Equal gradient spiral milling cutter design method based on workpiece elastic deformation rule

Abstract

The invention provides an equal gradient spiral milling cutter design based on a workpiece elastic deformation rule, and relates to the technical field of end milling cutters. The method includes the following steps that the stress condition of any parallel axial section of a weak-rigidity part in the cutting process is obtained, and the stress condition is simplified into a cantilever beam model to obtain the elastic deformation of a workpiece; according to the simplified cantilever beam model, the elastic deformation of the cutting depth ap section in the machining process of the weak-rigidity workpiece is obtained; and obtaining a function relationship between the elastic deformation and the cutting depth, and a function relationship between the helical angle and the cutting depth. When the equal gradual change spiral milling cutter is designed, the actual elastic deformation rule of the workpiece is considered, the deformation rule is mapped to the edge line of the equal gradual change spiral milling cutter, elastic deformation of the workpiece in the milling process is effectively compensated, deformation errors are reduced, and therefore the surface quality of parts is improved.

Description

Technical Field

[0001] The invention relates to the technical field of end mills, and in particular to the design of a constant-gradient spiral milling cutter based on the elastic deformation law of a workpiece. Background Art

[0002] Currently, the side milling process of weakly rigid parts causes significant elastic deformation due to the milling force, which in turn leads to large cutting vibrations and large machining errors, significantly affecting the surface quality and cutting stability of the parts. Furthermore, traditional milling methods have limited options for milling parameters, making it difficult to handle parts with large deformations. This not only affects machining efficiency, but also increases tool wear, shortening tool life and increasing machining costs.

[0003] At present, by changing the helix angle on the end mill so that the helix angle changes gradually, the cutting force can be reduced to a certain extent and the vibration of the cutting system can be reduced. Existing gradient spiral tools have been proven to have a very positive effect on reducing the cutting vibration and improving the processing quality of thin-walled deep cavity parts. However, during the design process, the tool is qualitatively analyzed as a uniform gradient, and is not quantitatively adapted to the processing conditions, making it impossible to maximize its applicability to the cutting process of such parts. Although the existing gradient spiral end mill design can improve the processing accuracy of weak rigid parts to a certain extent, it does not take into account the elastic deformation law of the parts and cannot more effectively map and control the elastic deformation of the parts. Therefore, how to control and optimize the elastic deformation of parts through the gradual change of the helix angle to improve the processing quality of thin-walled deep cavity parts has become a technical problem that needs to be solved urgently. Summary of the Invention

[0004] The present invention aims to solve the problem of large milling deformation during the milling process of weak rigidity parts and proposes a design method for a constant-gradient spiral milling cutter based on the elastic deformation law of the parts. The method aims to reduce the milling deformation and vibration during the milling process of weak rigidity parts such as thin-walled deep cavities, thereby improving the surface quality of the parts and extending the service life of the tool.

[0005] The design of this invention's uniformly variable spiral milling cutter is based on the elastic deformation of thin-walled, deep-cavity, and weakly rigid parts. By mapping the resulting elastic deformation patterns with the spatial curve of the cutter's cutting edge, an inverse design method for uniformly variable spiral milling cutters is proposed. This method enables the design of a uniformly variable spiral milling cutter that is highly compatible with the part's elastic deformation patterns, thereby reducing milling vibration and deformation.

[0006] Specifically, the design of the constant-gradient spiral milling cutter of the present invention includes the following steps:

[0007] Step 1: Simplify the force conditions of any plane cutter axis section of the weak rigid part during cutting into a cantilever beam model;

[0008] Step 2: Through the simplified cantilever beam model, the cutting depth a during the machining of weak rigid workpieces can be derived. p The elastic deformation of the segment is obtained, and the elastic deformation law is obtained. The expression of the elastic deformation is as follows:

[0009]

[0010] Where F is the cutting force, N; H is the height above the workpiece clamping surface, mm; E is the elastic modulus of the workpiece material, Pa; I is the moment of inertia of the workpiece in the processing area, mm 4 ; z is the axial cutting depth, mm; a p is the maximum axial cutting depth, mm;

[0011] Step 3: To achieve the goal of achieving uniform spiral tool design, the workpiece deformation is fully considered and the workpiece deformation law is mapped to the helix angle. The mapping relationship is as follows:

[0012] β(z)=ξ·δ w (z) (2)

[0013] Where ξ is the mapping coefficient; the calculation method is as follows:

[0014]

[0015] Where, β min is the starting angle of the spiral with equal gradient, °; δ w (0) is the initial elastic deformation, mm;

[0016] Substituting formula (3) into formula (2) yields:

[0017]

[0018] And β min and β max There are the following relationships:

[0019]

[0020] Where, β max is the termination angle of the uniformly tapered spiral, °;

[0021] Step 4: Based on step 3, we can derive the expression of the cutting edge line:

[0022]

[0023] Where β is the tool helix angle, °;

[0024] Since the helix angle β is the angle between the tangent line at any point on the development line and the Z axis, the reciprocal of tanβ is equal to the first-order derivative on the cutting edge development line. Therefore, the formula for the tool helix angle β is as follows:

[0025]

[0026] After sorting, we can get:

[0027] l′(β)=z′(β)tanβ (8)

[0028] The arc length l(β) can be obtained as follows:

[0029]

[0030] From the arc length formula we know that:

[0031]

[0032] Where D is the tool diameter, mm; θ(β) is the tool edge line rotation angle, degrees;

[0033] Furthermore, the equation of the gradual spiral P(x,y,z) is expressed as follows:

[0034]

[0035] After sorting, we can get:

[0036]

[0037] Next, the cutting edges in the N coordinate systems are converted to the same coordinate system O-XYZ.

[0038] Intertooth angle The following conditions are met:

[0039]

[0040] Where N is the number of tool edges / teeth;

[0041] Furthermore, the gradient spiral equation P(x, y, z) obtained from the above formula (12) is used as the first edge line equation. Then, the edge line space equation of the ith (2≤i≤N) edge line of the end mill with N teeth is:

[0042]

[0043] The expression of the edge line space equation is as follows:

[0044]

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] The existing technology does not take into account the actual elastic deformation law of the workpiece. When designing the tool, a quadratic function is used to replace the actual elastic deformation law of the workpiece. The tool designed by this solution cannot adapt to the elastic deformation law of the workpiece itself to the maximum extent, resulting in difficulty in further improving the workpiece processing accuracy and surface quality. When designing the equal-gradient spiral milling cutter, the present invention takes into account the actual elastic deformation law of the workpiece and maps the deformation law to the edge line of the equal-gradient spiral milling cutter, effectively compensating for the elastic deformation of the workpiece during the milling process, reducing deformation errors, and thus improving processing accuracy and surface quality. In addition, by rationally designing the milling parameters of the equal-gradient spiral milling cutter, the force on the tool is made more uniform, effectively reducing the phenomenon of local overload and extending the service life of the tool. At the same time, the equal-gradient spiral milling cutter design optimizes the distribution of cutting force on the basis of ensuring processing accuracy, improves cutting efficiency, reduces cutting vibration, and ensures processing stability. Considering the elastic deformation law of the workpiece helps to control temperature changes during the cutting process, reduce tool wear caused by cutting heat, effectively extend the service life of the tool, and reduce production costs. In the machining process of traditional tools, the deformation of the workpiece leads to a decrease in the machining accuracy of the parts. However, the design method based on the elastic deformation law of the workpiece can effectively reduce this adverse effect and improve the qualified rate of the parts.

[0047] In summary, this design method combines the elastic deformation law of the workpiece, which can reduce tool wear, reduce cutting heat, reduce production costs, and improve production efficiency while ensuring processing accuracy and cutting efficiency. Compared with existing technologies, it has better processing effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Simplified process of elastic deformation law of weak rigid workpiece based on cantilever beam model;

[0049] Figure 2 It is the mapping relationship between the elastic deformation law of the workpiece and the helix angle;

[0050] Figure 3 It is a process of obtaining the edge line of a spiral milling cutter with equal gradient based on the elastic deformation law of the workpiece. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0052] Example 1

[0053] This embodiment discloses a method for designing a uniformly variable spiral milling cutter based on the elastic deformation law of a workpiece, comprising the following steps:

[0054] Step 1: Simplify the stress of any parallel tool axis section during the cutting process of a weak rigid thin-walled part into a cantilever beam model, such as Figure 1 As shown, the elastic deformation of each position of the workpiece cross section is considered to be the deflection of each position of the cross section, so as to obtain the elastic deformation of the workpiece;

[0055] Step 2: Obtain elastic deformation law:

[0056] According to the simplified cantilever beam model in step 1, the cutting depth a during the machining of weak rigid workpieces can be derived. p Segment elastic deformation:

[0057]

[0058] Where F is the cutting force, N; H is the height above the workpiece clamping surface, mm; E is the elastic modulus of the workpiece material, Pa; I is the moment of inertia of the workpiece in the processing area, mm 4 ; z is the axial cutting depth, mm; a p is the maximum axial cutting depth, mm;

[0059] Step 3: Obtain the mapping relationship between the tool helix angle change law and the workpiece elastic deformation law:

[0060] like Figure 2 As shown in the figure, the functional relationship between the elastic deformation and the cutting depth, as well as the functional relationship between the helix angle and the cutting depth, in order to realize the design of the uniformly gradient helical tool, it is necessary to fully consider the deformation of the workpiece and map the deformation law of the workpiece to the helix angle. The mapping relationship is shown below:

[0061] β(z)=ξ·δ w (z) (2)

[0062] Where ξ is the mapping coefficient; the calculation method is as follows:

[0063]

[0064] Where, β min is the starting angle of the spiral with equal gradient, °; δ w (0) is the initial elastic deformation, mm;

[0065] Substituting formula (3) into formula (2) yields:

[0066]

[0067] And β min and β max There are the following relationships:

[0068]

[0069] Where, β max is the termination angle of the uniformly tapered spiral, °;

[0070] Step 4: Obtain the expansion line of the equal-gradient edge line based on the workpiece deformation law mapping, and then derive the spatial equation of the circumferential edge line:

[0071] From step 3, we can deduce the expression of cutting edge line:

[0072]

[0073] Where β is the tool helix angle, °;

[0074] Its image is Figure 3 As shown,

[0075] Since the helix angle β is the angle between the tangent line at any point on the development line and the Z axis, the reciprocal of tanβ is equal to the first-order derivative on the cutting edge development line. Therefore, we can get:

[0076]

[0077] After sorting, we can get:

[0078] l′(β)=z′(β)tanβ (8)

[0079] The arc length l(β) can be obtained as follows:

[0080]

[0081] From the arc length formula, we know that

[0082]

[0083] Where D is the tool diameter, mm; θ(β) is the tool edge line rotation angle, degrees;

[0084]

[0085] After sorting, we can get:

[0086]

[0087] Next, the cutting edges in the N coordinate systems are converted to the same coordinate system O-XYZ.

[0088] Intertooth angle The following conditions are met:

[0089]

[0090] Where N is the number of tool edges / teeth;

[0091] Furthermore, the gradient spiral equation P(x, y, z) obtained from the above formula (12) is used as the first edge line equation. Then, the edge line space equation of the ith (2≤i≤N) edge line of the end mill with N teeth is:

[0092]

[0093] After sorting:

[0094]

[0095] Step 5: Input the mathematical model established in steps 1 to 4 into MATLAB software, and then obtain a three-dimensional model of the uniformly variable spiral milling cutter based on the elastic deformation law of the workpiece.

[0096] Although the above describes the specific implementation methods of the invention in conjunction with the accompanying drawings, it 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 on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.

Claims

1. A method for designing a uniformly tapered spiral milling cutter based on the elastic deformation law of a workpiece, characterized by: The steps include: Step 1: Obtain the stress condition of any parallel axis section of a weakly rigid thin-walled part during the cutting process, and simplify the stress condition into a cantilever beam model; Step 2: According to the simplified cantilever beam model, the cutting depth a during the machining of weak rigid thin-walled parts is obtained. p Segment elastic deformation; Step 3: Obtain the functional relationship between elastic deformation and cutting depth, as well as the functional relationship between helix angle and cutting depth, and map the deformation law of weak rigidity thin-walled parts to the helix angle; Step 4: according to step 3, obtain the uniform gradient edge line expansion line mapped based on the deformation law of the weak rigid thin-walled part; Step 5: Based on the mathematical model, a three-dimensional model of a uniformly tapered spiral milling cutter is obtained that takes into account the elastic deformation law of weakly rigid thin-walled parts; The cutting depth a p The specific elastic deformation of the segment is: Where F is the cutting force, N; H is the height above the workpiece clamping surface, mm; E is the elastic modulus of the workpiece material, Pa; I is the moment of inertia of the workpiece in the processing area, mm 4 ; z is the axial cutting depth, mm; a p is the maximum axial cutting depth, mm.

2. The method for designing a uniformly tapered spiral milling cutter based on the elastic deformation law of a workpiece according to claim 1, characterized in that: The deformation law of the weakly rigid thin-walled part is mapped to the helix angle, specifically: β(z)=ξ·δ w (z) (2) Where ξ is the mapping coefficient.

3. The method for designing a uniformly variable spiral milling cutter based on the elastic deformation law of a workpiece according to claim 2, characterized in that: The mapping coefficient calculation method is as follows: Where, β min is the starting angle of the spiral with equal gradient, °; δ w (0) is the initial elastic deformation, mm.

4. The method for designing a uniformly variable spiral milling cutter based on the elastic deformation law of a workpiece according to claim 3, characterized in that: Substituting formula (3) into formula (2) yields:

5. The method for designing a uniformly variable spiral milling cutter based on the elastic deformation law of a workpiece according to claim 4, characterized in that: The β min and β max There are the following relationships: Where, β max is the termination angle of the uniformly tapered spiral, °.

6. The method for designing a uniformly tapered spiral milling cutter based on the elastic deformation law of a workpiece according to claim 5, characterized in that: The method of obtaining the uniformly gradient edge line expansion line based on the deformation law mapping of the weakly rigid thin-walled part is as follows: Since the helix angle β is the angle between the tangent line at any point on the development line and the Z axis, the reciprocal of tanβ is equal to the first-order derivative on the cutting edge development line. Therefore, we can get: After sorting, we can get: l′(β)=z′(β)tanβ (8) The arc length l(β) can be obtained as follows:

7. The method for designing a uniformly tapered spiral milling cutter based on the elastic deformation law of a workpiece according to claim 6, characterized in that: From the arc length l(β) formula, we can know that Where D is the tool diameter, mm; θ(β) is the tool edge line rotation angle, degrees; After sorting out, the expression of the space equation is:

8. The method for designing a uniformly tapered spiral milling cutter based on the elastic deformation law of a workpiece according to claim 7, characterized in that: Convert the number of cutting edges in N coordinate systems into the same coordinate system O-XYZ, According to the number of cutting edges, the tooth angle The following conditions are met: Where N is the number of tool edges.

9. The method for designing a uniformly tapered spiral milling cutter based on the elastic deformation law of a workpiece according to claim 8, characterized in that: The equation of the gradually changing spiral edge line obtained by formula (12) is taken as the first edge line equation. Then, the spatial equation of the peripheral edge line of the i-th (2≤i≤N) edge line of the end mill with N teeth is: After sorting out, the expression of the perimeter edge line space equation is obtained as follows:

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