Method and device for improving stability of side milling of thin-walled parts

Abstract

The application provides a method and device for improving the stability of side milling of a thin-walled part, and belongs to the technical field of ultrasonic vibration machining.The method comprises the following steps: determining the amplitude and frequency required by an ultrasonic vibration assisted milling device, designing the device, and exciting the device; analyzing the separation law and characteristics of ultrasonic longitudinal torsional vibration, and determining a cutting thickness expression; constructing a dynamic milling force model of ultrasonic longitudinal torsional vibration based on the cutting thickness expression; establishing an ultrasonic longitudinal torsional vibration milling thin-walled part dynamics model based on the dynamic milling force model of ultrasonic longitudinal torsional vibration; performing a modal experiment on the ultrasonic vibration assisted milling system, and obtaining the modal parameters of the thin-walled part; then, performing a groove milling experiment and calibrating the milling force coefficient; obtaining the machining parameters, tool parameters and ultrasonic vibration parameters of the thin-walled part to be side milled; then, solving the ultrasonic longitudinal torsional vibration milling thin-walled part dynamics model, and obtaining a stability lobe diagram; and the stability, machining precision and machining quality of the milling of the thin-walled part are improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of ultrasonic vibration machining, and particularly relates to a method and device for improving the stability of side milling of thin-walled parts. BACKGROUND

[0002] Complex thin-walled parts are widely used in the fields of aerospace, energy, precision instruments, automobile manufacturing, etc. due to their light weight and compact structure.

[0003] Non-universal thin-walled parts such as integral bulkheads, integral wallboards, turbine disc and turbine blade of an aero-engine, etc. are mostly machined by milling process. Due to the high performance requirement, complex structure and high material removal rate of such parts, the rigidity of the formed workpiece is reduced, which affects the stability of the thin-walled part during machining, reduces the machining precision and makes it difficult to guarantee the machining quality. SUMMARY

[0004] To solve the problems of poor stability, low machining precision and difficult to guarantee the machining quality of thin-walled parts in the prior art, the present application provides a method and device for improving the stability of side milling of thin-walled parts, which processes the thin-walled part by ultrasonic vibration assisted technology and predicts the ultrasonic machining stable milling parameters to improve the stability, machining precision and machining quality of the thin-walled part milling. The technical solution is as follows:

[0005] In a first aspect, a method for improving the stability of side milling of thin-walled parts is provided, which comprises:

[0006] Step 1: determining the amplitude and frequency required by the ultrasonic vibration assisted milling device according to the shape features and material properties of the thin-walled part to be side milled;

[0007] Step 2: designing the ultrasonic vibration assisted milling device;

[0008] Step 3: exciting the ultrasonic vibration assisted milling device using an ultrasonic power supply to realize stable ultrasonic longitudinal torsional vibration of the ultrasonic vibration assisted milling device;

[0009] Step 4: analyzing the separation law and characteristics of the ultrasonic longitudinal torsional vibration based on the tooth angle parameters of the ultrasonic longitudinal torsional vibration to determine the cutting thickness expression;

[0010] Step 5: constructing a dynamic milling force model of the ultrasonic longitudinal torsional vibration based on the cutting thickness expression;

[0011] Step 6: establishing a dynamic model of the ultrasonic longitudinal torsional vibration milling of the thin-walled part based on the dynamic milling force model of the ultrasonic longitudinal torsional vibration;

[0012] Step 7: performing modal experiment of the ultrasonic vibration assisted milling system to obtain the modal parameters of the thin-walled part;

[0013] Step 8, carry out groove milling experiment and calibrate milling force coefficient;

[0014] Step 9, obtain the machining parameters, tool parameters and ultrasonic vibration parameters of the thin-walled part to be side-milled;

[0015] Step 10, solve the dynamic model of ultrasonic longitudinal-torsional vibration milling of the thin-walled part by using the parameters in steps 7 to 9, and obtain the stability lobe diagram.

[0016] The step 2 specifically comprises:

[0017] Selecting a suitable machining tool;

[0018] Selecting a chuck cap according to the machining tool, and determining the small-end diameter of the amplitude rod;

[0019] Calculating the amplification factor according to the output amplitude of the transducer and the required amplitude, determining the type of the amplitude rod and the large-end diameter of the amplitude rod;

[0020] Selecting a piezoelectric ceramic and determining the diameter of the back cover plate;

[0021] Determining the frequency equations of each section by wave equation, and calculating the lengths of the back cover plate, the large end of the amplitude rod and the small end of the amplitude rod;

[0022] Establishing a three-dimensional model of the ultrasonic vibration unit according to the sizes and material properties of the back cover plate, the piezoelectric ceramic, the amplitude rod and the tool, and performing modal simulation;

[0023] Adjusting the sizes of the back cover plate and the amplitude rod to make the resonant frequency of the ultrasonic vibration unit close to the design frequency, and completing the design of the ultrasonic vibration machining unit.

[0024] The step 4 specifically comprises:

[0025] Establishing the kinematic equation expression of the ultrasonic longitudinal-torsional vibration side milling with the x-axis as the feed direction, the y-axis as the vertical feed direction and the z-axis as the spindle direction;

[0026] Based on the kinematic equation expression of the ultrasonic longitudinal-torsional vibration side milling, analyzing the trajectory of the ultrasonic longitudinal-torsional vibration milling to obtain the contact time and separation time of the tool and the workpiece in each vibration period, judging the cutting state and determining the cutting thickness expression.

[0027] The step 5 specifically comprises:

[0028] Analyzing the separation and contact relationship of the tool and the workpiece, and establishing a window function for judging the cutting state;

[0029] Based on the window function, determining the milling force of the ultrasonic vibration in the x and y directions according to the dynamic chip thickness and the tool tooth angle.

[0030] The modal parameters of the thin-walled part in step 7 include inherent frequency, damping and modal mass.

[0031] The milling force coefficients in step 8 include tangential and normal cutting force coefficients K t and K r , tangential and normal edge coefficients K te and K re .

[0032] The processing parameters of the thin-walled part in step 9 include feed speed v0.

[0033] The processing parameters of the thin-walled part in step 9 include feed speed v0.

[0034] The tool parameters include tool diameter D and tool tooth number N.

[0035] The ultrasonic vibration parameters include ultrasonic vibration frequency f, ultrasonic longitudinal vibration amplitude a and ultrasonic torsional vibration amplitude b.

[0036] In step 10, the improved full-discrete method is used to solve the dynamic model of ultrasonic longitudinal and torsional vibration milling of the thin-walled part by using the parameters in steps 7 to 9.

[0037] In the second aspect, an apparatus for improving the stability of side milling of a thin-walled part is provided, which comprises an ultrasonic vibration assisted milling processing device, and the ultrasonic vibration assisted milling processing device comprises an ultrasonic vibration processing unit and an integrated tool holder.

[0038] The ultrasonic vibration processing unit comprises a pre-tightening bolt, a rear cover plate, an electrode sheet, a piezoelectric ceramic, an amplitude transformer, an ER chuck, an ER pressure cap and a tool from back to front, and the rear cover plate, the electrode sheet and the piezoelectric ceramic are connected with the amplitude transformer through the pre-tightening bolt.

[0039] The amplitude transformer is a stepped amplitude transformer and is divided into two parts of a large end and a small end; the large end of the amplitude transformer is provided with an internal thread connected with the pre-tightening bolt; the large end of the amplitude transformer is further provided with a flange connected with the integrated tool holder; the small end of the amplitude transformer is provided with a spiral groove for degenerating an axial vibration mode into a torsional vibration; and the small end of the amplitude transformer is further provided with an external thread and an internal hole connected with the tool.

[0040] The integrated tool holder is provided with a stepped hole for ensuring coaxiality with the ultrasonic vibration processing unit.

[0041] The present application has at least the following beneficial effects:

[0042] An ultrasonic vibration assisted milling device is designed, the contact and separation relationship between the tool and the workpiece in the ultrasonic vibration milling movement process is analyzed, and a window function expressing the cutting state is defined to construct a dynamic milling force model of the ultrasonic longitudinal and torsional vibration, and the full discrete method is improved to solve the dynamic milling force model of the ultrasonic longitudinal and torsional vibration, the dynamic model of the ultrasonic longitudinal and torsional vibration milling of the thin-walled part is established, the stability lobe diagram is obtained, the stable machining parameters are given, the chatter phenomenon in the machining process can be inhibited, and the stability, machining precision and machining quality of the thin-walled part milling are improved. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 A flowchart of the method for improving the side milling stability of the thin-walled part;

[0044] Figure 2 An ultrasonic longitudinal and torsional vibration side milling schematic diagram;

[0045] Figure 3 A structural schematic diagram of the ultrasonic vibration machining unit;

[0046] Figure 4 A structural schematic diagram of the integrated tool holder;

[0047] Figure 5 A sectional view of the ultrasonic vibration assisted machining device;

[0048] Figure 6 A tool and workpiece separation and contact schematic diagram;

[0049] Figure 7 A comparison diagram of the stable lobe diagrams of ultrasonic milling and ordinary milling. DETAILED DESCRIPTION

[0050] The application will be further described in detail through specific embodiments and drawings.

[0051] Please refer to Figure 1 , which is a flowchart of the method for improving the side milling stability of the thin-walled part provided by the application, and the method comprises the following steps:

[0052] Step 1, determining the amplitude and frequency required by the ultrasonic vibration assisted milling device according to the shape characteristics and material properties of the thin-walled part to be side milled;

[0053] Step 2, designing the ultrasonic vibration assisted milling device;

[0054] Step 2 specifically comprises:

[0055] Step 21, selecting a suitable machining tool;

[0056] Step 22, selecting a chuck pressure cap according to the machining tool, and determining the diameter of the small end of the amplitude rod;

[0057] Step 23, calculate the amplification factor according to the output amplitude of the transducer and the required amplitude, determine the type of amplitude transformer and the diameter of the large end;

[0058] Step 24, select the piezoelectric ceramic and determine the diameter of the back cover plate;

[0059] Step 25, determine the length of the back cover plate, the large end of the amplitude transformer, and the small end of the amplitude transformer by the wave equation;

[0060] Step 26, according to the size and material properties of the back cover plate, piezoelectric ceramic, amplitude transformer and tool, establish a three-dimensional model of the ultrasonic vibration unit and carry out modal simulation;

[0061] Step 27, adjust the size of the back cover plate and the amplitude transformer to make the resonance frequency of the ultrasonic vibration unit close to the design frequency, complete the design of the ultrasonic vibration processing unit, see Figure 3 .

[0062] The size of the ultrasonic vibration processing unit is calculated based on the half wavelength theory, and the node is set at the front end of the piezoelectric ceramic, so the original front cover plate of the transducer is replaced by a quarter wavelength amplitude transformer. The specific size calculation process is as follows:

[0063] According to the one-dimensional longitudinal vibration wave equation of variable cross-section rod, in the case of cylindrical cross-section rod, the one-dimensional longitudinal vibration wave equation can be simplified as:

[0064]

[0065] Where, ξ = ξ(x) is the displacement function of the cross-section, k = ω / c, k is the wave number, ω is the circular frequency of vibration, is the propagation velocity of longitudinal wave.

[0066] Then the general solution of the one-dimensional longitudinal vibration wave equation is:

[0067] ξ = Hcoskx + J sinkx

[0068] Then the stress function σ in the rod is:

[0069]

[0070] According to the boundary conditions of the back cover plate and the piezoelectric ceramic:

[0071]

[0072] The frequency equation that the size of the back cover plate and the piezoelectric ceramic part meets is obtained:

[0073]

[0074] At the section change of the amplitude-varying rod, the displacement is considered to be continuous. If the section area ratio S4 / S5 is not too large, the force is considered to be continuous approximately, and then the boundary condition of the amplitude-varying rod is:

[0075]

[0076] The frequency equation of the amplitude-varying rod part is obtained:

[0077]

[0078] The specific size can be calculated according to the frequency equation of each section.

[0079] The integrated tool holder is designed according to the flange size set at the node position and the main shaft model, and the design of the ultrasonic vibration assisted milling machining device is finally completed.

[0080] Specifically, referring to Figure 5 , the ultrasonic vibration assisted milling machining device comprises an ultrasonic vibration machining unit and an integrated tool holder,

[0081] The ultrasonic vibration machining unit comprises, from back to front, a pre-tightening bolt 5, a back cover plate 6, an electrode sheet 7, a piezoelectric ceramic 8, an amplitude-varying rod 9, an ER chuck 10, an ER pressure cap 11 and a tool 12; the back cover plate 6, the electrode sheet 7 and the piezoelectric ceramic 8 are connected with the amplitude-varying rod 9 through the pre-tightening bolt 5; the amplitude-varying rod 9 is a stepped amplitude-varying rod, which is divided into a large end and a small end; the large end of the amplitude-varying rod is provided with an internal thread for connecting with the pre-tightening bolt 5; the large end of the amplitude-varying rod is provided with a flange for connecting with the integrated tool holder 1; the small end of the amplitude-varying rod is provided with a spiral groove for degenerating the axial vibration mode into a torsional vibration; the small end of the amplitude-varying rod is further provided with an external thread and an internal hole for connecting with the tool 12;

[0082] The integrated tool holder 1 is provided with a stepped hole 3 for ensuring the coaxiality of the connection with the ultrasonic vibration unit and a side hole 2 for passing a wire; the integrated tool holder 1 is connected with the ultrasonic vibration machining unit through a connecting bolt 4, as shown in Figure 4 .

[0083] Step 3, using an ultrasonic power supply to excite the ultrasonic vibration assisted milling machining device to realize stable ultrasonic longitudinal-torsional vibration of the ultrasonic vibration assisted milling machining device;

[0084] Step 4, based on the tool tooth rotation angle parameter of the ultrasonic longitudinal-torsional vibration, analyzing the separation law and characteristics of the ultrasonic longitudinal-torsional vibration to determine a cutting thickness expression;

[0085] Optionally, step 4 specifically comprises:

[0086] Step 41, taking the x-axis as the feed direction, the y-axis as the vertical feed direction and the z-axis as the spindle direction, referring to Figure 2, the kinematic equation expression of the ultrasonic longitudinal-torsional vibration side milling is established:

[0087]

[0088] Wherein, R is the tool radius, Ω is the spindle speed, θ is the initial rotation angle of the tool, v0 is the feed speed, α is the longitudinal vibration amplitude, β is the torsional vibration amplitude, f is the ultrasonic vibration frequency, and t is the time.

[0089] Step 42, based on the kinematic equation expression of the ultrasonic longitudinal-torsional vibration side milling, the trajectory of the ultrasonic longitudinal-torsional vibration milling is analyzed, the contact time and the separation time of the tool and the workpiece in each vibration period are obtained, the cutting state is judged, and the cutting thickness expression is determined.

[0090] Specifically, according to the kinematic equation expression of the ultrasonic longitudinal-torsional vibration milling, due to the effect of torsional vibration, the tool and the workpiece exist high-frequency contact and separation in the ultrasonic vibration milling process. According to the projection of the ultrasonic vibration tool tip trajectory on the torsional plane, t A , the tool moves to point A, the rotation direction of the tool and the rotation direction of the spindle become opposite, the tool and the workpiece begin to separate, see Figure 6 ; t B , the tool moves to point B, the rotation direction of the tool and the rotation direction of the spindle become the same, the tool and the workpiece are still in the separation state; t C , the tool moves to point C, the tool and the workpiece re-contact; t A1 , the tool moves to point A1, and one cycle of ultrasonic vibration is completed. Wherein, the tool speed at points A and B is 0, the feed amount in a single vibration period is ignored, it is considered that the arc lengths of AB segment and BC segment are equal, and the formula for calculating the contact time of the tool and the workpiece at point C is:

[0091]

[0092] Due to the periodicity of ultrasonic vibration, the contact time and the separation time of the tool and the workpiece in each vibration period can be obtained, and the cutting state can be judged.

[0093] Due to the torsional effect, the ultrasonic vibration tool tooth angle of the jth tooth of the tool is:

[0094] φ jum (t)=(2πΩ / 60)t-(j-1)×2π / N+β×cos(2πft)

[0095] Wherein, N is the number of tool teeth.

[0096] In the machining process of thin-walled parts, the material removal process of the workpiece can be considered as a slow time-varying process because the feed speed of the tool is much smaller than the rotational speed of the tool. Therefore, the instantaneous cutting thickness h jum (t) is expressed as:

[0097]

[0098] wherein, is the displacement vector of the tool at time t, is the displacement vector of the workpiece at time t.

[0099] Step 5, constructing a dynamic milling force model of ultrasonic longitudinal-torsional vibration based on the cutting thickness expression.

[0100] Step 5 specifically includes:

[0101] Step 51, analyzing the separation contact relationship of the tool and the workpiece, and establishing a window function for judging the cutting state;

[0102] Step 52, determining the milling force of ultrasonic vibration in x and y directions based on the dynamic chip thickness and the tooth angle of the tool according to the window function.

[0103] wherein, the window function l(t) and g(φ j (t)) for judging the cutting state are respectively:

[0104]

[0105]

[0106] wherein, t A is the separation time of the tool and the workpiece within a single period, t C is the contact time of the tool and the workpiece within a single period, mod(t / T um ) is the remainder after division operation of t and T um , T um is the period of ultrasonic vibration, φ st and φ ex are the cutting-in angle and cutting-out angle of the jth tooth respectively.

[0107] The milling force of ultrasonic vibration in x and y directions determined according to the dynamic chip thickness and the tooth angle of the tool is:

[0108]

[0109] wherein, a is the axial cutting depth, K t and K r are the tangential and normal cutting force coefficients respectively, K te and K re are the tangential and normal edge coefficients respectively.

[0110] Step 6, based on the dynamic milling force model of ultrasonic longitudinal-torsional vibration, a dynamic model of ultrasonic longitudinal-torsional vibration milling of thin-walled parts is established;

[0111] According to the dynamic milling force model of ultrasonic longitudinal-torsional vibration, the influence of static force component is ignored, and in the framework of structural dynamics, the workpiece dynamics equation can be expressed as a differential equation group containing both parameter excitation and time delay terms:

[0112]

[0113] Where M, C and K are the modal mass, damping and stiffness matrices of the workpiece, respectively; q(t) is the modal coordinate of the tool, and the mode shape coefficient is normalized at the tool tip point, i.e. T=60 / (NΩ) is the time delay, which is equal to the tool tooth cutting period. The coefficient matrix K c (t) is:

[0114]

[0115] The generalized coordinates of the "tool-workpiece" thin-walled part milling system are introduced:

[0116]

[0117] And let the change matrix

[0118]

[0119] Where [-χ1(CL),...,-χ Pw (CL)] is the row vector of the workpiece mode shape χ corresponding to the relative position CL of the tool to the workpiece, then the dynamics equation of the "workpiece-tool" coupling system can be obtained as:

[0120]

[0121] In the thin-walled part machining process, the workpiece stiffness is much smaller than the tool stiffness, and the stability boundary of the system is mainly determined by the dynamic characteristics of the workpiece, so the tool dynamics is ignored.

[0122] Step 7, modal experiment of ultrasonic vibration assisted milling system is carried out to obtain the modal parameters of thin-walled parts;

[0123] Specifically, the modal parameters of thin-walled parts include natural frequency, damping and modal mass.

[0124] Step 8, groove milling experiment is carried out and the milling force coefficients are calibrated;

[0125] Specifically, the milling force coefficients include: tangential and normal cutting force coefficients K t and K r, tangential and normal edge coefficients K te and K re .

[0126] Step 9, the processing parameters of the side milling thin-walled part, the tool parameters, and the ultrasonic vibration parameters are obtained.

[0127] Specifically, the processing parameters of the side milling thin-walled part include the feed speed v0.

[0128] The tool parameters include the tool diameter D and the tool tooth number N.

[0129] The ultrasonic vibration parameters include the ultrasonic vibration frequency f, the ultrasonic longitudinal vibration amplitude alpha, and the ultrasonic torsional vibration amplitude beta.

[0130] Step 10, the dynamic model of the ultrasonic longitudinal and torsional vibration milling thin-walled part is solved by using the parameters of steps 7 to 9, and the stability lobe diagram is obtained.

[0131] Specifically, the full-discrete method is improved, the dynamic model of the ultrasonic longitudinal and torsional vibration milling thin-walled part is solved by using the parameters of steps 7 to 9, and the stability lobe diagram is obtained. Figure 7 is the comparison diagram of the stability lobe diagrams of the ultrasonic milling and ordinary milling, and under the same rotational speed, the ultrasonic milling of the application generally has a larger stable axial depth of cut, and by selecting a suitable spindle speed for milling processing, stable cutting can be realized, the processing quality can be ensured, and the processing efficiency is improved.

[0132] The ultrasonic vibration auxiliary milling processing device is designed in the embodiment of the application, the contact and separation relationship between the tool and the workpiece in the ultrasonic vibration milling movement process is analyzed, and the window function for judging the cutting state is defined, the dynamic milling force model of the ultrasonic longitudinal and torsional vibration is constructed, the full-discrete method is improved, the dynamic milling force model of the ultrasonic longitudinal and torsional vibration is solved, the dynamic model of the ultrasonic longitudinal and torsional vibration milling thin-walled part is established, the stability lobe diagram is obtained, and the stable processing parameters are given, so that the chatter phenomenon in the processing process is inhibited, and the stability, the processing precision and the processing quality of the thin-walled part milling processing are improved.

[0133] In the application, the ultrasonic vibration auxiliary milling processing device has the characteristics of reducing the cutting force, reducing the cutting temperature, reducing the tool wear and improving the surface quality, etc.

[0134] The above merely expresses the embodiments of the present application, the description is more specific and detailed, but cannot be understood as the limitation of the patent scope. It should be noted that for ordinary skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, which all belong to the protection scope of the present application. In addition, the unexplained part of the present application is all the routine technology.

Claims

1. A method of improving the stability of side milling of thin-walled parts, characterized in that, The method comprises: Step 1, determining the amplitude and frequency required by the ultrasonic vibration assisted milling device according to the shape characteristics and material properties of the thin-walled part to be side milled; Step 2, designing the ultrasonic vibration assisted milling device: selecting a suitable machining tool; selecting a chuck pressure cap according to the machining tool, and determining the small end diameter of the amplitude transformer; calculating the amplification factor according to the output amplitude of the transducer and the required amplitude, determining the type and large end diameter of the amplitude transformer; selecting a piezoelectric ceramic and determining the diameter of the back cover plate; determining the frequency equation of each section through the wave equation, calculating the length of the back cover plate, the large end of the amplitude transformer and the small end of the amplitude transformer; establishing a three-dimensional model of the ultrasonic vibration unit according to the size and material properties of the back cover plate, piezoelectric ceramic, amplitude transformer and tool, and performing modal simulation; adjusting the size of the back cover plate and the amplitude transformer to make the resonant frequency of the ultrasonic vibration unit approach the design frequency, and completing the design of the ultrasonic vibration machining unit; The ultrasonic vibration assisted milling device comprises an ultrasonic vibration machining unit and an integrated tool shank, and the ultrasonic vibration machining unit comprises, from back to front, a pre-tightening bolt (5), a back cover plate (6), an electrode sheet (7), a piezoelectric ceramic (8), an amplitude transformer (9), an ER chuck (10), an ER pressure cap (11) and a tool (12); the amplitude transformer (9) is a stepped amplitude transformer, which is divided into a large end and a small end; the small end of the amplitude transformer is provided with a spiral groove for degenerating the axial vibration mode into a torsional vibration; Step 3, exciting the ultrasonic vibration assisted milling device to realize stable ultrasonic longitudinal torsional vibration of the ultrasonic vibration assisted milling device; Step 4, analyzing the separation law and characteristics of ultrasonic longitudinal torsional vibration based on the tooth angle parameters of the ultrasonic longitudinal torsional vibration, and determining the cutting thickness expression: taking the x-axis as the feed direction, the y-axis as the vertical feed direction and the z-axis as the spindle direction, establishing the kinematic equation expression of ultrasonic longitudinal torsional vibration side milling; based on the kinematic equation expression of ultrasonic longitudinal torsional vibration side milling, analyzing the trajectory of ultrasonic longitudinal torsional vibration milling to obtain the contact time and separation time of the tool and the workpiece in each vibration period, judging the cutting state and determining the cutting thickness expression; Step 5, constructing a dynamic milling force model of ultrasonic longitudinal torsional vibration based on the cutting thickness expression: analyzing the separation and contact relationship of the tool and the workpiece, establishing a window function for judging the cutting state; based on the window function, determining the ultrasonic vibration milling force in the x and y directions according to the dynamic chip thickness and the tooth angle; Step 6, establishing a dynamic model of ultrasonic longitudinal torsional vibration milling of thin-walled parts based on the dynamic milling force model of ultrasonic longitudinal torsional vibration; Step 7, performing modal experiments on the ultrasonic vibration assisted milling system to obtain the modal parameters of the thin-walled part, including the natural frequency, damping and modal mass; Step 8, slot milling experiments are conducted and the milling force coefficients are calibrated, including tangential and normal cutting force coefficients K t and K r , tangential and normal edge coefficients K te and K re ; Step 9, obtaining the machining parameters, tool parameters and ultrasonic vibration parameters of the thin-walled part to be side milled, the machining parameters of the thin-walled part to be side milled including the feed speed v0; the tool parameters including the tool diameter D and the tool tooth number N; the ultrasonic vibration parameters including the ultrasonic vibration frequency f, the ultrasonic longitudinal vibration amplitude α and the ultrasonic torsional vibration amplitude β. Step 10, using the parameters of step 7 to step 9, the improved full-discrete method is used to solve the dynamic model of ultrasonic longitudinal-torsional vibration milling thin-walled workpiece, and the stability lobe diagram is obtained.

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