Design method for precise'geometry-working condition 'matching of unequal gradient spiral milling cutter

Abstract

The invention discloses a design method for precise'geometry-working condition 'matching of an unequal gradient spiral milling cutter, and relates to the technical field of end milling cutters. The problems that when certain specific areas of titanium alloy weak-rigidity parts are machined at present, cutting force is not evenly distributed, and chatter is easily induced are solved. The design of the milling cutter comprises the following steps: simplifying the stress condition of any parallel cutter shaft section of the weak-rigidity thin-wall part in the cutting process into a cantilever beam model so as to obtain the elastic deformation of a cutting depth ap section in the machining process of the weak-rigidity thin-wall part; and obtaining a mapping relation between a cutter helical angle change rule and a weak-rigidity thin-wall part elastic deformation rule, and obtaining an unequal gradual change helical blade line expansion line according to the mapping relation. Meanwhile, in order to restrain flutter, the tooth space angle and the spiral starting angle of each blade line are designed to be not completely the same. The unequal gradient spiral milling cutter designed by the invention can optimize the cutting load of the cutter in a specific cutting area, reduce the elastic deformation and vibration in the cutting process and improve the machining precision of the specific area while suppressing the generation of flutter.

Description

Technical Field

[0001] The present invention relates to the technical field of end mills, and in particular to a design method for precise "geometry-working condition" matching of unequal-gradient spiral milling cutters. Background Art

[0002] At present, in the milling of weak-rigidity titanium alloy parts, the problem of low machining accuracy in special areas such as thin walls and deep cavities in some parts is particularly prominent. Due to the weak rigidity of such parts, the milling force is unevenly distributed during the milling process, and it is easy to induce vibration of the tool-tool system, which greatly affects the machining accuracy of the parts and may seriously affect the service performance of the parts. In addition, because the choice of milling parameters is limited, it is impossible to fully optimize the machining conditions, resulting in reduced machining efficiency of parts and shortened tool life, which increases the milling cost of parts. Therefore, higher requirements are placed on the milling capability, machining accuracy and machining efficiency of special areas of milling weak-rigidity titanium alloy parts.

[0003] While variable-pitch cutting tools can, to a certain extent, evenly distribute cutting forces, reduce chatter in the tool-tool system, and help extend tool life and improve cutting stability, they still cannot effectively address the problem of low machining accuracy in specific areas due to inherent elastic deformation in the part. Existing milling tools still have shortcomings when addressing this issue, especially when using uniform-pitch integral end mills. Because the milling force waveforms of the cutter teeth are uniform, they are prone to self-excited vibrations, which can reduce workpiece surface quality, resulting in lower part yield and work efficiency.

[0004] To address these issues, a design method for precise matching of the "geometry-working conditions" of unequal-gradient spiral milling cutters is proposed. The tool designed by this method can locally optimize the distribution of cutting force during the cutting process according to the elastic deformation characteristics of the workpiece. At the same time, the cutting intervals of its teeth are different, which can disrupt the periodicity of vibration and suppress the chatter of the tool-work system. It allows the use of higher cutting parameters for processing to adapt to different processing requirements. While improving the processing accuracy of parts, the processing efficiency and yield rate are also improved. It has important theoretical significance and practical application value. Summary of the Invention

[0005] This invention addresses the problem of low machining accuracy caused by milling deformation when milling thin-walled, deep cavities on weakly rigid titanium alloy parts. This invention proposes a design method for precisely matching the geometry and working conditions of a unequally tapered spiral milling cutter. This method aims to optimize the milling of thin-walled, deep cavities on weakly rigid parts, evenly distribute milling forces, reduce chatter in the cutter-tool system, and improve part dimensional accuracy while also boosting machining efficiency and yield.

[0006] The design of the unequal-grade spiral milling cutter in this invention is based on the elastic deformation of weakly rigid parts such as frame beams. By mapping the elastic deformation patterns obtained with the spatial curve of the cutting edge of the unequal-grade spiral milling cutter, a "form-property-function" inverse design method for the unequal-grade spiral milling cutter is proposed. This method can design an unequal-grade spiral milling cutter that adapts to the elastic deformation of the workpiece. This solves the problem of locally optimizing the distribution of cutting forces when milling thin-walled areas in deep cavities of weakly rigid titanium alloy parts, reducing chatter in the tool-tool system, adapting to different processing requirements, and improving part processing accuracy.

[0007] Specifically, the design of the unequal-gradient spiral milling cutter of the present invention includes the following steps:

[0008] Step 1: Simplify the model complexity and simplify the stress conditions of any parallel tool axis section of weakly rigid thin-walled parts during cutting into a cantilever beam model;

[0009] 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 is as follows:

[0010]

[0011] 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 axial cutting depth, mm;

[0012] Step 3: To fully consider the workpiece deformation during the design process of the unequally tapered spiral tool, the workpiece deformation law is mapped to the helix angle. The helix angle formula of any i-th cutting edge (where i is an integer and 1≤i≤N, N is the number of tool edges / teeth) is as follows:

[0013] β i (z) = ξ i ·δ w (z) (2)

[0014] Where, ξ i is the mapping coefficient of the i-th cutting edge; the calculation method is as follows:

[0015]

[0016] Where, β i min is the spiral starting angle of the i-th unequally tapered spiral blade, °; δ w (0) is the initial elastic deformation, mm;

[0017] Substituting formula (3) into formula (2), we can get:

[0018]

[0019] Therefore, the spiral termination angle β of the i-th unequally tapered spiral blade can be obtained i max as follows:

[0020]

[0021] Step 4: According to step 3, the i-th unequally gradient spiral edge line expansion line based on the deformation law mapping of the weakly rigid thin-walled part can be obtained:

[0022]

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

[0024] Since the helix angle β i is the angle between the tangent line at any point on the i-th cutting edge expansion line and the Z axis, tanβ i The reciprocal of is equal to the first-order derivative of the cutting edge expansion line, from which we can get:

[0025]

[0026] After sorting, we can get:

[0027] l i ′(β i )=z i ′(β i )tanβ i (8)

[0028] The formula for obtaining the arc length l(β) is 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] We can further obtain the equation of the unequally gradient spiral P(x i ,y i ,z i ) is represented as follows:

[0034]

[0035] After sorting, we can get:

[0036]

[0037] Furthermore, the cutting edges in N coordinate systems are converted into 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 unequally tapered spiral equation P(x i ,y i ,z i ) is taken 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] This invention overcomes the shortcomings of existing technologies by considering the elastic deformation of the workpiece during milling of special areas such as thin walls and deep cavities. It optimizes the cutting force distribution of the tool, effectively reducing machining problems caused by workpiece deformation and improving machining accuracy, especially for precision parts. Secondly, this design method, by designing an unequally tapered spiral milling cutter, enables the tool to more evenly distribute cutting force during milling, avoiding the chatter of the tool-workpiece system caused by traditional tools and significantly improving milling stability.

[0047] And because the cutting force is more evenly distributed, the tool can work stably at higher feed speeds and cutting depths, thereby improving overall cutting efficiency and shortening the processing cycle. The use of an unequal gradient spiral milling cutter design can reduce local wear and cutting heat of the tool during the processing process, thereby reducing the wear rate of the tool, extending the service life of the tool, and reducing production costs. Moreover, this method can flexibly adjust the geometric parameters of the tool according to the elastic properties of the workpiece, and can adapt to a wider range of materials and complex processing conditions, especially in the processing of weak rigidity parts of titanium alloys, which can reflect better processing adaptability. Due to the reduction of uneven distribution of cutting forces during the cutting process and the reduction of vibration of the tool-tool system, the processing accuracy of the workpiece in special deep cavity and thin-wall processing areas is improved, which improves the yield rate of the parts.

[0048] In summary, the unequal gradient spiral milling cutter design method based on precise matching of "geometry-working conditions" has obvious advantages over traditional tools in improving machining accuracy, extending tool life and improving cutting efficiency, especially in the non-uniform machining areas of weak rigidity titanium alloy parts. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a diagram of the elastic deformation process of a weakly rigid workpiece in the milling cantilever beam model;

[0050] Figure 2 It is the mapping relationship between the elastic deformation law of the workpiece and the helix angle;

[0051] Figure 3 It is the diagram of the elastic deformation law of the workpiece;

[0052] Figure 4 It is a process of obtaining the edge line of the unequally gradient spiral milling cutter based on the precise matching of "geometry-working conditions". DETAILED DESCRIPTION

[0053] 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.

[0054] Step 1: To obtain the elastic deformation process of the weak rigid workpiece in the milling cantilever beam model and simplify the model complexity, the stress conditions of the arbitrary parallel tool axis section cutting process of the weak rigid thin-walled part are simplified into a cantilever beam model, such as Figure 1 As shown, the elastic deformation at each position of the workpiece cross section can be arbitrarily defined as the deflection at each position of the cross section to obtain the elastic deformation of the workpiece;

[0055] Step 2: Obtain elastic deformation law:

[0056] Through the simplified cantilever beam model, 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 ;a p is the axial cutting depth, mm; z 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] In order to fully consider the deformation of the workpiece during the design process of the unequally tapered spiral tool, the deformation law of the workpiece is mapped to the helical angle. Figure 2 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, can be obtained. The specific helix angle formula for any i-th cutting edge (where i is an integer and 1≤i≤N, N is the number of tool edges / teeth) is as follows:

[0061] β i (z) = ξ i ·δ w (z) (2)

[0062] Where, ξ i is the mapping coefficient of the i-th cutting edge; the calculation method is as follows:

[0063]

[0064] Where, β imin is the spiral starting angle of the i-th unequally tapered spiral blade, °; δ w (0) is the initial elastic deformation, mm;

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

[0066]

[0067] And the spiral termination angle β of the i-th unequally tapered spiral blade imax The spiral starting angle β of the unequally tapered spiral blade imin The relationship is as follows:

[0068]

[0069] Step 4: Obtain the unfolded line of the unequally gradient spiral edge line based on the workpiece deformation law mapping:

[0070] According to step 3, the cutting edge line expression can be deduced as follows:

[0071]

[0072] Its image is Figure 3 As shown,

[0073] Helix angle β i is the angle between the tangent line at any point on the i-th cutting edge expansion line and the Z axis, tanβ i The reciprocal of is equal to the first-order derivative of the cutting edge expansion line, so we can get:

[0074]

[0075] After sorting, we can get:

[0076] l′ i (β i )=z′ i (β i )tanβ i (8)

[0077] The arc length l(β) can be obtained as follows:

[0078]

[0079] From the arc length formula, we know that

[0080]

[0081] Where D is the tool diameter, mm; θ(β) is the tool edge line rotation angle, degrees;

[0082]

[0083] After sorting, we can get:

[0084]

[0085] Next, the cutting edges in the N coordinate systems are converted to the same coordinate system O-XYZ.

[0086] Intertooth angle The following conditions are met:

[0087]

[0088] Where N is the number of tool edges / teeth;

[0089] In summary, the unequal gradient spiral equation P(x i ,y i ,z i ) is taken 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:

[0090]

[0091] After sorting:

[0092]

[0093] Step 5: Input the mathematical model established in steps 1 to 4 into MATLAB software, and then obtain a three-dimensional model of the unequal gradient spiral milling cutter based on the precise matching of "geometry-working conditions", such as Figure 4 shown.

[0094] 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 design method for precise matching of "geometry and working conditions" of unequally tapered spiral milling cutters, characterized by: The design steps are as follows; Step 1: Simplify the model complexity and simplify the stress conditions of any parallel tool axis section of weakly rigid thin-walled parts during cutting into a cantilever beam model; Step 2: Based on the simplified cantilever beam model above, obtain the cutting depth a during the machining of weak rigid thin-walled parts. p Segment elastic deformation; Step 3: Obtain the mapping relationship between the tool helix angle variation law and the elastic deformation law of the weak rigid thin-walled part; Step 4: Obtain the unfolding line of the unequally gradient spiral edge line based on the deformation law mapping of the weakly rigid thin-walled part; Step 5: Based on the mathematical models established in steps 1 to 4, a three-dimensional model of an unequally tapered spiral milling cutter based on the elastic deformation law of a weakly rigid thin-walled part is obtained; The cutting depth a during the machining of weak rigid thin-walled parts 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 design method for precise matching of "geometry and working conditions" of a unequally tapered spiral milling cutter according to claim 1 is characterized by: In order to fully consider the deformation of weak rigid thin-walled parts in the design process of unequally tapered spiral tools, the deformation law of weak rigid thin-walled parts is mapped to the helix angle. For any i-th cutting edge (where i is an integer and 1≤i≤N, N is the number of tool edges), the specific helix angle formula is: β i (z)=ξ i ·δ w (z) (2) Where, ξ i is the mapping coefficient of the i-th cutting edge.

3. The design method for precise matching of "geometry and working conditions" of a unequally tapered spiral milling cutter according to claim 2 is characterized by: The mapping coefficient calculation method is as follows: Where, β imin is the spiral starting angle of the i-th unequally tapered spiral blade, °; δ w (0) is the initial elastic deformation, mm.

4. The design method for precise matching of "geometry and working conditions" of a unequally tapered spiral milling cutter according to claim 3 is characterized by: Substituting formula (3) into formula (2), the specific relationship of the helix angle is:

5. The design method for precise matching of "geometry and working conditions" of a unequally tapered spiral milling cutter according to claim 4 is characterized by: The spiral termination angle β of the i-th unequally tapered spiral blade imax The spiral starting angle β of the unequally tapered spiral blade imin The relationship is as follows:

6. The design method for precise matching of "geometry and working conditions" of a unequally tapered spiral milling cutter according to claim 5, characterized in that: The method of obtaining the i-th unequally gradient spiral 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 i is the angle between the tangent line at any point on the i-th cutting edge expansion line and the Z axis, tanβ i The reciprocal of is equal to the first-order derivative of the cutting edge expansion line, so we can get: After sorting, we can get: l i ′(β i )=z i ′(β i )andβ i (8) The arc length l(β) can be obtained as follows:

7. The design method for precise matching of "geometry and working conditions" of a unequally tapered spiral milling cutter according to claim 6, characterized in that: From the arc length formula, we know that Where D is the tool diameter, mm; θ i (β i ) is the tool edge line rotation angle, °; After sorting, the expression of the space equation is:

8. The design method for precise matching of "geometry and working conditions" of a unequally tapered spiral milling cutter according to claim 7, characterized in that: Convert the 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 design method for precise matching of "geometry and working conditions" of a unequally tapered spiral milling cutter according to claim 8, characterized in that: The equation of the unequally tapered spiral edge line obtained by formula (12) is taken as the first edge line equation. Then, the spatial equation of the circumferential 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:

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