A spiral groove forming grinding wheel wear optimization method

Abstract

The application discloses a spiral groove forming grinding wheel wear optimization method, and particularly relates to the following steps: firstly, modeling the parameterized model and motion equation of the grinding wheel; secondly, quantifying the wear degree of the grinding wheel by adding the grinding curve length of each grinding wheel sheet through the envelope principle; finally, iteratively calculating the optimal grinding wheel installation position and the minimum wear forming grinding wheel profile by adopting the particle swarm optimization algorithm to the grinding wheel position. The application ensures the machining precision of the spiral groove by compensating the position of the grinding wheel according to the particularity of the spiral groove forming grinding process, improves the service life of the forming grinding wheel, and reduces the manufacturing cost of the numerical control cutter.

Description

Technical Field

[0001] This invention belongs to the field of integral CNC end mill machining technology, and particularly relates to a method for optimizing grinding wheel wear in spiral groove forming grinding. Background Technology

[0002] In the grinding process of helical grooves, the profiled wheel grinding process refers to the grinding wheel being designed according to the shape of the helical groove and then grinding it. This process offers the advantage of high grinding precision, ensuring not only the accuracy of the helical groove parameters but also that the resulting helical groove profile meets the accuracy requirements of the design. However, wear of the grinding wheel during the grinding process is unavoidable, affecting the machining accuracy of the helical groove. Currently, there is much research on wear detection and posture compensation for standard grinding wheels, but less research on wear of profiled grinding wheels. Due to the special nature of the profiled wheel grinding process, when the grinding wheel wears, it is difficult to ensure the machining accuracy of the helical groove by compensating for the wheel's posture. Summary of the Invention

[0003] To address the problem of grinding wheel wear in the spiral groove forming grinding process, this invention provides a method for optimizing grinding wheel wear in spiral groove forming grinding.

[0004] This invention discloses a grinding wheel wear optimization method for spiral groove forming grinding. First, a parametric model and motion equations of the grinding wheel are modeled. Second, using the envelope principle, the grinding wheel is discretized into several grinding wheel slices. The grinding curve lengths of each grinding wheel slice are summed to quantify the wear degree of the grinding wheel. Finally, a particle swarm optimization algorithm is used to iteratively calculate the optimal grinding wheel mounting posture and the forming grinding wheel profile with minimal wear. Specifically, the method includes the following steps:

[0005] Step 1: Parametric modeling of the end mill helical cutting edge and grinding wheel.

[0006] Establish workpiece coordinate system O W -X W Y W Z W The origin O is the coordinate system. W With X W Y W The plane is located on the end face of the tool, Z W The axis and the tool's axis vector coincide. Point P is defined as any point on the helical cutting edge, β is the helix angle of the tool, r is the radius of the tool, L is the cutting edge length, and ζ is the rotation angle corresponding to point P. The expression for point P is as follows:

[0007]

[0008] In the formula, ξ0 is the initial rotation angle corresponding to the starting point of the helical blade.

[0009] Define the grinding wheel coordinate system OG -X G Y G Z G coordinate axis Z G The axis coincides with the axis of the grinding wheel, and h is defined as the axial distance parameter of the grinding wheel. H is the rotation angle, and H is the grinding wheel thickness. The equations for the grinding wheel's rotating surface and the grinding wheel's profile are given by:

[0010]

[0011] Define the grinding wheel pose parameters (a x ,a y ,α), where a x and a y O is the origin of the grinding wheel coordinate system. G In the workpiece coordinate system, the installation angle α is the angle between the grinding wheel axis and the tool axis, δ is the rotational motion angle of the grinding wheel, and M is the motion matrix of the grinding wheel in the grinding motion. e Represented as:

[0012]

[0013] Step 2: Construct a model for solving the grinding curve length;

[0014] The grinding wheel is discretized into several thin discs along its axis. Each disc leaves a grinding curve within a certain cross-section of the cutting tool. The intersection of the grinding curve and the cutting tool represents the material removed by the grinding wheel. The envelope formed by the grinding curve is the cross-section of the helical groove. The specific model for determining the grinding curve length is as follows:

[0015] (1) Equation of the grinding wheel's rotating surface during the grinding process

[0016] After setting the installation pose (a) x ,a y After α), the transformation matrix M between the working coordinate system and the grinding wheel coordinate system can be obtained. W_G (a x ,a y ,α), can be expressed as:

[0017]

[0018] Spatial motion equation of grinding wheel According to equations (2), (3), and (4), they can be expressed in the workpiece coordinate system as follows:

[0019]

[0020] The cross-section of the helical groove is the same regardless of the cross-section, therefore the grinding curve left by the grinding wheel within any tool cross-section is the same; only the position changes. The spatial motion equation of the grinding wheel is taken as follows. In Z W =The grinding curve left within the Z0 section, and the inverse solution is obtained. As shown in the following formula:

[0021]

[0022] In the formula, k = r / tanβ;

[0023] Substituting equation (6) into equation (5), we can obtain the rotational surface of the grinding wheel at Z. W =The grinding curve left within the Z0 section, the specific expression of which is as follows:

[0024]

[0025] (2) Constructing the equation for calculating the grinding curve length

[0026] For the problem of determining the length of a curve, a line integral of the first kind is used to solve it. The length of the grinding curve of the discretized grinding wheel sheet is calculated by line integral. The specific expression of the line integral is as follows:

[0027]

[0028] Substituting equation (7) into equation (8), the grinding curve length of the grinding wheel thin slice can be obtained, and the specific expression is as follows:

[0029]

[0030] For equation (9), the integration intervals are the two angles corresponding to the two points where the grinding wheel slice intersects with the tool circle. and The characteristic that the two points lie on the grinding wheel and the tool circle respectively can be used to obtain two angles through equation (10). and Functional relationship regarding the axial parameter h of the grinding wheel and

[0031]

[0032] In the interval of integration where the line integral is obtained Then, by summing the lengths of the grinding curves of all the grinding wheel slices, the installation position of the grinding wheel can be obtained (a). x ,a y ,α) with respect to the grinding curve length S(a x ,a yThe functional relationship between α and α is given by the following expression:

[0033]

[0034] By applying an optimization algorithm to the above function to find its minimum value, the optimal grinding wheel pose and the forming grinding wheel profile with minimal wear can be obtained.

[0035] The beneficial technical effects of this invention are as follows:

[0036] This invention addresses the unique characteristics of the spiral groove forming grinding wheel process by compensating for the wheel's position and orientation to ensure the machining accuracy of the spiral groove, thereby improving the service life of the forming grinding wheel and reducing the manufacturing cost of CNC cutting tools. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the helical cutting edge of an end mill.

[0038] Figure 2 Schematic diagram of the rotating surface of a grinding wheel.

[0039] Figure 3 This is a schematic diagram of the motion equation of a grinding wheel.

[0040] Figure 4 This is a schematic diagram of the grinding curve of the grinding wheel.

[0041] Figure 5 This is a schematic diagram of the integration interval for solving the integral of the grinding curve.

[0042] Figure 6 These are the grinding wheels before and after wear optimization calculations.

[0043] Figure 7 This is a comparison chart of the wear of two shaped grinding wheels. Detailed Implementation

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0045] This invention discloses a method for optimizing grinding wheel wear in spiral groove forming grinding. First, a parametric model and motion equations of the grinding wheel are modeled. Second, using the envelope principle, the grinding wheel is discretized into several grinding wheel slices. The grinding curve lengths of each grinding wheel slice are summed to quantify the wear degree of the grinding wheel. Finally, a particle swarm optimization algorithm is used to iteratively calculate the optimal grinding wheel mounting posture and the forming grinding wheel profile with minimal wear. Specifically, the method includes the following steps:

[0046] Step 1: Parametric modeling of the end mill helical cutting edge and grinding wheel;

[0047] like Figure 1 As shown, establish the workpiece coordinate system O. W -XW Y W Z W The origin O is the coordinate system. W With X W Y W The plane is located on the end face of the tool, Z W The axis and the tool's axis vector coincide. Point P is defined as any point on the helical cutting edge, β is the helix angle of the tool, r is the radius of the tool, L is the cutting edge length, and ζ is the rotation angle corresponding to point P. The expression for point P is as follows:

[0048]

[0049] In the formula, ξ0 is the initial rotation angle corresponding to the starting point of the helical blade.

[0050] like Figure 2 As shown, the grinding wheel coordinate system O is defined. G -X G Y G Z G coordinate axis Z G The axis coincides with the axis of the grinding wheel, and h is defined as the axial distance parameter of the grinding wheel. H is the rotation angle, and H is the grinding wheel thickness. The equations for the grinding wheel's rotating surface and the grinding wheel's profile are given by:

[0051]

[0052] like Figure 3 As shown, the grinding wheel pose parameters (a) are defined. x ,a y ,α), where a x and a y O is the origin of the grinding wheel coordinate system. G In the workpiece coordinate system, the installation angle α is the angle between the grinding wheel axis and the tool axis, δ is the rotational motion angle of the grinding wheel, and M is the motion matrix of the grinding wheel in the grinding motion. e Represented as:

[0053]

[0054] Step 2: Construct a model for solving the grinding curve length;

[0055] like Figure 4 As shown, the grinding wheel is discretized into several thin grinding wheel blades along its axis. Each blade leaves a grinding curve within a certain cross-section of the tool. The intersection of the grinding curve and the tool represents the material removed by the grinding wheel. The envelope formed by the grinding curve is the cross-section of the helical groove. The specific model for calculating the grinding curve length is as follows:

[0056] (1) Equation of the grinding wheel's rotating surface during the grinding process

[0057] After setting the installation pose (a) x ,a y After α), the transformation matrix M between the working coordinate system and the grinding wheel coordinate system can be obtained. W_G (a x ,a y ,α), can be expressed as:

[0058]

[0059] Spatial motion equation of grinding wheel According to equations (2), (3), and (4), they can be expressed in the workpiece coordinate system as follows:

[0060]

[0061] The cross-section of the helical groove is the same regardless of the cross-section, therefore the grinding curve left by the grinding wheel within any tool cross-section is the same; only the position changes. The spatial motion equation of the grinding wheel is taken as follows. In Z W =The grinding curve left within the Z0 section, and the inverse solution is obtained. As shown in the following formula:

[0062]

[0063] In the formula, k = r / tanβ;

[0064] Substituting equation (6) into equation (5), we can obtain the rotational surface of the grinding wheel at Z. W =The grinding curve left within the Z0 section, the specific expression of which is as follows:

[0065]

[0066] (2) Constructing the equation for calculating the grinding curve length

[0067] For the problem of determining the length of a curve, a line integral of the first kind is used to solve it. The length of the grinding curve of the discretized grinding wheel sheet is calculated by line integral. The specific expression of the line integral is as follows:

[0068]

[0069] Substituting equation (7) into equation (8), the grinding curve length of the grinding wheel thin slice can be obtained, and the specific expression is as follows:

[0070] For equation (9), the integration intervals are the two angles corresponding to the two points where the grinding wheel slice intersects with the tool circle. and The characteristic that the two points lie on the grinding wheel and the tool circle respectively can be used to obtain two angles through equation (10). and Functional relationship regarding the axial parameter h of the grinding wheel and

[0071]

[0072] In the interval of integration where the line integral is obtained Then, by summing the lengths of the grinding curves of all the grinding wheel slices, the installation position of the grinding wheel can be obtained (a). x ,a y ,α) with respect to the grinding curve length S(a x ,a y The functional relationship between α and α is given by the following expression:

[0073]

[0074] By applying an optimization algorithm to the above function to find its minimum value, the optimal grinding wheel pose and the forming grinding wheel profile with minimal wear can be obtained.

[0075] Based on the above grinding algorithm, an algorithm module was developed in the VC++ environment. Taking the two sets of grinding wheel installation positions in Table 1 as examples, two different forming grinding wheels were calculated.

[0076] Table 1 Grinding wheel position parameter settings

[0077]

[0078] The grinding wheel calculated before wear optimization was 2-1, and the grinding wheel calculated after wear optimization was 2-2. Figure 6 As shown. Two shaped grinding wheels were machined with the same number of spiral grooves as shown in the diagram, and their wear was compared. The wear comparison is as follows: Figure 7 As shown.

Claims

1. A method for optimizing grinding wheel wear in spiral groove forming grinding, characterized in that, First, a parametric model and motion equations of the grinding wheel are modeled. Second, using the envelope principle, the grinding wheel is discretized into several grinding wheel slices. The grinding curve lengths of each grinding wheel slice are summed to quantify the wear degree of the grinding wheel. Finally, a particle swarm optimization algorithm is used to iteratively calculate the optimal grinding wheel mounting posture and the profile of the formed grinding wheel with minimal wear. Specifically, the following steps are included: Step 1: Parametric modeling of the end mill helical cutting edge and grinding wheel; Establish workpiece coordinate system O W -X W Y W Z W The origin O is the coordinate system. W With X W Y W The plane is located on the end face of the tool, Z W The axis and the tool's axis vector coincide. Point P is defined as any point on the helical cutting edge, β is the helix angle of the tool, r is the radius of the tool, L is the cutting edge length, and ζ is the rotation angle corresponding to point P. The expression for point P is as follows: In the formula, ξ0 is the initial rotation angle corresponding to the starting point of the helical blade; Define the grinding wheel coordinate system O G -X G Y G Z G coordinate axis Z G The axis coincides with the axis of the grinding wheel, and h is defined as the axial distance parameter of the grinding wheel. H is the rotation angle, and H is the grinding wheel thickness. The equations for the grinding wheel's rotating surface and the grinding wheel's profile are given by: Define the grinding wheel pose parameters (a) x ,a y ,α), where a x and a y O is the origin of the grinding wheel coordinate system. G In the workpiece coordinate system, the installation angle α is the angle between the grinding wheel axis and the tool axis, δ is the rotational motion angle of the grinding wheel, and M is the motion matrix of the grinding wheel in the grinding motion. e Represented as: Step 2: Construct a model for solving the grinding curve length; The grinding wheel is discretized into several thin discs along its axis. Each disc leaves a grinding curve within a certain cross-section of the cutting tool. The intersection of the grinding curve and the cutting tool represents the material removed by the grinding wheel. The envelope formed by the grinding curve is the cross-section of the helical groove. The specific model for determining the grinding curve length is as follows: (1) Equation of the grinding wheel's rotating surface during the grinding process After setting the installation posture (a) x ,a y After α), the transformation matrix M between the working coordinate system and the grinding wheel coordinate system can be obtained. W_G (a x ,a y ,α), can be expressed as: Spatial motion equation of grinding wheel According to equations (2), (3), and (4), they can be expressed in the workpiece coordinate system as follows: The cross-section of the helical groove is the same regardless of the cross-section, therefore the grinding curve left by the grinding wheel within any tool cross-section is the same; only the position changes. The spatial motion equation of the grinding wheel is taken as follows. In Z W =The grinding curve left within the Z0 section, and the inverse solution is obtained. As shown in the following formula: In the formula, k = r / tanβ; Substituting equation (6) into equation (5), we can obtain the rotational surface of the grinding wheel at Z. W =The grinding curve left within the Z0 section, the specific expression of which is as follows: (2) Constructing the equation for calculating the grinding curve length For the problem of determining the length of a curve, a line integral of the first kind is used to solve it. The length of the grinding curve of the discretized grinding wheel sheet is calculated by line integral. The specific expression of the line integral is as follows: Substituting equation (7) into equation (8), the grinding curve length of the grinding wheel thin slice can be obtained, and the specific expression is as follows: For equation (9), the integration intervals are the two angles corresponding to the two points where the grinding wheel slice intersects with the tool circle. and The characteristic that the two points lie on the grinding wheel and the tool circle respectively can be used to obtain two angles through equation (10). and Functional relationship regarding the axial parameter h of the grinding wheel and In the interval of integration where the line integral is obtained Then, by summing the lengths of the grinding curves of all the grinding wheel slices, the installation position of the grinding wheel can be obtained (a). x ,a y ,α) with respect to the grinding curve length S(a x ,a y The functional relationship between α and α is given by the following expression: By applying an optimization algorithm to the above function to find its minimum value, the optimal grinding wheel pose and the forming grinding wheel profile with minimal wear can be obtained.

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