A design method of unequal gradual change helical milling cutter based on elastic deformation law of workpiece uniform load

Abstract

This invention provides a design for an unequal-gradient helical end mill based on the elastic deformation law of a uniformly distributed load on a workpiece, relating to the field of end mill technology. The design includes the following steps: first, obtaining the elastic deformation law of the workpiece during the cutting process; second, obtaining the mapping relationship between the helical angle variation law of each cutting edge and the elastic deformation law of the workpiece; and finally, obtaining the unequal-gradient cutting edge development line based on the workpiece deformation law mapping relationship. In designing the unequal-gradient helical end mill, since the cutting force generated by the tool during the cutting process exists throughout the entire cutting depth range, simplifying it to a concentrated force would lead to significant deviations in the calculation results. Therefore, this invention assumes that the cutting force is a uniformly distributed load within the cutting depth range. By fully considering the actual elastic deformation law of the workpiece and mapping this deformation law onto the cutting edge of the unequal-gradient helical end mill, the elastic deformation of the workpiece during milling is effectively compensated, deformation errors are reduced, and thus the machining accuracy of the parts is improved.

Description

Technical Field

[0001] This invention relates to the field of end mill technology, and more specifically to a design method for unequal gradually varying spiral end mills based on the elastic deformation law of uniformly distributed load on the workpiece. Background Technology

[0002] Currently, during milling of titanium alloy parts, the parts themselves have relatively low rigidity, and the uneven distribution of milling forces during machining can easily cause vibrations in the tooling system, thus affecting the machining accuracy and, in severe cases, impacting the service performance of the parts. Therefore, effectively reducing the vibration of the tooling system during milling is of great significance to the machining accuracy of the parts.

[0003] Currently, although there is a "geometry-condition" precise matching design method using unequal gradient helical end mills, and although the tool designed by this method can optimize the cutting force distribution during the cutting process based on the elastic deformation characteristics of the part, effectively reducing the vibration of the tool system during milling, this method mainly considers the influence of concentrated forces. Since the cutting force generated by the tool during the cutting process exists throughout the entire cutting depth range, simplifying it to a concentrated force will lead to a large deviation in the calculation results.

[0004] In summary, to address the above problems, this invention proposes a design method for unequal gradually varying spiral end mills based on the elastic deformation law of uniformly distributed load on the workpiece. This design method assumes that the cutting force is a uniformly distributed load within the cutting depth range, which not only solves the problem of large deviations in results caused by the simplified concentrated force, but also effectively reduces the vibration of the tooling system during cutting and improves the machining accuracy of parts, thus having significant practical research value. Summary of the Invention

[0005] This invention addresses the problem of large milling deformation during the milling process of titanium alloy parts. It proposes a design method for unequal gradually varying spiral end mills based on the elastic deformation law of uniformly distributed load on the workpiece. The aim is to effectively reduce the vibration of the tooling system during milling, thereby improving the machining accuracy of the parts.

[0006] This invention discloses a design method for unequal-gradient helical end mills based on the elastic deformation law of a workpiece under uniformly distributed load. It assumes that the cutting force is a uniformly distributed load within the cutting depth range, thus solving the problem of large deviations in results caused by the simplification of concentrated forces. This method can design unequal-gradient helical end mills that are highly adapted to the elastic deformation law of the part, thereby achieving the goal of reducing milling vibration and improving the machining accuracy of the part.

[0007] Specifically, the unequal gradient helical end mill design of the present invention includes the following steps: Step 1: Obtain the elastic deformation law; Based on the simplified cantilever beam model, the load intensity can be determined. qIt can be represented as:

[0008] In the formula, F The cutting force is N; a p The axial cutting depth is in mm. By combining the cantilever beam model, the depth of cut during the machining of weakly rigid workpieces can be derived. a p segment elastic deformation d m ( z ):

[0009] In the formula, H The height above the workpiece clamping surface, in mm; a p The axial cutting depth is in mm. E Let be the elastic modulus of the workpiece material, in Pa; I Let the moment of inertia of the workpiece in the machining area be mm. 4 ; Therefore, an end blade can be obtained ( z Deformation at =0) d m (0) is as follows:

[0010] exist z =a p Deformation d m ( a p )as follows:

[0011] Step 2: Obtain the mapping relationship between the variation law of the helix angle of each cutting edge of the tool and the elastic deformation law of the workpiece; To ensure that the design process of unequal gradient helical cutting tools fully considers the workpiece deformation, the deformation law of the uniformly distributed load on the workpiece is mapped to the helix angle of each cutting edge as follows:

[0012] In the formula, β i ( z ) is the first i The helix angle of the cutting edge is about z The function, (1≤ i ≤ N ); N This represents the number of teeth / number of cutting edges of the cutting tool. x i For the first iMapping coefficient of the cutting edge, rad / mm; The calculation method is as follows:

[0013] In the formula, β imin For the first i The gradient helix starting angle of the cutting edge satisfies β i (0)= β imin rad; Then the mapping coefficients are obtained. x as follows:

[0014] After sorting, we can get the first... i helix angle of the cutting edge β i Regarding location z i function β i ( z ):

[0015] exist z = a p Place, No. i Helix angle of the cutting edge β i ap as follows:

[0016] No. i Gradual helix termination angle of the cutting edge β imax as follows:

[0017] In the formula, β imax satisfy β imax = β i ( l 1), rad; l 1 represents the effective cutting length (edge ​​length) of the tool, in mm; Step 3: Obtain the development line of the unequal gradient cutting edge based on the workpiece deformation law mapping; Due to the helix angle β i To expand the tangent line at any point on the line and Z The included angle of the axes. tan βi The reciprocal of is equal to the first derivative along the cutting edge development line. Furthermore, the chain rule yields:

[0018] After sorting, we get:

[0019] From formula (8), we get:

[0020] The arc length can be calculated. l i ( β i The formula is as follows:

[0021] After sorting, we get:

[0022] From the arc length formula, we know that:

[0023] In the formula, D The diameter of the cutting tool is in mm. i i ( β i () represents the rotation angle of the tool cutting edge, in °;

[0024] In the formula, z i ( β i ) is a function β i ( z i The inverse function of ). After sorting, we get:

[0025] Next, N The cutting edge in each coordinate system is transformed into the same coordinate system. O - XYZ .

[0026] Tooth angle f i The following conditions must be met:

[0027] In the formula, N This represents the number of cutting edges / number of teeth of the cutting tool. In summary, taking the above cutting edge lines as the equation for the first cutting edge line, let the number of teeth be... N The end mill i (2≤ i ≤ N The spatial equation of the perimeter of the cutting edge is:

[0028] Summarized as follows:

[0030] 1. This design method assumes that the cutting force is a uniformly distributed load within the cutting depth range. This not only solves the problem of large deviations in results caused by the simplified concentrated force, but also effectively reduces the vibration of the tooling system during cutting and improves the machining accuracy of parts. It has important practical research significance.

[0031] 2. This invention assumes that the cutting force is a uniformly distributed load within the cutting depth range, which solves the problem of large deviations in results caused by the simplified concentrated force. Furthermore, converting the concentrated force into a uniformly distributed load further improves the stability of the tooling system during milling, thereby further improving the machining accuracy of the parts and achieving better machining results compared to existing technologies. Attached Figure Description

[0032] Figure 1 It is a process of simplifying the elastic deformation law of uniformly distributed load on the workpiece and mapping it to the helix angle of the tool. Figure 2 It is a process for obtaining the cutting edge of an unequal, gradually changing spiral milling cutter based on the elastic deformation law of uniformly distributed load on the workpiece. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. Example

[0034] This embodiment discloses a design method for unequal gradually varying spiral end mills based on the elastic deformation law of uniformly distributed load on a workpiece, including the following steps: Step 1: Obtain the elastic deformation law; according to Figure 1 A simplified cantilever beam model of the cutting process of the workpiece shows the load intensity. q It can be represented as:

[0035] In the formula, F The cutting force is N; a p The axial cutting depth is in mm. By combining the cantilever beam model, the depth of cut during the machining of weakly rigid workpieces can be derived. a p segment elastic deformation d m ( z ):

[0036] In the formula, H The height above the workpiece clamping surface, in mm; a p The axial cutting depth is in mm. E Let be the elastic modulus of the workpiece material, in Pa; I Let the moment of inertia of the workpiece in the machining area be mm. 4 ; Therefore, an end blade can be obtained ( z Deformation at =0) d m (0) is as follows:

[0037] exist z =a p Deformation d m ( a p )as follows:

[0038] Step 2: Obtain the mapping relationship between the variation law of the helix angle of each cutting edge of the tool and the elastic deformation law of the workpiece; To ensure that the design process of unequal gradient helical cutting tools fully considers the workpiece deformation, the deformation law of the uniformly distributed load on the workpiece is mapped to the helix angle of each cutting edge, such as... Figure 1 As shown, the specific relationships are as follows:

[0039] In the formula, β i ( z ) is the first i The helix angle of the cutting edge is about z The function, (1≤ i ≤ N ); N This represents the number of teeth / number of cutting edges of the cutting tool. x i For the first iMapping coefficient of the cutting edge, rad / mm; The calculation method is as follows:

[0040] In the formula, β imin For the first i The gradient helix starting angle of the cutting edge satisfies β i (0)= β imin rad; Then the mapping coefficients are obtained. x as follows:

[0041] After sorting, we can get the first... i helix angle of the cutting edge β i Regarding location z i function β i ( z ):

[0042] exist z = a p Place, No. i Helix angle of the cutting edge β i ap as follows:

[0043] No. i Gradual helix termination angle of the cutting edge β imax as follows:

[0044] In the formula, β imax satisfy β imax = β i ( l 1), rad; l 1 represents the effective cutting length (edge ​​length) of the tool, in mm; Step 3: Obtain the development line of the unequal gradient cutting edge based on the workpiece deformation law mapping; Due to the helix angle β i To expand the tangent line at any point on the line and Z The included angle of the axes. tan β iThe reciprocal of is equal to the first derivative along the cutting edge development line. Furthermore, the chain rule yields:

[0045] After sorting, we get:

[0046] From formula (8), we get:

[0047] The arc length can be calculated. l i ( β i The formula is as follows:

[0048] After sorting, we get:

[0049] From the arc length formula, we know that:

[0050] In the formula, D The diameter of the cutting tool is in mm. i i ( β i () represents the rotation angle of the tool cutting edge, in °;

[0051] In the formula, z i ( β i ) is a function β i ( z i The inverse function of ). After sorting, we get:

[0052] Next, N The cutting edge in each coordinate system is transformed into the same coordinate system. O - XYZ .

[0053] Tooth angle f i The following conditions must be met:

[0054] In the formula, N This represents the number of cutting edges / number of teeth of the cutting tool. In summary, taking the above cutting edge lines as the equation for the first cutting edge line, let the number of teeth be...N The end mill i (2≤ i ≤ N The spatial equation of the perimeter of the cutting edge is:

[0055] Summarized as follows:

[0057] like Figure 2 As shown, the unequal gradually changing spiral end mill cutting edge line obtained above based on the elastic deformation law of uniformly distributed load on the workpiece is then applied to the actual end mill design to obtain the required unequal gradually changing spiral end mill.

[0058] While the specific embodiments of the invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the invention are still within the scope of protection of the invention.

Claims

1. A design method for unequal-gradient helical end mills based on the elastic deformation law of uniformly distributed load on a workpiece, characterized in that: Includes the following steps: Step 1: Obtain the elastic deformation law of the weakly rigid workpiece; Step 2: Obtain the mapping relationship between the variation law of the helix angle of each cutting edge of the tool and the elastic deformation law of the workpiece; Step 3: Obtain the development line of the unequal gradient cutting edge based on the workpiece deformation law mapping; The method for obtaining the elastic deformation law of a weakly rigid workpiece is as follows: Based on the simplified cantilever beam model, the load intensity can be obtained. q for: In the formula, F The cutting force is N; a p λ represents the axial cutting depth, in mm.

2. The design method for an unequal gradually varying helical end mill based on the elastic deformation law of a uniformly distributed load on a workpiece, as described in claim 1, is characterized in that: The method for obtaining the elastic deformation law of a weakly rigid workpiece also includes: deriving the cutting depth during the machining of the weakly rigid workpiece based on the cantilever beam model. a p segment elastic deformation δ m ( z )for: In the formula, H The height above the workpiece clamping surface, in mm; a p The axial cutting depth is in mm. E Let be the elastic modulus of the workpiece material, in Pa; I Let the moment of inertia of the workpiece in the machining area be mm. 4 Obtain the end blade ( z Deformation at =0) δ m (0) is as follows: get z =a p Deformation δ m ( a p )as follows: 。 3. The design method for an unequal gradually varying helical end mill based on the elastic deformation law of a uniformly distributed load on a workpiece, as described in claim 1, is characterized in that: The mapping relationship between the variation law of the helix angle of each cutting edge of the tool and the elastic deformation law of the workpiece is obtained; specifically, the deformation law under uniform load is mapped to each cutting edge helix angle as follows: In the formula, β i ( z ) is the first i The helix angle of the cutting edge is about z The function, (1≤ i ≤ N ); N This represents the number of teeth / number of cutting edges of the cutting tool. ξ i For the first i The mapping coefficient of the cutting edge, rad / mm; the calculation method is as follows: In the formula, β imin For the first i The gradient helix starting angle of the cutting edge satisfies β i (0)= β imin , rad; and then obtain the mapping coefficients. ξ as follows: After sorting, we can get the first... i helix angle of the cutting edge β i Regarding location z i function β i ( z ): exist z = a p Place, No. i Helix angle of the cutting edge β i ap as follows: No. i Gradual helix termination angle of the cutting edge β imax as follows: In the formula, β imax satisfy β imax = β i ( l 1), rad; l 1 represents the effective cutting length (blade length) of the tool, in mm.

4. The design method for an unequal gradually varying helical end mill based on the elastic deformation law of a uniformly distributed load on a workpiece, as described in claim 1, is characterized in that: The acquisition of the unequally gradual cutting edge development line based on the workpiece's elastic deformation law mapping; specifically: due to the helix angle β i To expand the tangent line at any point on the line and Z The included angle of the axes. tan β i The reciprocal of is equal to the first derivative along the cutting edge development line. Furthermore, the chain rule yields: After sorting, we get: From formula (8), we get: The arc length can be calculated. l i ( β i The formula is as follows: After sorting, we get: From the arc length formula, we know that: In the formula, D The diameter of the cutting tool is in mm. θ i ( β i () represents the rotation angle of the tool cutting edge, in °; In the formula, z i ( β i ) is a function β i ( z i The inverse function of ) is obtained; after simplification, we get: Will N The cutting edge in each coordinate system is transformed into the same coordinate system. O - XYZ Interdental angle φ i The following conditions must be met: Where, N Let the number of cutting edges be the number of teeth. In summary, taking the above cutting edges as the equation for the first cutting edge, let the number of teeth be... N The end mill i (2≤ i ≤ N The spatial equation of the perimeter of the cutting edge is: Summarized as follows: .

Images