A chatter-free tool axis vector generation method for five-axis machining with a ball-end tool

Abstract

The present invention proposes a method for generating chatter-free tool axis vectors for five-axis ball-end tool machining. First, representative tool axis vectors are determined at critical tool locations based on the Nyquist stability criterion to construct a critical tool axis vector set. Then, a four-element vector interpolation algorithm is used to interpolate the critical tool axis vector set within a general region to generate smooth tool axis vectors. The machining stability of each tool location is then checked. If chatter occurs, the steepest descent method is used at the tool location where chatter occurs to determine the chatter-free tool axis vector with the smallest angular change from the original tool axis vector. These chatter-free tool axis vectors are then added to the critical tool axis vector set. New tool axis vectors are then interpolated based on the critical tool axis vector set. This process is repeated until the tool axis vectors at all tool locations pass the cutting stability check. The present invention can generate a smooth and chatter-free tool path along the tool path, effectively suppressing cutting vibration during multi-axis machining.

Description

Technical Field

[0001] The present invention relates to a tool axis vector generation method, in particular to a method for generating a chatter-free tool axis vector for five-axis machining with a ball-end tool. Background Art

[0002] Thin-walled parts are widely used in the aerospace industry. However, cutting vibration is very likely to occur during their machining, making it a difficult problem in the manufacturing field. Optimizing the tool axis vector in multi-axis machining based on cutting dynamics is an effective way to suppress cutting vibration.

[0003] The document “Sun C, Altintas Y. Chatter-free tool orientations in 5-axis ball-end milling [J]. International Journal of Machine Tools and Manufacture, 2016, 106: 89-97.” discloses a method for optimizing the tool axis vector in a multi-axis machining process. The method avoids chatter along the tool machining path by establishing a stable tool axis vector domain of discrete tool position points and then performing tool axis smoothing. The document “Wang S, Geng L, Zhang Y, et al. Chatter-free cutter postures in five-axis machining [J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2016, 230 (8): 1428-1439.” discloses a method for selecting a chatter-free tool axis vector in a multi-axis machining process. The method guides the selection of tool postures by constructing a stability boundary map related to the tool axis vector.

[0004] These existing schemes are all based on Each The tool vector is smoothed after the stable tool axis optimization domain of the tool position point is determined. It is necessary to consume computing resources to determine the stable tool axis optimization domain of each tool position point first, resulting in low computational efficiency of the existing tool axis vector optimization method. Summary of the Invention

[0005] In order to overcome the shortcoming of low computational efficiency of existing tool axis vector optimization methods, the present invention provides a method for generating chatter-free tool axis vectors for five-axis machining with a ball-end tool. The basic principle of this method is: first, a smooth tool path is generated based on the chatter-free tool axis vectors of key tool positions, and then an iterative strategy of cutting chatter detection is performed on the tool path to optimize the tool axis vector.

[0006] The technical solution of the present invention is:

[0007] The method for generating a chatter-free tool axis vector for five-axis machining with a ball-end tool comprises the following steps:

[0008] Step 1: Select the critical tool location on the machining path; construct the stable tool axis vector domain of the critical tool location using the tool system characteristic equation, determine the representative tool axis vector of the critical tool location; add the representative tool axis vector of the critical tool location to the critical tool axis vector set;

[0009] Step 2: Use the key tool axis vector set to perform spherical interpolation to generate the tool axis vector of the general tool position point;

[0010] Step 3: Check the tool axis vector obtained in step 2 for chatter:

[0011] If the tool axis vector obtained in step 2 does not cause chatter, the obtained tool axis vector is used as the final tool axis vector for ball-end tool five-axis machining;

[0012] If the tool axis vector obtained in step 2 causes chatter, an optimization method is used to determine a chatter-free tool axis vector with the smallest angle change with the tool axis vector causing chatter at the tool position where chatter occurs, and the obtained chatter-free tool axis vector is used as the final tool axis vector for five-axis machining with a ball end tool.

[0013] Step 4: Add the tool axis vector that does not cause chatter after the chatter check in step 3 or the obtained chatter-free tool axis vector to the key tool axis vector set, and then return to step 2 until the tool axis vectors of all tool positions pass the chatter check, thereby generating smooth and chatter-free tool axis vectors along the machining path.

[0014] Furthermore, in step 1, the characteristic equation of the tool system is:

[0015] 1-Δz[(1-cosωT)(R(Φ xx )+R(Φ yy ))-(I(Φ xx )+I(Φ yy ))sinωT]+(Δz) 2 [(2(cosωT) 2 -2cosωT)R 0 -2I 0 (1-cosωT)sinωT]+i(-Δz[(1-cosωT)(I(Φ xx )+I(Φ yy ))+(R(Φ xx )+R(Φ yy ))sinωT]+(Δz) 2 [(2(cosωT) 2-2cosωT)I 0 +2R 0 (1-cosωT)sinωT])=0

[0016] in

[0017]

[0018] R 0 =R(Φ xx )R(Φ yy )-I(Φ xx )I(Φ yy )-R(Φ xy )R(Φ yx )+I(Φ xy )I(Φ yx )

[0019] I 0 =R(Φ xx )I(Φ yy )+I(Φ xx )R(Φ yy )-I(Φ xy )R(Φ yx )-R(Φ xy )I(Φ yx )

[0020] [A 0,xy ] represents the cutting force direction factor matrix, [Φ T (iω)] represents the tool frequency response function matrix, R(Φ xx )、R(Φ xy )、R(Φ yx ) and R(Φ yy ) represents the real part of the matrix Φ element, I(Φ xx )、I(Φ xy )、I(Φ yx ) and I(Φ yy ) represents the imaginary part of the matrix Φ element, Δz represents the height of the axial discrete element, ω is the excitation frequency, and T is the tooth-through period.

[0021] Furthermore, in step 1, under given machining conditions, the Nyquist stability criterion is applied to the characteristic equation of the tool system to construct the stable tool axis vector domain of the critical tool position.

[0022] Furthermore, in step 2, the key tool axis vector set is used to perform spherical quaternion interpolation to generate the tool axis vector of the general tool position point:

[0023]

[0024] Where θ = cos -1(A1·A n ), A1 and A n is the tool axis vector in the key tool axis vector set.

[0025] Furthermore, in step 3, the tool axis vector obtained in step 2 is subjected to a chatter check based on the Nyquist stability criterion.

[0026] Furthermore, in step 3, if the tool axis vector obtained in step 2 causes chatter, the tool axis inclination angle corresponding to the tool position where chatter occurs is (α i ,β i ) to minimize the non-chatter tool axis vector and the chatter tool axis inclination angle (α i ,β i ) is the optimization target, and the tool axis inclination angle without chatter is determined.

[0027] Furthermore, in step 3, the steepest descent method is used to solve the optimization problem and the chatter-free tool axis inclination angle is obtained.

[0028] A computer-readable storage medium stores a computer-executable program, wherein the computer-executable program is used to implement the above method when executed.

[0029] A computer system comprises: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above method.

[0030] Beneficial effects

[0031] The present invention does not need to obtain the vibration-free tool axis vector domain at each tool position point in advance, and only requires a limited number of iterative calculations to generate the vibration-free tool axis vector along the tool path. The calculation efficiency is high and the cutting vibration in the multi-axis machining process can be effectively suppressed.

[0032] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0034] Figure 1 This is the tool path for five-axis machining of a rectangular workpiece with a cutting depth of 0.6 mm in the embodiment of the method of the present invention.

[0035] Figure 2This is a flow chart of the algorithm for generating a stable cutting tool axis vector in an embodiment of the method of the present invention.

[0036] Figure 3 It is the feasible tool axis vector domain at the tool position point B1 calculated in the embodiment of the method of the present invention.

[0037] Figure 4 This is the process of generating a chatter-free tool axis vector along the tool path from a representative tool axis vector of a key tool position in the embodiment of the method of the present invention.

[0038] Figure 5 These are the vibration acceleration signals and their spectrum analysis results obtained by milling when the forward tilt angle is 10° and the side tilt angle is 5° in the embodiment of the method of the present invention.

[0039] Figure 6 It is the vibration acceleration signal and its spectrum analysis result obtained by tool axis vector milling generated by the proposed algorithm in the embodiment of the method of the present invention. DETAILED DESCRIPTION

[0040] The following describes in detail embodiments of the present invention. The embodiments are exemplary and intended to explain the present invention, but are not to be construed as limiting the present invention.

[0041] This embodiment provides a method for generating chatter-free tool axis vectors for five-axis ball-end tool machining. First, representative tool axis vectors are determined at critical tool locations based on the Nyquist stability criterion to construct a critical tool axis vector set. Then, using a four-element vector interpolation algorithm, a smooth tool axis vector is generated by interpolating the critical tool axis vector set within a general region. The machining stability of each tool location is then checked. If chatter occurs, the steepest descent method is used at the tool location where chatter occurs to determine the chatter-free tool axis vector with the smallest angular change from the original tool axis vector. These chatter-free tool axis vectors are then added to the critical tool axis vector set. New tool axis vectors are then interpolated based on the critical tool axis vector set. This process is repeated until the tool axis vectors at all tool locations pass the cutting stability check. The present invention can generate a smooth and chatter-free tool path along the tool path, effectively suppressing cutting vibration during multi-axis machining.

[0042] The workpiece model used in the embodiment is as follows Figure 1 As shown, the workpiece material is titanium alloy with a density of 4500kg / m 3 , elastic modulus is 104GPa, Poisson's ratio is 0.305. In the experiment, a 4-tooth ball-end cutter with a diameter of 8mm was selected along Figure 1 The workpiece is machined using the tool path in the figure. The selected spindle speed, feed rate and cutting depth are 6500rpm, 260mm / min and 0.6mm respectively. The algorithm flow for generating the chatter-free tool axis vector along the tool path is as follows: Figure 2 shown.

[0043] The milling cutter used in milling processing is clamped on the machine tool with a tool overhang length of 50 mm. A hammer test is carried out to measure the frequency response function of the tool. By performing modal analysis on the frequency response function, the natural frequency matrix ω, modal mass matrix M, modal stiffness matrix K, and damping ratio matrix ζ of the tool are obtained.

[0044] Step 1: Select the critical tool position on the cutting path; under given cutting conditions, apply the Nyquist stability criterion to the tool system characteristic equation to construct the stable tool axis vector domain of the critical tool position. The calculated stable tool axis vector domain at the critical tool position B1 is as follows: Figure 3 As shown, the representative tool axis vector of the key tool position is determined; the representative tool axis vector of the key tool position is added to the key tool axis vector set; the tool system characteristic equation is:

[0045] 1-Δz[(1-cosωT)(R(Φ xx )+R(Φ yy ))-(I(Φ xx )+I(Φ yy ))sinωT]+(Δz) 2 [(2(cosωT) 2 -2cosωT)R 0 -2I 0 (1-cosωT)sinωT]+i(-Δz[(1-cosωT)(I(Φ xx )+I(Φ yy ))+(R(Φ xx )+R(Φ yy ))sinωT]+(Δz) 2 [(2(cosωT) 2 -2cosωT)I 0 +2R 0 (1-cosωT)sinωT])=0

[0046] in

[0047]

[0048] R 0 =R(Φ xx )R(Φ yy )-I(Φ xx )I(Φ yy )-R(Φ xy )R(Φ yx )+I(Φ xy )I(Φ yx )

[0049] I 0 =R(Φxx )I(Φ yy )+I(Φ xx )R(Φ yy )-I(Φ xy )R(Φ yx )-R(Φ xy )I(Φ yx )

[0050] [A 0,xy ] represents the cutting force direction factor matrix, [Φ T (iω)] represents the tool frequency response function matrix, R(Φ xx )、R(Φ xy )、R(Φ yx ) and R(Φ yy ) represents the real part of the matrix Φ element, I(Φ xx )、I(Φ xy )、I(Φ yx ) and I(Φ yy ) represents the imaginary part of the matrix Φ element, Δz represents the height of the axial discrete element, ω is the excitation frequency, and T is the tooth-through period.

[0051] Step 2: Use the key tool axis vector set to perform spherical quaternion interpolation to generate the tool axis vector of the general tool position point;

[0052]

[0053] Where θ = cos -1 (A1·A n ), A1 and A n is the tool axis vector in the key tool axis vector set.

[0054] Side 3: Check the tool axis vector obtained in step 2 for chatter based on the Nyquist stability criterion:

[0055] If the tool axis vector obtained in step 2 does not cause chatter, the obtained tool axis vector is used as the final tool axis vector for ball-end tool five-axis machining;

[0056] If the tool axis vector obtained in step 2 causes chatter, let the tool axis inclination angle corresponding to the tool position where chatter occurs be (α i ,β i ) to minimize the non-chatter tool axis vector and the chatter tool axis inclination angle (α i ,β i ) is the optimization target, and the tool axis inclination angle without chatter is determined. Tool axis vector adjustment can be expressed as a minimization optimization problem as shown below:

[0057]

[0058] stchatter-free condition(Nyquist criterion)

[0059] The steepest descent method is used to solve the optimization problem of the above formula to obtain the chatter-free tool axis vector with the smallest angle change with the tool axis vector causing chatter. The obtained chatter-free tool axis vector is used as the final tool axis vector for five-axis machining with a ball-end tool.

[0060] Step 4: Add the tool axis vector that does not cause chatter after the chatter check in step 3 or the obtained chatter-free tool axis vector to the key tool axis vector set, and then return to step 2 until the tool axis vectors of all tool positions pass the chatter check, thereby generating smooth and chatter-free tool axis vectors along the machining path, such as Figure 4 shown.

[0061] The tool axis vector is not optimized, that is, the tool axis rake angle α = 10° and the side rake angle β = 5°. Figure 1 The vibration acceleration signal and spectrum analysis results obtained by machining the tool path shown are as follows Figure 5 As shown in the figure, the spectrum analysis shows that the vibration frequency is 2945Hz, which is caused by the vibration mode of the tool and chatter occurs during the cutting process. Figure 4 The optimized tool axis vector is shown along Figure 1 The vibration acceleration signal and spectrum analysis results obtained by machining the tool path shown are as follows Figure 6 As shown in the figure, the spectrum analysis shows that the vibration frequency is 433Hz, which is caused by the tooth pass frequency and the cutting process is stable. Figure 4-6 It can be seen that the present invention can quickly generate a smooth and chatter-free tool axis vector along the tool path, which proves the effectiveness of the method.

[0062] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A method for generating a chatter-free tool axis vector for five-axis machining using a ball-end tool, characterized by: The following steps are involved: Step 1: Select the critical tool location on the machining path; construct the stable tool axis vector domain of the critical tool location using the tool system characteristic equation, determine the representative tool axis vector of the critical tool location; add the representative tool axis vector of the critical tool location to the critical tool axis vector set; Step 2: Use the key tool axis vector set to perform spherical interpolation to generate the tool axis vector of the general tool position point; Step 3: Check the tool axis vector obtained in step 2 for chatter: If the tool axis vector obtained in step 2 does not cause chatter, the obtained tool axis vector is used as the final tool axis vector for ball-end tool five-axis machining; If the tool axis vector obtained in step 2 causes chatter, an optimization method is used to determine a chatter-free tool axis vector with the smallest angle change with the tool axis vector causing chatter at the tool position where chatter occurs, and the obtained chatter-free tool axis vector is used as the final tool axis vector for five-axis machining with a ball end tool. Step 4: Add the tool axis vector that does not cause chatter after the chatter check in step 3 or the obtained chatter-free tool axis vector to the key tool axis vector set, and then return to step 2 until the tool axis vectors of all tool positions pass the chatter check, thereby generating smooth and chatter-free tool axis vectors along the machining path.

2. The method for generating a chatter-free tool axis vector for five-axis machining with a ball-end tool according to claim 1, characterized in that: In step 1, the characteristic equation of the tool system is: 1-Δz[(1-cosωT)(R(Φ xx )+R(Φ yy ))-(I(Φ xx )+I(Φ yy ))sinωT] +(Δz) 2 [(2(cosωT) 2 -2cosωT)R 0 -2I 0 (1-cosωT)sinωT] +i(-Δz[(1-cosωT)(I(Φ xx )+I(Φ yy ))+(R(Φ xx )+R(Φ yy ))sinωT] +(Δz) 2 [(2(cosωT) 2 -2cosωT)I 0 +2R 0 (1-cosωT)sinωT])=0 in R 0 =R(Φ xx )R(Φ yy )-I(Φ xx )I(Φ yy )-R(Φ xy )R(Φ yx )+I(Φ xy )I(Φ yx ) I 0 =R(Φ xx )I(Φ yy )+I(Φ xx )R(Φ yy )-I(Φ xy )R(Φ yx )-R(Φ xy )I(Φ yx ) [A 0,xy ] represents the cutting force direction factor matrix, [Φ T (iω)] represents the tool frequency response function matrix, R(Φ xx )、R(Φ xy )、R(Φ yx ) and R(Φ yy ) represents the real part of the matrix Φ element, I(Φ xx )、I(Φ xy )、I(Φ yx ) and I(Φ yy ) represents the imaginary part of the matrix Φ element, Δz represents the height of the axial discrete element, ω is the excitation frequency, and T is the tooth-through period.

3. The method for generating a chatter-free tool axis vector for five-axis machining with a ball-end tool according to claim 1, characterized in that: In step 1, under given machining conditions, the Nyquist stability criterion is applied to the characteristic equation of the tool system to construct the stable tool axis vector domain of the critical tool position.

4. The method for generating a chatter-free tool axis vector for five-axis machining with a ball-end tool according to claim 1, characterized in that: In step 2, the key tool axis vector set is used to perform spherical quaternion interpolation to generate the tool axis vector of the general tool position point: Where θ = cos -1 (A1·A n ), A1 and A n is the tool axis vector in the key tool axis vector set.

5. The method for generating a chatter-free tool axis vector for five-axis machining with a ball-end tool according to claim 1, characterized in that: In step 3, the tool axis vector obtained in step 2 is checked for chatter based on the Nyquist stability criterion.

6. The method for generating a chatter-free tool axis vector for five-axis machining with a ball-end tool according to claim 1, characterized in that: In step 3, if the tool axis vector obtained in step 2 causes chatter, the tool axis inclination angle corresponding to the tool position where chatter occurs is (α i ,β i ) to minimize the non-chatter tool axis vector and the chatter tool axis inclination angle (α i ,β i ) is the optimization target, and the tool axis inclination angle without chatter is determined.

7. The method for generating a chatter-free tool axis vector for five-axis machining with a ball-end tool according to claim 6, characterized in that: In step 3, the steepest descent method is used to solve the optimization problem and obtain the chatter-free tool axis inclination angle 8. A computer-readable storage medium, characterized in that: A computer executable program is stored, and when the computer executable program is executed, it is used to implement the method according to any one of claims 1 to 7.

9. A computer system, characterized in that: include: One or more processors, the computer-readable storage medium of claim 8, used to store one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the method of any one of claims 1-7.

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