Method for designing tool path based on forming angle difference in machining of curved parts

Abstract

The method for designing tool path based on forming angle difference in curved surface part machining belongs to the technical field of sheet metal incremental forming, and aims to solve the problem of large part surface quality and contour error in the machining of curved surface parts in the prior art. The method includes two parts of contour line trajectory design and spiral line trajectory design. When the forming tool head is machining, it moves along the pre-designed part surface, the surface tool contact point of the tool head is in contact with the surface of the part to be formed, and a series of envelope lines formed by the movement of the tool head constitute the shape of the part. The position coordinates of the tool head movement are a series of tool position points composed of the center position of the spherical tool head, so the movement trajectory of the spherical tool head is the offset curve of the cross section curve of the formed part to the side of the tool head. The method considers the actual movement of the tool head and the shape parameters of the part, and completes the parametric accurate model of the trajectory by means of the analytical mathematical model of the residual wave height of the curved surface part.

Description

Technical Field

[0001] This invention belongs to the field of sheet metal progressive forming technology, specifically relating to a tool trajectory design method based on forming angle difference in the machining of curved parts. Background Technology

[0002] CNC sheet metal progressive forming technology is a flexible sheet metal forming process suitable for rapid prototyping and small-batch production. During the forming process, a computer numerical control (CNC) system is used to control a general forming tool to form the sheet metal layer by layer, ultimately achieving the required three-dimensional shape.

[0003] Chinese patent application number "201810955031.0" is titled "A Method for Generating Progressive Forming Machining Trajectory for Sheet Metal Using Secondary Interpolation." This method determines multi-layer part contour lines based on the geometry of the formed part, and then calculates the machining trajectory based on any contour line other than the first and second layer contour lines, as well as the two adjacent contour lines. This method uses three adjacent contour lines for interpolation to solve for trajectory points, resulting in a smoother trajectory and higher contour accuracy. However, analysis of the progressive forming tool during the machining process reveals that adjacent machining trajectories can create residual peak heights on the part, directly affecting the surface waviness and thus the surface quality. This is especially true for curved parts with continuously changing forming angles; the smaller the forming angle after machining, the more pronounced the residual peak heights and the greater the waviness. Furthermore, unmachined portions appear at the bottom of the part. This leads to significant surface quality and contour errors in curved parts. Summary of the Invention

[0004] To address the problem in existing technologies where small forming angles in the machining of curved parts easily generate large waviness, leading to significant surface quality and contour errors, this invention proposes a tool trajectory design method for machining curved parts with varying forming angles. This method comprehensively considers the tool head movement and part shape parameters during CNC machining of curved parts, utilizing an analytical mathematical model of the residual wave crest height of the curved part to create a precise parameterized trajectory model.

[0005] The technical solution of this invention to solve the technical problem is as follows:

[0006] A toolpath design method based on the forming angle difference in the machining of curved parts includes two parts: contour line path design and helical line path design.

[0007] (1) A contour trajectory design method based on the forming angle difference includes the following steps:

[0008] Step 1: Using the forming angle difference Δθ between two adjacent layers as a constant, layer the material to form contour lines. If the forming angle of the lowest layer is 0°, then the relationship between the forming angle of the tool contact point in the i-th layer and the forming angle difference is as follows:

[0009] θ i =iΔθ (1)

[0010] Combining the tool contact equation z′=f(x′), the forming angle of the tool head's tool contact point i on the workpiece cross-section is θ. i The coordinates of the location are:

[0011]

[0012] This allows us to obtain the tool head cutting point i at the part cross-section forming angle θ. i The coordinates of the location are:

[0013]

[0014] Step 2: The tool head makes the same angle on each layer. Based on the motion and formula (3), the coordinates of the j-th tool position of the tool head in the i-th layer are obtained as follows:

[0015]

[0016] In the formula —The tool head at each step of every layer;

[0017] Δθ — the fixed forming angle difference between two adjacent layers of the tool head trajectory;

[0018] r—radius of the spherical tool head;

[0019] Step 3: Combining the equation z′=f(x′) and formula (1), the radius of curvature of the knife contact point in the i-th layer is calculated as follows:

[0020]

[0021] In the formula ρ i — The radius of curvature of the curved surface part at point i;

[0022] f′ 2 (x i — The second derivative of the curved surface part at point i;

[0023] f″(x i — The second derivative of the curved surface part at point i;

[0024] Step 4: Analysis of the residual height of the curved surface reveals the relationship between the layer feed rate and the forming angle of the tool head trajectory between two adjacent layers:

[0025]

[0026] In the formula, r is the radius of the forming tool head.

[0027] Δz — Layer feed rate between two adjacent layers;

[0028] θ i-1 —The forming angle of the curved part at i-1;

[0029] Step 5: Based on the obtained forming trajectory, i.e. the tool position coordinate formula (4), output the coordinates in reverse order, and then obtain the contour trajectory of the tool head when machining on the curved part according to the difference of the forming angle of two adjacent trajectories.

[0030] (2) A spiral trajectory design method based on equal forming angle differences includes the following steps:

[0031] Step 1: Divide the helix into k subdivisions within one pitch according to Δγ, with each subdivision having a circumferential rotation angle of Δβ. This yields the tool contact point on the helix within each pitch:

[0032]

[0033] Step 2: Use the forming angle difference to perform layer design and obtain the relationship between the forming angles of adjacent layers:

[0034] θ i =θ i-1 +Δθ (8)

[0035] The number of machining layers N for the tool head used to complete this part is:

[0036]

[0037] In the formula α max —Maximum forming angle of curved surface parts

[0038] Δθ — the difference in the forming angle between two adjacent layers of trajectory.

[0039] θi — the forming angle of the curved surface part on the i-th layer of the trajectory;

[0040] Step 3: Using formula (6), obtain the perpendicular distance between the spiral lines at two adjacent nodes, parallel to the bottom plane:

[0041]

[0042] The tool head from the forming angle θ i The forming angle to any point within this pitch is θ i +kΔγ, the coordinates of its contact point are:

[0043]

[0044] Then the coordinates of its tool position point are obtained:

[0045]

[0046] Step 4: Based on the obtained forming trajectory, i.e., the tool position coordinate formula (12), output its coordinates, and then obtain the spiral trajectory of the tool head when processing the curved part according to the difference of the forming angle of two adjacent layers of trajectory.

[0047] The beneficial effects of this invention are:

[0048] (1) The trajectory points are solved by the trajectory method of forming angle difference. Since the trajectory points are relatively dense, the obtained trajectory lines are smoother and the contour accuracy is higher.

[0049] (2) The forming trajectory obtained by the trajectory method based on the forming angle difference can not only solve the problem of uneven surface waviness of curved parts and reduce the side wall error of parts, but also eliminate the downward pressure marks of the tool on the surface of the workpiece compared with the contour line tool trajectory, and significantly improve the processing efficiency.

[0050] (3) This processing method is applicable to all curved surface parts, and is economical, efficient and meets the requirements of batch processing. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the tool trajectory cross-section of the curved surface part described in this invention.

[0052] Figure 2 This is a schematic diagram of the contour line trajectory of the tool for the curved surface part described in this invention.

[0053] Figure 3 This is a schematic diagram of the spiral trajectory of the tool for curved parts according to the present invention.

[0054] Figure 4 This is a schematic diagram of the helical path within one pitch as described in this invention.

[0055] Figure 5 This is a cross-sectional view of the quadratic curve described in this invention. Detailed Implementation

[0056] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0057] A toolpath design method based on the forming angle difference in the machining of curved parts includes two parts: contour line path design and helical line path design.

[0058] (1) The contour trajectory design method based on the forming angle difference includes the following steps:

[0059] Step 1: A schematic diagram of the movement of the machining tool head at a certain cross section for curved parts, as shown below. Figure 1 As shown. Layering is performed using the forming angle difference Δθ between two adjacent layers as a constant to form contour lines. If the forming angle of the lowest layer is 0°, then the relationship between the forming angle of the tool contact point in the i-th layer and the forming angle difference is as follows:

[0060] θ i =iΔθ (1)

[0061] Combining the tool contact equation z′=f(x′), the forming angle of the tool head's tool contact point i on the workpiece cross-section is θ. i The coordinates of the location are:

[0062]

[0063] This allows us to obtain the tool head cutting point i at the part cross-section forming angle θ. i The coordinates of the location are:

[0064]

[0065] Step 2: The three-dimensional motion trajectory of the cutting tool, such as... Figure 2 As shown. The tool head makes the same angle at each layer. Based on the motion and formula (3), the coordinates of the j-th tool position of the tool head in the i-th layer are obtained as follows:

[0066]

[0067] In the formula —The tool head at each step of every layer;

[0068] Δθ — the fixed forming angle difference between two adjacent layers of the tool head trajectory;

[0069] r—radius of the spherical tool head;

[0070] Step 3: Combining the equation z′=f(x′) and formula (1), the radius of curvature of the knife contact point in the i-th layer is calculated as follows:

[0071]

[0072] In the formula ρ i — The radius of curvature of the curved surface part at point i;

[0073] f′(x i — The first derivative of the curved surface part at point i;

[0074] f″(x i — The second derivative of the curved surface part at point i;

[0075] Step 4: Analysis of the residual height of the curved surface reveals the relationship between the layer feed rate and the forming angle of the tool head trajectory between two adjacent layers:

[0076]

[0077] In the formula, r is the radius of the forming tool head.

[0078] Δz — Layer feed rate between two adjacent layers.

[0079] θ i-1 —The forming angle of the curved part at i-1;

[0080] Step 5: Based on the obtained forming trajectory, i.e. the tool position coordinate formula (4), output the coordinates in reverse order, and then obtain the contour trajectory of the tool head when processing the curved part according to the difference of the forming angle of two adjacent trajectories.

[0081] (2) A spiral trajectory design method based on equal forming angle differences includes the following steps:

[0082] Step 1: Schematic diagram of the helix of the curved surface part, as shown below. Figure 3 As shown. The helix is ​​subdivided into k parts within one pitch according to Δγ, with each circumferential rotation angle being Δβ. The tool contact point on the helix within each pitch is then obtained as follows:

[0083]

[0084] Step 2: Use the forming angle difference to perform layer design and obtain the relationship between the forming angles of adjacent layers:

[0085] θ i =θ i-1 +Δθ (8)

[0086] The number of machining layers N for the tool head used to complete this part is:

[0087]

[0088] In the formula α max —Maximum forming angle of curved surface parts

[0089] Δθ — the difference in the forming angle between two adjacent layers of trajectory.

[0090] θ i —The forming angle of the curved part on the i-th layer trajectory.

[0091] Step 3: Using formula (6), obtain the perpendicular distance between the spiral lines at two adjacent nodes, parallel to the bottom plane:

[0092]

[0093] A schematic diagram of the helical path of the tool head's contact point within one pitch, as shown below. Figure 4 As shown. The tool head is positioned from the forming angle θ. i The forming angle to any point within this pitch is θ i +kΔγ, the coordinates of its contact point are:

[0094]

[0095] Then the coordinates of its tool position point are obtained:

[0096]

[0097] Step 4: Based on the obtained forming trajectory, i.e., the tool position coordinate formula (12), output its coordinates, and then obtain the spiral trajectory of the tool head when processing the curved part according to the difference of the forming angle of two adjacent layers of trajectory.

[0098] Example:

[0099] like Figure 5 As shown, taking a quadratic curve cross-section as an example, a common quadratic curve with a forming angle between 0° and 30° is selected. x is the x-coordinate of the cross-sectional arc curve, and z is the z-coordinate of the cross-sectional arc curve. Let z = 0.005 * x 2 .

[0100] Contour trajectory: Process parameters selected for the forming angle difference method: r is the tool head radius, Δθ is the forming angle difference, α max For the maximum forming angle, α min For the minimum forming angle, For the turning angle. Set the above parameters as follows: r = 5mm, Δθ = 1°, α max =30°, α min =0°,

[0101] Substituting the process parameters into formula (1) yields θ i =i;

[0102] Substituting the process parameters into formula (2), we obtain the forming angle θ of the tool head contact point i on the part cross section. i The coordinates of the point are: x′ i =(0.01 tanθ) i ) -1 z′=0.005(0.01 tanθ) i ) -1

[0103] Substituting the process parameters into formula (3) yields the tool head cutting point i at the part cross-section forming angle θ. i The coordinates of the location are x i=0.01 tan i-5 sin i, z i =0.005(0.01 tanθ) i ) -1 -5 cos i.

[0104] Substituting the process parameters into formula (4), we obtain the coordinates of the j-th tool position of the tool head in the i-th layer.

[0105]

[0106] Spiral trajectory: Process parameters selected for the forming angle difference method: r is the tool head radius, Δθ is the forming angle difference, α max For the maximum forming angle, α min The minimum forming angle is given, Δβ is the rotation angle, and Δγ is 10°. The parameters are set as follows: r = 5mm, Δθ = 1°, α... max =30°, α min =0°, Δβ =1°.

[0107] Substituting the process parameters into formula (10) yields the vertical distance between the helix and the bottom plane at two adjacent nodes:

[0108] Substituting the process parameters into formula (11) yields the coordinates of the tool contact point:

[0109]

[0110] Substituting the process parameters into formula (12) yields the coordinates of the tool position:

[0111]

[0112] The contour lines and spiral lines of the tool position are made into a CNC machining program to process the sheet material. After processing, the tool is removed, the sheet material is taken off, and then the next sheet material to be formed is processed, and the operation is repeated.

Claims

1. A tool path design method based on forming angle difference in the machining of curved parts, characterized by: It includes two parts: contour line trajectory design and spiral trajectory design. (1) The contour trajectory design method based on the forming angle difference includes the following steps: Step 1: Based on the forming angle difference between two adjacent trajectory layers To form a contour line trajectory, layers are created for a fixed value. If the forming angle of the lowest layer is 0°, then the relationship between the forming angle and the forming angle difference at the blade contact point in the i-th layer is as follows: （1） Combining knife contact equation The forming angle of the tool head contact point i on the part cross section is obtained as follows: The coordinates of the location are: （2） This allows us to obtain the tool head cutting point i at the forming angle of the part cross section. The coordinates of the location are: （3） Step 2: The tool head makes the same angle on each layer. Based on the motion and formula (3), the coordinates of the j-th tool position of the tool head in the i-th layer are obtained as follows: （4） In the formula —The tool head at each step of every layer; —The fixed forming angle difference between two adjacent layers of the tool head trajectory; r—radius of the forming tool head; Step 3: Combining the equations The radius of curvature of the blade contact point in the i-th layer is calculated using formula (1): （5） In the formula —The radius of curvature of the curved surface part at point i; —The square of the first derivative of the curved part at point i; —The second derivative of the curved surface part at point i; Step 4: Analysis of the residual height of the curved surface reveals the relationship between the layer feed rate and the forming angle of the tool head trajectory between two adjacent layers: （6） In the formula, r is the radius of the forming tool head. —The layer feed rate between two adjacent layers; —The forming angle of the curved part at i-1; Step 5: Based on the obtained forming trajectory, i.e. the tool position coordinate formula (4), output the coordinates in reverse order, and then obtain the contour trajectory of the tool head when processing the curved part according to the difference of the forming angle of two adjacent layers of trajectory. (2) A spiral trajectory design method based on equal forming angle difference, including the following steps: Step 1: align the helix within one pitch according to... Subdivide into k times, each time with a circumferential turning angle of... The tool contact point on the helix within each pitch is obtained as follows: （7） Step 2: Use the forming angle difference to perform layer design and obtain the relationship between the forming angles of adjacent layers: （8） The number of machining layers N for the tool head used to complete this part is: （9） In the formula —Maximum forming angle of curved surface parts —Difference in the trajectory forming angle between adjacent layers, —The forming angle of the curved part in the i-th layer trajectory; Step 3: Using formula (6), obtain the perpendicular distance between the planes containing two adjacent nodes and the bottom plane: （10） tool head from forming angle The forming angle to any point within this pitch is The coordinates of its blade contact point are: （11） Then the coordinates of its tool position point are obtained: （12） Step 4: Based on the obtained forming trajectory, i.e., the tool position coordinate formula (12), output its coordinates, and then obtain the spiral trajectory of the tool head when processing the curved part according to the difference of the forming angle of two adjacent layers of trajectory.

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