A longitudinal-torsional composite ultrasonic vibration assisted high-speed milling machining optimization design method

Abstract

The application relates to a longitudinal-torsional composite ultrasonic vibration auxiliary high-speed milling processing optimization design method, which simplifies a single rotary ultrasonic vibration process into straight-line motions in X and Z directions, obtains a single longitudinal-torsional ultrasonic vibration displacement expression, and further obtains a single longitudinal-torsional ultrasonic vibration periodic trajectory diagram and a single longitudinal-torsional ultrasonic vibration velocity expression. The longitudinal-torsional ultrasonic vibration velocity is decomposed to obtain a velocity expression perpendicular to the direction of a cutting edge. The cutting separation time ratio is calculated, and the cutting separation time ratio is inversely proportional to the rotating speed and is proportional to the ultrasonic vibration frequency, the longitudinal ultrasonic amplitude, the torsional ultrasonic amplitude and the spiral angle. The milling speed required to be reached in the processing process, the amplitude and the frequency of the ultrasonic tool handle are selected. The cutting separation time ratio is calculated to evaluate the ultrasonic processing effect, which is the ratio of the separation time of the cutting edge and the workpiece to the ultrasonic vibration period in the single ultrasonic vibration process. The longer the cutting separation time is, the better the ultrasonic effect is. The application improves the milling speed and the processing efficiency.

Description

Technical Field

[0001] This invention belongs to the fields of milling technology and special machining technology, and particularly relates to a design method for high-speed milling assisted by longitudinal torsional ultrasonic vibration. Background Technology

[0002] As the performance requirements for components of fourth / fifth generation high thrust-to-weight ratio aero-engines gradually increase, severe challenges are posed to the machining performance of key high-temperature resistant materials such as Ti2AlNb intermetallic compounds and nickel-based superalloys. Milling is the main machining process for these materials, but the process suffers from problems such as high milling forces and high milling temperatures. Especially under high-speed conditions, the machining temperature increases significantly, which can easily lead to accelerated tool wear and a significant reduction in the surface quality of the machined material.

[0003] Ultrasonic vibration-assisted milling is a two-dimensional ultrasonic machining method that combines longitudinal and torsional ultrasonic vibrations. By applying ultrasonic vibrations to the cutting tool or workpiece, high-frequency periodic separation occurs between the cutting edge and the workpiece during the machining process. Longitudinal-torsional ultrasonic vibration-assisted milling, due to the presence of ultrasonic vibrations in both the longitudinal and torsional directions, facilitates the entry of coolant into the machining area during the separation process, enhancing heat transfer and improving the cooling environment, thus reducing the temperature and cutting force during milling. Simultaneously, the ultrasonic impact promotes chip breaking during the removal of difficult-to-machine materials, facilitating chip flow out of the machining area and reducing surface damage. In summary, longitudinal-torsional ultrasonic vibration-assisted milling, with these advantages, has become an effective method for solving the machining challenges of difficult-to-machine materials.

[0004] However, the advantages or effects of longitudinal torsional ultrasonic vibration machining are limited by its critical speed. For difficult-to-machine materials, the separation time between the cutting edge of the tool and the workpiece is short or even disappears under high-speed conditions (v≥100m / min), resulting in a sharp decline in the ultrasonic effect. Therefore, in actual machining processes, in order to ensure a certain ultrasonic machining effect, the cutting speed must be reduced, and the milling speed is usually controlled below 70m / min, resulting in low machining efficiency and severely limiting the application and promotion of this method. Summary of the Invention

[0005] Purpose of the invention: In order to overcome the shortcomings of the prior art, the present invention provides an optimized design method for high-speed milling assisted by longitudinal torsion composite ultrasonic vibration. This method can coordinate and optimize the machining conditions according to the target cutting speed, breaking through the existing level of longitudinal torsion ultrasonic vibration assisted machining technology and significantly improving machining efficiency. This method provides a new approach for high-efficiency machining of difficult-to-machine materials.

[0006] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] The single rotational ultrasonic vibration process is simplified into linear motion in the X and Z directions, resulting in the displacement expression for a single longitudinal torsional ultrasonic vibration. From this expression, the periodic trajectory diagram and the velocity expression for a single longitudinal torsional ultrasonic vibration are obtained.

[0008] The velocity expression perpendicular to the cutting edge direction is obtained by decomposing the longitudinal torsional ultrasonic vibration velocity;

[0009] The cutting separation time ratio Q is calculated, which is the ratio of the time it takes for the cutting edge to separate from the workpiece during a single ultrasonic vibration process to the ultrasonic vibration period. The cutting separation time ratio Q is inversely proportional to the rotational speed n and directly proportional to the ultrasonic vibration frequency f, the longitudinal ultrasonic amplitude A, the torsional ultrasonic amplitude B, and the helix angle β.

[0010] Based on the relationship between the cutting separation time ratio Q and various parameters, the milling speed, ultrasonic tool holder amplitude and frequency to be achieved in the machining process are selected.

[0011] The cutting separation time ratio Q is used to evaluate the ultrasonic machining effect; the longer the cutting separation time, the better the ultrasonic effect.

[0012] The proposed longitudinal-torsional composite ultrasonic vibration-assisted high-speed milling method breaks through the conventional longitudinal-torsional ultrasonic milling speed and significantly improves the processing efficiency.

[0013] Specifically, the technical solution of this invention is as follows:

[0014] A design method for high-speed milling assisted by longitudinal torsional ultrasonic vibration, comprising the following steps:

[0015] Step 1: Solve for the displacement expression of a single longitudinal torsional ultrasonic vibration.

[0016] In the machining process, the torsional ultrasonic vibration velocity and milling speed are much greater than the feed rate. Therefore, neglecting the influence of the feed rate, a single rotary ultrasonic vibration process can be simplified as linear motion. Using the concept of "substituting straight lines for curves," a single longitudinal torsional ultrasonic vibration process can be simplified into motion in the X and Z directions. The displacement expression for a single longitudinal torsional ultrasonic vibration can then be obtained as follows:

[0017]

[0018]

[0019]

[0020] Among them, v c Let t be the milling speed of the cutting tool, t be the time variable, A and B be the longitudinal and torsional amplitudes of the longitudinal-torsional ultrasonic vibration, respectively, and f be the ultrasonic vibration frequency. R is the initial phase angle of the tool, R is the radius of the machining tool, and n is the spindle speed.

[0021] Step 2: Solve for the periodic trajectory of a single longitudinal-torsional ultrasonic vibration.

[0022] The tool motion trajectory diagram can be obtained by using MATLAB program from equations (1) and (2).

[0023] Step 3: Solve for the expression of a single longitudinal torsional ultrasonic vibration velocity.

[0024] By differentiating the displacement expression in step one, we can obtain the cutting speed expressions for the tool in the X and Z directions during a single longitudinal torsional ultrasonic vibration process.

[0025] Step 4: Decomposition of longitudinal torsional ultrasonic vibration velocity

[0026] Based on the simplification principle in step one, it can be seen that a single longitudinal torsional ultrasonic vibration results in a tool having a rotational speed from the spindle, a rotational speed from the torsional ultrasonic vibration, and a motion speed from the longitudinal ultrasonic vibration. The ultrasonic vibration velocity can be decomposed using kinematic relationships.

[0027] Step 5: Solve for the velocity expression perpendicular to the cutting edge direction.

[0028] The expression for the velocity perpendicular to the cutting edge of the tool can be obtained from step four.

[0029] Step 6: Solving for the cutting separation time ratio Q

[0030] The milling speed is 0 at the point where the cutting edge is tangent to the trajectory. The time at this point can be obtained from the decomposed expression.

[0031] The slope of the straight line containing the point c where the cutting edge is tangent to the trajectory, and the intersection point d of the cutting edge and the trajectory diagram, are related to the tool helix angle and satisfy the linear equation. Therefore, the time t corresponding to the intersection point d can be calculated. d .

[0032] The cutting separation time Q is the ratio of the time it takes for the cutting edge to separate from the workpiece to the ultrasonic vibration period during a single ultrasonic vibration process. The longer the cutting separation time, the better the ultrasonic effect. The cutting separation time Q can be obtained from the time difference between the point c where the cutting edge is tangent to the trajectory and the intersection point d of the cutting edge and the trajectory diagram.

[0033] Step 7: Solve the correspondence between the variables involved and the cutting separation time ratio.

[0034] The MATLAB program can be used to solve the relationship between each variable in the above equation and the cutting separation time ratio. Specifically, the cutting separation time ratio Q is inversely proportional to the rotational speed n and directly proportional to the ultrasonic vibration frequency f, the longitudinal ultrasonic amplitude A, the torsional ultrasonic amplitude B, and the helix angle β.

[0035] Step 8: Select the milling speed required for the machining process.

[0036] Determine the tool diameter and spindle speed according to the machining requirements, and obtain the milling speed according to formula (3).

[0037] Step 9: Select the amplitude and frequency of the ultrasonic tool holder during the machining process.

[0038] The ultrasonic vibration frequency, longitudinal ultrasonic amplitude, and torsional ultrasonic amplitude are determined according to the processing requirements.

[0039] Step 10: Calculate the cutting separation time ratio Q to evaluate the ultrasonic machining effect.

[0040] The cutting separation time ratio is calculated based on the machining parameters in steps eight and nine.

[0041] Beneficial effects:

[0042] (1) The longitudinal-torsional composite ultrasonic vibration-assisted high-speed milling method designed in this invention breaks through the conventional longitudinal-torsional ultrasonic milling speed in terms of milling speed. Through comparison, it is found that the processing efficiency is significantly improved, with a specific value of 76%, providing a new idea for high-efficiency processing of difficult-to-machine materials.

[0043] (2) This invention has developed multiple solution programs for the designed machining method. In the actual design process, the critical speed of longitudinal torsional ultrasonic vibration milling that can be achieved can be quickly solved according to the test conditions. The cutting separation time of the machining process can be quickly solved to evaluate and predict the machining effect. The test conditions can be coordinated and optimized according to the expected cutting speed target, thereby greatly reducing the design time of the machining method and making the design process fast. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the process of separating the cutting edge from the workpiece in this invention;

[0045] Figure 2 This is a schematic diagram of the velocity decomposition of the cutting edge at point c in this invention;

[0046] Figure 3 This is a graph showing the relationship between spindle speed and cutting separation time ratio, where the horizontal axis represents spindle speed in r / min and the vertical axis represents cutting separation time ratio.

[0047] Figure 4 This is a graph showing the relationship between ultrasonic vibration frequency and cutting separation time ratio, where the horizontal axis represents ultrasonic vibration frequency in Hz, and the vertical axis represents cutting separation time ratio.

[0048] Figure 5 This is a graph showing the relationship between longitudinal ultrasonic amplitude and cutting separation time ratio, where the horizontal axis represents longitudinal ultrasonic amplitude in mm, and the vertical axis represents cutting separation time ratio.

[0049] Figure 6 This is a graph showing the relationship between torsional ultrasonic amplitude and cutting separation time ratio, where the horizontal axis is the torsional ultrasonic amplitude in mm and the vertical axis is the cutting separation time ratio.

[0050] Figure 7 This is a graph showing the relationship between the helix angle and the cutting separation time ratio, where the horizontal axis is the helix angle in degrees and the vertical axis is the cutting separation time ratio. Detailed Implementation

[0051] The technical solution of the present invention will be described in detail below with reference to the embodiments and accompanying drawings.

[0052] Example 1

[0053] The designed longitudinal-torsional composite ultrasonic vibration-assisted high-speed milling method comprises the following steps:

[0054] Step 1: Solve for the displacement expression of a single longitudinal torsional ultrasonic vibration.

[0055] The torsional ultrasonic vibration speed and milling speed during the machining process are much greater than the feed speed. Therefore, the influence of the feed speed can be ignored. Then, a single rotational ultrasonic vibration process can be simplified as linear motion. Using the idea of ​​"replacing curve with straight line", the single longitudinal torsional ultrasonic vibration process can be simplified into motion in the X and Z directions.

[0056] The expression for the displacement of a single longitudinal torsional ultrasonic vibration can then be obtained as follows:

[0057]

[0058]

[0059]

[0060] Among them, v c Let t be the milling speed of the cutting tool, t be the time variable, A and B be the longitudinal and torsional amplitudes of the longitudinal-torsional ultrasonic vibration, respectively, and f be the ultrasonic vibration frequency. R is the initial phase angle of the tool, R is the radius of the machining tool, and n is the spindle speed.

[0061] Step 2: Solve for the periodic trajectory of a single longitudinal-torsional ultrasonic vibration.

[0062] The tool motion trajectory diagram can be obtained from expressions (1) and (2) using the MATLAB program (Appendix 1), as shown below. Figure 1 Therefore, point bcde represents one ultrasonic vibration cycle.

[0063] Appendix 1

[0064] clear

[0065] clc

[0066] t=0.0001:0.000001:0.0003;

[0067] r=3

[0068] n = 3366

[0069] A1 = 0.007

[0070] A2 = 0.004

[0071] f1 = 35000

[0072] Phi1=0

[0073] Phi2=0

[0074] vc = 6 * pi * n

[0075] xt1=vc*t / 60+A2*sin(2*pi*f1*t+Phi1);

[0076] zt1=A1*sin(2*pi*f1*t+Phi2);

[0077] figure(′color′,′w′)

[0078] plot(xtl,ztl,′-′,′linewidth′,2,′color′,′m′)

[0079] hold on

[0080] xlabel('x(mm)')

[0081] zlabel('z(mm)')

[0082] set(gca,′fontsize′,50,′fontname′,′Times New Roman′)

[0083] hold off

[0084] Step 3: Solve for the expression of a single longitudinal torsional ultrasonic vibration velocity.

[0085] Differentiating the displacement expression in step one yields the cutting velocities V1(t) and V2(t) of the tool in the X and Z directions during a single longitudinal torsional ultrasonic vibration process, as follows:

[0086]

[0087]

[0088] Step 4: Decomposition of longitudinal torsional ultrasonic vibration velocity

[0089] Based on the simplification principle of step one, it can be seen that a single longitudinal-torsional ultrasonic vibration results in a tool with a rotational velocity Vc from the spindle, a rotational velocity V1(t) from the torsional ultrasonic vibration, and a motion velocity V2(t) from the longitudinal ultrasonic vibration. The ultrasonic vibration velocity can be decomposed into velocity components using kinematic relationships, as follows: Figure 2 .

[0090] Step 5: Solve for the velocity expression perpendicular to the cutting edge direction.

[0091] According to step four, the velocity V perpendicular to the cutting edge of the tool can be obtained. t The expression for (t) is:

[0092] V t (t)=V1cosβ+V2sinβ (6)

[0093] V1sinβ=V2cosβ (7)

[0094] Step 6: Solving for the cutting separation time ratio Q

[0095] Figure 2 In the example, the milling speed at point c (the position where the cutting edge is tangent to the trajectory) is V. t =0, then according to equation (6), the time t at this time is c It can be obtained from the following expression:

[0096] V1cosβ+V2sinβ=0 (8)

[0097] Seek

[0098] Points c and d lie on the cutting edge, and the slope of the line they form is related to the helix angle of the tool. Therefore, the following equation applies:

[0099]

[0100] The time t corresponding to the intersection point d can be obtained using formulas (1), (8), and (9) via the maltab program (Appendix 2). d .

[0101] Appendix 2

[0102] n = 6400% (unit: r / min)

[0103] a = 0.004% (unit: mm)

[0104] b = 0.007% (unit: mm)

[0105] r = 3% (unit: mm)

[0106] tanC=tan(54*2*3.141592653589 / 360)

[0107] cotC=cot(54*2*3.141592653589 / 360)

[0108] f = 35000% (unit: Hz)

[0109] w = 2 * 3.1415926535 * f

[0110] v = 2 * 3.141592653589 * r * n / 60% (unit: mm / s)

[0111] tc = acos(-v / ((a+b*tanC)*2*3.141592653589*f)) / w % Unit is s

[0112] symst

[0113] tl=solve((a*cotC+b)*(sin(w*tc)-sin(t))+v*cotC*(tc-t / w),t)

[0114] td = t1 / w % Unit is s

[0115] Q = (td - tc) * f%

[0116] The cutting separation time Q ratio is defined as the ratio of the time it takes for the cutting edge to separate from the workpiece in a single ultrasonic vibration process to the ultrasonic vibration period. The longer the cutting separation time, the better the ultrasonic effect. Its expression is as follows:

[0117]

[0118] T = 1 / f (12)

[0119] The cutting separation time Q can be obtained by the procedure in (Appendix 2 above).

[0120] Step 7: Solve for the relationship between each variable in the equation and the cutting separation time ratio.

[0121] Using MATLAB programs (Appendices 3-7), the relationships between the main variables and the cutting separation time ratio in these formulas can be solved from equations (1), (8), (9), (10), (11), and (12). Figures 3-7 As shown in the figure, the cutting separation time ratio Q is inversely proportional to the rotational speed n and directly proportional to the ultrasonic vibration frequency f, the longitudinal ultrasonic amplitude A, the torsional ultrasonic amplitude B, and the helix angle β.

[0122] Appendix 3 (Relationship between spindle speed and cutting separation time ratio)

[0123] clear

[0124] clc

[0125] a = 0.004; % Torsional vibration amplitude

[0126] b = 0.007; % longitudinal vibration amplitude

[0127] r = 3; % Tool radius (mm)

[0128] A = 0; % Initial phase angle of longitudinal vibration (rad)

[0129] B = 0; % Initial phase angle of torsional vibration (rad)

[0130] tan_C = tan(54 * 2 * 3.1415926535 / 360); % Tan value of tool helix angle

[0131] cot_C=cot(54*2*3.1415926535 / 360);

[0132] f = 35000; % Ultrasonic frequency

[0133] x=(a+b*tan_C)*2*3.1415926535*f;

[0134] w = 2 * 3.1415926535 * f; %

[0135] i = 1;

[0136] %%

[0137] for n=1:200:9000%spindle speed r / min

[0138] v = 2 * 3.1415926535 * r * n / 60; % Milling speed

[0139] y = v / x;

[0140] t1 = acos(-y); % tb * w

[0141] t2 = t1 / w; %tb

[0142] syms t

[0143] assume(t>3.1415926535&t<5*3.1415926535 / 2)%range

[0144] f=(a*cot_C+b)*(sin(w*t2)-sin(t))+v*cot_C.*(t2-t / w);

[0145] te = solve(f);

[0146] D(i)=(te-t1) / (2*3.1415926535);

[0147] i = i + 1

[0148] cleart

[0149] end

[0150] %%

[0151] figure

[0152] N = 1:200:9000;

[0153] plot(N, D)

[0154] hold on

[0155] scatter(N, D)

[0156] Appendix 4 (Relationship between ultrasonic vibration frequency and cutting separation time ratio)

[0157]

[0158] Appendix 5 (Relationship between longitudinal ultrasonic amplitude and cutting separation time ratio)

[0159]

[0160] Appendix 6 (Relationship between torsional ultrasonic amplitude and cutting separation time ratio)

[0161]

[0162] Appendix 7 (Relationship between helix angle and cutting separation time ratio)

[0163]

[0164] Step 8: Select the milling speed required for the machining process.

[0165] Based on the machining requirements, the tool diameter d = 6mm and the spindle speed n = 6400r / min are determined. The milling speed v is obtained according to formula (3). c =120.6 m / min.

[0166] Step 9: Select the amplitude and frequency of the ultrasonic tool holder during the machining process.

[0167] Based on the correspondence between each variable and the cutting separation time ratio obtained in step seven, the ultrasonic vibration frequency f = 35000Hz, the longitudinal ultrasonic amplitude A = 7μm, and the torsional ultrasonic amplitude B = 4μm are determined according to the processing requirements.

[0168] Step 10: Calculate the cutting separation time ratio Q to evaluate the ultrasonic machining effect.

[0169] Substituting the machining parameters from steps eight and nine into formula (11), the cutting separation time ratio Q = 0.41 is calculated. This indicates that the cutting edge separates from the workpiece for 41% of the ultrasonic vibration cycle, which helps reduce milling force and allows the cutting fluid to enter the machining area, enhancing heat exchange and reducing cutting heat. Conclusion: The cutting speed obtained in Example 1 is 120 m / min, and the cutting separation time ratio is 41%. Based on the published SCI paper "Surface microstructure of titanium alloy thin-walled parts at ultrasonic vibration-assisted milling" (DOI number 10.1007 / s00170-018-3005-7), steps eight to ten were repeated with horizontal parameters, resulting in a cutting speed of 68 m / min and a cutting separation time ratio of 44%. Comparison shows that, with similar cutting separation time ratios, the cutting speed in Example 1 is 1.77 times that of the published horizontal cutting speed, significantly improving machining efficiency.

[0170] Table 1. Comparison of Example Parameters with Existing Processing Level Parameters and Calculation Results

[0171]

Claims

1. A method for optimizing the design of high-speed milling assisted by longitudinal-torsional composite ultrasonic vibration, characterized in that, The steps are as follows: Step 1: Solve for the displacement expression of a single longitudinal torsional ultrasonic vibration. The single rotational ultrasonic vibration process is simplified to linear motion in the X and Z directions, resulting in the following expression for the displacement of a single longitudinal torsional ultrasonic vibration: (1) (2) (3) in, t is the milling speed of the tool, A and B are the longitudinal and torsional amplitudes of the longitudinal-torsional ultrasonic vibration, f is the ultrasonic vibration frequency, φ1 and φ2 are the initial phase angles of the tool, R is the radius of the machining tool, and n is the spindle speed. Step 2: Solve for the periodic trajectory of a single longitudinal-torsional ultrasonic vibration. Using equations (1) and (2) and a MATLAB program, a schematic diagram of the tool motion trajectory is obtained; Step 3: Solve for the expression of a single longitudinal torsional ultrasonic vibration velocity. Differentiating the displacement expression in step one yields the cutting speed expressions for the tool in the X and Z directions during a single longitudinal torsional ultrasonic vibration process. Step 4: Decomposition of longitudinal torsional ultrasonic vibration velocity Velocity decomposition of ultrasonic vibration velocity using kinematic relationships; Step 5: Solve for the velocity expression perpendicular to the cutting edge direction. Based on step four, the velocity expression perpendicular to the cutting edge of the tool is obtained; Step 6: Solving for the cutting separation time ratio Q The position of the point where the cutting edge is tangent to the trajectory and the milling speed. =0, then the time at this moment It can be obtained from the following decomposition expression: (8) Seek (9) The relationship between the slope of the line containing the cutting edge at point c (where the cutting edge is tangent to the trajectory) and the intersection point d (where the cutting edge intersects the trajectory) and the tool helix angle satisfies the following linear equation. (10) Therefore, the time corresponding to intersection point d can be calculated. ; The cutting separation time Q is the ratio of the time it takes for the cutting edge to separate from the workpiece in a single ultrasonic vibration process to the ultrasonic vibration period. The longer the cutting separation time, the better the ultrasonic effect. The cutting separation time can be obtained from the time difference between the point c where the cutting edge is tangent to the trajectory and the intersection point d of the cutting edge and the trajectory diagram, according to the following expression: (11) T = 1 / f (12); Step 7: Solve the relationship between the variables involved and the cutting separation time ratio. The variables are rotational speed n, ultrasonic vibration frequency f, longitudinal ultrasonic amplitude A, torsional ultrasonic amplitude B, and helix angle β; Step 8: Select the milling speed required for the machining process. Determine the tool diameter and spindle speed according to the machining requirements, and calculate the milling speed according to formula (3): (3) Step 9: Select the amplitude and frequency of the ultrasonic tool holder during the machining process. Based on the correspondence between each variable and the cutting separation time ratio obtained in step seven, the ultrasonic vibration frequency, longitudinal ultrasonic amplitude, and torsional ultrasonic amplitude are determined according to the processing requirements. Step 10: Calculate the cutting separation time ratio Q to evaluate the ultrasonic machining effect. Based on the processing parameters, the cutting separation time ratio is calculated by substituting into formula (11); then it can be known that the time ratio of the cutting edge to the workpiece to separate within the ultrasonic vibration cycle is longer, which is more conducive to reducing milling force and also conducive to the entry of cutting fluid into the processing area, enhancing the heat exchange effect and reducing cutting heat.

2. The optimized design method for high-speed milling assisted by longitudinal-torsional composite ultrasonic vibration according to claim 1, characterized in that, The cutting separation time ratio Q is inversely proportional to the rotational speed n and directly proportional to the ultrasonic vibration frequency f, the longitudinal ultrasonic amplitude A, the torsional ultrasonic amplitude B, and the helix angle β.

3. The optimized design method for high-speed milling assisted by longitudinal-torsional composite ultrasonic vibration according to claim 1, characterized in that, In step three, the expression for the cutting speed is as follows: (4) (5) V1(t) is the cutting speed in the X direction; V2(t) is the cutting speed in the Z direction.

4. The optimized design method for high-speed milling assisted by longitudinal-torsional composite ultrasonic vibration according to claim 1, characterized in that, The speed V perpendicular to the milling cutting edge of the tool, as described in step five. t (t) expression: (6) (7)。

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