Milling processing monitoring method
By analyzing cutting torque signals to separate torque components based on tool eccentricity and depth of cut, the method addresses the challenge of monitoring these parameters in milling, enhancing machining precision and reducing tool wear.
Patent Information
- Application Number
- JP2024000250
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2024-01-04
- Publication Date
- 2025-07-16
AI Technical Summary
Existing methods struggle to monitor the depth of cut and tool eccentricity in milling processes, particularly in complex machining scenarios, leading to decreased machining surface accuracy and tool wear due to uneven loads and mechanical vibrations.
A method involving the acquisition of tool information before milling, frequency analysis of cutting torque signals to identify harmonic components, and separation of torque components based on tool eccentricity and depth of cut, allowing real-time monitoring of these parameters.
Enables accurate and real-time monitoring of depth of cut and tool eccentricity, improving machining precision and reducing tool wear by separating torque components at different frequencies, facilitating efficient milling processes.
Smart Images
Figure 2025106713000001_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates to a technique for monitoring parameters such as the depth of cut and tool eccentricity in milling (milling).
Background Art
[0002] In order to avoid a decrease in productivity in cutting using a machine tool, it is necessary to select appropriate cutting conditions to suppress machine vibration. The depth of cut (cutting depth) is a parameter that affects machine vibration. Non-Patent Document 1 discloses a method for theoretically obtaining a stability limit diagram representing the relationship between the rotational speed of the spindle and the limit depth of cut of a tool that does not cause chatter vibration by solving the characteristic equation of a closed loop using the compliance transfer function of the machine structure of the machine tool and the specific cutting resistance.
Prior Art Documents
Non-Patent Documents
[0003]
Non-Patent Document 1
Summary of the Invention
Problems to be Solved by the Invention
[0004] In machining where the tool path and workpiece shape are simple, it is possible to monitor the depth of cut using pre-simulation by CAM software. However, in general machining, the tool path and workpiece shape are complex, and the shape of the material is inaccurate, so it is not easy to monitor the depth of cut in real time.
[0005] The eccentricity of the tool is one of the important parameters in machining. If the tool is eccentric, not only will the machining surface accuracy decrease, but uneven loads will be applied to the tool edge, which may cause phenomena such as mechanical vibration and tool wear. Currently, in order to monitor the eccentricity of the tool, it is necessary to attach expensive sensors such as displacement gauges.
[0006] This disclosure has been made in view of such circumstances, and its object is to provide a technique for easily monitoring parameters such as the depth of cut and tool eccentricity in milling.
Means for Solving the Problems
[0007] One aspect of this disclosure is a method for monitoring the positional relationship between a tool and a workpiece in milling. Before starting the milling, tool information is acquired. During the milling, a signal indicating the cutting torque is acquired. The signal indicating the cutting torque is frequency-analyzed to identify the harmonic components of the cutting edge passing frequency. The notch frequency is identified from the shapes of a plurality of harmonic components of the cutting edge passing frequency, and the axial depth of cut of the tool is identified from the notch frequency.
[0008] In addition, any combination of the above components, and those obtained by converting the expressions of this disclosure between methods, apparatuses, systems, etc. are also effective as aspects of this disclosure.
Brief Description of the Drawings
[0009]
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Mode for Carrying Out the Invention
[0010] Figure 1(a) shows a model of milling. In the milling (milling) of the embodiment, the rotary tool is a square end mill, and the radial depth of cut (RDOC: Radial Depth Of Cut) is d r , and the axial depth of cut (ADOC: Axial Depth Of Cut) is d aLet it be so. When the square end mill rotates at an angular velocity (tool rotation frequency) ω n the twisted blades sequentially cut the workpiece (workpiece) from the lower side.
[0011] Figure 1(b) shows the coordinate system of the milling model. The rotating tool has a constant twist angle (helix angle) β and a nominal radius r nom The X-axis, Y-axis, and Z-axis correspond to the feed direction of machining, the radial direction of the tool, and the axial direction of the tool, respectively. Here, the positive direction of the X-axis is set to coincide with the feed direction. When one of the plurality of cutting edges is set as the reference cutting edge and the lower end of the reference cutting edge is set as the Y'-axis, the Y'-axis and the X'-axis perpendicular to the Y'-axis rotate with the rotation of the tool. Hereinafter, the reference cutting edge is referred to as the "first cutting edge".
[0012] The angle φ (i.e., the angular delay) due to the twist (helix) of the reference cutting edge (first cutting edge) at an arbitrary height z is calculated by Equation (1).
Equation
Equation
[0013] Figure 2 shows the state of an eccentric tool. In milling, the eccentricity (runout) of the tool causes a change in the effective radius and affects the trajectory of the cutting edge. Figure 2(a) shows the trajectory of the cutting edge tip on the bottom surface, and Figure 2(b) shows the trajectory of the cutting edge at a position at height z from the bottom surface. As shown in the figure, the eccentricity displacement vector ε has the magnitude of eccentricity, i.e., the eccentricity amount |ε|, and the angle θ with respect to the Y-axis ecis defined by two parameters. The effective radius vector r of the locus along which the i-th cutting edge moves i is approximated as the sum of the eccentricity vector ε and the nominal radius vector r of the cutting edge nom, i . Therefore, the magnitude of the effective radius vector r i is derived as follows. [Number]
[0014] Here, since the direction of the nominal radius vector r nom, i depends on φ, as a result, the magnitude of the effective radius vector r i becomes a function of z. That is, the radius of the locus affected by tool eccentricity varies with height even for the same cutting edge (see Figs. 2(a) and (b)).
[0015] The tangential component of the cutting force can be modeled as a linear function of the instantaneous cross-sectional area of the uncut chip and the specific cutting resistance. Fig. 3(a) shows the state of milling without the influence of tool eccentricity, and Fig. 3(b) shows the state of milling with the influence of tool eccentricity. c is the feed per tooth, h i is the instantaneous uncut chip thickness of the i-th cutting edge (the i-th cutting edge), θ st , θ ex are the tool entry angle and the tool exit angle, respectively. The tool entry angle θ st and the tool exit angle θ ex define the angle range (cutting angle range) in which the tool cuts the workpiece. From the geometric relationship, the instantaneous uncut chip thickness h i is obtained as follows. [Number]
[0016] In Fig. 3(a), since there is no tool eccentricity, r i-1 and r i are the nominal radius r nomIt becomes the same. On the other hand, when there is an influence of tool eccentricity, the deviation between the nominal radius and the effective radius affects the instantaneous uncut chip thickness. Therefore, Equation (4) is converted into Equation (5) by substituting Equation (3).
Number
[0017] Here, the function of the instantaneous chip thickness of each cutting edge is expressed by two separate components: the chip thickness h due to tool rotation s and the chip thickness h due to tool eccentricity ec The cutting edge only engages with the workpiece within the range of θ st and θ ex Therefore, a switching function named the tool engagement function g is used to represent the engagement of the tool. The engagement range can be expressed as in Equation (6) using the radial depth of cut (RDOC). Here, as an example, the situation of down milling and clockwise rotation is shown.
Number
[0018] Strictly speaking, the engagement range is affected by tool eccentricity, but in a model for general cutting situations where the eccentricity ε is sufficiently smaller than the nominal radius r nom it is approximated by Equation (6). Furthermore, although the engagement range increases slightly due to the relative feed motion, since the feed rate c is sufficiently smaller than the nominal radius r nom this effect can also be ignored. From Equations (5) and (6), the tangential micro-cutting force and cutting torque can be expressed as follows using the tangential specific cutting resistance K t of the single mechanical force model.
Number
[0019] The micro-cutting force function df t,i and the micro-cutting torque function dτ irepresents the tangential cutting force and cutting torque applied to the i-th cutting edge in the discretized z-plane, respectively. dz represents the distance between the discretized planes. Therefore, the total cutting torque applied to the i-th cutting edge can be obtained by integrating the micro-cutting torque in the axial direction. In Equation (8), the operator * and the operator ● represent the convolution product and the general multiplication operation, respectively. [Number]
[0020] λ i is called the helical gradient function and is defined to convert the integration operation in the axial direction of Equation (8) into the angular domain. λ i represents the ratio of the height of the i-th cutting edge to the angular delay. Subsequently, the total cutting torque loaded on the entire tool can be obtained by the sum of the torques acting on all the cutting edges. [Number]
[0021] For the sake of convenience, let the first term independent of tool eccentricity in Equation (9) be τ s , and the second term dependent on tool eccentricity be τ ec . Then, the total cutting torque is expressed as follows. [Number]
[0022] The cutting torque can be converted into frequency components by Fourier transform. According to the superposition integral theorem, the convolution in the time domain is converted into a simple multiplication, and vice versa. Therefore, when Equation (10) is converted into the frequency domain, it becomes as follows (θ = ω n t). Here, the capital function represents the function in the frequency domain converted using the Fourier transform. [Number]
[0023] As a result of Fourier-transforming Eqs. (5) and (6), the functions that make up the cutting torque can be described as mathematical expressions in the frequency domain as follows.
Number
[0024] Equation (12) shows the Fourier transform of the function that constitutes the cutting torque signal. Since the mathematical model assumes a steady state, it is assumed that the cutting torque signal is infinitely periodic. In the embodiment, the measured signal is processed for each cycle of data. This means that it is possible to monitor the cutting state in real time. The cutting torque can be expressed in the form of a Fourier series.
[0025] Λ consists only of the harmonic components of the cutting edge passing angle frequency ω N (=Nω n ) and can be rewritten as a periodic impulse function.
Number
[0026] On the other hand, the torque T that depends on tool eccentricity ec is composed only of the frequency components of (Nk - 1)ω n and (Nk + 1)ω n , that is, only the components in the vicinity of the harmonic components of the cutting edge passing angle frequency. That is, the torque T that does not depend on tool eccentricity s and the torque T that depends on tool eccentricity ec are independent frequency components and can be observed separately from each other. However, in the case of a two-flute end mill, the components in the vicinity of different cutting edge passing frequencies will overlap. Therefore, the equations for monitoring are different for a two-flute rotary tool and a rotary tool with three or more flutes.
[0027] Figure 4 shows an example in which the cutting torque of a four-flute end mill is obtained by simulation in the frequency domain. The simulation conditions are shown in Table 1. [Table 1]
[0028] As shown in Figure 4, the torque T s that does not depend on tool eccentricity and the torque T ec that depends on tool eccentricity appear independently. Specifically, the torques at frequencies 0, ω N , 2ω N , 3ω N are the torque T s that does not depend on tool eccentricity, and the torques at frequencies ω n , ω N -ω n , ω N +ω n , 2ω N -ω n , 2ω N +ω n , 3ω N -ω n , 3ω N +ω n are the torque T ec that depends on tool eccentricity. Therefore, it can be seen that the parameters related to the depth of cut and tool eccentricity (runout) can be separately extracted from the harmonic components of the cutting edge passing angle frequency and the frequencies in the vicinity thereof.
[0029] Figure 5 shows the processing system 1 of the embodiment. The processing system 1 includes a processing device 10 and a control device 100. The control device 100 controls the operation of the processing device 10 according to a processing program. In the embodiment, the control device 100 may be a numerical control (NC) device that analyzes a numerical control (NC) program to control the operation of the processing device 10, and the processing device 10 and the control device 100 constitute a numerical control (NC) machine tool. In the processing system 1, the processing device 10 and the control device 100 may be connected by a cable or the like, or may be integrally configured.
[0030] The machining apparatus 10 includes a bed portion 12 and a column portion 14 which are main body parts. On the bed portion 12, a first table 16 and a second table 18 are movably supported. The first table 16 is movably supported in the Y-axis direction by a rail portion formed on the bed portion 12, and the second table 18 is movably supported in the X-axis direction by a rail portion formed on the first table 16. A workpiece installation surface is provided on the upper surface of the second table 18, and the workpiece 62 is fixed to the workpiece installation surface.
[0031] The Y-axis motor 22 rotates a ball screw mechanism to move the first table 16 in the Y-axis direction, and the X-axis motor 20 rotates a ball screw mechanism to move the second table 18 in the X-axis direction. The Y-axis sensor 32 detects the position of the first table 16 in the Y-axis direction, and the X-axis sensor 30 detects the position of the second table 18 in the X-axis direction.
[0032] Above the second table 18, a spindle 46 is provided, and a tool holder 48 is attached to the tip of the spindle 46. The tool holder 48 holds a tool 50, and an end mill tool is attached to the tool holder 48. The spindle motor 40 rotates the spindle 46, and the spindle sensor 42 detects the rotational speed of the spindle motor 40. The spindle 46 and the spindle motor 40 are fixed to a spindle support portion 44.
[0033] The spindle support portion 44 is movably supported in the Z-axis direction by a rail portion formed on the column portion 14 on the back side thereof. The Z-axis motor 24 rotates a ball screw mechanism to move the spindle 46 in the Z-axis direction. The Z-axis sensor 34 detects the position of the spindle 46 in the Z direction.
[0034] The first tilt motor 52 rotates a gear mechanism to tilt the spindle support portion 44 around an axis perpendicular to the spindle 46 and the Y-axis. The tilt sensor 56 detects the tilt angle of the spindle 46. The second tilt motor 54 rotates a gear mechanism to tilt the spindle support portion 44 around an axis parallel to the Y-axis. A tilt sensor (not shown) different from the tilt sensor 56 detects the tilt angle of the spindle 46.
[0035] The control device 100 is equipped with a computer that analyzes a machining program and drives and controls the machining device 10 based on the analysis result. The control device 100 may include one or more processors (CPUs). Specifically, the control device 100 drives and controls the X-axis motor 20, Y-axis motor 22, Z-axis motor 24, first tilt motor 52, second tilt motor 54, and spindle motor 40 according to the machining program. The control device 100 acquires the detection values detected by the X-axis sensor 30, Y-axis sensor 32, Z-axis sensor 34, tilt sensor, and spindle sensor 42, respectively, and reflects them in the drive control of each motor.
[0036] In the machining device 10, the workpiece 62 is moved in the X-axis direction and Y-axis direction by the X-axis motor 20 and Y-axis motor 22, respectively, and the tool 50 is moved in the Z-axis direction by the Z-axis motor 24. However, these movements only need to be relative between the tool 50 and the workpiece 62. That is, in the machining device 10, the tool 50 may be moved in the X-axis direction and Y-axis direction, and the workpiece 62 may be moved in the Z-axis direction. Also, in the machining device 10, the tool 50 is tilted with respect to the workpiece 62 by the first tilt motor 52 and the second tilt motor 54. However, these tilt motors may be provided on the bed portion 12 side. Thus, it does not matter whether the tool 50 or the workpiece 62 is moved. As long as they can move relatively in each movement direction and each rotation direction. The mechanism for realizing the relative movement between the tool 50 and the workpiece 62 is generically called a "feed mechanism".
[0037] The control device 100 of the embodiment has a function of monitoring parameters such as the cutting amount and tool eccentricity in real time while performing milling. Hereinafter, the parameter monitoring function by the control device 100 will be described.
[0038] FIG. 6 shows a functional block for realizing the monitoring function of the control device 100. The control device 100 includes a tool information acquisition unit 102, a machining condition acquisition unit 104, a cutting torque signal acquisition unit 106, a depth of cut specifying unit 108, an eccentricity specifying unit 110, a reliability index derivation unit 112, and a holding unit 114. The holding unit 114 is a memory that holds mathematical formulas, tables, etc. used for calculating the depth of cut and tool eccentricity.
[0039] The control device 100 includes a computer, and each function in the control device 100 is realized by the computer executing a program. The computer includes, as hardware, a memory for loading the program, one or more processors for executing the loaded program, an auxiliary storage device, and other LSIs. The processor is composed of a plurality of electronic circuits including semiconductor integrated circuits and LSIs, and the plurality of electronic circuits may be mounted on one chip or may be mounted on a plurality of chips.
[0040] Before the start of milling, the tool information acquisition unit 102 acquires tool information indicating the specifications of the tool 50. The tool information includes the number of teeth, the helix angle, and the diameter of the tool 50. Before the start of milling, the user inputs the tool information to the control device 100, and the tool information acquisition unit 102 acquires the input tool information and provides it to the depth of cut specifying unit 108.
[0041] The machining condition acquisition unit 104 acquires the machining conditions of the milling. The machining condition acquisition unit 104 acquires the spindle rotation speed and the feed rate as the machining conditions. The machining device 10 controls the spindle rotation speed and the feed rate, and thus the machining condition acquisition unit 104 acquires the machining conditions from the machining device 10. The machining condition acquisition unit 104 may acquire the machining conditions every rotation of the spindle 46. The machining condition acquisition unit 104 acquires the machining conditions and provides them to the depth of cut specifying unit 108.
[0042] During milling, the cutting torque signal acquisition unit 106 acquires a signal indicating the cutting torque. The cutting torque signal acquisition unit 106 may acquire a signal indicating the cutting torque, for example, from the current value of the spindle motor 40. Note that the cutting torque signal acquisition unit 106 may acquire a signal indicating the cutting torque itself (cutting torque signal) as a signal indicating the cutting torque, but may also acquire a signal corresponding to the cutting torque. The signal corresponding to the cutting torque may be any signal that has a correlation with the cutting torque and can derive the cutting torque, for example, a signal having a magnitude proportional to the cutting torque. Therefore, the cutting torque signal acquisition unit 106 may acquire a signal indicating the cutting force, or may also acquire a signal indicating the cutting load in the tangential direction. The cutting torque signal acquisition unit 106 provides a signal indicating the cutting torque to the depth of cut specifying unit 108.
[0043] (Calculation of Axial Depth of Cut) As described above, the torque T independent of tool eccentricity s is composed of the harmonic components of the cutting edge passing angle frequency ω of the cutting torque T N (i.e., integer multiples of ω N ). According to Equation (11), the torque T s is expressed using the helical gradient function Λ indicating the influence of the axial depth of cut (ADOC) d a on the cutting torque, the tool engagement function G indicating the influence of the radial depth of cut (RDOC) d r on the cutting torque, and the static instantaneous chip thickness H indicating the influence of the feed rate on the cutting torque. s Therefore, by calculating Λ from T s , the axial depth of cut (ADOC) d a can be monitored, and by calculating G*H s , the radial depth of cut (RDOC) d r can be monitored.
[0044] Fig. 7(a) shows an example of the simulation of the amplitude of Λ. Fig. 7(a) shows the result of performing FFT analysis on one rotation period in the infinite time domain. The vertical lines with × marks indicate the frequency components of the periodic signal Λ. The dotted line is scaled on the vertical axis with respect to the vertical line so that the × mark is located on the dotted line. As shown in this example, the frequency spectrum of Λ is periodic notches at the frequency kω notch =k·(2πω n r nom ) / (d a tanβ) (where k = 0, 1, 2,..., ∞). This means that since λ has the form of a rectangular step function in the time domain, the ratio of the height and angular delay of the helical cutting edge is constant during the engagement of the cutting edge and the workpiece. Since the frequency of the notch is determined by d a (ADOC), conversely, d a can be calculated from the notch frequency estimated from the cutting torque signal.
[0045] Fig. 7(b) shows an example of the simulation of G*H s . As shown in Fig. 7(b), although G is a step function, G*H s has no notches. This is because the convolution product operation is performed between G and H s .
[0046] Fig. 7(c) shows an example of the simulation of T s . As shown in Fig. 7(c), notches occur in the cutting torque due to the helical gradient function Λ. The dotted line in Fig. 7(c) is the result of performing FFT analysis on one rotation period in the infinite frequency domain, and the vertical line with the × mark as the peak value indicates the frequency components of the periodic signal. As shown in the figure, T s also has multiple notches at the same notch frequency as Λ. Based on the idea that T s has a notch-shaped shape transferred from Λ, the depth-of-cut specifying unit 108 searches for ω notch from the shape of the frequency components of the cutting torque. When ω notch is specified, d a is calculated by Equation (14).
Number
[0047] The depth of cut specifying unit 108 performs frequency analysis on the signal indicating the cutting torque per revolution supplied from the cutting torque signal acquisition unit 106, and determines the notch frequency ω notch from the magnitude of each frequency component. First, the depth of cut specifying unit 108 refers to the magnitude (amplitude indicated by the × mark) of each frequency component (kω N ) and specifies the frequency component at which the magnitude of the frequency component changes from decreasing to increasing. In this example, the amplitude of the frequency component from 0 to 5ω N gradually decreases, and the amplitude of the frequency component of 6ω N is larger than the amplitude of the frequency component of 5ω N . Therefore, the depth of cut specifying unit 108 determines that the amplitude of the frequency component of 5ω N is a minimum, and recognizes that the notch frequency exists in the vicinity of 5ω N . In this case, it can be seen that the notch frequency is a frequency greater than 4ω N and less than 6ω N .
[0048] Next, the depth of cut specifying unit 108 checks whether the notch frequency is 5ω N or higher, or 5ω N or lower. A method for checking whether the notch frequency is 5ω N or higher is shown. The depth of cut specifying unit 108 generates a line passing through the peak value (× mark) of the frequency component of 5ω N or lower and a line passing through the peak value of the frequency component greater than 5ω N . If the intersection of the two lines is between 5ω N and 6ω N , the frequency of the intersection is specified as the notch frequency. For example, a straight line passing through the peak values of 4ω N and 5ω N , and a straight line passing through the peak values of 6ω N and 7ω NThe intersection of the straight line passing through the peak value is 5ω N and 6ω N When it is between, the notch amount specifying unit 108 may specify the frequency of the intersection as the notch frequency. In the example shown in FIG. 7(c), since the intersection is not between 5ω N and 6ω N it is confirmed that the notch frequency is not 5ω N or more.
[0049] A method for checking whether the notch frequency is 5ω N or less is shown. The notch amount specifying unit 108 generates a line passing through the peak value of a frequency component smaller than 5ω N and a line passing through the peak value of a frequency component of 5ω N or more. When the intersection of the two lines is between 4ω N and 5ω N the frequency of the intersection is specified as the notch frequency. For example, the intersection of the line passing through the peak values of 3ω N and 4ω N and the line passing through the peak values of 5ω N and 6ω N is between 4ω N and 5ω N the notch amount specifying unit 108 may specify the frequency of the intersection as the notch frequency. In the example shown in FIG. 7(c), the intersection is 4.5ω N and is between 4ω N and 5ω N so the notch frequency ω notch is specified as 4.5ω N Note that ω N =Nω n is the case.
[0050] In the above example, the notch amount specifying unit 108 sets a straight line passing through two adjacent peak values and specifies the notch frequency from the intersection of the two straight lines. However, a curve passing through three or more peak values may be set and the notch frequency may be specified from the intersection of the two curves. For example, the notch amount specifying unit 108 may use the curve passing through the peak values of 2ω N and 3ω N and 4ω N and the curve passing through the peak value of 5ωN and 6ω N and 7ω N When the intersection point of the curve passing through the peak values of is 4ω N and 5ω N is between, the notch amount specifying unit 108 may specify the frequency of the intersection point as the notch frequency.
[0051] Also, the notch amount specifying unit 108 may search for the notch frequency ω notch using the amplitude of the high harmonic component. In this example, the notch amount specifying unit 108, after specifying that the magnitude of the frequency component changes from decreasing to increasing at 9ω N confirms whether 2ω notch is greater than or equal to 9ω N or less than or equal to 9ω N to specify the notch frequency ω notch . By using the peak value of the harmonic component, it becomes possible to improve the estimation accuracy of the notch frequency ω notch .
[0052] As described above, the notch amount specifying unit 108 is provided with tool information including the number of teeth N, the twist angle β, and the diameter 2r nom of the tool 50. Therefore, when the notch amount specifying unit 108 specifies the notch frequency, it can specify the axial feed amount d a using the formula (14) held by the holding unit 114. As described above, the notch amount specifying unit 108 can monitor the axial feed amount d a by specifying the notch frequency from the shape of the integer multiple component of the cutting edge passing frequency obtained by frequency analyzing the cutting torque signal.
[0053] (Calculation of the radial feed amount) When the axial feed amount d a is calculated, Λ can be estimated using the formula (13). Subsequently, G*H s is calculated by the formula (15).
Number
[0054] Specific cutting resistance Kt is an unknown parameter, but G*H s If the ratio Ψ between adjacent frequency components of t is common to all components, then K t The influence of can be removed. In the embodiment, as shown in Equation (16), the first harmonic component and the second harmonic component of the cutting edge passing frequency are used for the calculation of the ratio Ψ. Referring to FIG. 4, the first harmonic component is ω N component, and the second harmonic component is 2ω N component.
Number
[0055] FIG. 8(a) shows the cutting state of the tool. In FIG. 8(a), (i) to (iii) show the cutting states in which the tool rotates clockwise, where (i) is downcut, (ii) is upcut, and (iii) is the transition state. (iv) to (vi) show the cutting states in which the tool rotates counterclockwise, where (iv) is upcut, (v) is downcut, and (vi) is the transition state. Practical cutting operations are often performed clockwise as viewed from the negative z direction of the machining center.
[0056] Fig. 8(b) shows the relationship between the tool entry angle θ st and the tool exit angle θ ex in the cutting states of (i) to (vi). For example, in the cutting state of (i), the tool exit angle θ ex is always 180 degrees, and the tool entry angle θ st is determined by the cutting conditions. Also, in the cutting state of (ii), the tool entry angle θ st is always 180 degrees, and the tool exit angle θ ex is determined by the cutting conditions.
[0057] Fig. 9(a) shows the relationship of the cutting angle range of a single-flute end mill, Fig. 9(b) shows the relationship of the cutting angle range of a two-flute end mill, and Fig. 9(c) shows the relationship of the cutting angle range of a four-flute end mill. In Figs. 9(a) to (c), the left figure shows the ratio Ψ of G*H s (2ω N ) to G*H s (ω N ), and the right figure shows the phase difference between the first harmonic component and the second harmonic component. Theoretically, the ratio Ψ depends on the tool entry angle θ st , the tool exit angle θ ex , and the number of flutes N. Therefore, in the embodiments, for each number of flutes N, the ratio Ψ of G*H s , the relationship between the tool entry angle θ st and the tool exit angle θ ex , the phase difference between the first harmonic component and the second harmonic component, and the relationship between the tool entry angle θ st and the tool exit angle θ ex are obtained in advance and recorded in the holding unit 114 as a look-up table.
[0058] That is, the holding unit 114 records a look-up table that defines the relationships in the two figures shown in Fig. 9(a) for a single-flute end mill, records a look-up table that defines the relationships in the two figures shown in Fig. 9(b) for a two-flute end mill, and records a look-up table that defines the relationships in the two figures shown in Fig. 9(c) for a four-flute end mill.
[0059] Therefore, if the number of cutting edges N is specified, the cutting depth specifying unit 108 uses the relationship shown in FIG. 9 to determine the tool entry angle θ st and the tool exit angle θ ex . Specifically, when the number of cutting edges N is 4, the cutting depth specifying unit 108 reads a look-up table showing the relationship between the ratio Ψ in FIG. 9(c), the tool entry angle θ st and the tool exit angle θ ex , a look-up table showing the relationship between the phase difference and the tool entry angle θ st and the tool exit angle θ ex . The cutting depth specifying unit 108 obtains the ratio Ψ and the phase difference from the first harmonic component and the second harmonic component of the cutting edge passing frequency.
[0060] The cutting depth specifying unit 108 refers to the look-up table regarding the ratio Ψ and derives the corresponding tool entry angle θ st and the tool exit angle θ ex . Also, the cutting depth specifying unit 108 refers to the look-up table regarding the phase difference and derives the corresponding tool entry angle θ st and the tool exit angle θ ex . The cutting depth specifying unit 108 determines the common tool entry angle θ st and the tool exit angle θ ex from the tool entry angles θ st and the tool exit angles θ ex derived from both look-up tables, and specifies the radial cutting depth d st and the tool exit angle θ ex based on the specified tool entry angle θ r . Note that the tool entry angle θ st and the tool exit angle θ ex define the cutting angle range, and the radial cutting depth d r is uniquely determined from the cutting angle range. In this way, the cutting depth specifying unit 108 uses the look-up table showing the relationship in FIG. 9 to specify the tool entry angle θ st and the tool exit angle θ ex and can monitor the radial cutting depth d r in real time.
[0061] Note that the depth-of-cut specifying unit 108 can also specify whether the milling process is an up-cut, a down-cut, or in a transition state by specifying the tool entry angle θ st and the tool exit angle θ ex (see Fig. 8(b)). That is, the depth-of-cut specifying unit 108 can monitor the milling process by specifying the tool entry angle θ st and the tool exit angle θ ex .
[0062] (Calculation of tool eccentricity) As shown in Fig. 4, T ec can be observed independently of T s . In the embodiment, the eccentricity specifying unit 110 uses only the ω n component for the calculation of tool eccentricity. The rotational component of the torque T(ω n ) can be derived as follows from Eqs. (11) to (13) when N is not 1. In the case of a single-edge tool, there is no tool eccentricity. Note that the eccentricity specifying unit 110 may also use other harmonic components simultaneously to reduce the monitoring error. [Number]
[0063] The tool eccentricity parameters ε and θ ec can be calculated as follows from Eqs. (12) and (17) when N ≥ 3, that is, when Λ(2ω n ) = 0, using T(ω n ). [Number] The holding unit 114 stores Eq. (18).
[0064] Here, note that d a , θ st and θ ex have already been obtained from the previous monitoring. Note that the remaining unknown parameter, the specific cutting resistance K tcan be derived from G and Λ using Equation (11). Here, only the cutting edge passing frequency component is utilized. The specific cutting resistance K t is a parameter that is convenient to know in practice because it reflects the influence of tool shape, work material strength, and cutting fluid. [Number]
[0065] When N = 2, Equation (17) can be rewritten as Equation (20) using the following relationship. [Number] In the relational expression, H with an overline ec is the complex conjugate of H ec and j is the imaginary unit.
[0066] By comparing the real and imaginary parts on both sides of Equation (20), H ec is calculated as follows. [Number]
[0067] As a result, the tool eccentricity parameters ε and θ ec are calculated as follows. [Number] The holding unit 114 stores Equation (18). As described above, the eccentricity specifying unit 110 can specify the tool eccentricity parameters ε and θ ec using the spindle rotation speed.
[0068] (Reliability index) In the machining system 1 of the embodiment, a reliability index σ is introduced to evaluate the reliability of the monitored parameters. The reliability index represents the similarity between the actual frequency components and the frequency components of the simulation based on the monitored parameters (cutting conditions). As an example, the reliability indices for evaluating the reliability of ADOC and RDOC are defined as in Equation (23).
Equation
[0069] Here, the reliability index derivation unit 112 calculates the total of the absolute errors between the magnitude of the harmonic components of the cutting edge passing frequency of the actual cutting torque signal T(kω N ) and the magnitude of the harmonic components of the cutting edge passing frequency of the simulated cutting torque T’(kω N ) using the monitored cutting conditions. To ensure that the cutting conditions do not affect the reliability index, the reliability index derivation unit 112 normalizes the total of the absolute errors by dividing it by the sum of the magnitudes of T(kω N ) and subtracts the normalized total of the absolute errors from 1. The higher the value of the reliability index σ, the smaller the error, indicating that the reliability of the monitored cutting conditions is higher.
[0070] As shown in Equation (23), the reliability index σ is affected by the integer m indicating the frequency range. In the embodiment, m is set such that mω N is near the notch frequency of Λ to fully evaluate the influence of both ADOC and RDOC. In Equation (23), floor(ω notch / ω n ) means the largest integer less than or equal to ω notch / ω n . The effectiveness of this index σ is confirmed by the cutting experiments described later.
[0071] Figure 10 shows a flowchart of the monitoring method according to the embodiment. Before the start of milling, the user inputs tool information representing the specifications of tool 50 to control device 100. The tool information includes at least the number of teeth, the helix angle, and the diameter of tool 50. Tool information acquisition unit 102 acquires the tool information input by the user (S12) and provides it to depth of cut specification unit 108.
[0072] When milling starts, machining condition acquisition unit 104 acquires machining conditions including the spindle rotation speed and the feed rate from machining device 10 (S14) and provides them to depth of cut specification unit 108. Machining condition acquisition unit 104 may acquire the machining conditions each time spindle 46 rotates.
[0073] During milling, cutting torque signal acquisition unit 106 acquires a signal indicating the cutting torque (S16). Cutting torque signal acquisition unit 106 may acquire a signal indicating the cutting torque from, for example, the current value of spindle motor 40 or control information. Cutting torque signal acquisition unit 106 may acquire a signal indicating the cutting torque itself (cutting torque signal) as the signal indicating the cutting torque, or may acquire a signal corresponding to the cutting torque. For example, cutting torque signal acquisition unit 106 may acquire a signal indicating the cutting force, or may also acquire a signal indicating the tangential cutting load. A dynamometer may be arranged below workpiece 62 in machining device 10, and cutting torque signal acquisition unit 106 may acquire the cutting force in the z-axis direction (proportional to the cutting torque) measured by the dynamometer. Cutting torque signal acquisition unit 106 provides the acquired signal indicating the cutting torque to depth of cut specification unit 108.
[0074] Depth of cut specification unit 108 performs frequency analysis on the signal indicating the cutting torque to identify the harmonic components of the cutting edge passing frequency of the cutting torque (see Fig. 7(c)). Depth of cut specification unit 108 identifies notch frequency ω notch from the shapes (sizes) of a plurality of harmonic components, and uses formula (14) to identify axial depth of cut d a (S18).
[0075] Axial depth of cut d ais known, Λ can be estimated from Equation (13), so G*H s can be calculated by Equation (15). The depth of cut specifying unit 108 calculates the ratio Ψ of G*H s (ω N ) to G*H s (2ω N ) and obtains the phase difference between the 2ω N component and the ω N component of the cutting torque. Then, the depth of cut specifying unit 108 refers to the look-up table recording the relationship shown in FIG. 9 to determine the tool entry angle θ st and the tool exit angle θ ex of the cutting angle range. The depth of cut specifying unit 108 may specify the radial depth of cut d r from the cutting angle range (S20).
[0076] When the axial depth of cut d a and the cutting angle range are known, the eccentricity specifying unit 110 calculates the tool eccentricity parameters ε and θ ec using Equation (18) or Equation (22) (S22).
[0077] Subsequently, the reliability index derivation unit 112 derives a reliability index σ to evaluate the reliability of the specified parameters (S24). The reliability index σ is an index for evaluating the degree of agreement between the actually input cutting torque and the cutting torque simulated using the specified parameters. The reliability index σ has a value from 0 to 1, and the closer it is to 1, the smaller the difference between the two, meaning that the reliability of the specified parameters is high.
[0078] The processes of S18 to S24 may be performed each time the spindle 46 makes one revolution during milling (N in S26). Thereby, the control device 100 can monitor the axial depth of cut d a , the radial depth of cut d r , the tool eccentricity parameters ε and θ ec in real time. Note that the control device 100 may perform this monitoring every multiple revolutions of the spindle 46. When the milling is completed (Y in S26), the monitoring of the parameters ends.
[0079] According to the monitoring method of the embodiment, by performing frequency analysis on the signal indicating the cutting torque, the torque caused by the depth of cut and the torque caused by tool eccentricity can be separated, and it becomes possible to easily realize the state monitoring of milling.
[0080] The present inventor conducted a cutting experiment to confirm the effectiveness of the monitoring method of the embodiment. Fig. 11 shows a photograph of the experimental apparatus. A general free-cutting brass (CuZn39Pb3) was used as the workpiece, and coated single-edge, two-edge, and four-edge carbide square end mills (helix angle 35 degrees) were used as the rotary tools. The experimental conditions are shown in Table 2.
Table 2
[0081] In the experiment, instead of measuring the cutting torque, the cutting force in the z-axis direction is measured with a dynamometer installed under the workpiece. This is because in the case of a square end mill, the cutting force in the z-axis direction is proportional to the cutting torque. The cutting force in the z-axis direction can be converted into the cutting torque using the nominal radius r of the end mill nom and the cutting force ratio k z , that is, the ratio of the z-axis component to the tangential force. Therefore, the signal indicating the normalized cutting force in the z-axis direction can be regarded as the signal indicating the cutting torque. In this experiment, the magnitude of tool eccentricity is measured in advance using a dial gauge for comparison. Also, the shape of the workpiece after cutting is measured using an image measuring machine.
[0082] The following shows three types of experimental conditions. The first type is the experimental condition where both RDOC and ADOC are constant, the second type is the experimental condition where ADOC is constant while RDOC is changed, and the third type is the experimental condition where RDOC is constant while ADOC is changed.
[0083] FIG. 12 shows a schematic diagram of a first type of experiment in which both RDOC and ADOC are constant. The cutting experiment was conducted using single-flute, two-flute, and four-flute end mills, and a plurality of conditions shown in Tables 3 to 5 were evaluated. [Table 3] Table 3 shows the experimental results using a single-flute end mill. The measured values (monitor values) are average values calculated in the tool path excluding the transitional state where the tool enters the workpiece and the transitional state where the tool exits the workpiece. Note that there is no tool eccentricity in the single-flute end mill. In this experiment, d r (RDOC) and d a (ADOC) are measured, and the reliability index σ is obtained.
[0084] [Table 4] Table 4 shows the experimental results using a two-flute end mill. During the experiment using the two-flute end mill, the two-flute end mill was detached and attached, so Table 4 includes two measured tool eccentricities ε. In this experiment, d r (RDOC) and d a (ADOC) and the value of tool eccentricity ε are measured, and the reliability index σ is obtained.
[0085] [Table 5] Table 5 shows the experimental results using a four-flute end mill. In this experiment, d r (RDOC) and d a (ADOC) and the value of tool eccentricity ε are measured, and the reliability index σ is obtained.
[0086] FIG. 13 is an example of monitoring data in four-flute end mill machining where d r (RDOC) is 3 mm, d a (ADOC) is 0.5 mm, and the eccentricity is 1.5 μm. As shown in FIG. 13, it can be seen that according to the monitoring method of the embodiment, each parameter (cutting amount and eccentricity amount) can be monitored well.
[0087] Figure 14 shows the relationship between the reliability index σ of the experimental results and the errors of the axial depth of cut (ADOC) and the radial depth of cut (RDOC). The error of the depth of cut is calculated as a percentage by comparing the measured value with the monitored value. As shown in Figure 14, the smaller the error, the more the reliability index σ tends to be a large value close to 1. From this, it can be seen that the reliability index σ can be useful information for evaluating the monitoring error.
[0088] Figure 15 shows a schematic diagram of a second type of experiment in which the RDOC is linearly changed and the ADOC is set constant in the tool path. In this experiment, a four-flute end mill is used.
[0089] Figure 16 shows the parameters monitored in the second type of experiment and the calculated reliability index. In this experiment, d a (ADOC) is 1 mm and the eccentricity is 1.5 μm. Although the depth of cut changes rapidly in the transition state, it can be seen that the parameters of the depth of cut are well monitored when focusing on the range where the reliability index is relatively high.
[0090] Figure 17 shows a schematic diagram of a third type of experiment in which the ADOC is linearly changed and the RDOC is set constant in the tool path. In this experiment, a four-flute end mill is used.
[0091] Figure 18 shows the parameters monitored in the third type of experiment and the calculated reliability index. In this experiment, d r (RDOC) is 1 mm and the eccentricity is 1.5 μm. Although the depth of cut changes rapidly in the transition state, it can be seen that the parameters of the depth of cut are well monitored when focusing on the range where the reliability index is relatively high.
[0092] In this experiment, the radial depth of cut d r (RDOC), the axial depth of cut d a(ADOC), the calculation processes of tool eccentricity ε and reliability index σ are completed in a short time of 1 ms or less. Since this time is much shorter than the 50 ms rotation period of the tool, the monitoring process of each parameter can be carried out in real time during cutting. The sampling rate of the cutting force signal in the z-axis direction is 1 MHz. Considering that the sampling rate is in a trade-off relationship with the calculation cost, by selecting an appropriate sampling rate, the calculation speed can be improved, and the monitoring of milling with a higher spindle rotation speed can be carried out. In the embodiment, although the monitoring is performed at the rotation period of the tool, the monitoring period may be carried out, for example, at multiple rotation periods of the tool.
[0093] In the embodiment, based on the frequency domain analysis of the cutting torque in end milling, a method for real-time monitoring (monitoring) of the depth of cut and tool eccentricity is proposed. This monitoring method utilizes the feature that the cutting torque components independent of tool eccentricity and the cutting torque components dependent on tool eccentricity are observed at different frequencies. The cutting torque component independent of tool eccentricity is observed at a frequency that is an integer multiple of the tooth passing frequency, while the cutting torque component dependent on tool eccentricity is observed in the vicinity of a frequency that is an integer multiple of the tooth passing frequency. Based on this feature, first, the notch frequency due to tool twist is searched from the shape of the torque component that is an integer multiple of the tooth passing frequency, and after identifying the notch frequency, the axial depth of cut ADOC is calculated. Next, from the ratio and phase difference of the magnitudes of the tooth passing frequency components of the cutting torque, the tool entry angle θ st and the tool exit angle θ ex are calculated using the monitored value of the axial depth of cut ADOC. Then, using the monitored axial depth of cut ADOC, tool entry angle θ st and tool exit angle θ ex , the specific cutting resistance and tool eccentricity are calculated from the frequency components independent of tool eccentricity and the frequency components dependent on tool eccentricity, respectively. Finally, an index for evaluating the reliability of the monitored output is calculated.
[0094] As described above, the present disclosure has been explained based on the embodiments. It should be understood by those skilled in the art that these embodiments are illustrative, and various modifications are possible for each component and combination of each process, and such modifications are also within the scope of the present disclosure.
[0095] The outline of the aspect of the present disclosure is as follows. One aspect of the present disclosure is a method for monitoring the positional relationship between a tool and a workpiece in milling, which includes acquiring tool information before the start of milling, acquiring a signal indicating cutting torque during milling, performing frequency analysis on the signal indicating cutting torque to identify harmonic components of the cutting edge passing frequency, identifying a notch frequency from the shapes of a plurality of harmonic components of the cutting edge passing frequency, and identifying the axial depth of cut of the tool from the tool information and the notch frequency.
[0096] According to this aspect, by performing frequency analysis on the signal indicating cutting torque, the axial depth of cut of the tool can be easily identified. The tool information may include the number of tool teeth, the helix angle, and the diameter of the tool.
[0097] This milling monitoring method may acquire the spindle rotation speed, identify the ratio and phase difference of the magnitudes of two or more harmonic components of the cutting edge passing frequency, and based on the spindle rotation speed, the axial depth of cut of the tool, the ratio of magnitudes, and the phase difference, identify the cutting angle range in which the tool enters the workpiece and exits the workpiece. Further, the milling monitoring method may identify the radial depth of cut of the tool from the cutting angle range.
[0098] This milling monitoring method may identify the tool eccentricity parameter using the axial depth of cut of the tool, the cutting angle range, and the harmonic components of the tool rotation frequency.
Explanation of Reference Numerals
[0099] 1... Machining system, 10... Machining device, 50... Tool, 62... Workpiece, 100... Control device, 102... Tool information acquisition unit, 104... Machining condition acquisition unit, 106... Cutting torque signal acquisition unit, 108... Depth of cut specifying unit, 110... Eccentricity specifying unit, 112... Reliability index derivation unit, 114... Holding unit.
Claims
1. A method for monitoring the positional relationship between a tool and a workpiece in milling, comprising: acquiring tool information before the start of milling; acquiring a signal indicating cutting torque during milling; performing frequency analysis on the signal indicating cutting torque to identify harmonic components of the tooth passing frequency; identifying a notch frequency from the shapes of a plurality of harmonic components of the tooth passing frequency; identifying the axial depth of cut of the tool from the tool information and the notch frequency; a milling monitoring method.
2. The tool information includes the number of teeth, helix angle, and diameter of the tool; The milling monitoring method according to Claim 1.
3. acquiring the spindle rotational speed; identifying the ratio and phase difference of the magnitudes of two or more harmonic components of the tooth passing frequency; identifying the cutting angle range in which the tool enters the workpiece and exits the workpiece based on the spindle rotational speed, the axial depth of cut of the tool, the ratio of magnitudes, and the phase difference; The milling monitoring method according to Claim 1.
4. identifying the radial depth of cut of the tool from the cutting angle range; The milling monitoring method according to Claim 3.
5. identifying a tool eccentricity parameter using the axial depth of cut of the tool, the cutting angle range, and harmonic components of the tool rotation frequency; The milling monitoring method according to Claim 3.