An ultrasonic assisted milling force modeling method suitable for round corner tools

Abstract

The application discloses a kind of ultrasonic auxiliary milling force modeling methods suitable for round corner cutter, three-dimensional cutting force measured by cutting force measuring system is converted to the normal force and friction force suffered by tool rake face, and break through the limitation of traditional right-angle cutter model, innovatively introduce the geometric correction to tool round corner radius, decompose cutting edge into linear segment and circular arc segment respectively for mechanical analysis and synthesis, so that the model can more truly reflect the complex stress state of round corner cutter, significantly improve the calculation precision of normal force and friction force, and has fundamental significance for in-depth study of tribological behavior, wear mechanism and chip formation process.

Description

Technical Field

[0001] This invention belongs to the field of metal cutting and machining, and specifically relates to an ultrasonic-assisted milling force modeling method suitable for rounded corner cutting tools. Background Technology

[0002] In ultrasonic-assisted milling, especially for difficult-to-machine materials such as titanium alloys and high-temperature alloys, accurately characterizing the stress state of the tool is crucial for optimizing process parameters, controlling machining quality, analyzing tool wear, and extending tool life.

[0003] Patent CN103646141B discloses a cutting force modeling method for orthogonal milling of shaft-type workpieces using a flat-bottomed spiral end mill. This method accurately obtains the cutting force during orthogonal milling of shaft-type parts, enabling parameter optimization based on the cutting force. Patent CN113536543B discloses a cutting force modeling method for milling tools with a fine PCD (Positioning Controlled Cutting) without a side clearance angle. This method establishes a micro-element cutting force model, enabling prediction and optimization of the milling tool's cutting force under different machining parameters. Patent CN105426697B discloses a precise prediction method for milling force in five-axis spiral end mill machining. This method combines the instantaneous tool tip position and the yoke axis angle position to establish a cutting edge trajectory equation with eccentricity parameters to calculate the cutting layer thickness. Thin-plate milling experiments are used to calibrate the tool eccentricity parameters and specific cutting force coefficient, achieving accurate prediction of the total cutting force acting on the workpiece. The aforementioned invention patents mostly focus on specific cutting tools or machining processes, but they fail to solve the problem of universally converting the force measured in the workpiece coordinate system to the actual force experienced in the tool coordinate system, especially given the high-precision modeling requirements under the coupling of two key factors: ultrasonic vibration intervention and tool fillet geometry. Therefore, establishing a modeling method that can accurately convert the triaxial cutting force collected by the force gauge in the workpiece coordinate system into the normal force and frictional force experienced by the rake face of a fillet tool under ultrasonic assistance has significant theoretical value and engineering application significance. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and to provide an ultrasonic-assisted milling force modeling method suitable for rounded corner cutting tools. The aim is to accurately convert the triaxial cutting force measured in the workpiece coordinate system into the normal force and friction force of the rake face of the rounded corner cutting tool, so as to more realistically reflect the actual stress state of the tool and provide a reliable basis for process optimization and wear analysis.

[0005] The specific technical solution of the present invention is as follows: An ultrasonic-assisted milling force modeling method suitable for fillet tools includes the following steps: S1: The cutting forces in three mutually orthogonal directions during ultrasonic-assisted milling are obtained through a cutting force measurement system; S2: Establish the workpiece coordinate system XYZ and the auxiliary coordinate system X'Y'Z'; S3: Normal force N and friction f Project the forces onto the X', Y', and Z' directions respectively and perform force analysis; normal force N The frictional force acts on the rake face of the tool, and its direction is always perpendicular to the rake face of the tool. f It acts on the rake face of the tool, and its direction is parallel to the flow direction of the chips; S4: Transform the auxiliary coordinate system X'Y'Z' to the workpiece coordinate system XYZ through the rotation transformation matrix to obtain the resultant force along the X, Y, and Z directions during ultrasonic-assisted milling with a right-angle tool under ideal conditions; S5: By modifying the tool geometry, the resultant force along the X, Y, and Z directions is obtained during ultrasonic-assisted milling of fillet tools under actual conditions; S6: Obtain the cutting forces in three mutually orthogonal directions during ultrasonic-assisted milling through a cutting force measurement system. F X(圆角) , F Y(圆角) , F Z(圆角) Substituting this into the model formula obtained in S5, the normal force acting on the tool is calculated by reverse calculation. N and friction f。

[0006] Specifically, S1 is: The cutting force measurement system includes a force gauge, a charge amplifier, and a data acquisition unit. The force gauge measures the cutting force in three mutually orthogonal directions during milling based on the piezoelectric principle. Combined with the output voltage signal from the charge amplifier and the cutting force acquisition signal from the data acquisition unit, the system ultimately collects the cutting force.

[0007] Specifically, S2 is: The established workpiece coordinate system XYZ has the positive X-axis as the feed direction, the positive Z-axis as the tool axis direction, and the positive Y-axis as the direction following a right-hand Cartesian coordinate system. The workpiece coordinate system XYZ is rotated around the Y (Y') axis. β An auxiliary coordinate system X'Y'Z' is established, with its Z' axis parallel to the main cutting edge of the tool.

[0008] Specifically, S3 is: In the auxiliary coordinate system X'Y'Z', the normal force N and friction f By projecting the forces onto the X', Y', and Z' directions respectively and performing force analysis, we can obtain: (1) (2) (3) In the formula, F X’ , F Y’ , F Z’ These are the resultant forces along the X', Y', and Z' directions, respectively. f This refers to the frictional force acting on the rake face of the cutting tool; N This is the normal force acting on the rake face of the tool; α This is the absolute value of the radial rake angle of the cutting tool; β The helix angle of the cutting tool; θ This is the angle through which the tool rotates from entry to exit. ω Angular velocity; t For time.

[0009] Specifically, S4 is: The auxiliary coordinate system X'Y'Z' is transformed to the workpiece coordinate system XYZ using a rotation transformation matrix, that is, rotated about the Y-axis. β Angle, we can get: (4) Right now: (5) (6) (7) In the formula, F X(直角) , F Y(直角) , F Z(直角) These represent the resultant forces along the X, Y, and Z directions during milling with a right-angle tool under ideal conditions; The resultant force along the X, Y, and Z directions during ultrasonic-assisted milling with a right-angle tool under ideal conditions is obtained by solving the system of equations (1)(2)(3)(5)(6)(7), that is:

[0010] (8) (9)

[0011] (10).

[0012] Specifically, S5 is: The mechanical model of ultrasonic assisted milling with a right-angle tool under ideal conditions is modified to obtain the mechanical model of ultrasonic assisted milling with a rounded-corner tool under actual conditions. In this modification, the main cutting edge is changed from a straight segment to a combination of a straight segment and a quarter-circle segment. Therefore, the resultant force along the X-axis after modification consists of these two parts. When the tool geometry in the mechanical model changes from right-angle to rounded, the rounded portion of its cutting edge will be subjected to forces along both the Y and Z axes. Finally, through calculation, the resultant force along the X, Y, and Z directions of ultrasonic assisted milling with a rounded-corner tool under actual conditions can be obtained, namely: (11) (12) (13) In the formula, F X(圆角) , F Y(圆角) , F Z(圆角) These are the resultant forces along the X, Y, and Z directions during ultrasonic milling with rounded corner tools in actual conditions; a p This refers to the axial depth of cut. R The radius of the fillet; F 抗力 This represents the resistance experienced by the tool when it comes into contact with the workpiece along the Z-axis. By solving the system of equations (8), (9), (10), (11), (12), and (13), we can obtain: (14) (15)

[0013] (16).

[0014] By adopting the above scheme, this invention converts the triaxial cutting force collected by the cutting force measurement system into the normal force and friction force on the rake face of the tool. It also breaks through the limitations of the traditional right-angle tool model and innovatively introduces geometric correction for the fillet radius of the tool. The cutting edge is decomposed into straight line segments and arc segments for mechanical analysis and synthesis, so that the model can more realistically reflect the complex force state of the fillet tool. It significantly improves the calculation accuracy of the normal force and friction force, which is of fundamental significance for in-depth research on tribological behavior, wear mechanism and chip formation process. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of a milling experiment using cutting tools. Figure 2 The milling force data acquisition diagram for milling Ti-6Al-4V with and without ultrasonic tools; Figure 3 A mechanical model for milling machining (right-angle tool); Figure 4 For the mechanical model of milling machining (rounded corner tool); Figure 5 To convert milling force into frictional and normal forces acting on the cutting tool, whether or not ultrasonic is used. Detailed Implementation

[0016] This invention provides a modeling method for ultrasonic-assisted milling forces applicable to rounded corner cutting tools, which solves the problems of existing models being unable to accurately handle the geometry of rounded corner cutting tools and not considering ultrasonic assistance conditions. By establishing a systematic coordinate system transformation and geometric correction process, a high-precision conversion from the force measured in the workpiece coordinate system to the actual force on the cutting tool is achieved, providing a reliable mechanical analysis tool for the optimization and analysis of ultrasonic-assisted milling processes.

[0017] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, including the following steps: Step S1: Obtain the cutting forces in three mutually orthogonal directions during ultrasonic-assisted milling using a cutting force measurement system.

[0018] The cutting force measurement system includes a force gauge, a charge amplifier, and a data acquisition unit. The force gauge measures the cutting force in three mutually orthogonal directions during milling based on the piezoelectric principle. It features high stiffness, a high natural frequency (3.5kHz), and high resolution. Combined with the output voltage signal of the charge amplifier and the cutting force acquisition signal from the data acquisition unit, the system ultimately completes the acquisition and analysis of the cutting force. Figure 1 As shown. The workpiece is fixed on the force gauge, which is mounted on the machine tool table. Driven by an ultrasonic vibration device, the cutting tool generates high-frequency vibrations along its axis, and a milling experiment is performed. The system's sampling frequency should be significantly higher than the ultrasonic vibration frequency and the frequency corresponding to the machine tool spindle speed; therefore, it is set to 20kHz to ensure accurate acquisition of dynamic force signals. Figure 2 As shown, the milling force data of the tool in milling Ti-6Al-4V from entry to exit in one cycle, with or without ultrasonic application, shows that the milling force changes along the X, Y, and Z directions during the milling process. This is because the undeformed cutting thickness also changes gradually and decreases with the application of ultrasonic amplitude.

[0019] Step S2: Establish the workpiece coordinate system XYZ and the auxiliary coordinate system X'Y'Z'.

[0020] Since the force gauge and workpiece are mounted and fixed on the machine tool worktable, the milling force measured by the force gauge is the milling force along the X, Y, and Z directions in the workpiece coordinate system XYZ. For example... Figure 3 As shown, to convert the milling forces along the X, Y, and Z directions in the workpiece coordinate system into normal forces and frictional forces acting on the tool in the tool coordinate system, a workpiece coordinate system XYZ is first established, with the positive X-axis as the feed direction, the positive Z-axis as the tool axis direction, and the positive Y-axis following the right-hand Cartesian coordinate system. The workpiece coordinate system XYZ is then rotated around the Y (Y') axis. β An auxiliary coordinate system X'Y'Z' was established, with its Z' axis parallel to the main cutting edge of the tool. It is also known that the direction of the normal force N acting on the rake face of the coated tool is always perpendicular to the rake face, and the direction of the frictional force f acting on the rake face of the coated tool is parallel to the chip flow direction.

[0021] Step S3, Normal Force N and friction f Project the forces onto the X', Y', and Z' directions respectively and perform force analysis.

[0022] In the auxiliary coordinate system X'Y'Z', the normal force N and friction f By projecting the forces onto the X', Y', and Z' directions respectively and performing force analysis, we can obtain: (1) (2) (3) In the formula, F X’ , F Y’ , F Z’ These are the resultant forces along the X', Y', and Z' directions, respectively. f This refers to the frictional force acting on the rake face of the cutting tool; N This is the normal force acting on the rake face of the tool; α The absolute value of the radial rake angle of the tool ( α =13°); β The helix angle of the tool ( β =8°); θ The angle through which the tool rotates from entry to exit ( θ =90°). ω Angular velocity; t For time.

[0023] Step S4: Transform the auxiliary coordinate system X'Y'Z' to the workpiece coordinate system XYZ using a rotation transformation matrix to obtain the resultant force along the X, Y, and Z directions during ultrasonic-assisted milling with a right-angle tool under ideal conditions.

[0024] The auxiliary coordinate system X'Y'Z' is transformed to the workpiece coordinate system XYZ using a rotation transformation matrix, that is, rotated about the Y-axis. β Angle, we can get: (4) Right now: (5) (6) (7) In the formula, F X(直角) , F Y(直角) , F Z(直角) These are the resultant forces along the X, Y, and Z directions during milling with a right-angle tool under ideal conditions.

[0025] The resultant force along the X, Y, and Z directions during ultrasonic-assisted milling with a right-angle tool under ideal conditions is obtained by solving the system of equations (1)(2)(3)(5)(6)(7), that is:

[0026] (8) (9)

[0027] (10) Step S5: By modifying the tool geometry, obtain the resultant force along the X, Y, and Z directions during ultrasonic-assisted milling of rounded corner tools under actual conditions.

[0028] The aforementioned model is based on the assumption of right-angled tools, while the actual tools used (in this embodiment, the fillet radius) R =0.8mm), therefore, the mechanical model for right-angle milling under the ideal conditions described above needs to be modified. For example Figure 4 As shown, it can be observed that the main cutting edge consists of a straight line segment (length is...) a p ) becomes a part of a straight line segment (length is a p - R Add a quarter-circle arc segment (radius is) RTherefore, it can be seen that the resultant force along the X-axis after correction consists of these two parts. Furthermore, when the tool geometry in the mechanical model changes from right angles to rounded corners, the rounded corner portion of its cutting edge will be subjected to forces along both the Y and Z axes. Finally, through calculation, the resultant force along the X, Y, and Z directions in the corrected mechanical model of rounded corner milling can be obtained, namely: (11) (12) (13) In the formula, F X(圆角) , F Y(圆角) , F Z(圆角) These are the resultant forces along the X, Y, and Z directions during ultrasonic milling with rounded corner tools in actual conditions; a p This refers to the axial depth of cut. R The radius of the fillet; F 抗力 This represents the resistance experienced by the tool when it comes into contact with the workpiece along the Z-axis.

[0029] By solving the system of equations (8), (9), (10), (11), (12), and (13), we can obtain: (14) (15)

[0030] (16) Step S6: Calculate the normal force acting on the tool. N and friction f .

[0031] The cutting forces in three mutually orthogonal directions during ultrasonic-assisted milling are obtained using a cutting force measurement system. F X(圆角) , F Y(圆角) , F Z(圆角) Substitute these values ​​into formulas (14)-(16) to calculate the normal force acting on the tool. N and friction f。

[0032] Based on the above analysis of the milling machining mechanics model, the milling force data with and without ultrasonic application are converted into frictional force acting on the cutting tool according to the derived formula. fWith normal force N ,like Figure 5 As shown, it can be observed that the frictional force acting on the tool during milling is... f The normal force acting on the tool remains basically stable. N The cutting force gradually decreases from its maximum value to zero because the undeformed cutting thickness also gradually decreases from its maximum value to zero during the milling process. Furthermore, the periodic tool-workpiece separation generated by ultrasonic vibration reduces the overall cutting force, accurately reflecting the complex stress state of the fillet tool.

[0033] In summary, this invention converts the triaxial cutting force collected by the cutting force measurement system into the normal force and frictional force on the rake face of the tool. It also breaks through the limitations of traditional right-angle tool models by innovatively introducing geometric correction for the fillet radius of the tool. The cutting edge is decomposed into straight line segments and arc segments for mechanical analysis and synthesis, enabling the model to more realistically reflect the complex force state of the fillet tool. This significantly improves the calculation accuracy of the normal force and frictional force, and is of fundamental significance for in-depth research on tribological behavior, wear mechanism and chip formation process.

Claims

1. A method for modeling ultrasonic-assisted milling forces suitable for fillet-type cutting tools, characterized in that, Includes the following steps: S1: The cutting forces in three mutually orthogonal directions during ultrasonic-assisted milling are obtained through a cutting force measurement system; S2: Establish the workpiece coordinate system XYZ and the auxiliary coordinate system X'Y'Z'; S3: Normal force N and friction f Project the forces onto the X', Y', and Z' directions respectively and perform force analysis; normal force N The frictional force acts on the rake face of the tool, and its direction is always perpendicular to the rake face of the tool. f It acts on the rake face of the tool, and its direction is parallel to the flow direction of the chips; S4: Transform the auxiliary coordinate system X'Y'Z' to the workpiece coordinate system XYZ through the rotation transformation matrix to obtain the resultant force along the X, Y, and Z directions during ultrasonic-assisted milling with a right-angle tool under ideal conditions; S5: By modifying the tool geometry, the resultant force along the X, Y, and Z directions is obtained during ultrasonic-assisted milling of fillet tools under actual conditions; S6: Obtain the cutting forces in three mutually orthogonal directions during ultrasonic-assisted milling through a cutting force measurement system. F X(圆角) , F Y(圆角) , F Z(圆角) Substituting this into the model formula obtained in S5, the normal force acting on the tool is calculated by reverse calculation. N and friction f。 2. The ultrasonic-assisted milling force modeling method for fillet tools as described in claim 1, characterized in that, Specifically, S1 is: The cutting force measurement system includes a force gauge, a charge amplifier, and a data acquisition unit. This force gauge measures the cutting force in three mutually orthogonal directions during milling based on the piezoelectric principle. It works in conjunction with the output voltage signal of the charge amplifier and the cutting force acquisition signal of the data acquisition unit to finally complete the acquisition of the cutting force.

3. The ultrasonic-assisted milling force modeling method for fillet tools as described in claim 1, characterized in that, Specifically, S2 is: The established workpiece coordinate system XYZ has the positive X-axis as the feed direction, the positive Z-axis as the tool axis direction, and the positive Y-axis as the direction following a right-hand Cartesian coordinate system. The workpiece coordinate system XYZ is rotated around the Y (Y') axis. β An auxiliary coordinate system X'Y'Z' is established, with its Z' axis parallel to the main cutting edge of the tool.

4. The ultrasonic-assisted milling force modeling method for fillet tools as described in claim 1, characterized in that, Specifically, S3 is: In the auxiliary coordinate system X'Y'Z', the normal force N and friction f By projecting the forces onto the X', Y', and Z' directions respectively and performing force analysis, we can obtain: (1) (2) (3) In the formula, F X’ , F Y’ , F Z’ These are the resultant forces along the X', Y', and Z' directions, respectively. f This refers to the frictional force acting on the rake face of the cutting tool; N This is the normal force acting on the rake face of the tool; α This is the absolute value of the radial rake angle of the cutting tool; β The helix angle of the cutting tool; θ This is the angle through which the tool rotates from entry to exit. ω Angular velocity; t For time.

5. The ultrasonic-assisted milling force modeling method for fillet tools as described in claim 1, characterized in that, Specifically, S4 is: The auxiliary coordinate system X'Y'Z' is transformed to the workpiece coordinate system XYZ using a rotation transformation matrix, that is, rotated about the Y-axis. β Angle, we can get: (4) Right now: (5) (6) (7) In the formula, F X(直角) , F Y(直角) , F Z(直角) These represent the resultant forces along the X, Y, and Z directions during milling with a right-angle tool under ideal conditions; The resultant force along the X, Y, and Z directions during ultrasonic-assisted milling with a right-angle tool under ideal conditions is obtained by solving the system of equations (1)(2)(3)(5)(6)(7), that is: (8) (9) (10)。 6. The ultrasonic-assisted milling force modeling method for fillet tools as described in claim 5, characterized in that, Specifically, S5 is: The mechanical model of ultrasonic assisted milling with a right-angle tool under ideal conditions is modified to obtain the mechanical model of ultrasonic assisted milling with a rounded-corner tool under actual conditions. In this modification, the main cutting edge is changed from a straight segment to a combination of a straight segment and a quarter-circle segment. Therefore, the resultant force along the X-axis after modification consists of these two parts. When the tool geometry in the mechanical model changes from right-angle to rounded, the rounded portion of its cutting edge will be subjected to forces along both the Y and Z axes. Finally, through calculation, the resultant force along the X, Y, and Z directions of ultrasonic assisted milling with a rounded-corner tool under actual conditions can be obtained, namely: (11) (12) (13) In the formula, F X(圆角) , F Y(圆角) , F Z(圆角) These are the resultant forces along the X, Y, and Z directions during ultrasonic milling with rounded corner tools in actual conditions; a p This refers to the axial depth of cut. R The radius of the fillet; F 抗力 This represents the resistance experienced by the tool when it comes into contact with the workpiece along the Z-axis. By solving the system of equations (8), (9), (10), (11), (12), and (13), we can obtain: (14) (15) (16)。

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