A method for calculating the mounting eccentricity of a milling cutter based on the texture of the generated surface

Abstract

By analyzing the micro-texture of the machined surface, inverse estimation of tool mounting eccentricity is realized on the machine tool. [Solution] Under predetermined workpiece parameters, simulation machining is performed based on multiple parameter sets obtained based on different tool parameters, tool attitude parameter settings, and cutting parameters, and the surface shape after machining for each parameter set is obtained. An optimization variable set is constructed based on each parameter set, and the optimization variable set when waviness is most sensitive to changes in tool mounting eccentricity is determined. The tool mounting eccentricity during machining of the workpiece sample is calculated using the constructed relationship between the tool mounting error and the peak-to-peak value of waviness. If the tool mounting eccentricity exceeds the predetermined value, the bull nose end mill is reattached and the workpiece sample is replaced so that the workpiece can be actually machined, and this calculation of tool mounting eccentricity is repeated until the tool mounting eccentricity becomes smaller than the predetermined value.

Description

[Technical Field]

[0001] The present invention belongs to the technical field of subtractive manufacturing, and in particular to a method for calculating the mounting eccentricity of a milling tool based on the texture of the generating surface. [Background technology]

[0002] As equipment in fields such as aerospace, nuclear power, and biomedical sciences becomes more high-end and intelligent, the demands for product manufacturing precision are increasing. Precision milling technology has attracted attention due to its ability to efficiently machine high-precision products and functional surface textures. Conventional hydrostatic guide rail technology and liquid-cooled spindle technology have significantly improved the accuracy and reliability of actual machining by numerically controlled machine tools. However, for products requiring extremely high precision, it is still difficult to achieve the desired surface quality.

[0003] This is primarily due to mounting errors (mounting eccentricity) that exist during the milling process, which are present in the tool-tool holder-spindle assembly process. This error causes the actual center of rotation of the tool to deviate from its theoretical center when the spindle rotates, resulting in tool eccentricity. In terms of milling stability, tool eccentricity can cause multiple periodic time-lag chatter vibrations. This means that the teeth of the current cutter may cut the machined surface left behind by the teeth of previous cutters. Furthermore, even in stable milling conditions, tool eccentricity can cause the actual cutting radii of each cutter tooth to differ from each other. Furthermore, this can cause periodic variations in the micromorphology of the machined surface of the part compared to when the tool is not eccentric, ultimately resulting in poor surface roughness.

[0004] Currently, milling tool eccentricity measurement methods include using a laser tool measuring instrument to obtain the actual cutting radii of different cutting edges and then comprehensively calculate the tool mounting eccentricity. Other methods use dial indicators or eddy current sensors. However, the accuracy of these measurement methods remains to be improved. Eddy current sensors are susceptible to the uniformity of the tool material, causing jitter in the electrical signal, making it difficult to quickly and accurately obtain eccentricity. There are also several indirect measurement methods, such as building a relationship model between cutting tool eccentricity and the frequency domain characteristics of cutting force and utilizing frequency domain information from experimental data to identify cutting tool eccentricity. However, these methods generally require the use of multiple types of sensors, limiting their versatility.

[0005] As described above, existing cutting tool eccentricity measurement methods have obvious limitations, such as the low cost and convenience of the measurement process and the difficulty in quickly obtaining the tool eccentricity status, which limits the goal of achieving high-precision milled surface quality of the product. Summary of the Invention

[0006] The object of the present invention is to overcome the drawbacks of the prior art by providing a method for calculating the mounting error of a milling cutter based on the texture (surface waviness pattern or periodic unevenness pattern of the machined surface) of the generated surface, and to inversely estimate the mounting eccentricity of the milling cutter by measuring the waviness of the workpiece surface shape.

[0007] The method for calculating the mounting eccentricity of a milling tool based on the texture of a generated surface in the present invention specifically includes the following steps:

[0008] S1: Establish the coordinate expression of the points on the spiral cutting line of the cutter tooth in the workpiece coordinate system. The radius R1 of the edge of the flat part of the cutting edge of the milling cutter, the radius R2 of the arc part of the cutting edge of the milling cutter, and the number of teeth n of the cutter are tand tool parameters including the helix angle γ of the helical cutting edge of the cutter tooth, tool attitude parameters including the side inclination angle α and the forward inclination angle β, spindle rotation speed N, feed rate f of each tooth z , cutting depth a p , cutting step f p and adjustment amount ε κ Set the cutting parameters including the number of cutter teeth n t While keeping constant, the cutting parameters, tool attitude parameters, tool mounting eccentricity ρ and remaining tool parameters are changed to obtain multiple parameter sets, and simulation machining is performed for each parameter set, and the waviness of the milled surface is calculated to obtain the peak-to-peak value of the waviness.

[0009] S2: Optimization variable set X={N, f z , f p , a p , ε κ , α, β, γ, R1, R2}, and an optimization variable set Х=Х is defined based on each parameter set. i The peak value of the swell W t (ρ, Х) is expressed as W0(Х) when the tool mounting eccentricity ρ = 0, and the waviness prominence index affected by the tool mounting eccentricity ρ is defined as follows:

number

[0010] Next, the first-order sensitivity index is used to determine each optimization variable set Х=Х i The degree of influence of the above on the waviness conspicuousness index O(ρ, X) is evaluated. The primary sensitivity index is calculated as follows:

number

[0011] Here, V() indicates that the variance is to be calculated.

[0012] Finally, we use an optimization algorithm to ρ (ρ, Х iThe optimization goal is to maximize the waviness conspicuousness index O(ρ, Х), and the set of optimization variables is solved when the waviness conspicuousness index O(ρ, Х) is most sensitive (highly sensitive) to changes in the tool mounting eccentricity ρ.

[0013] S3: A parameter set having each parameter value in the optimization variable set is selected, and the peak-to-peak value of the waviness obtained by simulating machining with these parameter sets is used to derive a relational expression between the tool mounting eccentricity and the peak-to-peak value of the waviness by fitting. t A milling cutter is selected based on the optimization variable set, and the machine tool is allowed to machine the workpiece sample under the conditions of the optimization variable set, the three-dimensional shape of the machined surface of the workpiece sample after machining is obtained, and the peak-to-peak value of the waviness is obtained. The relationship between the tool mounting error and the peak-to-peak value of the waviness is used to calculate the tool mounting eccentricity when machining the workpiece sample, and if the tool mounting eccentricity exceeds a predetermined value, the milling cutter is re-mounted, the workpiece sample is replaced, and the calculation of the tool mounting eccentricity when machining the workpiece sample is repeated until the tool mounting eccentricity is smaller than the predetermined value, and the final tool mounting eccentricity is obtained.

[0014] Preferably, in step S1, establishing the coordinate representation of the points on the helical cutting line of the cutter tooth in the workpiece coordinate system is specifically as follows:

[0015] S11: A step of creating a reference coordinate system. The reference coordinate system is Coordinate origin O T is the center of the circle U where the arc surface part and the cylindrical surface part of the milling cutter intersect, and the intersection point of the spiral cutting edge of the first cutter tooth and the circle U is point K1, and the coordinate axis X T The direction is vector O T The K1 direction is the coordinate axis Z T The direction is the axis of the milling cutter from the cutting edge to the tool holder, and the coordinate axis Y T is determined by the right-hand system, the cutter tooth local coordinate system O T -X T Y T Z Tand, Coordinate origin O C and the coordinate origin O T The intersection of the helical cutting edge of the j-th cutter tooth and the circle is called point K. j and the coordinate axis X C The direction is vector O C K j The direction is the coordinate axis Z. C The direction is the axis of the milling cutter from the cutting edge to the tool holder, and the coordinate axis Y C is determined by the right-hand system, the local coordinate system of the cutter, O C -X C Y C Z C and, Coordinate origin O S is the intersection of the rotation axis of the spindle of the machine tool and the plane containing the circle U, and the coordinate axis Z S and the rotation axis of the spindle of the machine tool overlap, and the positive direction is the direction away from the workpiece, and the coordinate axis X S and coordinate axis X C are parallel and in the same direction, and the coordinate axis Y S and the coordinate axis Y C The machine tool spindle movement coordinate system O is parallel to and in the same direction. S -X S Y S Z S and, Coordinate origin O I is the lowest contact point between the cutting edge and the workpiece, and the coordinate axis X I is the feed direction along one line of the running blade (the machining direction along one cutting feed path), and the coordinate axis Y I is the feed direction when switching between different rows (the direction of moving to the next machining column), and the coordinate axis Z I is determined by the right-hand system, and the instantaneous feed coordinate system O I -X I Y I Z I and, Coordinate system origin O W is the starting point of machining the workpiece, and the coordinate axis X W , Y W , Z W are parallel to the three motion directions of the machine tool drive jig, and the coordinate axis X Iand coordinate axis X W are parallel and in the same direction, and the coordinate axis Y I and the coordinate axis Y W are parallel and in the same direction, and the coordinate axis Z I and the Z axis W and are parallel and in the same direction, W -X W Y W Z W Includes:

[0016] S12: Constructing a coordinate representation of the points on the helical cutting line of the first cutter tooth in the local coordinate system of the cutter tooth.

[0017] S13: A step of constructing a coordinate representation of the points on the helical cutting line of the cutter tooth in the workpiece coordinate system.

[0018] More preferably, step S12 specifically includes: The projection of point Q on the circular arc helix segment of the first cutter tooth helical cutting edge line onto the plane containing circle U is called point Q', and the coordinate origin O T and point Q' is connected to line O T Let Q' be the projection of the flat edge of the cutting edge onto the plane containing the circle U and the line segment O T The intersection point with Q' is point O', and the O'Q connection line is connected to the coordinate axis Z. T The angle with the negative direction of is λ, and the coordinate origin O T and the line segment O connecting point Q on the cylindrical spiral line of the first cutter tooth spiral cutting edge. T Let θ be the angle between Q and the plane containing the circle U, and the arc helical segment of the helical cutting edge of the first cutter tooth is shown as follows:

number

[0019] The cylindrical helical line segment of the helical cutting edge of the first cutter tooth is shown as follows:

number

[0020] More preferably, step S13 is specifically as follows: The phase difference between the j-th cutter tooth and the first cutter tooth is φ j year,

number

[0021] where j is the cutter tooth number and n t is the number of teeth of the cutter, and the transformation matrix MC T of the local coordinate system of the cutter teeth to the local coordinate system of the cutter is as follows:

number

[0022] Coordinate matrix T of any point p on the jth cutter tooth in the cutter's local coordinate system C The coordinates are obtained as follows:

number

[0023] where xT j, yT j and zT j are the three-axis coordinates of any point p of the j-th cutter tooth on the milling cutter in the cutter's local coordinate system.

[0024] The transformation matrix MS C of the cutter's local coordinate system relative to the machine tool spindle's moving coordinate system is as follows:

number

[0025] where ω is the rotational angular velocity of the milling cutter, t is the current time, and ρ is the tool mounting eccentricity.

[0026] The transformation matrix MI S of the moving coordinate system of the machine tool spindle relative to the instantaneous feed coordinate system is as follows:

number

[0027] where T γ is the coordinate origin O of the moving coordinate system of the machine tool spindle S From the coordinate origin O of the instantaneous feed coordinate system I is the translation matrix that moves along the Z coordinate axis. S Coordinate plane Y I O I Z I Projection onto the Z axis I The angle between the coordinate axis Z is defined as the side tilt angle α. S Coordinate plane X I O I Z I Projection onto the Z axis I The angle between these is defined as the forward tilt angle β, and the matrix R β' The coordinate system of the machine tool spindle is the coordinate axis Y I is the rotation matrix that rotates around the angle β', β'=arctan(tanβcosα), R α The coordinate system of the machine tool spindle is the coordinate axis X I is a rotation matrix that rotates around the angle α.

[0028] The transformation matrix MW I of the instantaneous feed coordinate system relative to the workpiece coordinate system is as follows:

number

[0029] where q is the number of feeds of the milling cutter, q=1,2,3,…,n q and n q is the total number of feeds, L is the feed length per feed, and w h is the height of the workpiece, and the adjustment amount ε κ ∈(0, f z n t )

[0030] At the current time t, the coordinate matrix T of the lowest contact point between the milling cutter and the workpiece in the workpiece coordinate system W is as follows:

number

[0031] Here, xW j,q, yW j,q, and zW j,q are the three-axis coordinates of the lowest point of contact between the milling cutter and the workpiece in the workpiece coordinate system at the current time t.

[0032] Preferably, the workpiece is subjected to simulation machining, and the waviness of the milled surface is calculated to obtain the peak-to-peak value of the waviness. (1) The workpiece is discretized into a grid, and the grid index of a grid point is denoted as (ix, iy), and the variable Z map (ix,iy) stores the height of the workpiece at the grid point, and each Z map (ix,iy) is the matrix Z map Configure.

[0033] (2) At the current time t, the three-axis coordinates xW j,q, yW j,q and zW j,q of the lowest point of contact between the milling cutter and the workpiece in the work coordinate system are stored in the following vector.

number

[0034] At the current time t, the coordinate X of the lowest contact point between the milling cutter and the workpiece in the work coordinate system current and Y current to grid indices.

number

[0035] round() is a rounding function calculated by rounding off. If the mapped grid index is inside the workpiece, further judgment is performed to find the coordinate Z of the lowest contact point between the milling cutter and the workpiece in the workpiece coordinate system at the current time t. current <Z mapIf it is (ix,iy), update the height of the workpiece at the grid point.

number

[0036] (3) For each parameter set, the following steps are performed: Traverse all grid points of the workpiece according to the set tool parameters, tool attitude parameters, and cutting parameters, perform simulation machining, and calculate the grid index and updated Z map Based on the matrix, the three-dimensional shape of the machined surface is drawn and the peak-to-peak value of the waviness is calculated.

[0037] More preferably, in steps S3 and (3), the process of obtaining the peak-to-peak value of the waviness by machining the three-dimensional shape of the surface is as follows: the lowest point of the three-dimensional shape of the machined surface is identified, a cross section passing through this lowest point is created along the feed direction of one cutter run, the intersection line between the cross section and the workpiece surface is taken as the contour line, the waviness of the contour line is calculated, and the peak-to-peak value of the waviness (ripple degree) is obtained.

[0038] Preferably, before performing step S3, the method further includes the following steps: for each parameter set, select milling cutters with different aspect ratios to perform actual machining comparisons, detect vibrations, calculate average values ​​of radial vibration amplitudes when machining using each parameter set at each aspect ratio, determine the aspect ratio corresponding to the smallest average value as the optimal aspect ratio, and use the optimal aspect ratio as the aspect ratio of the milling cutter when selecting a milling cutter in step S3.

[0039] The beneficial effects of the present invention are as follows:

[0040] In the present invention, under predetermined workpiece parameters, simulation machining is performed based on multiple parameter sets obtained based on different tool parameters, tool attitude parameter settings, and cutting parameters, to obtain the three-dimensional shape of the machined surface after machining with each parameter set. Then, an optimization variable set is constructed based on each parameter set, and the optimization variable set at which the waviness is most sensitive to changes in tool mounting eccentricity is determined. The constructed relationship between the tool mounting error and the peak-to-peak value of the waviness is then used to calculate the tool mounting eccentricity when machining the workpiece sample. If the tool mounting eccentricity exceeds the predetermined value, the bull nose end mill is re-mounted and the workpiece sample is replaced so that the workpiece can be actually machined. The calculation of the tool mounting eccentricity when machining the workpiece sample is repeated until the tool mounting eccentricity becomes smaller than the predetermined value. Therefore, the present invention realizes the inverse estimation of tool mounting eccentricity on a machine tool by analyzing the periodic features of the micro-texture of the machined surface, eliminating the need to re-mount the tool during actual machining, and avoiding the dependence on the equipment and working conditions of traditional metrology, laser or electromagnetic measurement methods, and requiring no additional sensors. It can be applied to multiple types of tools, especially bullnose end mills, providing a new, efficient and intelligent method for quality control of high-precision milling, which is low-cost, easy to operate, and inexpensive. [Brief explanation of the drawings]

[0041] [Figure 1] 1 is a schematic diagram of a reference coordinate system in the present invention. [Figure 2] 1 is a flowchart of coordinate system transformation in the present invention. [Figure 3] 1 is an output flowchart of the waviness of a milled surface in the present invention. [Figure 4] 1 is a flowchart for selecting a bull nose end mill with an optimal aspect ratio according to the present invention. [Figure 5] FIG. 10 is a graph showing the relationship between the peak-to-peak value of waviness and the amount of tool mounting eccentricity, which is created using different sets of optimization variables in the present invention. [Figure 6]FIG. 10 is a curve diagram showing the relationship between tool mounting eccentricity and waviness peak-to-peak value obtained by linear fitting using an optimization variable set when the waviness conspicuousness index of the present invention is most sensitive to changes in tool mounting eccentricity. DETAILED DESCRIPTION OF THE INVENTION

[0042] The present invention will now be further described with reference to the drawings.

[0043] A method for calculating the mounting eccentricity of a milling tool based on the texture of a generated surface, the specific steps of which are as follows:

[0044] S1: Establish the coordinate representation of the points on the spiral cutting line of the cutter tooth in the workpiece coordinate system, perform simulation machining on the workpiece with multiple parameter sets, and calculate the waviness of the milled surface.

[0045] S11: The present invention completes the modeling of the kinematic model of the milling process of a bullnose end mill (also known as a bullnose cutter, R-angle end mill, or round-nose milling cutter, which refers to an end mill with a circular arc surface portion on the cutting edge) based on homogeneous coordinate transformation, and further establishes an expression for the relative positional relationship between the cutting point of each cutter tooth and the workpiece during the cutting process of the tool, thereby simulating the entire milling process. For this purpose, a reference coordinate system is created as shown in Figure 1 to describe the kinematic process and its matrix changes. The reference coordinate system includes the following:

[0046] (1) Local coordinate system O of the cutter teeth T -X T Y T Z T( abbreviated as {T}) and is used to define the expression of the helical cutting line of the cutter tooth. Tis the center of circle U where the arc surface part (part A in Fig. 1) and cylindrical surface part (part B in Fig. 1) of the bull nose end mill intersect. The intersection point of the spiral cutting edge of the first cutter tooth and circle U is point K1, and the coordinate axis X T The direction is vector O T The K1 direction is the coordinate axis Z T The direction is the axis of the bull nose end mill from the cutting edge to the tool holder, and the coordinate axis Y T is determined by the right-hand system.

[0047] (2) Cutter local coordinate system O C -X C Y C Z C (abbreviated as {C}), and the cutter's local coordinate system is fixedly connected to the bull nose end mill (relatively stationary), and the coordinate origin O C and the coordinate origin O T The intersection of the helical cutting edge of the j-th cutter tooth and the intersecting circle is called point K. j and the coordinate axis X C The direction is vector O C K j The direction is the coordinate axis Z. C The direction is the axis of the bull nose end mill from the cutting edge to the tool holder, and the coordinate axis Y C is determined by the right-hand system.

[0048] (3) Machine tool spindle movement coordinate system O S -X S Y S Z S (abbreviated as {S}) and the coordinate origin O S is the intersection of the rotation axis of the spindle of the machine tool and the plane containing the circle U, and the coordinate axis Z S and the rotation axis of the spindle of the machine tool overlap, and the positive direction is the direction away from the workpiece, and the coordinate axis X S and coordinate axis X C are parallel and in the same direction, and the coordinate axis Y S and the coordinate axis Y C are parallel and in the same direction. S From the coordinate origin O C The distance to the tool mounting eccentricity ρ (coordinate axis ZS and the Z axis T The offset between

[0049] (4) Instantaneous feed coordinate system O I -X I Y I Z I (abbreviated as {I}) is used to define various directions during feeding, and the coordinate origin O I is the lowest point of contact between the cutting edge and the workpiece (where the bull nose end mill does not mill vertically). The present invention uses a multi-stage row cutting method to move the cutter, and the coordinate axis X I is the feed direction along one row of running blades, and the coordinate axis Y I is the feed direction when switching between different rows, and the coordinate axis Z I is determined by the right-hand system.

[0050] (5) Work coordinate system O W -X W Y W Z W (abbreviated as {W}) is used to define the spatial position of the workpiece, and the coordinate system origin O W is the starting point of machining the workpiece, and the coordinate axis X W , Y W , Z W are parallel to the three motion directions of the machine tool drive jig, and the coordinate axis X I and coordinate axis X W are parallel and in the same direction, and the coordinate axis Y I and the coordinate axis Y W are parallel and in the same direction, and the coordinate axis Z I and the Z axis W are parallel and in the same direction.

[0051] S12: Local coordinate system of the cutter teeth O T -X T Y T Z TThis is the step of constructing the coordinate representation of the points on the helical cutting edge of the first cutter tooth in . The cutting edge of a bull nose end mill consists of a flat surface portion and an arc surface portion, and the radius of the edge (which is a circle) of the flat surface portion is R1 ≠ 0, and the radius of the arc surface portion is R2 ≠ 0. The helical cutting edge is divided into two parts: an arc helical line segment located on the arc surface portion and a cylindrical helical line segment located on the cylindrical surface portion.

[0052] (1) The projection of point Q on the circular arc spiral segment of the first cutter tooth spiral cutting edge onto the plane containing circle U is set as point Q', and the coordinate origin O T and point Q' is connected to line O T Let Q' be the projection of the flat edge of the cutting edge onto the plane containing the circle U and the line segment O T The intersection point with Q' is point O', and point O' is the center of the arc on the vertical cross section that passes through point Q of the bull nose end mill cutter. T , point O', and point Q' are on the same line. The circular arc helical line of the first cutter tooth helical cutting edge (local coordinate system O T -X T Y T Z T The coordinates of point Q on the arc spiral segment at are given as follows:

number

[0053] Here, λ is the distance between the O'Q connecting line and the coordinate axis Z T is the angle with the negative direction of λ∈[0,π / 2], and γ is the helix angle of the helical cutting edge of the cutter tooth.

[0054] (2) Cylindrical surface spiral segment The cylindrical surface spiral segment of the first cutter tooth is shown as follows.

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[0055] Here, θ is the coordinate origin O T and the line segment O connecting point Q T This is the angle between Q and the plane containing the circle U, where θ≧0.

[0056] S13: This is the step of constructing the coordinate representation of the points on the spiral cutting line of the cutter teeth in the workpiece coordinate system. The cutter teeth of the bull nose end mill are uniformly distributed (equally spaced), so the phase difference between the jth cutter tooth and the first cutter tooth is φ j is.

number

[0057] where j is the cutter tooth number and n t is the number of teeth of the cutter. During the cutting motion process, the homogeneous coordinate transformation matrix MC T of the local coordinate system of the cutter teeth to the local coordinate system of the cutter is as follows:

number

[0058] Coordinate matrix T of any point p on the jth cutter tooth in the cutter's local coordinate system C The coordinates are obtained as follows:

number

[0059] Here, xT j, yT j, and zT j are the three-axis coordinates of an arbitrary point p on the j-th cutter tooth of the bull nose end mill in the cutter local coordinate system.

[0060] Describing the kinematic relationship of the cutter tooth rotation, and considering the eccentricity of the cutter installation error, the transformation matrix MS C of the cutter's local coordinate system to the moving coordinate system of the machine tool spindle is obtained as follows:

number

[0061] Here, ω is the rotational angular velocity of the bull nose end mill, t is the current time, that is, the time required from the start of the initial cutting of the bull nose end mill to the current position, and ρ is the amount of tool mounting eccentricity.

[0062] The transformation matrix MI S of the moving coordinate system of the machine tool spindle relative to the instantaneous feed coordinate system is as follows:

number

[0063] where T γ is the coordinate origin O of the moving coordinate system of the machine tool spindle S From the coordinate origin O of the instantaneous feed coordinate system I is the translation matrix that moves to the coordinate origin O S and the coordinate origin O I After the overlap, the coordinate axis Z S Coordinate plane Y I O I Z I Projection onto the Z axis I The angle between the coordinate axis Z is defined as the side tilt angle α. S Coordinate plane X I O I Z I Projection onto the Z axis I The angle between these is defined as the forward tilt angle β. β' The coordinate system of the machine tool spindle is the coordinate axis Y I is the rotation matrix that rotates around the angle β', and R α The coordinate system of the machine tool spindle is the coordinate axis X I The rotation matrix is ​​a rotation matrix that rotates around the axis by an angle α. That is, the moving coordinate system of the machine tool spindle is first T γ Then, move the coordinate origin in parallel using the coordinate Y axis. I Rotate around β' and then rotate along the coordinate axis X I Rotating around α transforms it into the instantaneous feed coordinate system. Note that we need to introduce a rotation angle β', where β' = arctan(tanβcosα).

[0064] The transformation matrix MW I of the instantaneous feed coordinate system relative to the workpiece coordinate system is as follows:

number

[0065] where q is the number of feeds of the bull nose end mill (i.e., the current row number), and q=1,2,3,…,n q …(total number of feeds) and f z is the feed rate of each tooth, and f p is the cutting pitch, and L is the feed length per step, which is 30 mm in this embodiment. h is the height of the workpiece, and w h = 10 mm. p is the cutting depth, N is the rotational speed of the spindle, εκ is the adjustment amount, and ε κ ∈(0, f z n t )

[0066] At the current time t, the coordinate matrix T of the lowest contact point between the bull nose end mill cutter and the workpiece in the workpiece coordinate system (assuming that one point of the jth cutter tooth moves to the lowest contact point position with the workpiece at the current time t) W is as follows:

number

[0067] Here, xW j,q, yW j,q, and zW j,q are the three-axis coordinates of the lowest point of contact between the bull nose end mill and the workpiece in the workpiece coordinate system at the current time t.

[0068] Any point p of the jth cutter tooth of the bull nose end mill is obtained by performing coordinate transformation based on the corresponding point of the first cutter tooth. The process of transforming any point p of the jth cutter tooth from the cutter local coordinate system to the workpiece coordinate system is shown in Figure 2.

[0069] S14: As shown in Figure 3, the workpiece is subjected to simulated machining to generate a surface shape after the simulated machining (using the Z-map method).

[0070] (1) Setting tool parameters and tool attitude parameters of a bull nose end mill, and setting cutting parameters, where the tool parameters are radius R1, radius R2, number of teeth of the cutter n t The tool attitude parameters include the side inclination angle α and the front inclination angle β. The cutting parameters include the spindle rotation speed N, the feed rate f z , cutting depth a p , cutting step f p and an adjustment amount εκ.

[0071] (2) Setting workpiece parameters: Set the workpiece size to w x ×w y ×w h Let the workpiece be discretized into an m × n grid, where the coordinate axes X W The grid step size along x = wx / m, and the coordinate axis Y W The grid step size along y = wy / n, and the grid index of the grid point is denoted as (ix, iy), and the variable Z map (ix,iy) stores the height of the workpiece at the grid point, and each Z map (ix,iy) is the matrix Z map Configure.

[0072] (3) At the current time t, the three-axis coordinates xW j,q, yW j,q and zW j,q of the lowest point of contact between the bull nose end mill cutter and the workpiece in the work coordinate system are stored in the following vector.

number

[0073] At the current time t, the coordinate X of the lowest contact point between the bull nose end mill and the workpiece in the work coordinate system current and Y current to grid indices.

number

[0074] round() is a rounding function calculated by rounding off. If the mapped grid index is inside the workpiece (i.e., if ix∈[1,m+1]∪iy∈[1,n+1]), the cutting state judgment (i.e., cutting interference judgment in Figure 3) is performed, and the coordinate Z of the lowest contact point between the bull nose end mill and the workpiece in the work coordinate system at the current time t is calculated. current <Z map If it is (ix,iy), update the height of the workpiece at the grid point.

number

[0075] (4) Traverse (scan) all grid points of the workpiece according to the set tool parameters, tool attitude parameters, and cutting parameters, and perform simulation machining on the workpiece. The grid index and the updated Z map Based on the matrix, the three-dimensional shape of the machined surface after the simulation machining is finally drawn using the surf() 3D surface generation function in MATLAB (registered trademark).

[0076] S15: Milled surface (surface after simulation processing) waviness output Workpiece parameters and number of cutter teeth n t(usually 3 or 4, 3 is used in this embodiment) is set to be constant, and the cutting parameters, tool attitude parameters, tool mounting eccentricity ρ, and remaining tool parameters are changed to obtain multiple parameter sets. Step S14 is repeated for each parameter set to obtain the corresponding 3D shape of the machined surface after simulated machining, and the lowest point of the 3D shape of the machined surface after simulated machining is identified. A cross section passing through this lowest point along the feed direction during one line of cutter travel is created, and the intersection line between the cross section and the workpiece surface is taken as the contour line. The waviness of the contour line is calculated to obtain the peak-to-peak value of the waviness.

[0077] S2: As shown in Figure 4, for each parameter set, select bull nose end mills with different aspect ratios within the range of 2 to 5, perform actual machining comparisons, detect vibrations using an acceleration sensor during machining, calculate the average radial vibration amplitude values ​​when machining using each parameter set at each aspect ratio, determine the aspect ratio corresponding to the smallest average value as the optimal aspect ratio, and set the aspect ratio of the bull nose end mill as this optimal aspect ratio, thereby suppressing interference of vibration factors with waviness.In addition, since the vibration amplitude generated in a magnesium alloy workpiece under the same parameter set is significantly lower than that of aluminum alloy and copper alloy, it is recommended to select a magnesium alloy as the workpiece material to further suppress interference of vibration factors with waviness.

[0078] S3: Find the optimal variable set when waviness is most sensitive to changes in tool mounting eccentricity.

[0079] S31: Optimization variable set Х={N, f z , f p , a p , ε κ , α, β, γ, R1, R2}, and an optimization variable set Х=Х is defined based on each parameter set. i The peak value of the swell W t(ρ, Х) is expressed as W0(Х) when the tool mounting eccentricity ρ = 0, and the waviness prominence index (significance index) affected by the tool mounting eccentricity ρ is defined as follows:

number

[0080] Here, the tool mounting eccentricity ρ in equation (14) traverses the tool mounting eccentricity ρ included in each parameter set in step S15.

[0081] S32: Using the first-order sensitivity index, each optimization variable set Х = Х i The degree of influence of the swell prominence index O(ρ, X) on the swell prominence index is evaluated. The first-order sensitivity index (based on the Sobol method) is calculated as follows:

number

[0082] Here, V( ) represents the variance, and E[O(ρ,Х)|Х=Х i ] is Х i represents the expectation value of O(ρ,Х) under the condition S ρ (ρ, Х i ) value, the larger the waviness conspicuousness index O(ρ, Х), the more the parameter Х changes with the tool mounting eccentricity ρ. i shows that it is more sensitive to

[0083] S33: Using an optimization algorithm (e.g., particle swarm algorithm), ρ (ρ, Х i The optimization goal is to maximize the waviness conspicuousness index O(ρ, Х), and the optimization variable set is solved when the waviness conspicuousness index O(ρ, Х) is most sensitive to the change in the tool mounting eccentricity ρ. * The optimization variable set X obtained by solving the solution in this embodiment is written as follows: * The parameters in are shown in Table 1.

[0084] [Table 1]

[0085] S4: Using the relationship between the tool mounting error and the waviness peak-to-peak value, calculate the tool mounting eccentricity during machining of the workpiece sample. If the tool mounting eccentricity exceeds a predetermined value, re-mount the bull nose end mill, replace the workpiece sample, and calculate the tool mounting eccentricity during machining of the workpiece sample. This process is repeated until the tool mounting eccentricity becomes smaller than the predetermined value, and then the workpiece is actually machined. Specifically, the process is as follows:

[0086] S41: Optimization variable set X * Each parameter set having each parameter value in the above is selected, and the peak-to-peak value W of the waviness obtained by simulating machining of the workpiece with these parameter sets is calculated. t (ρ,Х * ) to obtain the peak-to-peak value of the swell W t (ρ,Х * ) and tool mounting eccentricity ρ, and the tool mounting eccentricity ρ and the peak-to-peak value W of the waviness obtained by fitting were plotted. t (ρ,Х * ) is as follows:

number

[0087] As shown in Fig. 5, the relationship between the peak-to-peak value of waviness and the tool mounting eccentricity plotted using six different sets of optimization variables is created and compared. (f) in Fig. 5 shows the peak-to-peak value W t (ρ,Х * ) and tool mounting eccentricity ρ. As can be seen from this, the optimization variable set Х * The peak value of the swell is W t (ρ,Х * ) is sensitive to each value of tool mounting eccentricity ρ, and the peak-to-peak value of waviness W t (ρ,Х *) and tool eccentricity ρ are close to a linear change relationship, and the peak-to-peak value of waviness in the remaining optimization variable set fluctuates greatly with changes in tool eccentricity, but is not sensitive to all values ​​of tool eccentricity ρ. The tool eccentricity ρ and peak-to-peak value of waviness W obtained by linear fitting based on the data in Fig. 5(f) t (ρ,Х * The relationship between the temperature and the temperature is shown in Figure 6.

[0088] S42: Optimization variable set X * and selecting a bull nose end mill based on the optimum aspect ratio (as an alternative embodiment, step S2 may not be included, in which case the step of selecting the optimum aspect ratio is not included here), and the number of teeth n of the cutter. t A bull nose end mill for which the setting is made is selected, and this bull nose end mill and the work sample are mounted on the machine tool.

[0089] S43: Optimization variable set X for machine tools * Under these conditions, a workpiece sample is machined using the workpiece parameters in step S14, and the three-dimensional shape of the machined surface of the machined workpiece sample is obtained using a white light interferometer or a laser contour measuring device. The lowest point of the three-dimensional shape of the machined surface is identified, and a cross section passing through this lowest point along the feed direction during one line of cutter travel is created. The intersection of the cross section and the workpiece surface is taken as the contour line, and the waviness of the contour line is calculated to obtain the peak-to-peak value of the waviness. This is then substituted into equation (16) to find a solution and obtain the corresponding tool mounting eccentricity ρ.

[0090] S44: If the tool mounting eccentricity ρ exceeds the predetermined value, re-mount the bull nose end mill, replace the workpiece sample, and repeat step S43 until the tool mounting eccentricity ρ is smaller than the predetermined value, and then the actual machining of the workpiece can be performed.

Claims

1. A method for calculating the amount of mounting eccentricity of a milling tool based on the texture of a generated surface in milling processing, in which the feed of a milling cutter in a row direction of a predetermined length at a predetermined feed rate is repeated for a plurality of rows at predetermined pitch intervals in a switching direction perpendicular to the row direction, S1: Establish the coordinate representation of the points on the spiral cutting line of the cutter tooth in the workpiece coordinate system, and the radius R of the edge of the cutting edge plane of the milling cutter 1 , the radius of the arc surface of the milling cutter cutting edge R 2 , number of cutter teeth n t and tool parameters including the helix angle γ of the helical cutting edge of the cutter tooth, tool attitude parameters including the side inclination angle α and the forward inclination angle β, spindle rotation speed N, and feed rate f per tooth z , cutting depth a p , the predetermined pitch interval is the cutting pitch f p and an adjustment amount ε which is the amount of feed deviation in the row direction between adjacent rows. κ Set the cutting parameters including the number of teeth of the cutter, n t Step S1: while keeping constant, changing cutting parameters, tool attitude parameters, tool mounting eccentricity ρ and remaining tool parameters to obtain a plurality of parameter sets, performing simulation machining for each of the parameter sets, and calculating the waviness of the milled surface to obtain a peak-to-peak value of the waviness; S2: Optimization variable set X={N, f z , f p , a p , ε κ , α, β, γ, R 1 , R 2 }, and one optimization variable set Х=Х is defined based on each parameter set. i The peak value of the swell W t (ρ, Х) is W when the tool mounting eccentricity ρ=0 0 (X), and the waviness conspicuousness index affected by tool mounting eccentricity ρ is defined as follows: [Equation 1] Next, each optimization variable set Х=Х is calculated using the first-order sensitivity index, which is calculated as follows: i The degree of influence on the swell prominence index O(ρ,Х) is evaluated. [Equation 2] Here, V( ) represents the variance, and E[O(ρ,Х)|Х=Х i ] represents the expected value of O(ρ,Х) under the condition Х i . Finally, we use an optimization algorithm to ρ (ρ, Х i Step S2: Solving a set of optimization variables when the waviness conspicuousness index O(ρ, X) is most sensitive to changes in the tool mounting eccentricity ρ, with the optimization goal being to maximize the waviness conspicuousness index O(ρ, X); S3: A parameter set having each parameter value in the optimization variable set is selected, and the peak-to-peak value of the waviness obtained by simulating machining with these parameter sets is used to derive a relational expression between the tool mounting eccentricity and the peak-to-peak value of the waviness by fitting, and the number of teeth n of the set cutter is determined. t and (S3) selecting a milling cutter based on the optimization variable set, allowing the machine tool to machine the workpiece sample under the conditions of the optimization variable set, obtaining the three-dimensional shape of the machined surface of the workpiece sample after machining, obtaining the peak-to-peak value of the waviness, and calculating the tool mounting eccentricity during machining of the workpiece sample using the relationship between the tool mounting error and the peak-to-peak value of the waviness; if the tool mounting eccentricity exceeds a predetermined value, re-mounting the milling cutter, replacing the workpiece sample, and calculating the tool mounting eccentricity during machining of the workpiece sample, this process is repeated until the tool mounting eccentricity becomes smaller than the predetermined value, thereby obtaining a final tool mounting eccentricity.

2. In step S1, establishing a coordinate representation of a point on the helical cutting line of the cutter tooth in the workpiece coordinate system includes: S11: A step of creating a reference coordinate system, the reference coordinate system being: Coordinate origin O T is the center of the circle U where the arc surface portion and the cylindrical surface portion of the milling cutter intersect, and the intersection point between the spiral cutting edge of the first cutter tooth and the circle U is point K 1 and the coordinate axis X T The direction is vector O T K 1 The direction is the coordinate axis Z. T The direction is the axis of the milling cutter from the cutting edge to the tool holder, and the coordinate axis Y T is determined by the right-hand system, the cutter tooth local coordinate system O T -X T Y T Z T and, Coordinate origin O C and the coordinate origin O T The intersection of the helical cutting edge of the j-th cutter tooth and the circle is called point K. j and the coordinate axis X C The direction is vector O C K j The direction is the coordinate axis Z. C The direction is the axis of the milling cutter from the cutting edge to the tool holder, and the coordinate axis Y C is determined by the right-hand system, the local coordinate system of the cutter, O C -X C Y C Z C and, Coordinate origin O S is the intersection of the rotation axis of the spindle of the machine tool and the plane containing the circle U, and the coordinate axis Z S and the rotation axis of the spindle of the machine tool overlap, and the positive direction is the direction away from the workpiece, and the coordinate axis X S and coordinate axis X C are parallel and in the same direction, and the coordinate axis Y S and the coordinate axis Y C The machine tool spindle movement coordinate system O is parallel to and in the same direction. S -X S Y S Z S and, Coordinate origin O I is the lowest contact point between the cutting edge and the workpiece, and the coordinate axis X I is the feed direction along one row of running blades, and the coordinate axis Y I is the feed direction when switching between different rows, and the coordinate axis Z I is determined by the right-hand system, and the instantaneous feed coordinate system O I -X I Y I Z I and, Coordinate system origin O W is the starting point of machining the workpiece, and the coordinate axis X W , Y W , Z W are parallel to the three motion directions of the machine tool drive jig, and the coordinate axis X I and coordinate axis X W are parallel and in the same direction, and the coordinate axis Y I and the coordinate axis Y W are parallel and in the same direction, and the coordinate axis Z I and the Z axis W and are parallel and in the same direction, W -X W Y W Z W Step S11 including: S12: constructing a coordinate representation of a point on the helical cutting line of the first cutter tooth in the local coordinate system of the cutter tooth; 2. The method for calculating the mounting eccentricity of a milling tool based on the texture of the generated surface according to claim 1, further comprising the step of: S13: constructing a coordinate representation of points on the helical cutting line of the cutter tooth in the workpiece coordinate system.

3. In step S12, The projection of point Q on the circular arc helix segment of the first cutter tooth helical cutting edge line onto the plane containing circle U is called point Q', and the coordinate origin O T and point Q' is connected to line O T Let Q' be the projection of the flat edge of the cutting edge onto the plane containing the circle U and the line segment O T The intersection point with Q' is point O', and the O'Q connection line is connected to the coordinate axis Z. T The angle with the negative direction of is λ, and the coordinate origin O T and the line O connecting point Q on the cylindrical spiral line of the first cutter tooth spiral cutting edge. T Let θ be the angle between Q and the plane containing the circle U, and the arc helical segment of the helical cutting edge of the first cutter tooth is expressed as follows: [Equation 3] The method for calculating the mounting eccentricity of a milling tool based on the texture of the generated surface according to claim 2, characterized in that the cylindrical surface helical line segment of the helical cutting edge of the first cutter tooth is expressed as follows: [Equation 4]

4. In step S13, the phase difference between the j-th cutter tooth and the first cutter tooth is defined as φ j year, [Equation 5] where j is the cutter tooth number and n t is the number of teeth of the cutter, and the transformation matrix MC T of the local coordinate system of the cutter teeth to the local coordinate system of the cutter is as follows: [Equation 6] Coordinate matrix T of any point p on the jth cutter tooth in the cutter's local coordinate system C The coordinates are obtained as follows: [Equation 7] where xTj, yTj and zTj are the three-axis coordinates of any point p of the jth cutter tooth on the milling cutter in the cutter's local coordinate system; The transformation matrix MS C of the cutter's local coordinate system relative to the machine tool spindle's moving coordinate system is as follows: [Equation 8] where ω is the rotational angular velocity of the milling cutter, t is the current time, and ρ is the tool mounting eccentricity. The transformation matrix MI S of the machine tool spindle movement coordinate system relative to the instantaneous feed coordinate system is as follows: [Equation 9] where T γ is the coordinate origin O of the moving coordinate system of the machine tool spindle S From the coordinate origin O of the instantaneous feed coordinate system I is the translation matrix that moves along the Z coordinate axis. S Coordinate plane Y I O I Z I Projection onto the Z axis I The angle between the coordinate axis Z is defined as the side tilt angle α. S Coordinate plane X I O I Z I Projection onto the Z axis I The angle between these is defined as the forward tilt angle β, and the matrix R β' The coordinate system of the machine tool spindle is the coordinate axis Y I is the rotation matrix that rotates around the angle β', β'=arctan(tanβcosα), R α The coordinate system of the machine tool spindle is the coordinate axis X I is a rotation matrix that rotates around the angle α, The transformation matrix MW I of the instantaneous feed coordinate system relative to the workpiece coordinate system is as follows: [Equation 10] Here, q is the number of times the milling cutter is fed in the row direction, and q=1, 2, 3, ..., n q and n q is the total number of feeds, L is the feed length in one pass in the row direction, and w h is the height of the workpiece, 0≦adjustment amount ε κ ≦fznt, At the current time t, the coordinate matrix T of the lowest contact point between the milling cutter and the workpiece in the workpiece coordinate system W is as follows: [0011] 3. The method for calculating the mounting eccentricity of a milling tool based on the texture of the generated surface according to claim 2, wherein xW j,q, yW j,q and zW j,q are the three-axis coordinates of the lowest point of contact between the milling cutter and the workpiece in the workpiece coordinate system at the current time t.

5. By performing simulation machining on the workpiece and calculating the waviness of the milled surface, the peak-to-peak value of the waviness can be obtained. (1) The workpiece is discretized into a grid, and the grid index of the grid point is denoted as (ix, iy), and the variable Z map (ix,iy) stores the height of the workpiece at the grid point, and each Z map (ix,iy) is the matrix Z map Step (1) of constructing (2) At the current time t, the three-axis coordinates xW j,q, yW j,q and zW j,q of the lowest contact point between the milling cutter and the workpiece in the workpiece coordinate system are stored in the following vector: [0012] At the current time t, the coordinate X of the lowest contact point between the milling cutter and the workpiece in the work coordinate system current and Y current to grid indices, [0013] round() is a rounding function calculated by rounding off. If the mapped grid index is inside the workpiece, further judgment is performed to find the coordinate Z of the lowest contact point between the milling cutter and the workpiece in the workpiece coordinate system at the current time t. current <Z map (ix,iy), then update the height of the workpiece at the grid point (2); and [0014] (3) For each parameter set, traverse all grid points of the workpiece according to the set tool parameters, tool attitude parameters, and cutting parameters, perform simulation machining, and obtain the grid index and updated Z map The method for calculating the mounting eccentricity of a milling tool based on the texture of the generated surface according to claim 1, further comprising the step (3) of drawing a three-dimensional shape of the machining surface based on the matrix and calculating a peak-to-peak value of the waviness.

6. 6. The method for calculating the mounting eccentricity of a milling tool based on the texture of a generated surface according to claim 5, wherein in step S3 and step (3), the process of obtaining the peak-to-peak value of the waviness by machining the three-dimensional shape of the surface comprises identifying the lowest point of the three-dimensional shape of the machined surface, creating a cross section passing through this lowest point along the feed direction during one line of cutter travel, defining the intersection line between the cross section and the workpiece surface as a contour line, calculating the waviness of the contour line, and obtaining the peak-to-peak value of the waviness.

7. 2. The method for calculating the mounting eccentricity of a milling tool based on the texture of the generated surface according to claim 1, further comprising, before performing step S3, the steps of selecting milling cutters with different aspect ratios for each parameter set and comparing actual machining to detect vibrations, calculating average values ​​of radial vibration amplitude values ​​when machining using each parameter set at each aspect ratio, determining the aspect ratio corresponding to the smallest average value as the optimal aspect ratio, and setting the aspect ratio of the milling cutter to the optimal aspect ratio when selecting the milling cutter in step S3.

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