duration of the off-time voltage pulse. Shortening the duration of the off-time voltage pulse reduces the off time per unit time, which can lead to increased processing energy.

[0121] The processing energy is kept constant and voltage feedback control is applied to control the processing speed of the workpiece 102. Voltage feedback control is employed to control the speed so that the machining voltage is kept constant. Furthermore, the processing speed may be controlled so that a lower target value for the machining voltage results in a faster processing speed and an increase in the machining voltage results in a slower processing speed. Additionally, the current may be controlled to control the machining energy.

[0122] FIG. 17 shows a flowchart 1700 illustrating a method for machining a workpiece 102 according to some embodiments of the present disclosure.

[0123] In step 1702, the method for machining the workpiece 102 may include transporting a wire electrode 104 near the workpiece 102. The wire electrode 104 may be utilized to machine the workpiece 102. Details about transporting the wire electrode 104 near the workpiece 102 are provided, for example, in FIG. 1B.

[0124] In step 1704, the method for machining the workpiece 102 may include generating an electrical discharge between the wire electrode 104 and the workpiece 102. The electrical discharge may be required to remove metal from the workpiece 102. Details about generating an electrical discharge between the wire electrode 104 and the workpiece 102 are provided, for example, in FIG. 1B.

[0125] In step 1706, the method for machining the workpiece 102 may include illuminating the wire electrode 104 with a coded illumination pattern. The coded illumination pattern can generate a constant illumination pattern or a pseudo-random sequence of on and off light pulses. Details about generating a constant illumination pattern or a pseudo-random sequence of on and off light pulses are provided, for example, in FIGS. 1B, 4B, and 4C.

[0126] In step 1708, the method for machining the workpiece 102 may include acquiring a set of images 702 showing the wire electrode illuminated with the coded illumination pattern at different positions. The set of images 702 may be captured by the camera 126. Details about acquiring the set of images 702 are provided, for example, in FIG. 1B .

[0127] In step 1710, the method for machining the workpiece 102 may include utilizing compressed sensing with sparse reconstruction techniques to reconstruct positions of at least segments of the wire electrode 104 at a reconstruction rate that is higher than the acquisition rate of the camera 126 that acquires the set of images 702. Details about reconstructing positions of at least segments of the wire electrode 104 are provided, for example, in FIGS.

[0128] In step 1712, the method for machining the workpiece 102 may include controlling at least one of a transport system 118 that transports the wire electrode 104 near the workpiece 102 and an energy source 108 that generates the electrical discharge based on the position of at least the segment of the wire electrode 104 restored at the restoration rate. Details about controlling the transport system 118 and the energy source 108 are provided, for example, in Figures 1B, 14, 15, and 16.

[0129] Numerous modifications and other embodiments of the inventions described herein will occur to one skilled in the art to which the inventions pertain having the benefit of the teachings presented in the above description and the associated drawings. It is to be understood that the invention is not limited to the particular embodiments disclosed, and that modifications and other embodiments are intended to be included within the scope of the appended claims. In addition, while the above description and the associated drawings describe example embodiments in the context of certain example combinations of elements and / or functions, it is to be recognized that different combinations of elements and / or functions may be provided by alternative embodiments without departing from the scope of the appended claims. In this regard, combinations of elements and / or functions different from those expressly set forth in the above description are also contemplated, for example, as may be set forth in some of the appended claims. Although specific terms have been used herein, these terms are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

1. 1. A wire electric discharge machine (EDM) for machining a workpiece, the wire EDM comprising: a transport system for contacting one or a combination of a wire electrode and the workpiece and transporting the wire electrode and the workpiece close together; an energy source configured to generate an electrical discharge between the wire electrode and the workpiece; a wire electrode position measurement system, a light source configured to illuminate the wire electrodes with a coded illumination pattern; a camera having an image sensor positioned to capture a set of images showing the wire electrode illuminated with the coded illumination pattern at different positions, the wire EDM further comprising: a processor configured to reconstruct positions of at least segments of the wire electrode at a reconstruction rate higher than an acquisition rate of the camera by utilizing compressed sensing with sparse reconstruction; a controller configured to control at least one of the delivery system and the energy source based on a position of at least a segment of the wire electrode restored at the restoration rate.

2. the energy source is further configured to generate a waveform consisting of a sequence of on-time voltage pulses and off-time voltage pulses; processing energy is reduced by shortening the duration of the on-time voltage pulse or lengthening the duration of the off-time voltage pulse; the processing energy is increased by extending the duration of the on-time voltage pulse or shortening the duration of the off-time voltage pulse; The wire EDM of claim 1 , wherein the process energy is held constant and voltage feedback control is applied to control the process speed of the workpiece.

3. the image sensor is a two-dimensional (2D) sensor that captures the segment of the wire including a plurality of points, and the coded illumination pattern of the light source is configured to generate a pseudo-random sequence of on and off light pulses; a duration of each pulse in the pseudo-random sequence of on and off light pulses is less than or equal to a Nyquist sampling rate of a frequency of vibration of the wire electrode; 10. The wire EDM of claim 1, wherein a total duration of the pseudo-random sequence of on and off light pulses is less than or equal to a duration of a frame exposure of the camera.

4. the light source and the camera of the wire electrode position measuring unit are disposed on both sides of the wire electrode; 2. The wire EDM of claim 1, wherein the image sensor of the camera is configured to acquire a set of images of a sum of shadows of the wire electrode encoded by the illumination pattern as the wire electrode moves across the image sensor of the camera.

5. The compressed sensing with sparse recovery is buffering the set of images acquired from the camera; generating a set of bubble-free images of the wire electrode encoded with the coded illumination pattern by removing a shadow of a bubble from a shadow of the wire electrode moving across the image sensor captured in the set of images acquired from the camera; compressing the pixel dimensions of the set of bubble-free images by multiplying the pixel dimensions by a Gaussian random matrix to equal the number of images in the set of images, and outputting a set of compressed images; and computing a spectral matrix of the wire electrode from the set of compressed images by solving a Group 1-norm sparse recovery problem, wherein the wire electrode vibrates while moving across the image sensor, and the compressive sensing with sparse recovery further comprises: identifying a reduced set of frequency bins corresponding to the location of the row of the spectral matrix that has the largest Euclidean norm; reconstructing a high temporal resolution set of images of the wire electrode movement with a spatial resolution equal to the spatial resolution of the image sensor of the camera by solving a least squares reconstruction problem using the reduced set of frequency bins; and outputting positions of at least the segments of the wire electrode from a high time resolution set of reconstructed images of the wire electrode movement.

6. Removing the shadows of bubbles from the set of images acquired from the camera to generate a set of bubble-free images is performed by solving a robust principal component analysis problem, which further includes: modeling the set of images as consisting of low-rank matrix elements and sparse matrix elements, the low-rank matrix elements corresponding to the vibrating wire electrode without bubbles and the sparse elements corresponding to the bubbles; and The wire EDM of claim 5 including outputting the low-rank matrix elements as the set of bubble-free images.

7. Solving the group 1-norm sparse retrieval problem minimizing the difference between the set of compressed images and a composite set of compressed images formed by the product of a spectral matrix of the vibrating wire electrode and a Fourier transform applied in the upsampled time domain; regularizing the minimization of the difference by the sum of the Euclidean norms of the rows of the spectral matrix of the vibrating wire electrode; and outputting the spectral matrix in an upsampled time domain that is sparse in the frequency bins by having a small number of non-zero row norms.

8. The controller further comprises: the frequency of vibration of the wire electrode; and and determining at least one of an amplitude of vibration of the wire electrode; the frequency of vibration of the wire electrode is determined by converting a reduced set of frequency bins into physical frequency values; 2. The wire EDM of claim 1, wherein the amplitude of vibration of the wire electrode is determined by converting the position of a segment of the wire electrode on a sensor array into a physical position of the wire electrode according to the geometry of elements of the wire electrode position measuring unit.

9. The controller further comprises: analyzing the determined frequency and amplitude of vibration of the wire electrode for significant changes; reducing processing energy input to the wire electrode based on detection of one or more of the significant changes; 10. The wire EDM of claim 8, configured to reduce the likelihood of the wire electrode breaking during rough machining by performing one or more control actions based on detecting one or more of the significant changes and reducing a processing speed of the workpiece and the transport system.

10. The controller further comprises: analyzing the amplitude of the vibration of the wire and detecting that the amplitude is greater than a threshold; reducing a processing speed of the workpiece and the transport system to reduce an amplitude of vibration of the wire electrode when the shape of the wire electrode is estimated to be convex; increasing the processing speed of the workpiece and the transport system to increase the amplitude of vibration of the wire electrode when the shape of the wire electrode is estimated to be concave; 10. The wire EDM of claim 8, configured to control the amount of cut straightness and size error during skimming by performing control actions based on varying machining energy as a function of the distance between the wire electrode and the workpiece.

11. The controller further comprises: analyzing the amplitude of vibration of the wire electrode to detect variations in the vibration; reducing a processing speed of the workpiece and the transport system to reduce an amplitude of vibration of the wire electrode when the shape of the wire electrode is estimated to be convex; increasing the processing speed of the workpiece and the transport system to increase the amplitude of vibration of the wire electrode when the shape of the wire electrode is estimated to be concave; 10. The wire EDM of claim 8, configured to control streaks of cut during skim machining by performing a control action based on varying machining energy as a function of the distance between the wire electrode and the workpiece.

12. 1. A method for machining a workpiece, the method comprising: transporting a wire electrode adjacent to the workpiece; generating an electric discharge between the wire electrode and the workpiece; illuminating the wire electrode with a coded illumination pattern; acquiring a set of images showing the wire electrode illuminated with the coded illumination pattern at different positions; Reconstructing positions of at least segments of the wire electrodes at a reconstruction rate that is higher than an acquisition rate of a camera that acquires the set of images by using compressed sensing with sparse reconstruction; based on the position of at least a segment of the wire electrode restored at the restoration rate; a transport system for transporting the wire electrode to the vicinity of the workpiece; and and controlling at least one of the energy sources that generates the discharge.

13. generating a waveform consisting of a sequence of on-time voltage pulses and off-time voltage pulses; processing energy is reduced by shortening the duration of the on-time voltage pulse or lengthening the duration of the off-time voltage pulse; the processing energy is increased by extending the duration of the on-time voltage pulse or shortening the duration of the off-time voltage pulse; 13. The method of claim 12, wherein the processing energy is kept constant and a voltage feedback control is applied to control the processing speed of the workpiece.

14. generating a pseudo-random sequence of on and off light pulses; a duration of each pulse in the pseudo-random sequence of on and off light pulses is less than or equal to a Nyquist sampling rate of a frequency of vibration of the wire electrode; The method of claim 12 , wherein the total duration of the pseudo-random sequence of on and off light pulses is less than or equal to the duration of a frame exposure of the camera.

15. acquiring a set of images of the sum of shadows of the wire electrode encoded by the illumination pattern as the wire electrode moves across an image sensor of the camera; The method of claim 12 , wherein the light source and the camera of the wire electrode position measurement unit are positioned on either side of the wire electrode.

16. The compressed sensing with sparse recovery is buffering the set of images acquired from the camera; generating a set of bubble-free images of the wire electrode encoded with the coded illumination pattern by removing a shadow of a bubble from a shadow of the wire electrode moving across the image sensor captured in the set of images acquired from the camera; compressing the pixel dimensions of the set of bubble-free images by multiplying the pixel dimensions by a Gaussian random matrix to equal the number of images in the set of images, and outputting a set of compressed images; and computing a spectral matrix of the wire electrode from the set of compressed images by solving a Group 1-norm sparse recovery problem, wherein the wire electrode vibrates while moving across the image sensor, and the compressive sensing with sparse recovery further comprises: identifying a reduced set of frequency bins corresponding to the location of the row of the spectral matrix that has the largest Euclidean norm; reconstructing a high temporal resolution set of images of the wire electrode movement with a spatial resolution equal to the spatial resolution of the image sensor of the camera by solving a least squares reconstruction problem using the reduced set of frequency bins; and outputting the positions of at least the segments of the wire electrode from a high temporal resolution set of reconstructed images of the wire electrode movement.

17. Removing bubble shadows from the set of images to generate a set of bubble-free images further includes solving a robust principal component analysis problem, the solving comprising: modeling the set of images as consisting of low-rank matrix elements and sparse matrix elements, the low-rank matrix elements corresponding to the vibrating wire electrode without bubbles and the sparse elements corresponding to the bubbles; and The method of claim 16 , comprising outputting the low-rank matrix elements as the set of bubble-free images.

18. Solving the group 1-norm sparse retrieval problem minimizing the difference between the set of compressed images and a composite set of compressed images formed by the product of a spectral matrix of the vibrating wire electrode and a Fourier transform applied in the upsampled time domain; regularizing the minimization of the difference by the sum of the Euclidean norms of the rows of the spectral matrix of the vibrating wire electrode; and outputting the spectral matrix in an upsampled time domain that is sparse in the frequency bins by having a small number of non-zero row norms.

19. the frequency of vibration of the wire electrode; and determining at least one of the amplitude of vibration of the wire electrode; the frequency of vibration of the wire electrode is determined by converting a reduced set of frequency bins into physical frequency values; 13. The method of claim 12, wherein the amplitude of vibration of the wire electrode is determined by converting the position of a segment of the wire electrode on a sensor array into a physical position of the wire electrode according to the geometric shape of an element of a wire electrode position measuring unit.

20. 1. A non-transitory computer readable medium storing computer executable instructions for machining a workpiece, the computer executable instructions comprising: transporting the wire electrode adjacent to the workpiece; generating an electric discharge between the wire electrode and the workpiece; illuminating the wire electrode with a coded illumination pattern; acquiring a set of images showing the wire electrode illuminated with a coded illumination pattern at different positions; Reconstructing positions of at least segments of the wire electrodes at a reconstruction rate that is higher than an acquisition rate of a camera that acquires the set of images by using compressed sensing with sparse reconstruction; based on the position of at least a segment of the wire electrode restored at the restoration rate; a transport system for transporting the wire electrode to the vicinity of the workpiece; and and controlling at least one of the energy sources that generate the discharge.

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