Five-axis side milling surface roughness prediction method

Abstract

The invention discloses a five-axis side milling machining surface roughness prediction method. Firstly, a workpiece, a cutter location point, a main shaft and a cutter coordinate system are established; secondly, the tool is dispersed in the ZW axis direction of a workpiece coordinate system, and elliptical sections with different geometric parameters are obtained; then tool nose point coordinates, tool axis vectors and eccentric parameters of the current feeding position are extracted, and geometric parameters of an elliptic model are determined according to the tool nose point coordinates, the tool axis vectors and the eccentric parameters; constructing a space trajectory of the elliptical model in combination with a tool machining path and a feeding speed; and finally, deriving to obtain the surface appearance of the workpiece for calculating the overall surface roughness. According to the five-axis side milling simulation method based on the elliptical model, the calculation efficiency can be effectively improved by establishing the elliptical model for five-axis side milling, and the prediction precision is ensured. According to the method, surface roughness control in the complex curved surface machining process is facilitated, and theoretical support is provided for optimizing machining process parameters and improving machining precision.

Description

Technical Field

[0001] The present invention relates to the field of five-axis side milling, and in particular to a method for predicting surface roughness during five-axis side milling. Background Art

[0002] Five-axis side milling is widely used in metal removal processes in the automotive, aerospace and other fields. Especially in the finishing process, surface roughness, as one of the key machining quality indicators, has a significant impact on the performance of parts and the subsequent assembly accuracy. With the continuous improvement of product quality requirements in the manufacturing industry, the accurate prediction and control of machining surface roughness has become a research focus. Accurately predicting the surface roughness of workpieces is conducive to research in the field of precision manufacturing, and provides theoretical support for optimizing machining parameters, improving machining quality and reducing production costs. Especially in the machining process of complex components, their contours are usually composed of straight lines and convex and concave arc segments with different curvature radii. Since the change in curvature will affect the residual height of the surface during machining, it will affect the quality of the machined surface. Therefore, in the five-axis side milling of complex contour workpieces, accurate prediction of surface roughness is particularly important.

[0003] In the prior art, the trochoid model and the discrete point trajectory model are the two main mathematical models used for milling surface topography prediction. The trochoid model is based on the superposition relationship between the tool's rotational motion and feed motion, and describes the trochoid trajectory formed by any specified point on the tool on the workpiece surface. During the milling process, the tool rotates around the spindle while moving relative to the workpiece at a set feed speed, so that the motion trajectory of each point on the cutting edge exhibits trochoid characteristics. This trajectory directly determines the micro-geometric topography of the machined surface, so the trochoid model can be used to predict surface roughness. The discrete point trajectory model predicts the milling surface topography by discretizing the tool edge into multiple points, calculating the trajectory formed during the tool rotation and feed process, and solving the minimum envelope curve. By considering the discretization of the tool trajectory, the details of the contact between the tool and the workpiece can be more accurately reflected. It is particularly suitable for predicting the surface topography of complex components and provides an effective mathematical tool for optimizing surface quality in high-precision milling processing. However, the trochoid model and the discrete point trajectory model have the problems of high computational difficulty and low computational efficiency in the simulation and calculation process of five-axis side milling processing, making it difficult to meet the needs of efficient and high-precision prediction.

[0004] The existing technology requires a method for accurately predicting the surface roughness of five-axis side milling, which can improve the calculation efficiency while ensuring the calculation accuracy. Summary of the Invention

[0005] The purpose of the present invention is to propose a surface roughness prediction method for five-axis side milling, which can reduce the amount of calculation in surface topography and roughness prediction, improve calculation efficiency, and ensure calculation accuracy.

[0006] To achieve the above object, the technical solution of the present invention is: a method for predicting surface roughness of five-axis side milling, comprising the following steps:

[0007] S1. First, establish the workpiece, tool location, spindle and tool coordinate system;

[0008] S2, move the tool along the workpiece coordinate system Z W Discretization in the axial direction yields elliptical sections with different geometric parameters;

[0009] S3. Determine the geometric parameters of the elliptical model based on the extracted tool tip point position, tool axis vector, and eccentricity parameters;

[0010] S4, based on the tool processing path and feed speed, obtaining the elliptical space trajectory of each tool position point;

[0011] S5, assembling the elliptical spatial trajectory into the processed surface topography;

[0012] S6. Calculate the surface roughness based on the obtained surface morphology.

[0013] Preferably, the coordinate system in S1 is established as follows:

[0014] Workpiece coordinate system X W Y W Z W From the origin O W Move to origin O P Get the tool position coordinate system X P Y P Z P , where the moving distance is known through the tool position parameter; due to the existence of the swing angle, through point O P The axis Z P Rotate to be parallel to the tool axis vector to obtain the spindle coordinate system X S Y S Z S , where the axis Z S In line with the spindle axis direction; determine the eccentricity ρ and angle Get tool coordinate system X T Y T Z T At point O T Add auxiliary coordinate system X E Y E Z E With the workpiece coordinate system X W Y W Z W parallel.

[0015] Preferably, the process of calculating the geometric parameters of the ellipse model in S3 specifically includes the following steps:

[0016] 1) Move the tool along the workpiece coordinate system Z W The axial direction is discrete, and each cross section is an ellipse of different size and direction, and the distance between each ellipse is the feed per tooth f. z :

[0017] f z =f / (n·N t )

[0018] Among them, f represents the feed rate, n represents the spindle speed, N t Represents the number of tool teeth;

[0019] 2) The position of the tool position is measured by [X D Y D Z D I D J D K D ] These six parameters are used to represent the tool tip position in the workpiece coordinate system. D Represents the tool axis vector in X D Projection in the axial direction, J D Represents the tool axis vector in Y D Projection in the axis direction, K D Represents the tool axis vector in Z D Axis projection;

[0020] 3) Calculate the oblique ellipse whose geometric parameters change with the tool axis vector. The change rule is as follows:

[0021]

[0022] Among them, k represents the feed tool position number of each tooth; a (i,k) 、b (i,k) and R (i,k) They represent the major axis, minor axis and actual cutting radius of the oblique ellipse at the kth tool position in the i-th layer respectively; the rotation angle α represents the angle between the major axis of the oblique ellipse and the main axis coordinate system X S The angle between the axes; the tilt angle β represents the angle between the tool axis vector and the workpiece coordinate system Z W Axis angle.

[0023] Preferably, the elliptical space trajectory of each tool position point calculated in S4 is obtained by the following formula:

[0024]

[0025]

[0026]

[0027] in, and Represents the height In the plane, the center of the elliptical model is in the workpiece coordinate system X W Y W Z W The coordinate value of the following; and Represents any point on the elliptical trajectory in the auxiliary coordinate system X E Y E Z E Coordinate value of x W 、y W and z W Represents any point on the elliptical trajectory in the workpiece coordinate system X W Y W Z W The coordinate value of the following; W T E Represents the transformation matrix from the auxiliary coordinate system to the workpiece coordinate system.

[0028] Preferably, the calculation of the roughness in S6 includes the following steps:

[0029] 1) In order to establish the relationship between surface topography and roughness, an auxiliary parameter surface profile height R is introduced max As the trajectory profile feature value;

[0030] 2) By establishing a geometric relationship between the cutting surface and the surface topography, the calculation formula for the surface profile height is derived as follows:

[0031]

[0032]

[0033] Among them, l (i,k) represents the distance from any point on the ellipse trajectory to the center of the ellipse at the kth tool position on the i-th layer; λ represents the independent variable in the ellipse equation; p and q represent the serial number of the current cutting tooth and the serial number of the next cutting tooth that produces the effective surface topography, respectively; the intersection point of the paths of cutting tooth p and cutting tooth q is taken as M, the lowest point of the ellipse trajectory corresponding to tooth p is N, and the center of the ellipse trajectory of tooth q is O q , the center of the elliptical trajectory of the blade tooth p is O p , The reverse extension line of The angle is represent The reverse extension line of Angle; represent and The angle between (i,p)represents the distance from any point on the ellipse trajectory to the center of the ellipse at the p-th tool position on the i-th layer; l (i,q) represents the distance from any point on the ellipse trajectory to the center of the ellipse at the qth tool position on the i-th layer; f z Feed per tooth; Δl represents the distance between the center points of adjacent effective elliptical paths at a certain height; K represents the curvature of the workpiece surface corresponding to the current tool position; Δf represents the distance between adjacent effective tool tip points, that is, Δf = (pq)·f z ; α p and α q represents the inclination angle of the cutting teeth p and q; h represents the height value of the cutting element in the Z-axis direction.

[0034] 3) The surface roughness calculation method is as follows:

[0035]

[0036] Among them, Z p (x) and Z v (x) represents the highest point and the lowest point of the contour within the basic measurement range, and x represents the position coordinates on the measurement contour line.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] This paper provides a five-axis side milling simulation method based on an elliptical model. By establishing an elliptical model for five-axis side milling, this method effectively improves computational efficiency and ensures prediction accuracy. This method facilitates surface roughness control during the machining of complex curved surfaces and provides theoretical support for optimizing machining parameters and improving machining accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Flowchart of the method for predicting the surface topography of a side milling process of a curved surface according to the present invention;

[0040] Figure 2a A schematic diagram of a coordinate system according to an embodiment of the present invention;

[0041] Figure 2b A schematic diagram of tool eccentricity parameter definition according to an embodiment of the present invention;

[0042] Figure 3 Schematic diagram of the discrete state of a tool in a workpiece coordinate system according to an embodiment of the present invention;

[0043] Figure 4 This is a diagram of the ellipse model parameter steps according to an embodiment of the present invention;

[0044] Figure 5 A schematic diagram of the surface profile height of an embodiment of the present invention;

[0045] Figure 6 A schematic diagram of the surface profile height of a complex curved surface according to an embodiment of the present invention;

[0046] Figure 7 A processing diagram of an embodiment of the present invention;

[0047] Figure 8 A roughness measurement point position diagram according to an embodiment of the present invention;

[0048] Figure 9 A comparison diagram of roughness simulation results and measured data of an embodiment of the present invention;

[0049] Figure 10 2 is a deviation rate comparison diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The following is combined with Figure 1-10 , the technical solution of the present invention is described in detail.

[0051] The present invention proposes a method for predicting the surface morphology of cutting process, such as Figure 1 As shown, the specific steps include:

[0052] Establish workpiece coordinate system, tool location coordinate system, spindle coordinate system and tool coordinate system;

[0053] Workpiece coordinate system X W Y W Z W From the origin O W Move to origin O P Get the tool position coordinate system X P Y P Z P , where the moving distance is determined by the tool position parameter [X D Y D Z D ] is known. Secondly, due to the existence of the swing angle, it is necessary to pass through point O P The axis Z P Rotate to the same direction as the tool axis vector [I D J D K D ] parallel to obtain the principal axis coordinate system X S Y S Z S , where the axis Z S The direction of the axis is consistent with the spindle axis. S Take a plane perpendicular to the axis Z at any position in the direction S , respectively, the intersection axis Z T and axis Z S At points A and B, the length of line segment AB is ρ; axis X S With axis ZS The plane is P1, axis X T With axis Z T The plane is P2, and the angle between planes P1 and P2 is The tool coordinate system X can be obtained by the above two eccentric parameters. T Y T Z T Finally, at point O T Add auxiliary coordinate system X E Y E Z E With the workpiece coordinate system X W Y W Z W Parallel, such as Figure 2a shown.

[0054] In the spindle coordinate system, the distance between the spindle axis and the tool axis is as follows: Figure 2b As shown;

[0055] Calculate the geometric parameters of the ellipse model. Give priority to the workpiece coordinate system. At the same height, since the tool axis vector is no longer perpendicular to the workpiece surface, the cross section of the tool cylinder is an ellipse, that is, the cross section of the tool cylinder changes from a circle with a fixed geometric size to an oblique ellipse with geometric parameters that change with the tool axis vector, such as Figure 3 As shown, its changing rule is calculated by the following formula:

[0056]

[0057] Among them, k represents the feed tool position number of each tooth; a (i,k) 、b (i,k) and R (i,k) They represent the major axis, minor axis and actual cutting radius of the oblique ellipse at the kth tool position in the i-th layer respectively; the rotation angle α represents the angle between the major axis of the oblique ellipse and the main axis coordinate system X S The angle between the two axes; the tilt angle β represents the angle between the tool axis vector and the workpiece coordinate system Z W Axis angle.

[0058] In theory, the tool axis and the spindle axis are consistent, and the theoretical tool radius is valid. However, in the actual processing process, due to the installation error of the tool, the tool axis and the spindle axis are inevitably eccentric. Among them, the tool eccentricity is composed of two main parameters: eccentricity ρ and positioning angle According to the actual cutting radius and tool axis vector obtained by the eccentricity parameter, the length of the major axis and minor axis of the ellipse can be obtained respectively. Figure 4 shown.

[0059] The elliptical space trajectory of each tool position point is calculated. By analyzing the overall elliptical model and combining the actual cutting radius and tool axis vector, the trajectory of the elliptical model can be obtained as shown below:

[0060]

[0061]

[0062]

[0063] in, and Represents the height In the plane, the center of the elliptical model is in the workpiece coordinate system X W Y W Z W The coordinate value of the following; and Represents any point on the elliptical trajectory in the auxiliary coordinate system X E Y E Z E Coordinate value of x W 、y W and z W Represents any point on the elliptical trajectory in the workpiece coordinate system X W Y W Z W The coordinate value of the following; W T E Represents the transformation matrix from the auxiliary coordinate system to the workpiece coordinate system.

[0064] The obtained elliptical spatial trajectories are assembled into the processed surface topography.

[0065] In order to establish the relationship between surface topography and roughness, an auxiliary parameter surface profile height R is introduced. max As the trajectory profile characteristic value, such as Figure 5 and Figure 6 shown.

[0066] A geometric relationship is established between the cutting surface and the surface topography, and the calculation formula for the surface profile height is derived as follows:

[0067]

[0068]

[0069] Among them, l (i,k)represents the distance from any point on the ellipse trajectory to the center of the ellipse at the kth tool position on the i-th layer; λ represents the independent variable in the ellipse equation; p and q represent the serial number of the current cutting tooth and the serial number of the next cutting tooth that produces the effective surface topography, respectively; the intersection point of the paths of cutting tooth p and cutting tooth q is taken as M, the lowest point of the ellipse trajectory corresponding to tooth p is N, and the center of the ellipse trajectory of tooth q is O q , the center of the elliptical trajectory of the blade tooth p is O p , The reverse extension line of The angle is represent The reverse extension line of Angle; represent and The angle between (i,p) represents the distance from any point on the ellipse trajectory to the center of the ellipse at the p-th tool position on the i-th layer; l (i,q) represents the distance from any point on the ellipse trajectory to the center of the ellipse at the qth tool position on the i-th layer; f z Feed per tooth; Δl represents the distance between the center points of adjacent effective elliptical paths at a certain height; K represents the curvature of the workpiece surface corresponding to the current tool position; Δf represents the distance between adjacent effective tool tip points, that is, Δf = (pq)·f z ; α p and α q represents the inclination angle of the cutting teeth p and q; h represents the height value of the cutting element in the Z-axis direction.

[0070] During the measurement process, select the maximum height R of the profile Z As a representative of surface roughness, the calculation method is as follows:

[0071]

[0072] Among them, Z p (x) and Z v (x) represents the highest point and the lowest point of the contour within the basic measurement range, and x represents the position coordinates on the measurement contour line.

[0073] When obtaining the surface profile height R of each tool position max Finally, combined with the calculation formula of the elliptical path, the surface profile height of any point on the elliptical path can be obtained, and then the profile height of each tool position of the entire processing surface can be obtained by gathering the discrete layers of the elliptical path into a surface. z , the roughness prediction value of the machined surface can be obtained.

[0074] In the experiment, the workpiece material used for processing is aluminum alloy 7075-T7451, and the tool is a two-tooth carbide end mill with a tool radius of 16 mm, a helix angle of 45°, a tool eccentricity of 0.005 mm, and an eccentricity angle of 30°. The processing diagram is shown in the figure. Figure 7 As shown. The surface roughness of each measuring point on the workpiece surface is detected using a surface profiler (Form Talysurf I-120). When measuring the workpiece, first divide it into three layers along the height direction and measure them separately. Then, according to the curvature characteristics of the workpiece, 9 measuring points are selected on the processing surface of the same layer, as shown in the figure. Figure 8 shown.

[0075] When selecting measurement points, points ②, ③, and ④ correspond to the concave region, points ⑥, ⑦, and ⑧ correspond to the convex region, and points ①, ⑤, and ⑨ correspond to the flat region. The measurement points are evenly distributed across the three curvature regions. Because the S specimen is a non-developable ruled surface, the curvature at different heights of the same tool position varies. The roughness data obtained from the measurements is shown in Table 1.

[0076] Table 1 Surface roughness measurement data

[0077]

[0078] The simulation results of the upper area of ​​the S specimen are compared with the measured data, such as Figure 9 As shown in the comparison chart, it can be seen that the change trends of the simulation results and the measured data are consistent.

[0079] In order to avoid large deviations caused by large cardinality, the deviation rate R is introduced. error (Deviation value ÷ measured value) is used as a reference for the deviation between simulation and measurement, such as Figure 10 By comparison, the simulation results and the measured results are basically consistent in the plane area; the maximum deviation rate in the concave and convex areas is 20%, which is controlled within a small range, verifying that the roughness prediction of the present invention has good accuracy.

[0080] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions and effects do not exceed the scope of the technical solution of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A method for predicting surface roughness during five-axis side milling, characterized in that: The following steps are involved: S1. First, establish the workpiece, tool location, spindle and tool coordinate system; S2, move the tool along the workpiece coordinate system Z W Discretization in the axial direction yields elliptical sections with different geometric parameters; S3. Determine the geometric parameters of the elliptical model based on the extracted tool tip point position, tool axis vector, and eccentricity parameters; S4, based on the tool processing path and feed speed, obtaining the elliptical space trajectory of each tool position point; S5, assembling the elliptical spatial trajectory into the processed surface topography; S6. Calculate the surface roughness based on the obtained surface morphology.

2. The surface roughness prediction method for five-axis side milling according to claim 1, characterized in that: The establishment of the coordinate system in S1 is as follows: Workpiece coordinate system X W Y W Z W From the origin O W Move to origin O P Get the tool position coordinate system X P Y P Z P , where the moving distance is known through the tool position parameter; due to the existence of the swing angle, through point O P The axis Z P Rotate to be parallel to the tool axis vector to obtain the spindle coordinate system X S Y S Z S , where the axis Z S In line with the spindle axis direction; determine the eccentricity ρ and angle Get tool coordinate system X T Y T Z T At point O T Add auxiliary coordinate system X E Y E Z E With the workpiece coordinate system X W Y W Z W parallel.

3. The surface roughness prediction method for five-axis side milling according to claim 1, characterized in that: The process of calculating the geometric parameters of the ellipse model in S3 specifically includes the following steps: 1) Move the tool along the workpiece coordinate system Z W The axial direction is discrete, and each cross section is an ellipse of different size and direction, and the distance between each ellipse is the feed per tooth f. z : f z =f / (n·N t ) Among them, f represents the feed rate, n represents the spindle speed, N t Represents the number of tool teeth; 2) The position of the tool position is measured by [X D Y D Z D I D J D K D ] These six parameters are used to represent the tool tip position in the workpiece coordinate system. D Represents the tool axis vector in X D Projection in the axial direction, J D Represents the tool axis vector in Y D Projection in the axis direction, K D Represents the tool axis vector in Z D Axis projection; 3) Calculate the oblique ellipse whose geometric parameters change with the tool axis vector. The change rule is as follows: Among them, k represents the feed tool position number of each tooth; a (i,k) 、b (i,k) and R (i,k) They represent the major axis, minor axis and actual cutting radius of the oblique ellipse at the kth tool position in the i-th layer respectively; the rotation angle α represents the angle between the major axis of the oblique ellipse and the main axis coordinate system X S The angle between the axes; the tilt angle β represents the angle between the tool axis vector and the workpiece coordinate system Z W Axis angle.

4. The method for predicting surface roughness during five-axis side milling according to claim 3, wherein: The elliptical space trajectory of each tool position point calculated in S4 is obtained by the following formula: in, and Represents the height In the plane, the center of the elliptical model is in the workpiece coordinate system X W Y W Z W The coordinate value of the following; and Represents any point on the elliptical trajectory in the auxiliary coordinate system X E Y E Z E Coordinate value of x W 、y W and z W Represents any point on the elliptical trajectory in the workpiece coordinate system X W Y W Z W The coordinate value of the following; W T E Represents the transformation matrix from the auxiliary coordinate system to the workpiece coordinate system.

5. The method for predicting surface roughness during five-axis side milling according to claim 4, wherein: The calculation of the roughness in S6 includes the following steps: 1) In order to establish the relationship between surface topography and roughness, an auxiliary parameter surface profile height R is introduced max As the trajectory profile feature value; 2) By establishing a geometric relationship between the cutting surface and the surface topography, the calculation formula for the surface profile height is derived as follows: Among them, l (i,k) represents the distance from any point on the ellipse trajectory to the center of the ellipse at the kth tool position on the i-th layer; λ represents the independent variable in the ellipse equation; p and q represent the serial number of the current cutting tooth and the serial number of the next cutting tooth that produces the effective surface topography, respectively; the intersection point of the paths of cutting tooth p and cutting tooth q is taken as M, the lowest point of the ellipse trajectory corresponding to tooth p is N, and the center of the ellipse trajectory of tooth q is O q , the center of the elliptical trajectory of the blade tooth p is O p , The reverse extension line of The angle is represent The reverse extension line of Angle; represent and The angle between (i,p) represents the distance from any point on the ellipse trajectory to the center of the ellipse at the p-th tool position on the i-th layer; l (i,q) represents the distance from any point on the ellipse trajectory to the center of the ellipse at the qth tool position on the i-th layer; f z Feed per tooth; Δl represents the distance between the center points of adjacent effective elliptical paths at a certain height; K represents the curvature of the workpiece surface corresponding to the current tool position; Δf represents the distance between adjacent effective tool tip points, that is, Δf = (pq)·f z ; α p and α q represents the inclination angle of the cutting teeth p and q; h represents the height value of the cutting element in the Z-axis direction. 3) The surface roughness calculation method is as follows: Among them, Z p (x) and Z v (x) represents the highest point and the lowest point of the contour within the basic measurement range, and x represents the position coordinates on the measurement contour line.

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