A micro-milling surface roughness model prediction method considering multi-factor influence

Abstract

The application discloses a micro-milling surface roughness model prediction method considering multi-factor influence, which takes micro-milling tool parameters and machining parameters as inputs, establishes a contact model between a micro-milling tool tip and a workpiece, integrates workpiece material elastic recovery into a surface generated by previous tooth cutting of the workpiece after considering the influence of tool runout in the micro-milling process, and is used for calculating the workpiece surface profile when the runout effect exists; the generated surface is simplified into a two-dimensional profile, the minimum cutting thickness is coupled into a micro-milling tool cutting edge milling track equation, and a micro-milling surface roughness model considering multi-factor influence is established. Through the application, the problem of inaccurate surface roughness model prediction in the current micro-milling process is solved, and a theoretical reference is provided for further evaluation of the surface profile in the micro-milling process.

Description

Technical Field

[0001] This invention belongs to the field of micro-cutting manufacturing simulation technology, and in particular, it is a method for predicting the surface roughness of micro-milling surfaces that considers the influence of multiple factors. Background Technology

[0002] Surface roughness simulation and prediction during micro-milling is fundamental to the rational optimization of process parameters. Furthermore, surface roughness, as a crucial evaluation criterion for workpiece quality, is difficult to control precisely during micro-milling; therefore, predictive analysis of the resulting surface roughness is necessary.

[0003] Since the surface roughness model of micro-milling differs from that of traditional milling, in order to improve the prediction accuracy of the surface roughness model of micro-milling, it is necessary to take into account the effects of minimum cutting thickness, tool runout, and elastic recovery of workpiece material. However, most current modeling techniques for surface roughness of micro-milling consider the influence of single factors. Therefore, establishing a surface roughness model that considers multiple factors can improve the prediction accuracy of surface roughness in the micro-milling process and also provide favorable support for the optimization of the micro-milling process. Summary of the Invention

[0004] The purpose of this invention is to provide a micro-milling surface roughness prediction method that considers the influence of multiple factors. The key feature of this prediction method is that it integrates the elastic recovery of the material into the surface produced by the previous cutting tooth. During this process, the influence of minimum cutting thickness, tool runout, and workpiece material elastic recovery on surface roughness is fully considered. A surface roughness model for micro-milling workpieces is established, improving the accuracy of surface roughness prediction in the micro-milling process and providing favorable support for process optimization. To achieve the above objective, the technical solution adopted by this invention includes: a micro-milling surface roughness prediction method that considers the influence of multiple factors, comprising the following steps:

[0005] Step 1: Obtain the micro-milling cutter parameters and cutting parameters for the micro-milling process.

[0006] Step 2: Considering the influence of tool runout, calculate the coordinate x(k) of the k-th tool tip of the micro-milling cutter at the current position.

[0007] Step 3: Determine the relationship between the uncut thickness and the minimum cutting thickness during the micro-milling process. If the uncut thickness is less than the minimum cutting thickness, first obtain the relationship between the current cutting edge k trajectory and the previous cutting edge (k-1) trajectory: the previous cutting edge trajectory point is located on the surface generated by the current cutting edge. Then, after considering the influence of tool runout and material elastic recovery, calculate its tool tip coordinate x(k-1).

[0008] Step 4: When the rotation angle (ωt)k When -2πk / K)=(2Nπ+π / 2) (N is an integer), the uncut thickness can be approximately expressed as σ. k l The feed distance from the previous tooth (k-1) to the current tooth k can be expressed as f. e (k); and then define Z as the critical line for the minimum cutting thickness. hmin ,

[0009] Step 5: Based on the tool edge geometry, considering the influence of minimum cutting thickness and material elastic recovery, determine the final surface profile as Z. f If h≤h min Then update the surface profile if h > h min The current surface contour is obtained directly; then, the surface contour of the workpiece generated by micro-milling is represented by the surface formed by the sampling points on the cutting edge trajectory of the end mill.

[0010] As an improvement to the method of this invention, in step one, the micro-milling cutter parameters include the number of flutes, the cutter radius, etc., and the micro-milling machining process cutting parameters include the feed per tooth, the spindle speed, etc. The influence of each machining process parameter on surface roughness is obtained based on the trajectory equation analysis of the micro-milling cutter cutting edge.

[0011] As an improvement to the method of the present invention, in step two, the k-groove cutter is at t k The coordinate x(k) of the tool tip at time k can be determined by the following parametric equation:

[0012]

[0013] As an improvement to the method of the present invention, in step three, when the uncut thickness is less than the minimum cutting thickness, due to the influence of elastic recovery, the actual generated surface deviates from the tool cutting trajectory. The cutting edge and the blunt part of the side exert friction and pressure on the surface, and the resulting elastic recovery directly determines the surface quality, specifically including:

[0014] Determine the equation of the cycloidal trajectory of the micro-milling cutter's cutting edge:

[0015] x(t,z,x(k))=x0(t,z,x(k))+x r (t,z,x(k))+x de (t,z,x(k))+x dy (t,z,x(k))

[0016] y(t,z,x(k))=y0(t,z,x(k))+y r (t,z,x(k))+y de (t,z,x(k))+y dy (t,z,x(k))

[0017] Where x0(t,z,x(k)) and y0(t,z,x(k)) are the cutting edge coordinates under ideal conditions, x r (t,z,x(k)) and y r (t,z,x(k)) represents the offset value caused by the runout of the micro-milling cutter, x de (t,z,x(k)) and y de (t,z,x(k)) represents the instantaneous deflection deformation of the micro-milling cutter, x dy (t,z,x(k)) and y dy (t,z,x(k)) is the contour of the machined surface R. h It can be represented as:

[0018] R h =h1-h2

[0019] Where h1 is the plastic deformation height and h2 is the elastic recovery height.

[0020] After considering elastic recovery, the tool tip coordinates are updated as follows:

[0021]

[0022] As an improvement to the method of the present invention, in step four, when the rotation angle (ωt) k When -2πk / K)=(2Nπ+π / 2) (N is an integer), the tool tip coordinate x(k) reaches its maximum. Uncut thickness σ k l It can be approximated as:

[0023]

[0024] Whether the cutting edge participates in milling the workpiece is obvious and can be determined using the following formula:

[0025]

[0026] As an improvement to the method of this invention, in step four, during macro-milling, all teeth participate in cutting the workpiece. However, when the uncut thickness of the k-th tooth is less than the minimum cutting thickness, σ will occur in micro-milling. k <0, which means that not all teeth participate in cutting the workpiece during a single rotation, when all σ k When both are less than 0, no chips can form on any of the teeth within one revolution. σ has already been determined in step three. k l Therefore, the distance that the current tooth k advances from the previous tooth (k-1) in the feed direction can be obtained as follows:

[0027]

[0028] Furthermore, the blade tip profile can be represented by its radius r. e The tool clearance angle γ is defined as:

[0029]

[0030] To determine whether chips have formed, the critical line for minimum cutting thickness should be defined as follows:

[0031]

[0032] As an improvement to the method of this invention, in step five, based on the tool edge geometry and considering the influence of minimum cutting thickness and elastic recovery, the generated surface profile can be described according to the following steps, specifically including:

[0033] Obtain the surface profile (Z) formed by the current cutting edge cutting the workpiece. e,k The contours (Z) formed by the cutting of the workpiece by the previous cutting edge are respectively compared with those formed by the previous cutting edge. e,k-1 The surface profile (Z) formed by the next cutting edge cutting the workpiece. e,k+1 The intersection of the points is used to determine the final surface profile Z based on the tool edge geometry, taking into account the minimum cutting thickness and the elastic recovery of the workpiece material. f The surface profile can be summarized as follows:

[0034]

[0035] The arithmetic mean deviation R of the workpiece surface from the profile during micro-milling a for:

[0036]

[0037] Substituting Zf, initial values ​​are selected in the solution process:

[0038]

[0039] During the movement of the micro-end mill cutting edge, the time corresponding to the tip of the k-th micro-end mill cutting edge reaching point x(k) is t. k , can be derived from x i Performing a first-order Taylor expansion at the location of the nearest extreme point, and retaining the first-order terms, yields the following expression:

[0040]

[0041] Substituting the above formula into the arithmetic mean deviation R of the workpiece surface from the contour during micro-milling... a We can obtain:

[0042]

[0043] This invention provides a micro-milling surface roughness prediction method that considers the influence of multiple factors. It integrates the elastic recovery of the workpiece material into the surface generated by the previous cutting tooth, takes into account the effects of tool runout and elastic recovery, and fully describes the process of workpiece surface contour generation. Thus, a milling surface roughness model is established. This model fully considers the influence of minimum cutting thickness, tool runout, and workpiece material elastic recovery on surface roughness, improves the surface roughness prediction accuracy of micro-milling, and provides technical support for process parameter optimization and milling cutter structure selection for surface roughness control. Attached Figure Description

[0044] Figure 1 This is a simplified flowchart of a micro-milling surface roughness model prediction method that considers the influence of multiple factors according to the present invention.

[0045] Figure 2 This is a diagram showing the cycloidal trajectory of the tip of the two-tooth end mill of the present invention.

[0046] Figure 3 This is a diagram illustrating the formation mechanism of plastic deformation of the workpiece material during the milling process of this invention.

[0047] Figure 4 The tool profile diagram considering the minimum cutting thickness for this invention.

[0048] Figure 5 This is a diagram illustrating the surface contour formation process of the present invention. Detailed Implementation

[0049] To better explain and facilitate understanding of the present invention, a detailed description of the invention is provided below with reference to the accompanying drawings.

[0050] This invention provides a method for predicting surface roughness in micro-milling that considers the influence of multiple factors, such as... Figure 1 As shown, it includes the following steps:

[0051] Step 1: Obtain the micro-milling cutter parameters and cutting parameters for the micro-milling process.

[0052] Micro-milling cutter parameters include tool radius and number of teeth, while micro-milling machining process parameters include feed per tooth and spindle speed.

[0053] Step 2: Considering the influence of tool runout, calculate the coordinate x(k) of the k-th tool tip of the micro-milling cutter at the current position.

[0054] like Figure 2 As shown, O and O' are the spindle center and tool center, respectively. Due to tool runout, the actual trajectory of the tool center is not a linear trajectory, but a cycloidal trajectory. The corresponding tool center points O and O' can be represented as:

[0055]

[0056]

[0057] Therefore, the k-groove cutter at t k The coordinate x(k) of the tool tip at time k can be determined by the following parametric equation:

[0058]

[0059] Where K, R, f, ω, and n are the number of teeth, tool radius, feed per tooth, and spindle speed, respectively, and ρ and λ are the transition length and transition angle, respectively.

[0060] Step 3: Determine the relationship between the uncut thickness and the minimum cutting thickness during the micro-milling process. If the uncut thickness is less than the minimum cutting thickness, first obtain the relationship between the current cutting edge k trajectory and the previous cutting edge (k-1) trajectory: the previous cutting edge trajectory point is located on the surface generated by the current cutting edge. Then, considering the influence of tool runout and material elastic recovery, calculate its tool tip coordinate x(k-1), combined with... Figure 2 and Figure 3 As shown, the contour height R of the machined surface h The height of plastic deformation h1 and the height of elastic recovery h2, generated by the cutting force, are formed by their combined action.

[0061] R h =h1-h2

[0062] The height of plastic deformation h1 can be determined by friction and wear calculation methods:

[0063]

[0064] r is the fillet radius of the cutting edge, ψ is the degree of deformation, HB is the Brinell hardness of the workpiece material, σ is the flow stress, and h1 can then be expressed as:

[0065]

[0066] σ is the flow stress, which can be obtained from the JC constitutive equation:

[0067]

[0068] Where A, B, C, m, and n are constitutive parameters of the workpiece material; T is the workpiece temperature. r At room temperature (30℃), T m ε0 is the melting temperature of the workpiece; ε0 is the reference plastic strain rate, which can be defined as 0.001 s-1; ε and ε1 are the equivalent plastic strain and plastic strain rate, respectively, and can be calculated by the following formula:

[0069]

[0070]

[0071] Combining the above formula, the elastic recovery height h2 can be determined as follows:

[0072]

[0073] After considering elastic recovery, the tool tip coordinates are updated as follows:

[0074]

[0075] Where P e For the elastic recovery rate, step four: when the rotation angle (ωt) k When -2πk / K)=(2Nπ+π / 2) (N is an integer), the uncut thickness can be approximately expressed as σ. k l The feed distance from the previous tooth (k-1) to the current tooth k can be expressed as f. e (k); and then define Z as the critical line for the minimum cutting thickness. hmin In macro milling, all teeth participate in cutting the workpiece. However, when the instantaneous uncut chip thickness of the k-th tooth is less than the minimum cutting thickness, a σ phenomenon occurs in micro milling. k <0, which means that not all teeth participate in cutting the workpiece during a single rotation, when all σ k When both are less than 0, no chips can form on any of the teeth within one revolution. σ has already been determined in step three. k l Therefore, the distance that the current tooth k advances from the previous tooth (k-1) in the feed direction can be expressed as:

[0076]

[0077] The tool tip position is derived based on homogeneous matrix transformation (HTM) at point O. t -X t Y t Z t The coordinates of the cutting edge are:

[0078]

[0079] X T and Y T Aligned with the feed direction and cross feed direction respectively, Z T Parallel to Z t The origin of the tool coordinate system is the same as the origin of the local tool coordinate system.

[0080] The homogeneous matrix transformation of the tool coordinate system from Ot-XtYtZt to OT-XTYTZT can be expressed as:

[0081]

[0082] θ is the relative rotation angle, defined as:

[0083]

[0084] in For X t With X T The initial angle between them

[0085] Principal coordinate system, from O t -X t Y t Z t To O S -X S Y S Z S The homogeneous matrix transformation can be expressed as:

[0086]

[0087] Where Δα and Δd are the radial runout amplitude and initial phase angle, and Δh and Δβ are the axial runout and initial phase angle, respectively. The workpiece coordinate system starts from O. t -X t Y t Z t To O W -X W Y W Z W The homogeneous matrix transformation can be expressed as:

[0088]

[0089] Combining the three coordinates above, the knife-edge equation can be expressed as:

[0090]

[0091] like Figure 3 As shown, combining the coordinates of the tool tip equation, the position of the tool tip can be represented by its radius r. e The tool clearance angle γ is defined as:

[0092] To determine whether chips have formed, the critical line for minimum cutting thickness should be defined as follows:

[0093]

[0094] Step 5: Based on the tool edge geometry, considering the influence of minimum cutting thickness and material elastic recovery, determine the final surface profile as Z. f If h≤h min Then update the surface profile if h > h min The current surface contour is obtained directly; then, the surface contour of the workpiece generated by micro-milling is represented by the surface formed by the sampling points on the cutting edge trajectory of the end mill.

[0095] Based on the tool edge geometry, and considering the effects of minimum cutting thickness and workpiece material elastic recovery, the generated surface profile can be described by the following process.

[0096] like Figure 5 As shown, the surface profile (Z) formed by the current cutting edge cutting the workpiece. e ,k) respectively with the surface profile (Z) formed by the previous cutting edge cutting the workpiece. e The surface profile (Z) formed by the next cutting edge cutting the workpiece (k-1) and k-1) is also shown. e The cutting edge (k+1) intersects at points A and D. Simultaneously, the minimum cutting thickness critical line (Z) of the surface profile formed by the current cutting edge cutting the workpiece is... hmin The surface profile (Z) formed by the previous cutting edge and the cutting edge (k) e If the lines BC and BC intersect at point B, and point B corresponds to point C on the surface profile of the current cutting edge, then the length of BC is equal to h. min ,

[0097] To the left of point C, due to the surface profile (Z) formed by the next cutting edge cutting the workpiece. e The uncut thickness (k+1) is less than the minimum cutting thickness, therefore no chips are formed. The final profile in region BC is generated by the elastic recovery of the material after the next cutting edge passes through the surface, but the surface material can be completely removed in the next stage. To the right of point C, the surface material between points C and D is continuously removed, and the resulting profile coincides with CD.

[0098] The final surface profile can be expressed as:

[0099]

[0100] The surface formed by sampling points along the cutting edge trajectory of the end mill is the workpiece surface profile generated by micro-milling. The arithmetic mean deviation value R of the workpiece surface profile generated by micro-milling is... a for:

[0101]

[0102] Substitute Z f Initial value selection in the solution process:

[0103]

[0104] During the movement of the micro-end mill cutting edge, the time corresponding to the tip of the k-th micro-end mill cutting edge reaching point x(k) is t. k Can be derived from x k Performing a first-order Taylor expansion at the location of the nearest extreme point, and retaining the first-order terms, yields the following expression:

[0105]

[0106] Substituting the above formula into the arithmetic mean deviation R of the workpiece surface from the contour during micro-milling... a We can obtain:

[0107]

[0108] It should be understood that the above description of specific embodiments of the present invention is only for illustrating the technical approach and features of the present invention, and is intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. However, the present invention is not limited to the specific embodiments described above. All changes or modifications made within the scope of the claims of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for predicting the surface roughness of a micro-milling cutter considering the influence of multiple factors, characterized in that: The method includes the following steps: Step 1: Obtain the micro-milling cutter parameters and cutting parameters for the micro-milling process; Step 2: Considering the influence of tool runout, calculate the coordinate x(k) of the kth tool tip of the micro-milling cutter at the current position; Step 3: Determine the relationship between the uncut thickness and the minimum cutting thickness during the micro-milling process. If the uncut thickness is less than the minimum cutting thickness, first obtain the relationship between the current cutting edge k motion trajectory and the previous cutting edge (k-1) motion trajectory: the previous cutting edge trajectory point is located on the surface generated by the current cutting edge. Then, after considering the influence of tool runout and material elastic recovery, calculate its tool tip coordinate x(k-1). Step 4: When the rotation angle (ωt) k When -2πk / K)=(2Nπ+π / 2) (N is an integer), the uncut thickness can be approximately expressed as σ. k l The feed distance from the previous tooth (k-1) to the current tooth k can be expressed as f. e (k); and then define Z as the critical line for the minimum cutting thickness. hmin , Step 5: Based on the tool edge geometry, considering the influence of minimum cutting thickness and material elastic recovery, determine the final surface profile as Z. f If h≤h min Then update the surface profile if h > h min The current surface profile is obtained directly; then the surface profile of the workpiece generated by micro-milling is represented by the surface formed by the sampling points on the cutting edge trajectory of the end mill.

2. The method according to claim 1, characterized in that, In step one, the micro-milling cutter parameters include the number of flutes and the cutter radius. The cutting parameters of the micro-milling process include the feed per tooth and the spindle speed. The influence of each machining process parameter on the surface roughness is obtained based on the trajectory equation analysis of the micro-milling cutter cutting edge.

3. The method according to claim 1, characterized in that, In step two, the k-groove cutter is at t k The coordinate x(k) of the tool tip at time k can be determined by the following parametric equation: Where ρ is the amplitude of the sine wave, and λ is the fixed phase shift of the sine wave.

4. The method according to claim 2, characterized in that, In step three, when the uncut thickness is less than the minimum cutting thickness, due to the influence of elastic recovery, the actual generated surface deviates from the tool cutting trajectory. The cutting edge and the blunt part of the side exert friction and compression on the surface, and the resulting elastic recovery directly determines the surface quality, specifically including: Determine the equation of the cycloidal trajectory of the micro-milling cutter's cutting edge: x(t,z,x(k))=x0(t,z,x(k))+x r (t,z,x(k))+x de (t,z,x(k))+x dy (t,z,x(k)) y(t,z,x(k))=y0(t,z,x(k))+y r (t,z,x(k))+y de (t,z,x(k))+y dy (t,z,x(k)) Where x0(t,z,x(k)) and y0(t,z,x(k)) are the cutting edge coordinates under ideal conditions, x r (t,z,x(k)) and y r (t,z,x(k)) represents the offset value caused by the runout of the micro-milling cutter, x de (t,z,x(k)) and y de (t,z,x(k)) represents the instantaneous deflection deformation of the micro-milling cutter, x dy (t,z,x(k)) and y dy (t,z,x(k)) represents the vibration value of the micro-milling cutter caused by the dynamic micro-milling system; The profile R of the machined surface h It can be represented as: R h =h1-h2 Where h1 is the plastic deformation height and h2 is the elastic recovery height; After considering elastic recovery, the tool tip coordinates are updated as follows: In step four, when the rotation angle (ωt) k When -2πk / K)=(2Nπ+π / 2) (N is an integer), the tool tip coordinate x(k) reaches its maximum coordinate, and the uncut thickness σ k l It can be approximated as: Whether the cutting edge participates in milling the workpiece is obvious and can be determined using the following formula: This formula can accurately determine whether the cutting edge is involved in cutting at the current angle.

5. The method according to claim 1, characterized in that, In step three, during macro-milling, all teeth participate in cutting the workpiece. However, when the uncut thickness of the k-th tooth is less than the minimum cutting thickness, a σ-problem occurs in micro-milling. k <0, which means that not all teeth participate in cutting the workpiece during a single rotation, when all σ k When both are less than 0, none of the teeth can form a cut within one revolution. σ has already been obtained in step three. k l Therefore, the distance that the current tooth k advances from the previous tooth (k-1) in the feed direction can be obtained as follows: Furthermore, the blade tip profile is defined by its radius r. e The tool clearance angle γ is defined as: To determine whether chips have formed, the critical line for minimum cutting thickness should be defined as follows: The calculated result of the arithmetic mean deviation of the profile serves as a key indicator for evaluating the surface quality of micro-milled workpieces.

6. The method according to claim 1, characterized in that, In step five, based on the tool edge geometry and considering the effects of minimum cutting thickness and elastic recovery, the generated surface profile is described according to the following steps, specifically including: Obtain the surface profile (Z) formed by the current cutting edge cutting the workpiece. e (k) and the contour (Z) formed by the previous cutting edge cutting the workpiece are respectively connected. e The surface profile (Z) formed by the next cutting edge cutting the workpiece (k-1) and k-1) is also shown. e,k+1 The intersection of the points is used to determine the final surface profile Z based on the tool edge geometry, taking into account the minimum cutting thickness and the elastic recovery of the workpiece material. f The surface profile can be summarized as follows: The arithmetic mean deviation R of the workpiece surface from the profile during micro-milling a for: Substitute Z f Initial value selection in the solution process: During the movement of the micro-end mill cutting edge, the time corresponding to the tip of the k-th micro-end mill cutting edge reaching point x(k) is t. k , can be derived from x i Performing a first-order Taylor expansion at the location of the nearest extreme point, and retaining the first-order terms, yields the following expression: Substituting the above formula into the arithmetic mean deviation R of the workpiece surface from the contour during micro-milling... a We can obtain: The surface profile model constructed by this piecewise function accurately characterizes the elastoplastic deformation behavior of the material under the critical condition of minimum cutting thickness, thereby significantly improving the prediction accuracy of the surface morphology of micro-milled workpieces.

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