Damping Modeling Method for Milling Thin-Walled Components under Multiple Factors of Velocity Direction Variation

Abstract

This invention discloses a damping modeling method for the milling process of thin-walled components under multi-factor velocity direction variation, belonging to the field of electromechanical technology. First, based on the actual cutting speed affected by the multi-directional vibration effects of the milling system's feed direction, feed normal, and tool axis direction, the chip load matrix and force coordinate transformation matrix are characterized. Then, based on the periodic milling force expression and Taylor expansion simplification at the forced vibration point, the dynamic force components, process damping force components, and static force components of milling are solved to obtain the resultant cutting force matrix. Finally, the resultant cutting force expression is substituted into the dynamic control equation of the milling system and solved using the time-domain semi-discrete method to obtain a stability leaflet diagram of the damping effect of the milling process of thin-walled components including multi-factor velocity direction variation. This application considers multi-factor velocity direction variation, significantly improving the applicability of the model under different working conditions.

Description

Technical Field

[0001] This invention belongs to the field of electromechanical technology, specifically relating to a damping modeling method for the milling process of thin-walled components under multi-factor velocity direction changes. Background Technology

[0002] Interference and compression between the tool flank and the workpiece surface, as well as changes in cutting velocity direction caused by tool-workpiece system vibration, both generate process damping effects, leading to increased cutting stability at low speeds. Existing modeling of milling process damping largely focuses on the plowing effect caused by interference and compression. Because it fails to consider the deformation of the milling system for thin-walled components and thus doesn't correct for the actual intrusion area, the predicted axial limit depth of cut in the stability prediction of thin-walled components is often higher than the experimentally observed value. A few studies have addressed the correction of dynamic cutting forces by considering changes in cutting velocity direction caused by cutting vibration; however, current methods only consider the feed direction / feed normal direction cutting vibration effects, failing to consider the coupling effect of multi-factor velocity direction changes, such as the tool-workpiece dual flexible system, multi-directional vibration of feed direction, feed normal, and tool axis direction, and the combined characterization of lateral cutting force and axial cutting force. The applicability of these models needs further expansion. Therefore, establishing a milling process damping model considering multi-factor velocity direction changes has significant theoretical and engineering application value for predicting the stability of thin-walled components.

[0003] Reference 1, "Eksioglu C, Kilic ZM, 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 flexible milling systems considering multi-directional vibration and multi-edge cutting coupling. However, because this method does not consider the correction of the actual cutting speed direction by tool-workpiece vibration, it is not applicable to the stability prediction problem of thin-walled components considering process damping effects.

[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 modeling process damping based on the actual cutting speed direction to characterize dynamic cutting force and establish a method for modeling process damping by varying the cutting speed direction. However, this method fails to consider multiple factors affecting speed direction variations, resulting in a limited applicability of the model; for example, it can only consider the influence of radial / normal cutting vibration effects on process damping during side milling of thin-walled components.

[0005] The typical characteristics of the aforementioned references are: stability prediction methods that consider multi-directional vibrations in the feed direction, feed normal direction, and tool axis direction, and the comprehensive characterization of lateral cutting force and axial cutting force, do not yet include the process damping effect caused by changes in the cutting speed direction. Furthermore, the process damping model for thin-walled components with changing cutting speed direction fails to consider the coupling effect of the tool-workpiece dual flexible system, multi-directional vibrations in the feed direction, feed normal direction, and tool axis direction, and the comprehensive characterization of lateral cutting force and axial cutting force. Summary of the Invention

[0006] To address the problems mentioned in the background art, the present invention provides a damping modeling method for the milling process of thin-walled components under multi-factor velocity direction variation, so as to solve the problem that the existing technology does not consider multi-factor velocity direction variation in the damping modeling process.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A damping modeling method for the milling process of thin-walled components under multi-factor velocity direction variation includes the following steps:

[0009] S1: The cutting load of each tool involved in milling is infinitesimally calculated along the axial depth of cut, using the tool rotation angle θ. ij (t), angle of entry θ st , tangent angle θ ex and window function g ij Determine whether the i-th infinitesimal element on the j-th cutting edge participates in the cutting process;

[0010] S2: Axial intrusion angle κ of the tool i and the tool rotation angle θ ij (t) Calculate the chip load matrix V corresponding to the dynamic force components. 1,ij (t);

[0011] S3: The chip load matrix V corresponding to the dynamic force components1,ij (t) Projecting from the rotating coordinate system to the Cartesian coordinate system yields the transformation matrix T of the dynamic force components. 1,ij (t);

[0012] S4: Rotate the tool by angle θ ij (t) Calculation process: Chip load matrix V corresponding to damping force component. 2,ij (t);

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

[0014] 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 dynamic force component matrix for calculating the vibration displacement of the milling system [F] xyz,i (t)] dy ;

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

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

[0017] S9: The resultant cutting force [F], which considers the changes in velocity direction due to multiple factors and includes static force, dynamic force, and process damping force components, is calculated using the following formula. xyz,i (t)]:

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

[0019] The cutting resultant force [F] xyz,i Substituting (t) into the dynamic control equation of the milling system, the stability of the equation is solved by the semi-discrete time-domain method, and the stability lobe diagram of the damping effect of the milling process of thin-walled components considering the velocity direction changes of multiple factors is obtained.

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

[0021] .

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

[0023] .

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

[0025] .

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

[0027] .

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

[0029] .

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

[0031] ;

[0032] Where dz is the axial height of the infinitesimal element, and x i (t) represents the vibration displacement of the milling system in the x-direction at the current moment, and y i (t) represents the vibration displacement of the milling system in the y-direction at the current moment, z i (t) represents 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 moment of the cutting tooth, y i(tT) is the vibration displacement of the milling system in the y-direction at the previous moment of the cutting tooth, z i (tT) is the vibration displacement of the milling system in the z direction at the previous moment of the cutting tooth.

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

[0034] ;

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

[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 chip load matrix and force coordinate transformation matrix are first characterized based on the actual cutting speed affected by the multi-directional vibration effects of the milling system's feed direction, feed normal, and tool axis direction. Then, based on the periodic milling force expression and the Taylor expansion simplification at the forced vibration point, the dynamic force components, process damping force components, and static force components of the milling are solved to obtain the resultant cutting force matrix. Finally, the resultant cutting force expression is substituted into the dynamic control equation of the milling system and solved using the time-domain semi-discrete method to obtain the stability leaflet diagram of the damping effect in the milling process of thin-walled components that includes multiple factors of velocity direction variation.

[0040] This application considers the coupling effect of the tool-workpiece dual flexible system, multi-directional vibration of feed direction-feed normal-tool axis direction, and comprehensive characterization of lateral cutting force and axial cutting force, and establishes a process damping model for thin-walled components with changing cutting speed direction, which significantly improves the applicability of the model under different working conditions. Attached Figure Description

[0041] Figure 1This is a schematic diagram comparing the stability lobe diagram (feed normal vibration) of the side milling process of titanium alloy thin-walled components predicted by the embodiments of the present invention with the dynamic measured chatter data;

[0042] Figure 2 This is a schematic diagram comparing the stability lobe diagram (vibration in the tool axis direction) of the bottom milling process of titanium alloy thin-walled components predicted by the embodiments of the present invention with the dynamic measured chatter data. Detailed Implementation

[0043] To facilitate understanding of the technical content of this invention by those skilled in the art, the invention will be further described in detail below with reference to the accompanying drawings and specific examples. It should be understood that the specific examples described herein are merely illustrative and not intended to limit the scope of the invention.

[0044] Example 1:

[0045] This embodiment uses a common industrial titanium alloy thin-walled blade structure to conduct milling chatter experiments, verifying the predictive effect of the proposed method on the damping stability of the lobe diagram during the milling process of thin-walled components with multi-factor velocity direction variations. The workpiece material is titanium alloy TC4, with a first natural frequency of 1309 Hz, a damping ratio of 0.82%, and a mass-normalized mode shape of 17.76; a second natural frequency of 3315 Hz, a damping ratio of 1.28%, and a mass-normalized mode shape of 23.45. A ball end mill with a tool radius R = 4 mm and a number of teeth N = 3 is used.

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

[0047] S1: The cutting load of each tool involved in milling is infinitesimally calculated along the axial depth of cut, using the tool rotation angle θ. ij (t), angle of entry θ st , tangent angle θ ex and window function g ij To determine whether the i-th infinitesimal element on the j-th cutting edge participates in cutting, the window function g... ij Specifically:

[0048] ;

[0049] S2: Axial intrusion angle κ of the tool i and the tool rotation angle θ ij (t) Calculate the chip load matrix V corresponding to the dynamic force components. 1,ij (t), chip load matrix V 1,ij The specific calculation method for (t) is as follows:

[0050] ;

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

[0052] ;

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

[0054] ;

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

[0056] ;

[0057] 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 dynamic force component matrix for calculating the vibration displacement of the milling system [F] xyz,i (t)] dy ; Dynamic force component matrix [F xyz,i (t)] dy The specific calculation method is as follows:

[0058] ;

[0059] Where dz is the axial height of the infinitesimal element, and x i (t) represents the vibration displacement of the milling system in the x-direction at the current moment, and y i (t) represents the vibration displacement of the milling system in the y-direction at the current moment, z i (t) represents 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 moment of the cutting tooth, y i (tT) is the vibration displacement of the milling system in the y-direction at the previous moment of the cutting tooth, z i(tT) is the vibration displacement of the milling system in the z direction at the previous cutter tooth moment;

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

[0061] ;

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

[0063] S8: Using the number of tool teeth N and the window function g ij , Tool feed per tooth c, Transformation matrix T 1,ij (t), Cutting force coefficient matrix K rta and rotation angle θ ij (t) Calculate the static force component matrix [F xyz,i (t)] st ; Static force component matrix [F xyz,i (t)] st The specific calculation method is as follows:

[0064] ;

[0065] S9: The resultant cutting force [F], which considers the changes in velocity direction due to multiple factors and includes static force, dynamic force, and process damping force components, is calculated using the following formula. xyz,i (t)]:

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

[0067] The cutting resultant force [F] xyz,i Substituting (t) into the dynamic control equation of the milling system, the stability of the equation is solved by the semi-discrete time-domain method, and the stability lobe diagram of the damping effect of the milling process of thin-walled components considering the velocity direction changes of multiple factors is obtained.

[0068] like Figure 1 As shown, for the side milling process of thin-walled titanium alloy components (feed normal vibration), the present invention is used at a radial depth of cut a e =0.4 mm, and the predicted stability lobe diagram under cutting parameters of c=0.05 mm per tooth feed can match the measured chatter results well;

[0069] like Figure 2 As shown, for the bottom milling process of thin-walled titanium alloy components (vibration in the tool axis direction), the present invention is used at a radial depth of cut a e The predicted stability lobe diagram under cutting parameters of 0.4 mm per tooth feed and c=0.05 mm also matches the measured chatter results well.

[0070] The above results demonstrate that the proposed multi-factor velocity direction variation damping modeling method for thin-walled component milling process can be applied to the process damping effect caused by feed normal vibration or tool axis vibration. This expands the applicability of the thin-walled component stability prediction model to complex scenarios involving tool-workpiece dual flexible systems, multi-directional vibrations in the feed direction, feed normal, and tool axis directions, and the coupling effects of lateral cutting force and axial cutting force.

[0071] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A damping modeling method for the milling process of thin-walled components under multi-factor velocity direction variation, characterized in that, Includes the following steps: S1: The cutting load of each tool involved in milling is infinitesimally calculated along the axial depth of cut, using the tool rotation angle θ. ij (t), angle of entry θ st , tangent angle θ ex and window function g ij Determine whether the i-th infinitesimal element on the j-th cutting edge participates in the cutting process; S2: Axial intrusion angle κ of the tool i and the tool rotation angle θ ij (t) Calculate the chip load matrix V corresponding to the dynamic force components. 1,ij (t); S3: The chip load matrix V corresponding to the dynamic force components 1,ij (t) Projecting from the rotating coordinate system to the Cartesian coordinate system yields the transformation matrix T of the dynamic force components. 1,ij (t); S4: Rotate the tool by angle θ ij (t) Calculation process: Chip load matrix V corresponding to damping force component. 2,ij (t); S5: The chip load matrix V corresponding to the process damping force component. 2,ij (t) Projecting from the rotating coordinate system to the Cartesian coordinate system, we obtain the transformation matrix T of the process damping force components. 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 dynamic force component matrix for calculating the vibration displacement of the milling system [F] xyz,i (t)] dy ; S7: Using the number of tool teeth N and the window function g ij Tool radius R, tool feed per tooth c, machine spindle speed Ω, transformation matrix T 2,ij (t), Cutting force coefficient matrix K rta Chip load matrix V 2,ij (t) and the calculation process of vibration velocity of the milling system and damping force component matrix [F] xyz,i (t)] pr ; S8: Using the number of tool teeth N and the window function g ij , Tool feed per tooth c, Transformation matrix T 1,ij (t), Cutting force coefficient matrix K rta and rotation angle θ ij (t) Calculate the static force component matrix [F xyz,i (t)] st ; S9: The resultant cutting force [F], which considers the changes in velocity direction due to multiple factors and includes static force, dynamic force, and process damping force components, is calculated using the following formula. xyz,i (t)]: [F xyz,i (t)]=[F xyz,i (t)] st +[F xyz,i (t)] dy +[F xyz,i (t)] pr ; The cutting resultant force [F] xyz,i Substituting (t) into the dynamic control equation of the milling system, the stability of the equation is solved by the semi-discrete time-domain method, and the stability lobe diagram of the damping effect of the milling process of thin-walled components considering the velocity direction changes of multiple factors is obtained.

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

8. The damping modeling method for milling thin-walled components under multi-factor velocity direction variation according to claim 7, characterized in that, In S7, the process damping force component matrix [F] xyz,i (t)] pr The specific calculation method is as follows: ； in, It is the vibration velocity of the milling system in the x-direction at the current moment. It is the vibration velocity of the milling system in the y-direction at the current moment. It is the vibration velocity of the milling system in the z-direction at the current moment. It is the forced vibration velocity of the milling system in the x-direction at the current moment. It 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 milling thin-walled components under multi-factor velocity direction variation according to claim 8, characterized in that, In S8, the static force component matrix [F] xyz,i (t)] st The specific calculation method is as follows: 。

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