Damping modeling method for milling process of thin-wall component under multi-factor speed direction change

Abstract

The invention discloses a damping modeling method for a milling process of a thin-wall component under multi-factor speed direction change, which belongs to the technical field of electromechanics, and comprises the following steps of: firstly, representing a chip load matrix and a force coordinate transformation matrix according to an actual cutting speed influenced by a multi-directional vibration effect in a feeding direction, a feeding normal direction and a cutter shaft direction of a milling system; then, based on a periodic milling force expression and Taylor expansion simplification processing at a forced vibration position, solving of a milling dynamic force component, a process damping force component and a static force component is carried out, a cutting resultant force matrix is obtained, finally, a cutting resultant force expression is substituted into a milling system dynamics control equation, solving is carried out according to a time domain semi-discrete method, and a milling system dynamic control equation is obtained. According to the stability lobe graph of the damping effect in the milling process of the thin-wall component, the multi-factor speed direction change is considered, and the application range of the model under different working conditions is remarkably widened.

Description

Technical Field

[0001] The present invention belongs to the field of mechatronics technology, and particularly relates to a damping modeling method for the milling process of thin-walled components under the change of multi-factor speed direction. Background Art

[0002] The interference extrusion between the flank face of the cutting tool and the workpiece surface, as well as the change in the cutting speed direction caused by the vibration of the tool-workpiece system, will both generate a process damping effect, resulting in an increase in cutting stability at low rotational speeds. Existing modeling of the milling process damping mostly focuses on the plowing effect caused by interference extrusion. Since the deformation of the thin-walled component milling system is not considered and the actual penetration area is not corrected accordingly, the predicted axial limit cutting depth in the stability prediction of thin-walled components is usually higher than the observed value of the experimental results. A few literatures have carried out corrections on the dynamic cutting force considering the change in the cutting speed direction caused by cutting vibration, but currently only the correction considering the cutting vibration effect in the feed direction / feed normal direction has been realized, and the change in the multi-factor speed direction, such as the coupling effect of the double-flexible system of the tool-workpiece, the multi-directional vibration in the feed direction-feed normal direction-spindle direction, and the comprehensive characterization of the lateral cutting force-axial cutting force, has not been considered, and the applicable range of the model needs to be further expanded. Therefore, establishing a milling process damping model considering the change in the multi-factor speed direction has important theoretical significance and engineering application value for the stability prediction of thin-walled components.

[0003] Document 1 "Eksioglu C, Kilic Z M, Altintas Y, Discrete-time prediction of chatter stability, cutting forces, and surface location errors in flexible milling systems, Transactions of ASME Journal of Manufacturing Science and Engineering 134 (2012) 061006." discloses a stability prediction method for a flexible milling system considering the coupling effect of multi-directional vibration and multi-edge cutting. Since this method does not consider the correction of the actual cutting speed direction by the tool-workpiece vibration, it is not applicable to the problem of predicting the stability of thin-walled components considering the process damping effect.

[0004] Reference 2 "Feng J, Wan M, Gao TQ, Zhang WH, Mechanism of process damping in milling of thin walled workpiece, International Journal of Machine Tools and Manufacture 134 (2018) 1-19." discloses a method for characterizing dynamic cutting forces based on the actual cutting velocity direction and establishing a process damping modeling method for the change of the cutting velocity direction. Since this method fails to consider the change of the cutting velocity direction in multiple factors, the applicable range of the model is limited. For example, it can only consider the influence of the radial / normal cutting vibration effect on the process damping in the side milling of thin-walled components.

[0005] The typical characteristics of the above reference are as follows: The stability prediction method considering the multi-directional vibration of the feed direction - feed normal direction - tool axis direction and the comprehensive characterization of the lateral cutting force - axial cutting force does not include the process damping effect caused by the change of the cutting velocity direction. The process damping model of the thin-walled component with the change of the cutting velocity direction fails to consider the coupling effect of the tool-workpiece double-flexible system, the multi-directional vibration of the feed direction - feed normal direction - tool axis direction, and the comprehensive characterization of the lateral cutting force - axial cutting force. Summary of the Invention

[0006] To solve the problems raised in the above background art, the present invention provides a method for modeling the process damping in the milling of thin-walled components under the change of multiple-factor velocity directions, so as to solve the problem that the prior art does not consider the change of multiple-factor velocity directions in the damping modeling process.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A method for modeling the process damping in the milling of thin-walled components under the change of multiple-factor velocity directions, comprising the following steps:

[0009] S1: Micro-elementize the cutting load of each tool participating in milling along the axial depth of cut direction, and judge whether the i-th micro-element on the j-th cutting edge participates in cutting through the rotation angle θ ij (t), the entry angle θ st , the exit angle θ ex and the window function g ij ;

[0010] S2: Calculate the chip load matrix V i corresponding to the dynamic force component through the axial engagement angle κ ij of the tool and the rotation angle θ 1,ij (t);

[0011] S3: The chip load matrix V corresponding to the dynamic force component1,ij (t) is projected from the rotating coordinate system to the Cartesian coordinate system to obtain the transformation matrix T of the dynamic force components 1,ij (t);

[0012] S4: Calculate the chip load matrix V corresponding to the process damping force components through the tool rotation angle θ ij (t); 2,ij (t);

[0013] S5: Project the chip load matrix V corresponding to the process damping force components from the rotating coordinate system to the Cartesian coordinate system to obtain the transformation matrix T of the process damping force components 2,ij (t); 2,ij (t);

[0014] S6: Calculate the dynamic force component matrix [F ij , the number of tool teeth N, the transformation matrix T 1,ij (t), the cutting force coefficient matrix K rta , the chip load matrix V 1,ij (t) and the vibration displacement of the milling system xyz,i (t)] dy ;

[0015] S7: Calculate the process damping force component matrix [F ij , the number of tool teeth N, the window function g 2,ij (t), the tool radius R, the feed per tooth c of the tool, the spindle speed Ω of the machine tool, the transformation matrix T rta (t), the cutting force coefficient matrix K 2,ij (t) and the vibration velocity of the milling system xyz,i (t)] pr ;

[0016] S8: Calculate the static force component matrix [F ij , the number of tool teeth N, the window function g 1,ij (t), the feed per tooth c of the tool, the transformation matrix T rta (t), the cutting force coefficient matrix K ij (t) and the rotation angle θ xyz,i (t)] st ;

[0017] S9: Calculate the cutting resultant force [F xyz,i (t)] considering the change of the velocity direction with multiple factors, including static force, dynamic force, and process damping force components, through the following formula

[0018] [F xyz,i (t)] = [F xyz,i (t)] st + [F xyz,i (t)]dy + [F xyz,i (t)] pr ;

[0019] Substitute the cutting resultant force [F xyz,i (t)] into the dynamic control equation of the milling system, and solve the stability of the equation according to the semi-discrete method in the time domain, to obtain the stability lobe diagram of the damping effect in the milling process of thin-walled components considering the change of the velocity direction under multiple factors.

[0020] Preferably, the window function g in S1 ij is specifically:

[0021] .

[0022] Preferably, in S2, the specific calculation method of the chip load matrix V 1,ij (t) is:

[0023] .

[0024] Preferably, the specific calculation method of the transformation matrix T 1,ij (t) in S3 is:

[0025] .

[0026] Preferably, in S4, the specific calculation method of the chip load matrix V 2,ij (t) is:

[0027] .

[0028] Preferably, in S5, the specific calculation method of the transformation matrix T 2,ij (t) is:

[0029] .

[0030] Preferably, in S6, the specific calculation method of the dynamic force component matrix [F xyz,i (t)] dy is:

[0031] ;

[0032] where, dz is the axial height of the microelement, x i (t) is the vibration displacement of the milling system in the x direction at the current moment, y i (t) is the vibration displacement of the milling system in the y direction at the current moment, z i (t) is the vibration displacement of the milling system in the z direction at the current moment, x i (t - T) is the vibration displacement of the milling system in the x direction at the previous tooth moment, y i(t - T) is the vibration displacement of the milling system in the y-direction at the previous tooth moment, z i (t - T) is the vibration displacement of the milling system in the z-direction at the previous tooth moment.

[0033] Preferably, in S7, the process damping force component matrix [F xyz,i (t)] pr The specific calculation method is as follows:

[0034] ;

[0035] Wherein, is the vibration velocity of the milling system in the x-direction at the current moment, is the vibration velocity of the milling system in the y-direction at the current moment, is the vibration velocity of the milling system in the z-direction at the current moment, is the forced vibration velocity of the milling system in the x-direction at the current moment, is the forced vibration velocity of the milling system in the y-direction at the current moment, is the forced vibration velocity of the milling system in the z-direction at the current moment.

[0036] Preferably, in S8, the static force component matrix [F xyz,i (t)] st The specific calculation method is as follows:

[0037] .

[0038] Compared with the prior art, the beneficial effects of the present invention are:

[0039] In this application, the actual cutting speed affected by the multi-directional vibration effects of the feed direction, feed normal direction, and tool axis direction of the milling system is first used to characterize the chip load matrix and the force coordinate transformation matrix; then, based on the periodic milling force expression and the Taylor expansion simplification at the forced vibration, the solution of the milling dynamic force component, process damping force component, and static force component is carried out to obtain the cutting force resultant matrix; finally, the cutting force resultant expression is substituted into the dynamic control equation of the milling system and solved according to the time-domain semi-discrete method to obtain the stability lobe diagram of the milling process damping effect of the thin-walled component including the change of the multi-factor velocity direction;

[0040] This application considers the coupling effects of the tool-workpiece double flexible system, multi-directional vibration of the feed direction-feed normal direction-tool axis direction, and the comprehensive characterization of the lateral cutting force-axial cutting force, and establishes a process damping model for thin-walled components with changing cutting speed directions, significantly improving the applicable range of the model under different working conditions. Description of the Drawings

[0041] Figure 1It is a schematic diagram comparing the stability lobe diagram of the side-edge milling process (feed normal vibration) of a titanium alloy thin-walled component predicted in the embodiment of the present invention with the measured chatter vibration data in dynamics;

[0042] Figure 2 It is a schematic diagram comparing the stability lobe diagram of the bottom-edge milling process (tool axis direction vibration) of a titanium alloy thin-walled component predicted in the embodiment of the present invention with the measured chatter vibration data in dynamics. Specific implementation manners

[0043] To facilitate those skilled in the art to understand the technical content of the present invention, the following further elaborates the present invention in detail with reference to the accompanying drawings and specific examples. It should be understood that the specific examples described herein are only used to explain the present invention and are not used to limit the present invention.

[0044] Embodiment 1:

[0045] In this embodiment, a milling chatter vibration experiment is carried out using a common titanium alloy thin-walled blade structure in the industrial field to verify the prediction effect of the method of the present application on the damping stability lobe diagram of the milling process with multi-factor velocity direction changes of thin-walled components. The workpiece material is titanium alloy TC4, with a first-order natural frequency of 1309 Hz, a damping ratio of 0.82%, a mass-normalized modal shape of 17.76, a second-order natural frequency of 3315 Hz, a damping ratio of 1.28%, and a mass-normalized modal shape of 23.45. A ball-end mill with a tool radius R = 4 mm and the number of teeth N = 3 is used.

[0046] The damping modeling method for the milling process of thin-walled components under multi-factor velocity direction changes includes the following steps:

[0047] S1: Micro-elementize the cutting load of each tool participating in milling along the axial depth of cut direction, and judge whether the i-th micro-element on the j-th cutting edge participates in cutting through the rotation angle θ ij (t), the entry angle θ st , the exit angle θ ex and the window function g ij . The window function g ij is specifically:

[0048] ;

[0049] S2: Calculate the chip load matrix V i corresponding to the dynamic force component through the axial engagement angle κ ij of the tool and the rotation angle θ 1,ij (t) of the tool. The specific calculation method of the chip load matrix V 1,ij (t) is:

[0050] ;

[0051] S3: Project the chip load matrix V corresponding to the dynamic force component 1,ij (t) from the rotating coordinate system to the Cartesian coordinate system to obtain the transformation matrix T 1,ij (t) of the dynamic force component. The specific calculation method of the transformation matrix T 1,ij (t) is as follows: 1,ij (t) from the rotating coordinate system to the Cartesian coordinate system to obtain the transformation matrix T 1,ij (t) of the dynamic force component. 1,ij (t), the transformation matrix T 1,ij (t) is as follows:

[0052] ;

[0053] S4: Calculate the chip load matrix V 2,ij (t) corresponding to the process damping force component through θ ij . The specific calculation method of the chip load matrix V 2,ij (t) is as follows: ij Calculate the chip load matrix V corresponding to the process damping force component 2,ij (t), the chip load matrix V 2,ij (t) is as follows:

[0054] ;

[0055] S5: Project the chip load matrix V 2,ij (t) corresponding to the process damping force component from the rotating coordinate system to the Cartesian coordinate system to obtain the transformation matrix T 2,ij (t) of the process damping force component. The specific calculation method of the transformation matrix T 2,ij (t) is as follows: 2,ij (t) from the rotating coordinate system to the Cartesian coordinate system to obtain the transformation matrix T 2,ij (t) of the process damping force component. 2,ij (t), the transformation matrix T 2,ij (t) is as follows:

[0056] ;

[0057] S6: Calculate the dynamic force component matrix [F xyz,i (t)] through the window function g ij , the number of tool teeth N, the transformation matrix T 1,ij (t), the cutting force coefficient matrix K rta , the chip load matrix V 1,ij (t), and the vibration displacement of the milling system. The specific calculation method of the dynamic force component matrix [F xyz,i (t)] is as follows: ij 、 the number of tool teeth N, the transformation matrix T 1,ij (t), the cutting force coefficient matrix K rta 、 the chip load matrix V 1,ij (t) and the vibration displacement of the milling system to calculate the dynamic force component matrix [F xyz,i (t)] dy ; The dynamic force component matrix [F xyz,i (t)] dy is as follows:

[0058] ;

[0059] Among them, dz is the axial height of the microelement, x i (t) is the vibration displacement of the milling system in the x direction at the current moment, y i (t) is the vibration displacement of the milling system in the y direction at the current moment, z i (t) is the vibration displacement of the milling system in the z direction at the current moment, x i (t - T) is the vibration displacement of the milling system in the x direction at the previous tooth moment, y i (t - T) is the vibration displacement of the milling system in the y direction at the previous tooth moment, z i (t - T) is i the vibration displacement of the milling system in the x direction at the current moment, y i the vibration displacement of the milling system in the y direction at the current moment, z i the vibration displacement of the milling system in the z direction at the current moment, x i (t - T) is the vibration displacement of the milling system in the x direction at the previous tooth moment, y i (t - T) is the vibration displacement of the milling system in the y direction at the previous tooth moment, z i(t - T) is the vibration displacement of the milling system in the z - direction at the moment of the previous cutting edge;

[0060] S7: Through the number of tool teeth N, window function g ij , tool radius R, feed per tooth c of the tool, spindle speed Ω of the machine tool, transformation matrix T 2,ij (t), cutting force coefficient matrix K rta , chip load matrix V 2,ij (t) and the vibration velocity of the milling system to calculate the process damping force component matrix [F xyz,i (t)] pr ; The specific calculation method of the process damping force component matrix [F xyz,i (t)] pr is:

[0061] ;

[0062] Among them, is the vibration velocity of the milling system in the x - direction at the current moment, is the vibration velocity of the milling system in the y - direction at the current moment, is the vibration velocity of the milling system in the z - direction at the current moment, is the forced vibration velocity of the milling system in the x - direction at the current moment, is the forced vibration velocity of the milling system in the y - direction at the current moment, is the forced vibration velocity of the milling system in the z - direction at the current moment;

[0063] S8: Through the number of tool teeth N, window function g ij , feed per tooth c of the tool, transformation matrix T 1,ij (t), cutting force coefficient matrix K rta and rotation angle θ ij (t) to calculate the static force component matrix [F xyz,i (t)] st ; The specific calculation method of the static force component matrix [F xyz,i (t)] st is:

[0064] ;

[0065] S9: Calculate the cutting resultant force [F xyz,i (t)] considering the change of the velocity direction with multiple factors, including static force, dynamic force, and process damping force components through the following formula:

[0066] [F xyz,i (t)] = [F xyz,i (t)] st + [F xyz,i (t)] dy + [Fxyz,i (t)] pr ;

[0067] Substitute the cutting resultant force [F xyz,i (t)] into the dynamic control equation of the milling system, and solve the stability of the equation according to the semi-discrete method in the time domain to obtain the stability lobe diagram of the damping effect in the milling process of thin-walled components considering the change of the velocity direction of multiple factors.

[0068] As Figure 1 shown, for the side-edge milling process (feed normal vibration) of titanium alloy thin-walled components, when using the present invention with the radial depth of cut a e = 0.4 mm and the feed per tooth c = 0.05 mm, the predicted stability lobe diagram can better match the measured chatter results;

[0069] As Figure 2 shown, for the bottom-edge milling process (tool axis direction vibration) of titanium alloy thin-walled components, when using the present invention with the radial depth of cut a e = 0.4 mm and the feed per tooth c = 0.05 mm, the predicted stability lobe diagram can also better match the measured chatter results.

[0070] The above results prove that the proposed damping modeling method for the milling process of thin-walled components considering the change of the velocity direction of multiple factors can be applied to the process damping effects caused by both feed normal vibration and tool axis direction vibration, and the applicable range of the stability prediction model for thin-walled components is extended to complex scenarios with coupled effects such as a double flexible system of tool-workpiece, multi-directional vibration in the feed direction - feed normal direction - tool axis direction, and lateral cutting force - axial cutting force.

[0071] The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A damping modeling method for thin-walled component milling process under multi-factor velocity direction changes, characterized in that: The following steps are involved: S1: The cutting load of each tool involved in milling is micro-elemented along the axial cutting depth direction, and the tool rotation angle θ is used to calculate the cutting load of each tool involved in milling. ij (t), cutting angle θ st , cut-out angle θ ex and the window function g ij Determine whether the i-th microelement on the j-th blade participates in cutting; S2: Axial penetration angle κ of the tool i and tool rotation angle θ ij (t) Calculate the chip load matrix V corresponding to the dynamic force component 1,ij (t); S3: The chip load matrix V corresponding to the dynamic force component 1,ij (t) Projecting from the rotating coordinate system to the Cartesian coordinate system, we get the transformation matrix T of the dynamic force component: 1,ij (t); S4: By tool rotation angle θ ij (t) Chip load matrix V corresponding to the damping force component during calculation 2,ij (t); S5: The chip load matrix V corresponding to the process damping force component 2,ij (t) Project the rotating coordinate system to the Cartesian coordinate system to obtain the transformation matrix T of the process damping force component 2,ij (t); S6: Through the window function g ij , number of tool teeth N, transformation matrix T 1,ij (t), cutting force coefficient matrix K rta , Chip load matrix V 1,ij (t) and the vibration displacement of the milling system to calculate the dynamic force component matrix [F xyz,i (t)] dy ; S7: Through the number of tool teeth N, window function g ij , tool radius R, tool feed per tooth c, machine tool spindle speed Ω, transformation matrix T 2,ij (t), cutting force coefficient matrix K rta , Chip load matrix V 2,ij (t) and the vibration velocity calculation process of the milling system damping force component matrix [F xyz,i (t)] pr ; S8: Through the number of tool teeth N, window function g ij , tool feed per tooth c, transformation matrix T 1,ij (t), cutting force coefficient matrix K rta and the rotation angle θ ij (t) Calculate the static force component matrix [F xyz,i (t)] st ; S9: The cutting force [F xyz,i (t)]: [F xyz,i (t)]=[F xyz,i (t)] st +[F xyz,i (t)] dy +[F xyz,i (t)] pr ; The cutting force [F xyz,i (t)] is brought into the dynamic control equation of the milling system, and the stability of the equation is solved according to the time domain semi-discrete method. The stability lobe diagram of the damping effect in the milling process of thin-walled components considering the multi-factor velocity direction changes is obtained.

2. The damping modeling method for thin-walled component milling process under multi-factor velocity direction change according to claim 1 is characterized in that: The window function g in S1 ij Specifically: 。 3. The damping modeling method for thin-walled component milling process under multi-factor velocity direction change according to claim 2 is characterized in that: In S2, the chip load matrix V 1,ij The specific calculation method of (t) is: 。 4. The damping modeling method for thin-walled component milling process under multi-factor velocity direction change according to claim 3 is characterized in that: Transformation matrix T in S3 1,ij The specific calculation method of (t) is: 。 5. The damping modeling method for thin-walled component milling process under multi-factor velocity direction change according to claim 4 is characterized in that: In S4, the chip load matrix V 2,ij The specific calculation method of (t) is: 。 6. The damping modeling method for thin-walled component milling process under multi-factor velocity direction change according to claim 5 is characterized in that: In S5, the transformation matrix T 2,ij The specific calculation method of (t) is: 。 7. The damping modeling method for thin-walled component milling process under multi-factor velocity direction change according to claim 6 is characterized in that: In S6, the dynamic force component matrix [F xyz,i (t)] dy The specific calculation method is: ； Among them, dz is the axial height of the microelement, x i (t) is the vibration displacement of the milling system in the x direction at the current moment, y i (t) is the vibration displacement of the milling system in the y direction at the current moment, z i (t) is the vibration displacement of the milling system in the z direction at the current moment, x i (tT) is the vibration displacement of the milling system in the x direction at the previous tooth moment, y i (tT) is the vibration displacement of the milling system in the y direction at the previous tooth moment, z i (tT) is the vibration displacement of the milling system in the z direction at the previous tooth moment.

8. The damping modeling method for thin-walled component milling process under multi-factor velocity direction change according to claim 7 is characterized in that: In S7, the process damping force component matrix [F xyz,i (t)] pr The specific calculation method is: ； in, is the vibration speed of the milling system in the x direction at the current moment, is the vibration speed of the milling system in the y direction at the current moment, is the vibration speed of the milling system in the z direction at the current moment, is the forced vibration velocity of the milling system in the x direction at the current moment, is the forced vibration velocity of the milling system in the y direction at the current moment, It is the forced vibration velocity of the milling system in the z direction at the current moment.

9. The damping modeling method for thin-walled component milling process under multi-factor velocity direction change according to claim 8 is characterized in that: In S8, the static force component matrix [F xyz,i (t)] st The specific calculation method is: 。

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