System and method for controlling a wire electrical discharge machining 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 (EDM), and more specifically to a method for controlling a wire EDM for machining a workpiece. Background Art

[0002] Electrical discharge machining (EDM) is a metal manufacturing process that obtains a desired shape of a metal workpiece by using discharges (or sparks). Material is removed from the metal workpiece by a series of rapidly repeated discharges between two electrodes separated by a dielectric liquid and to which a voltage is applied. One of the electrodes is a tool electrode or tool, and the other is a workpiece electrode or workpiece. The manufacturing process relies on the tool and the workpiece not being in physical contact with each other.

[0003] A wire electrical discharge machine (wire EDM) is a precision cutting device that uses the EDM manufacturing process to machine workpieces. The tool electrode of a wire EDM is a wire, and the workpiece functions as the second electrode. When the voltage between the wire and the workpiece increases, the electric field strength in the space between the wire and the workpiece increases, dielectric breakdown of the dielectric liquid occurs, and an arc is generated. As a result, material is removed from the electrodes, i.e., the wire and the workpiece.

[0004] Typically, in order to avoid wire wear that causes wire breakage, the wire is wound between two spools such that the effective portion of the wire is constantly changed. However, the occurrence of discharges and the relatively small diameter of the wire cause wire vibration, while the wire vibration is damped on two supports that limit the vibration length of the wire.

[0005] Generally, wire EDM systems have configurations 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 where the wire returns along the same path after rough cutting is complete. Therefore, skim cutting requires greater precision than rough cutting to achieve a more refined and accurate cut with surface integrity. In particular, although the purposes of rough cutting and skim cutting are different, the accuracy of the cutting in both depends on the vibration of the wire.

[0006] Traditionally, estimating such vibrations with the desired accuracy has been difficult due to the disturbances and various forces acting within the wire EDM. In addition, one or more conventional methods use an optical system to focus reflected light onto a one-dimensional sensor, which detects unidirectional vibrations of the wire as changes in the position of the sensor's imaging point. While such configurations allow for the detection of small wire vibrations, the vibration estimation results are inaccurate for controlling the wire EDM for precise machining processes.

[0007] Therefore, to address the above problem, a method is needed to estimate wire vibration with sufficient accuracy to maintain the precision of wire EDM during rough machining and skimming processes. [Overview of the Initiative]

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

[0009] Some embodiments are based on the understanding that vibrations of a wire electrode can be reconstructed in the frequency domain by detecting changes in the position of the imaging point of a camera's one-dimensional sensor. However, such reconstruction requires several assumptions. For example, one assumption is that the frequency of the timing of the linear position 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, as well as the machining of the workpiece, interfere with the wire electrode with multiple unknown frequency harmonics.

[0010] Therefore, controlling the machining of a workpiece based solely on vibration feedback determined on a straight line may provide insufficient information for control. Wire electrodes are soft continuum that deform significantly during machining. This deformation is transmitted to the machined surface of the workpiece, reducing workability. Thus, wire electrodes are affected by complex physical phenomena involving various factors such as explosions caused by electrical discharge and water pressure caused by the processing fluid, making it difficult to predict the behavior of wire electrodes. For this reason, it is necessary to estimate the physical behavior of wire electrodes to improve the control accuracy of wire EDM.

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

[0012] Some embodiments further rely on the understanding that the position of the wire electrode at different points in time can be reconstructed using a camera that observes the wire electrode in at least two dimensions (2D field of view: FoV). However, such solutions have several problems. For example, the vibration frequency of the wire electrode in a wire EDM is generally in the range of approximately 1 kilohertz (kHz), so accurately determining the position of the wire electrode would require a camera with an acquisition rate of at least 2000 frames per second (fps). Such a high-speed camera can significantly increase the cost of the wire EDM equipment. In addition, the discharge produces a wide, blurry white area that interferes with the acquisition of a 2D image. Moreover, bubbles or other transient objects can also form shadows that interfere with the acquisition of a 2D image. Therefore, the objective of some embodiments is to utilize compressed sensing with sparse reconstruction techniques to reduce the cost of using a wire EDM by eliminating the need for high-fps high-speed cameras, which can be expensive.

[0013] To this end, several embodiments are based on the realization of a wire EDM for machining a workpiece. The wire EDM comprises a transport system, such as pulleys, for contacting and moving the wire electrode and the workpiece, or a combination thereof, toward each other. The wire EDM further comprises an energy source configured to generate a discharge between the wire electrode and the workpiece. The EDM further comprises a wire electrode positioning system, which includes a camera having a light source configured to illuminate the wire electrode with an encoded illumination pattern, and an image sensor positioned to acquire a set of images showing the wire electrode at different positions illuminated by the encoded illumination pattern. The wire EDM further comprises a processor configured to restore the position of at least segments of the wire electrode at a restoration rate higher than the camera acquisition rate by utilizing compressed sensing with sparse restoration technique. The wire EDM further comprises a controller configured to control at least one of the transport system and the energy source based on the position of at least segments of the wire electrode restored at the restoration rate.

[0014] Some embodiments are based on the understanding 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. Processing energy is reduced by shortening the duration of the on-time voltage pulses or extending the duration of the off-time processing energy, and increased by extending the duration of the on-time voltage pulses or shortening the duration of the off-time voltage pulses. The processing energy is kept constant, and 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 understanding that the encoded 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 wire electrode vibrations. The total duration of the pseudo-random sequence of on and off light pulses is less than or equal to the duration of the camera frame exposure. By making the duration of each pulse in the sequence of on and off light pulses less than or equal to the Nyquist sampling rate of the frequency of the wire electrode vibrations, the cost of the camera can be reduced.

[0016] Some embodiments are based on the understanding that the light source and camera of the wire electrode positioning unit are positioned on both sides of the wire electrode. The camera's image sensor is configured to acquire a set of images of the sum of shadows of the wire electrode encoded by the illumination pattern as the wire electrode moves across the camera's image sensor. By acquiring a set of images of the sum of shadows, it is possible to determine whether the wire electrode is moving or vibrating.

[0017] Some embodiments are based on the understanding that compressed sensing using sparse restoration techniques involves buffering a set of images acquired from a camera. Compressed sensing using sparse restoration techniques further includes generating a set of bubble-free images of the wire electrode, encoded by an encoded illumination pattern, by removing bubble shadows from the shadows of the wire electrode moving across the image sensor, captured in the set of images acquired from the camera. By generating bubble-free images, spectral contamination of the purely vibrating wire electrode can be removed from the set of images. Compressed sensing using sparse restoration techniques further includes compressing the pixel dimensions of the set of bubble-free images to be equal to the number of images in the set of images by multiplying the pixel dimensions of the set of bubble-free images by a Gaussian random matrix, and outputting a set of compressed images. Compressed sensing using sparse restoration techniques further includes solving the Group 1-norm sparse restoration problem to compute the spectral matrix of the wire electrode from the set of compressed images. The wire electrode vibrates as it moves across the image sensor. Compressed sensing using sparse reconstruction techniques further includes identifying a reduced set of frequency bins corresponding to the row positions of a spectral matrix containing the maximum Euclidean norm. Compressed sensing using sparse reconstruction techniques further includes reconstructing a high-temporal-resolution set of images of wire electrode motion 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. Compressed sensing using sparse reconstruction techniques further includes outputting the positions of at least segments of the wire electrode from the reconstructed high-temporal-resolution set of images of wire electrode motion. 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 understanding that generating a set of bubble-free images by removing the shadows of bubbles from a set of images acquired from a camera is accomplished by solving a robust principal component analysis problem. The robust principal component analysis problem involves modeling the set of images as consisting of low-rank matrix components and sparse matrix components. The low-rank matrix components correspond to the vibrating wire electrodes without bubbles, and the sparse components correspond to bubbles. The robust principal component analysis problem further includes outputting the low-rank matrix components as a set of bubble-free images.

[0019] Some embodiments are based on the understanding that solving the Group 1-norm-sparse recovery problem involves minimizing the difference between a set of compressed images and a composite set of compressed images formed by the product of the spectral matrix of the oscillating wire electrode and the Fourier transform applied in the upsampled time domain. Solving the Group 1-norm-sparse recovery problem further involves regularizing the difference minimization by summing the row Euclidean norms of the spectral matrix of the oscillating wire electrode and outputting the spectral matrix in the upsampled time domain which is sparse in frequency bins by having a small number of non-zero row norms.

[0020] Some embodiments are based on the understanding that the controller is further configured to determine at least the frequency of the wire electrode vibration by converting a reduced set of frequency bins into physical frequency values. The controller is further configured to determine at least the amplitude of the wire electrode vibration by converting the position of the wire electrode segment on the sensor array into the physical position of the wire electrode, according to the geometric shape of the components of the wire electrode position measuring unit. The determined wire electrode vibration frequency and amplitude are used to control the wire EDM for precise machining of the workpiece.

[0021] Several embodiments are based on the understanding that the controller is configured to reduce the likelihood of wire electrode breakage during rough machining by performing control actions based on an analysis of significant changes in the frequency and amplitude of the determined wire electrode vibration, a reduction in the processing energy input to the wire electrode based on the detection of one or more significant changes, and a reduction in the processing speed of the workpiece and conveying system based on the detection of one or more significant changes. The reduction in processing energy input and the reduction in the processing speed of the workpiece and conveying system enable safe operation of the wire EDM.

[0022] Based on the understanding that some embodiments are further configured to control the straightness and size error of the cutting during skimming by having the controller perform control actions based on the following: analyzing the amplitude of wire vibration and detecting when the amplitude is greater than a threshold; reducing the amplitude of wire electrode vibration by reducing the processing speed of the workpiece and transport system when the shape of the wire electrode is estimated to be convex; increasing the amplitude of wire electrode vibration by increasing the processing speed of the workpiece and transport system when 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 improve the accuracy of skimming.

[0023] Some embodiments are based on the understanding that the controller is further configured to control cutting streaks during skimming by performing control actions based on: analyzing the amplitude of the vibration of the wire electrode to detect vibration fluctuations; reducing the processing speed of the workpiece and transport system to reduce the amplitude of the 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 transport system to increase the amplitude of the vibration of the wire electrode when 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 of cutting streaks during skimming can improve the accuracy of skimming.

[0024] Accordingly, several embodiments disclose methods for machining a workpiece. The method includes transporting a wire electrode near the workpiece. The method further includes generating a discharge between the wire electrode and the workpiece. The method further includes illuminating the wire electrode with an encoded illumination pattern. The method further includes acquiring a set of images showing the wire electrode illuminated with the encoded illumination pattern at different locations. The method further includes reconstructing the positions of at least segments of the wire electrode at a reconstruction rate higher than the acquisition rate of the camera acquiring the set of images by utilizing compressed sensing with sparse reconstruction technique. The method further includes controlling at least one of a transport system for transporting the wire electrode near the workpiece and an energy source for generating a 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 convey a wire electrode to the vicinity of a 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 an encoded illumination pattern. The computer-executable instructions are further configured to acquire a set of images showing the wire electrode illuminated with the encoded illumination pattern at different positions. The computer-executable instructions are further configured to reconstruct a position 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 using sparse reconstruction techniques. The computer-executable instructions are further configured to control at least one of a conveyance system that conveys the wire electrode to the vicinity of the workpiece and an energy source that generates the electrical discharge, based on the position of at least the segment of the wire electrode reconstructed at the reconstruction rate.

[0026] The present disclosure will be further described in the following detailed description with reference to a plurality of drawings, which are shown as non-limiting examples of specific embodiments of the present disclosure. Like reference numerals represent like parts in several of the drawings. The drawings shown are not necessarily to scale; rather, emphasis is generally placed on illustrating the principles of embodiments of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] [Figure 1A] FIG. 1 is a schematic diagram showing basic components of a wire electrical discharge machine (EDM) according to some embodiments of the present disclosure. [Figure 1B] FIG. 2 is a schematic diagram showing a wire EDM for machining a workpiece according to some embodiments of the present disclosure. [Figure 2]This figure shows inaccuracies that affect the quality of workpiece cutting in conventional wire EDMs, according to some embodiments of the present disclosure. [Figure 3A] A schematic diagram is shown illustrating the positions of various components of a wire electrode position measuring unit with respect to a wire electrode immersed in a processing fluid, according to some embodiments of the present disclosure. [Figure 3B] A schematic diagram of one of the images from a set of images acquired by a camera of a wire electrode position measurement unit according to some embodiments of the present disclosure is shown. [Figure 4A] The following are block diagrams illustrating, according to some embodiments of this disclosure, the control of a camera for determining trigger timing and the control of a light source for generating an illumination pattern. [Figure 4B] The diagram shows a certain illumination pattern generated by a light source, according to some embodiments of this disclosure. [Figure 4C] The diagram shows 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] This figure shows a pictorial representation of the position of a section of a wire electrode as it changes over time, and the corresponding sensor measurement observed by a camera, according to some embodiments of the present disclosure. [Figure 6A] The figure shows a measurement operator "A" corresponding to an illumination pattern having a pseudo-random sequence of on and off light pulses that begin at the same time as the camera exposure, according to some embodiments of the present disclosure. [Figure 6B] The figure shows a measurement operator "A" corresponding to an illumination pattern having a pseudo-random sequence of on and off light pulses that begin at random points in time within the exposure duration of the camera, according to some embodiments of the present disclosure. [Figure 7] The diagram shows a set of images of a moving wire electrode acquired by a camera according to some embodiments of the present disclosure. [Figure 8]A figure illustrating a comparison between the continuous motion of a wire electrode and a set of images acquired by a camera, according to some embodiments of this disclosure, is shown. [Figure 9] A concrete example block diagram is shown of a step used in compressed sensing using sparse restoration technique according to some embodiments of the present disclosure, for restoring the position of at least a segment of a wire electrode. [Figure 10] The diagram shows the presence of bubbles in the processing fluid around the wire electrode of a wire EDM according to some embodiments of this disclosure. [Figure 11] The diagram shows how, according to some embodiments of this disclosure, a set of bubble-free images is generated from a set of images acquired from a camera. [Figure 12] A concrete block diagram is shown for determining at least the frequency and amplitude of vibration of a wire electrode according to some embodiments of this disclosure. [Figure 13] A concrete example block diagram is shown of a method for reducing the possibility of wire electrode breakage during rough machining, according to some embodiments of this disclosure. [Figure 14] A concrete example block diagram is shown for controlling the straightness and size error of cuts during skimming, according to some embodiments of the present disclosure. [Figure 15] A concrete example block diagram for controlling cutting streaks during skimming, according to an embodiment of this disclosure, is shown. [Figure 16] This figure shows waveforms generated by an energy source according to some embodiments of the present disclosure. [Figure 17] This is a flowchart illustrating a method for machining a workpiece according to some embodiments of the present disclosure. [Modes for carrying out the invention]

[0028] (Detailed explanation) In the following description, numerous specific details are included for illustrative purposes to ensure a full understanding of this disclosure. However, it will be apparent to those skilled in the art that this disclosure can be implemented without these specific details. In other examples, apparatus and methods are shown in block diagram form solely for the purpose of avoiding obscuration of this disclosure. The intended modifications are those that may be made to the function and configuration of the elements, as described in the appended claims, without departing from the spirit and scope of the disclosed subject matter.

[0029] The terms “for example,” “for instance,” and “such as,” as used herein and in the claims, as well as the verbs “comprising,” “having,” and “including,” and each of these verbs in other forms, should be interpreted as open-ended, meaning that when used with an enumeration of one or more components or other items, the enumeration should not be considered to exclude any further components or items. The term “based on” means based at least partially. Furthermore, it should be understood that the style and terminology used herein are for illustrative purposes only and should not be considered restrictive. Any headings used herein are for convenience only and have no legal or restrictive effect.

[0030] Specific details are provided in the following description for a full understanding of the embodiments. However, those skilled in the art will understand that embodiments may be carried out without these specific details. For example, to avoid obscuring the embodiments with unnecessary details, systems, processes, and other elements in the disclosed subject matter may be shown as components in the form of block diagrams. In other examples, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the embodiments. Furthermore, similar reference numbers and names in different drawings refer to similar elements. (System Overview)

[0031] Figure 1A shows a schematic diagram 100A of a portion of a wire electrical discharge machine (EDM) according to some embodiments of the present disclosure. Schematic diagram 100A includes a workpiece 102, a wire electrode 104, a wire guide 106, and an energy source 108. Schematic diagram 100A further shows the direction of motion 110 of the workpiece 102 and the direction of motion 112 of the wire electrode 104. In different implementations, the EDM is configured to move either or a combination of the workpiece and / or the wire electrode itself. Therefore, in some embodiments, the machining speed is the relative speed between the wire and the workpiece. Schematic diagram 100A further shows the 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 single wire that can be used to manufacture the workpiece 102. The wire EDM utilizes a discharge 114 or spark to remove material from the workpiece 102 and obtain the desired shape of the workpiece 102. The wire electrode 104 acts as the first electrode, and the workpiece 102 acts as the second electrode. The wire electrode 104 and the workpiece 102 are separated by a dielectric liquid, and the application of a voltage from an energy source 108 generates a series of rapidly repeating 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 the motion direction 110, and the speed of movement of the workpiece 102 is the processing speed. The wire electrode 104 moves in the motion direction 112 for machining the workpiece 102, and the speed of movement of the wire electrode 104 is the feed rate of the wire electrode 104. The movement of the wire electrode 104 may be controlled via a wire guide 106. In addition, the generation of the discharge 114 and the relatively small diameter of the wire electrode 104 cause vibration of the wire electrode 104, while the vibration of the wire is damped on two supports that limit the length of the wire vibration. Details of the wire EDM and related components of this disclosure are further provided, for example, in Figure 1B.

[0034] Figure 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 may include a wire electrode 104, an energy source 108, a transport system 118, a machining fluid 120, and a wire electrode position measuring system 122. In some implementations, the transport system 118 is a wire bobbin configured to control the wire feed. In addition to or instead of this, in some embodiments, the wire feed rate 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 measuring 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 vibrations at a point in the wire. In some implementations, the image sensor is 2D, reconstructing sections of the wire that include multiple points. This implementation provides more accurate results. The wire EDM 116 may further include a processor 128 and a controller 130. In one embodiment, 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 conveying system 118 may include a pulley, also called a wire bobbin, which contacts one or both of the wire electrode 104 and the workpiece 102, and conveys the wire electrode 104 and the workpiece 102 toward each other. The conveying system 118 is configured to convey the wire electrode 104 toward the vicinity of the workpiece 102. The conveying system 118 may include a roll of the wire electrode 104, so that, if necessary, a portion of the wire electrode 104 is fed from the roll toward the workpiece 102. The wire electrode 104 and the workpiece 102 may be immersed in a processing fluid 120. In one embodiment, the processing fluid 120 may consist of either water or oil.

[0036] The energy source 108 is configured to generate a discharge 114 between the wire electrode 104 and the workpiece 102. When 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 dielectric breakdown of the dielectric liquid (such as the workpiece fluid 120) and generating an arc or discharge 114. As a result, material is removed from the electrodes. When the current stops, new liquid dielectric is introduced into the space between the electrodes, carrying away solid particles (or debris) and restoring the insulating properties of the dielectric liquid. Further addition of new liquid dielectric to the space between the electrodes is called flushing. After the current has flowed, the voltage between the electrodes recovers to the same level as before the dielectric breakdown, causing new liquid dielectric breakdown and repeating this cycle.

[0037] The wire electrode positioning system 122 includes a light source 124 configured to illuminate the wire electrode 104 with an encoded illumination pattern. In one embodiment, the light source 124 is a light-emitting diode (LED). In one or more embodiments, the wire electrode positioning system 122 may further include a lens 124A positioned in line of sight of the light source 124 to focus the light from the light source 124 toward the wire electrode 104. The wire electrode positioning 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 encoded illumination pattern at different positions. For example, the camera 126 may be positioned on the opposite side of the direction of the light source 124 to capture a set of images such that a segment of the wire electrode 104 is between the light source 124 and the image sensor of the camera 126. In one embodiment, the discharge 114 may produce a white, blurred area. The impact of the white, blurred areas in the acquired set of images may be reduced by generating an encoded lighting pattern that is in opposition to the white, blurred areas.

[0038] The processor 128 is configured 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 by utilizing compressed sensing with sparse reconstruction technique. The reconstruction rate can be defined as the rate at which the positions of at least segments of the wire electrode 104 are reconstructed by the processor 128. In addition, the acquisition rate can be defined as the rate at which the camera 126 acquires a set of images. Compressed sensing with sparse reconstruction technique is a computational technique that processes the acquired set of images using a computational technique that can enable the identification of the precise position of the wire electrode 104 by temporal upsampling of the position of the wire electrode 104 at a temporal sampling rate (or reconstruction rate) that matches or exceeds the Nyquist rate. The Nyquist rate can be associated with a sampling rate that may be equal to or twice the bandwidth of the frames (set of images, etc.) acquired by the camera 126. In this way, a set of images can be acquired at a low rate, i.e., a rate lower than the Nyquist rate. By acquiring sets of images at such low rates, the requirement for a potentially expensive high-frame-rate camera is eliminated, potentially reducing the cost of camera 126. Furthermore, compressed sensing with sparse reconstruction 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 reconstruction problem in order to not only determine the frequency of the vibration of the wire electrode 104 but also to reconstruct the high-frame-rate video. Such a solution can address disturbances caused by bubbles and / or small waves in the processing fluid 120 that have frequencies inconsistent with the sparsity of the vibration of the wire electrode 104. Further details of compressed sensing with sparse reconstruction are provided, for example, in Figure 10.

[0039] Returning to Figure 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 clean or smooth cutting of the workpiece 102 by determining the processing speed of the workpiece 102 and the amount of potential (or voltage) that can be applied during processing. The controller 130 may receive information regarding the position of the wire electrode 104 from the wire position measuring system 122. However, certain inaccuracies in the overall operation of the wire EDM 116 may impair the quality of cutting of the workpiece 102.

[0040] Figure 2 shows the inaccuracies that affect the quality of cutting of the workpiece 102 in the wire EDM 116. The wire EDM 116 may be configured to perform two types of cutting techniques: roughing and skimming. Roughing may involve roughly machining the workpiece 102. Skimming may involve additional work that allows the wire electrode 104 to return along the same path after roughing is complete. Therefore, skimming requires greater precision than roughing to achieve a finer and more accurate cut, along with surface integrity.

[0041] However, the quality of cutting the workpiece 102 may 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 cutting of the workpiece 102 may be affected, resulting in cutting inconsistencies. Furthermore, vibrations of the wire electrode 104 may cause streaks 204 to form in the workpiece 102. In addition, size errors 206 of the wire electrode 104 due to vibrations may result in an undesirable finished size of the workpiece 102. Moreover, wear and breakage of the wire electrode 104 due to vibrations may result in breaks 208 being observed in the wire electrode 104. The wire EDM 116 of this disclosure overcomes the above-listed inaccuracies by minimizing vibrations occurring in the wire electrode 104 using a wire position measurement system 122. Details of the wire EDM 116 that can control the vibration of the wire electrode 104 are further provided, for example, in Figures 3A to 17.

[0042] Figure 3A shows a schematic diagram 300A illustrating the positions of various components of a wire electrode position measuring system 122 relative to a wire electrode 104 immersed in a processing fluid 120, according to some embodiments of the present disclosure. The light source 124 and camera 126 of the wire electrode position measuring system 122 are positioned on both sides 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 shadows of the wire electrode 104 encoded by an illumination pattern as the wire electrode 104 moves across the image sensor 126A of the camera 126. The 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 may be positioned so that sections of the wire electrode 104 cut off the illumination. The positions where sections of the wire electrode 104 cut off the illumination can be acquired as the sum of shadows of the wire electrode 104 encoded by an illumination pattern.

[0043] Figure 3B shows a schematic diagram 300B of image 302, one of a set of images acquired by a camera 126 of a wire electrode position measuring system 122 according to some embodiments of the present disclosure. The camera 126 records the shadow 304 of the wire electrode 104 on the sensor surface (e.g., the indicated Y-axis). The shadow 304 can be formed by the illumination pattern incident on the wire electrode 104. Similarly, the sum of shadows such as shadow 304 is acquired in a set of images such as image 302.

[0044] Figure 4A shows a block diagram 400A for controlling a camera 126 to determine trigger timing and a light source 124 to generate an encoded illumination pattern, according to some embodiments of the present disclosure. A controller 130 may be connected to the light source 124. In one embodiment, the controller 130 may be connected to the light source 124 via an LED control unit 402. The controller 130 may be configured to trigger the encoded illumination pattern of the light source 124. The controller 130 may communicate with the LED control unit 402 to trigger the encoded illumination pattern of the light source 124.

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

[0046] Figure 4B shows Figure 400B illustrating a constant encoded illumination pattern 404 generated by a light source 124 according to some embodiments of the present disclosure. The constant encoded illumination pattern 404 may be generated during the period in which 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 with a duration of 0 to 0.5 milliseconds and an on-light pulse with a duration of 0.5 to 1 millisecond.

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

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

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

[0050] Figure 5 shows the position 502 of a section of the wire electrode 104 as it changes over time, and the corresponding sensor measurement 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 vibrations of the wire electrode 104. The observed sensor measurement 504 may represent a set of multiple frames or 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, the first image 504A shows the position of the section of the wire electrode 104 at a first time point, the second image 504B shows the position of the section of the wire electrode 104 at a second time point, the 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 measurement 504 observed by the camera 126 are further shown, for example, in Figures 6A and 6B.

[0051]

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[0052] Figure 600A further includes the exposure duration 604 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 602 may indicate the number of images in the acquired set. The illumination pattern, having a pseudo-random sequence of on and off light pulses, is generated at the same time as the exposure duration 604 of camera 126.

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

[0054] The generation of such illumination patterns, such as the illumination patterns in Figure 6A and Figure 6B, is necessary to determine the vibration of the wire electrode 104. Knowledge of the precise location and shape of the wire electrode 104 or cutting wire is important for determining the vibration or tension and cutting quality of the wire electrode 104. Typically, the vibration frequency 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 pinpoint the location of the wire electrode 104. Since such a high-speed camera would significantly increase the cost of the equipment, the wire EDM 116 uses a camera 126 with a standard frame rate along with time-coded illumination or aperture, and calculations, to recover the vibration frequency and precise location of the wire electrode 104.

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

[0056] The duration of the encoded illumination pattern may correspond to the exposure or acquisition interval of a low-rate camera, such as camera 126, during which the encoded illumination pattern may be active. Typically, the exposure or acquisition interval is actually each frame t, since camera 126 may require some time to send data as a reset. f The duration may be significantly less than that.

[0057]

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[0059]

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

[0061] Figure 7 shows Figure 700, which illustrates 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 of the moving wire electrode 104, or frames of video, are acquired using measurement operator A, shown in Figure 6A. The set of images 702 shows the blurred portion formed by each image of the wire electrode 104 as it moves through space while being 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 measurement 504 of the camera 126.

[0062] The set of images 702, such as the first image 702A, the second image 702B, the third image 702C, the fourth image 702D, and the fifth image 702E, is acquired from the vibrating wire electrode 104, with measurements corresponding to m=5, c=5, and n=100. Each frame, or one image in the set of images 702, may consist of 10 × 151 pixels. The set of images 702 shows the blurring effect resulting from observing the true vibrating wire electrode 104 through measurement operator A. Figure 700 further includes a graph 704 showing the average of the five observed frames, such as the set of images 702.

[0063] Figure 8 shows Figure 800, which illustrates a comparison of the continuous motion of a wire electrode 104 with a set of images 702 acquired by a camera, according to some embodiments of the present disclosure. Figure 800 includes a vibration sequence U802 of the wire electrode 104 (acquired as high frame rate video), which is compared with a measurement sequence Y804 observed through measurement operator A. The last row 806 of measurement sequence Y804 may correspond to the average of five observed video frames shown by graph 704. A set of five video frames captured through operator A of vibration sequence U is shown as an example. When the wire electrode 104 is moving, measurement operator A results in blurred artifacts. The average of the observed video frames may be added to the measurements as part of measurement operator A to help speed up the reconstruction of the DC component of the acquired vibration video.

[0064] As can be seen from equation (1), the measurement operator A can act in the same way on all pixels of the video, such as the vibration sequence U. Note that the problem in equation (1) can be very singular because there can be an infinite number of solutions for the vibration sequence U for the system. However, since the wire electrode 104 moves or vibrates within a narrow frequency band, the exact reconstruction of the true matrix of the vibration sequence U can be obtained by taking advantage of the sparsity in the frequency domain.

[0065]

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[0066] Since the intensity fluctuations in the acquired set of images or video are facilitated by the vibration of the wire electrode 104, the positions of significant non-zero coefficients in the columns of matrix X may be within the same frequency bin. As a result, a co-sparse structure can be utilized in matrix X, which may allow the utilization of multiple measurement vectors, such as columns of measurement sequence Y given by different pixels in the observed video, in order to restore support for the row norm of matrix X.

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[0069] Figure 9 shows a concrete example block diagram 900 of steps used in compressed sensing using sparse restoration technique to restore 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 to 916.

[0070] In step 902, a set of images or videos may be buffered into matrix Y by collecting the images or videos together, as shown in measurement sequence Y804. The set of images 702 may be acquired from camera 126.

[0071] In step 904, outliers caused by bubbles in the processing fluid 120 can be removed. In one embodiment, the shadows of bubbles are removed from the shadows of the wire electrode 104 moving across the image sensor, captured in a set of images 702 acquired from the camera 126. This makes it possible to generate a set of bubble-free images of the wire electrode 104 encoded by the encoded illumination pattern. Details of generating the set of bubble-free images are provided, for example, in Figures 10 and 11.

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

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[0074] In step 908, the spectral matrix of the wire electrode 104 can be calculated from the set of compressed images by solving the Group 1-norm-sparse recovery problem. For example, the compressed spectral matrix can be calculated by solving the Group 1-norm-sparse recovery problem or the sparse least squares problem. The wire electrode 104 may vibrate as it moves across the image sensor of the camera 126.

[0075]

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[0076] Further details regarding solving the Group 1-norm sparse recovery problem are provided, for example, in Figure 12.

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[0080] In step 912, identify the reduced set of frequency bins corresponding to the row positions in the spectral matrix containing the maximum Euclidean norm. The compressed spectral matrix may be used to identify support for the co-sparse signal X.

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

[0086] Figure 10 shows the presence of bubbles in the processing fluid 120 around the wire electrode 104 of a wire EDM 116 according to an embodiment of the present disclosure. In a real wire EDM 116 scenario, the wire electrode 104 may vibrate within the processing fluid 120, which can help lubricate and cool the mechanical components. The presence of the processing fluid 120 and the vibration of the wire often generate bubbles 1002, such as air bubbles, moving within the processing fluid 120. Since such bubbles 1002 can be captured by a video camera such as camera 126, their movement causes spectral components that contaminate the spectrum of the purely vibrating wire electrode 104. Fortunately, the movement of the bubbles 1002 is not periodic, and the occurrence of bubbles 1002 in the captured video is generally transient.

[0087]

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[0088] Figure 11 shows Figure 1100, which illustrates 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 a set of bubble-free images 1102 by removing the shadows of bubbles 1002 from a set of images 702 acquired from camera 126 is performed by solving a robust principal component analysis (PCA) problem. Furthermore, the robust principal component analysis problem may include modeling the set of images 702 as consisting of low-rank matrix components and sparse matrix components 1104. The low-rank matrix components correspond to the vibrating wire electrodes 104 without bubbles 1002 (such as the set of bubble-free images 1102), and the sparse matrix components 1104 correspond to the bubbles. The low-rank matrix components can be output as a set of bubble-free images 1102.

[0090]

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

[0092]

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[0093] In some embodiments, solving the group 1-norm sparse recovery problem may be necessary to compute 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 oscillating wire electrode 104 and the Fourier transform applied in the upsampled time domain may be minimized. This minimization may be described by using equation (4), as explained in step 908 of Figure 9.

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

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

[0096] Figure 12 shows a block diagram 1200 as a specific example 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 the corresponding sensing matrix A plays a crucial role in determining the restoration quality of the super-resolution video acquired by the camera 126. In particular, the instantiation and length of the encoded illumination pattern within the exposure duration of the video frame can affect its ability to determine accurate signal support.

[0097] Encoded lighting pattern a i If the strobes are triggered at equal intervals, the measurement operator A may exhibit a sparse spectrum in the frequency domain, which may be indistinguishable from the support of the reconstructed 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 break the periodicity of the sampling operator, resulting in a relatively flat spectrum that may not exhibit high coefficients at harmonic frequencies.

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

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

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

[0101] Figure 13 shows an exemplary block diagram 1300 for reducing the possibility of wire electrode 104 breakage during rough machining according to an embodiment of the present disclosure. In rough machining techniques, wire breakage is the most common problem. If the amplitude of wire vibration becomes large or the frequency of vibration fluctuates significantly during processing, the processing is considered to become unstable, which may increase the likelihood of wire breakage.

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

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

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

[0105] In step 1308, the control action may be based on the detection of one or more significant changes, or on a reduction in the processing speed of the workpiece 102 and the 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 the transport system 118 may be output by the controller 130. Furthermore, the machining energy is controlled by controlling the machining current and the pause time.

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

[0107] Regarding skimming, the processing energy is lower than that of roughing, so the possibility of wire breakage is low, but on the other hand, concerns may arise regarding deterioration of straightness, streaks, and size errors. The controller 130 may control the processing power and processing speed using frequency 1202, curvature 1212, and amplitude 1208.

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

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

[0110] In step 1406, the control action may be based on the control of the processing power. In one embodiment, the control action may be based on an increase in machining energy when the wire electrode 104 moves away from the workpiece 102, and a decrease in machining energy when the wire electrode 104 moves closer to the workpiece 102. The accuracy of the size error can 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, if the shape of the wire electrode 104 is estimated to be convex, the action may be based on reducing the processing speed of the workpiece 102 and the transport system 118 to reduce the amplitude of vibration 1208 in the wire electrode 104. Slowing down the processing speed reduces the explosive force due to the discharge as the discharge frequency decreases, 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, which may result in a concave straightness of the machined surface. In another embodiment, if the shape of the wire electrode 104 is estimated to be concave, the action may be based on increasing the processing speed of the workpiece 102 and the transport system 118 to increase the amplitude of vibration 1208 of the wire electrode 104. Increasing the processing speed increases the discharge frequency, and the explosive force from the discharge acts strongly on the wire electrode 104, causing the wire electrode 104 to bend away from the workpiece 102, resulting in a machined surface with 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 nature of wire vibration, the straightness accuracy can be improved. The same machining control used for straightness can also be used to improve dimensional error accuracy. Furthermore, regarding dimensional errors, it may be possible to modify the machining trajectory itself to match the desired shape based on the measured wire position.

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

[0114] In step 1502, the control action may be based on an analysis of the amplitude 1208 of the vibration of the wire electrode 104 to detect vibration fluctuations. To control the streak, 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 fluctuations in processing speed or increasing wire tension may be considered, as will be described in a later step. In one embodiment, the controller 130 may receive frequency 1202, curvature 1212, and amplitude 1208 as inputs for controlling the streak.

[0115] In step 1504, the control action may be based on the control of machining energy. In one embodiment, the control action may be based on an increase in machining energy when the wire electrode 104 moves away from the workpiece 102, and a decrease in 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 processing speed of the workpiece 102 and the transport system 118. In one embodiment, if the shape of the wire electrode 104 is estimated to be convex, the control action may be based on increasing 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. In another embodiment, if the shape of the wire electrode 104 is estimated to be concave, the control 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.

[0117] Furthermore, control of the energy source 108 by the controller 130, based on the position of at least segments of the wire electrode 104 restored at the restoration rate, is provided, for example, in Figure 16.

[0118] Figure 16 shows a waveform 1600 generated by an energy source 108 according to some embodiments of the present disclosure. The energy source 108 is further configured to generate a 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 voltage pulses and off-time voltage pulses includes alternating on-time voltage pulses 1602 and off-time voltage pulses 1604.

[0119] Processing energy is reduced by shortening the duration of the on-time voltage pulse or extending the duration of the off-time voltage pulse. A longer pause time or a shorter on-time voltage pulse duration reduces the on-time per unit time, which can lead to a reduction in processing energy.

[0120] 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 an increase in 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 remains constant. Furthermore, the processing speed may be controlled such that decreasing the target value of the machining voltage increases the processing speed, and increasing the machining voltage decreases the processing speed. In addition, the current may be controlled to control the machining energy.

[0122] Figure 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 the wire electrode 104 to the vicinity of the workpiece 102. The wire electrode 104 can be used to machine the workpiece 102. Details of transporting the wire electrode 104 to the vicinity of the workpiece 102 are provided, for example, in Figure 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 necessary to remove metal from the workpiece 102. Details of generating an electrical discharge between the wire electrode 104 and the workpiece 102 are provided, for example, in Figure 1B.

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

[0126] In step 1708, the method for machining the workpiece 102 may include obtaining a set of images 702 showing wire electrodes illuminated with encoded illumination patterns at different positions. The set of images 702 may be captured by a camera 126. Details on obtaining the set of images 702 are provided, for example, in Figure 1B.

[0127] In step 1710, the method for machining the workpiece 102 may include restoring the positions of at least segments of the wire electrode 104 at a restoration rate higher than the acquisition rate of the camera 126 that acquires the set of images 702, by utilizing compressed sensing with sparse restoration technique. Details on restoring the positions of at least segments of the wire electrode 104 are provided, for example, in Figures 1B and 9.

[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 to the vicinity of the workpiece 102, and an energy source 108 that generates a discharge, based on the position of at least a segment of the wire electrode 104 restored at a restoration rate. Details on controlling the transport system 118 and the energy source 108 are provided, for example, in Figures 1B, 14, 15, and 16.

[0129] A person skilled in the art who enjoys the benefits of the teachings presented in the above description and the accompanying drawings will come to mind numerous variations and other embodiments of these inventions. It should be understood that the present invention is not limited to the specific embodiments disclosed, and that variations and other embodiments are intended to be included within the scope of the appended claims. In addition, while the above description and the accompanying drawings illustrate examples of embodiments in the context of examples of several combinations of elements and / or functions, it should 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, for example, different combinations of elements and / or functions than those explicitly stated in the above description are also intended, which may be described in some of the appended claims. Specific terminology is used herein, but these terms are used only in a general and descriptive sense and are not intended to be limiting.

Claims

1. A wire electrical discharge machine (EDM) for machining a workpiece, wherein the wire EDM is A conveying system for contacting one or both of the wire electrode and the workpiece, and for transporting the wire electrode and the workpiece so that they approach each other, An energy source configured to generate a discharge between the wire electrode and the workpiece, The system comprises a wire electrode position measurement system, and the wire electrode position measurement system is A light source configured to illuminate the wire electrodes with an encoded illumination pattern, The wire EDM further includes a camera having an image sensor arranged to acquire a set of images showing the wire electrodes illuminated with the encoded illumination pattern at different positions, and the wire EDM further includes A processor configured to restore the position of at least segments of the wire electrode at a restoration rate higher than the acquisition rate of the camera by utilizing compressed sensing with sparse restoration, A wire EDM comprising a controller configured to control the transport system and at least one of the energy source based on the position of at least segments 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 extending 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 according to claim 1, wherein the processing energy is kept constant and the processing speed of the workpiece is controlled by applying voltage feedback control.

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

4. The light source and camera of the wire electrode position measurement system are arranged on both sides of the wire electrode. The wire EDM according to claim 1, wherein 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.

5. The compressed sensing using the aforementioned sparse reconstruction is, Buffering the set of images acquired from the camera, By removing the shadow of the bubble from the shadow of the wire electrode moving across the image sensor, which is captured in the set of images acquired from the camera, a set of bubble-free images of the wire electrode encoded by the encoded illumination pattern is generated. The pixel dimensions of the set of bubble-free images are multiplied by a Gaussian random matrix to compress the pixel dimensions so that they are equal to the number of images in the set, and a set of compressed images is output. Group 1 – Includes solving the norm-sparse recovery problem to calculate the spectral matrix of the wire electrode from the set of compressed images, wherein the wire electrode vibrates as it moves across the image sensor, and the compressed sensing using the sparse recovery further, Identifying a reduced set of frequency bins corresponding to the row positions of the spectral matrix containing the maximum Euclidean norm, By solving the least-squares reconstruction problem using the reduced set of frequency bins, a high-temporal-resolution set of images of the movement of the wire electrodes is reconstructed with a spatial resolution equal to the spatial resolution of the image sensor of the camera. The wire EDM according to claim 1, further comprising outputting the position of at least the segment of the wire electrode from a high-time-resolution set of images of the restored motion of the wire electrode.

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

7. Solving the aforementioned Group 1 - Norm Sparse Recovery Problem is, Minimizing the difference between the set of compressed images and the composite set of compressed images formed by the product of the spectral matrix of the vibrating wire electrode and the Fourier transform applied in the upsampled time domain, The minimization of the difference is regularized by summing the Euclidean norms of the rows of the spectral matrix of the vibrating wire electrode, The wire EDM according to claim 5, comprising outputting the spectral matrix in an upsampled time domain that is sparse in the frequency bin by having a small number of non-zero row norms.

8. The controller further, The frequency of vibration of the wire electrode, and It is configured to determine at least one of the amplitudes of the vibration of the wire electrode, The vibration frequency of the wire electrode is determined by converting a reduced set of frequency bins into physical frequency values. The wire EDM according to claim 1, wherein the amplitude of the vibration of the wire electrode is determined by converting the position of the wire electrode segment on the sensor array into the physical position of the wire electrode, according to the geometric shape of the elements of the wire electrode position measurement system.

9. The controller further, Analysis of significant changes in the frequency and amplitude of the vibration of the wire electrode obtained, Based on the detection of one or more of the aforementioned significant changes, the processing energy input to the wire electrode is reduced, The wire EDM according to claim 8, configured to reduce the possibility of the wire electrode breaking during rough machining by performing one or more control actions based on the detection of one or more of the aforementioned significant changes, and based on a reduction in the processing speed of the workpiece and the transport system.

10. The controller further, The amplitude of the vibration of the wire is analyzed and it is detected that the amplitude is greater than a threshold, If the shape of the wire electrode is presumed to be convex, the processing speed of the workpiece and the transport system is reduced to reduce the amplitude of vibration of the wire electrode. If the shape of the wire electrode is estimated to be concave, the processing speed of the workpiece and the transport system is increased to increase the amplitude of the vibration of the wire electrode. The wire EDM according to claim 8, configured to control the straightness of the cutting and the amount of size error during skimming by performing a control action based on changing the machining energy according to the distance between the wire electrode and the workpiece.

11. The controller further, The amplitude of the vibration of the wire electrode is analyzed to detect the fluctuation of the vibration, If the shape of the wire electrode is presumed to be convex, the processing speed of the workpiece and the transport system is reduced to reduce the amplitude of vibration of the wire electrode. If the shape of the wire electrode is estimated to be concave, the processing speed of the workpiece and the transport system is increased to increase the amplitude of the vibration of the wire electrode. The wire EDM according to claim 8, configured to control cutting streaks during skimming by performing a control action based on varying the machining energy according to the distance between the wire electrode and the workpiece.

12. A method for machining a workpiece, wherein the method is Transporting the wire electrode to the vicinity of the workpiece, To generate a discharge between the wire electrode and the workpiece, Illuminating the wire electrodes with an encoded illumination pattern, Obtaining a set of images showing the wire electrodes illuminated with the encoded illumination pattern at different locations, By utilizing compressed sensing with sparse reconstruction, the position of at least segments of the wire electrode is reconstructed at a reconstruction rate higher than the acquisition rate of the camera that acquires the set of images, Based on the position of at least the segments of the wire electrode restored at the aforementioned restoration rate, A conveying system for transporting the wire electrode to the vicinity of the workpiece, and A method comprising controlling at least one of the energy sources that generate the discharge.

13. The method further includes 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 extending 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 method according to claim 12, wherein the processing energy is kept constant and the processing speed of the workpiece is controlled by applying voltage feedback control.

14. This further includes generating a pseudo-random sequence of on and off light pulses, The duration of each pulse in the pseudo-random sequence of the on and off light pulses is less than or equal to the Nyquist sampling rate of the vibration frequency of the wire electrode. The method according to 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 the camera's frame exposure.

15. The method further includes obtaining 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, The method according to claim 12, wherein the light source and the camera of the wire electrode position measurement unit are arranged on both sides of the wire electrode.

16. The compressed sensing using the aforementioned sparse reconstruction is, Buffering the set of images acquired from the camera, By removing the shadow of the bubble from the shadow of the wire electrode moving across the image sensor of the camera, which is captured in the set of images acquired from the camera, a set of bubble-free images of the wire electrode encoded by the encoded illumination pattern is generated. The pixel dimensions of the set of bubble-free images are multiplied by a Gaussian random matrix to compress the pixel dimensions so that they are equal to the number of images in the set, and a set of compressed images is output. Group 1 – Includes solving the norm-sparse recovery problem to calculate the spectral matrix of the wire electrode from the set of compressed images, wherein the wire electrode vibrates as it moves across the image sensor, and the compressed sensing using the sparse recovery further, Identifying a reduced set of frequency bins corresponding to the row positions of the spectral matrix containing the maximum Euclidean norm, By solving the least-squares reconstruction problem using the reduced set of frequency bins, a high-temporal-resolution set of images of the movement of the wire electrodes is reconstructed with a spatial resolution equal to the spatial resolution of the image sensor of the camera. The method according to claim 12, further comprising outputting the position of at least the segment of the wire electrode from a high-time-resolution set of images of the restored motion of the wire electrode.

17. Generating a set of bubble-free images by removing the bubble shadows from the aforementioned set of images further involves solving a robust principal component analysis problem, which means that This includes modeling the set of images as consisting of a low-rank matrix component and a sparse matrix component, wherein the low-rank matrix component corresponds to the wire electrode vibrating without bubbles, and the sparse component corresponds to the bubbles, and further, The method according to claim 16, comprising outputting the low-rank matrix component as the set of bubble-free images.

18. Solving the aforementioned Group 1 - Norm Sparse Recovery Problem is, Minimizing the difference between the set of compressed images and the composite set of compressed images formed by the product of the spectral matrix of the vibrating wire electrode and the Fourier transform applied in the upsampled time domain, The minimization of the difference is regularized by summing the Euclidean norms of the rows of the spectral matrix of the vibrating wire electrode, The method according to claim 16, comprising outputting the spectral matrix in an upsampled time domain that is sparse in the frequency bin by having a small number of non-zero row norms.

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

20. A non-temporary computer-readable medium for storing computer-executable instructions for machining a workpiece, wherein the computer-executable instructions are: Transporting the wire electrode to the vicinity of the workpiece, To generate a discharge between the wire electrode and the workpiece, Illuminating the wire electrodes with an encoded illumination pattern, Obtaining a set of images showing the wire electrodes illuminated with encoded illumination patterns at different positions, By utilizing compressed sensing with sparse reconstruction, the position of at least segments of the wire electrode is reconstructed at a reconstruction rate higher than the acquisition rate of the camera that acquires the set of images, Based on the position of at least the segments of the wire electrode restored at the aforementioned restoration rate, A conveying system for transporting the wire electrode to the vicinity of the workpiece, and A non-temporary computer-readable medium configured for controlling at least one of the energy sources that generate the aforementioned discharge.

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