Ultrasonic vibration assisted five-axis ultra-precise single-point diamond turning face gear method

Abstract

The invention discloses an ultrasonic vibration assisted five-axis ultra-precise single-point diamond turning face gear method, which comprises the following steps of: 1, planning an initial cutter contact point path of an enveloping face gear tooth surface: carrying out inversion on tooth surface discrete points through an NURBS (Non-Uniform Rational B-Spline) algorithm, and determining node vectors in combination with a centripetal parameterization method, the Archimedes spiral is projected to an NURBS parameter space, and an initial cutter contact of an enveloping tooth surface is generated; step 2, determining a machining condition of the minimum residual height: calculating elliptical trajectories of a cutter in a cutting direction and a cutting depth direction according to ultrasonic vibration parameters, analyzing a coincidence condition of the cutter and an initial contact point of a workpiece, and optimizing a G code running speed of a machine tool to enable the number of spiral trajectories between adjacent cutter contacts to meet a time synchronization relationship; and thirdly, cutter contact point distribution is adjusted and controlled to achieve normal separation of the cutter and the workpiece, the initial cutter contact point path is adjusted through a golden section method, it is ensured that the cutting speed is smaller than the vibration speed of the cutter in the cutting direction, and periodic separation of the cutter and the workpiece is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical processing, and specifically relates to a method for ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning of face gears. Background Art

[0002] Face gears have the advantages of high transmission efficiency, large load-bearing capacity, no axial force generated during transmission, and insensitivity to axial installation errors of the pinion. Therefore, they have gradually replaced bevel gears in spatial shaft transmission and become a key basic component of high-end equipment such as new helicopter main reducers and turboshaft engines. However, the tools required for face gear processing are difficult to manufacture and are prone to wear, making it difficult to meet the requirements for processing accuracy and surface quality at the same time. Existing research shows that ultra-precision single-point diamond turning technology can achieve higher shape accuracy; five-axis turning can improve the flexibility of tool movement and avoid face gear cutting interference; ultrasonic vibration-assisted processing can reduce chemical wear when diamond tools are processing gear steel; but there is no method in the existing technology that combines these three to achieve face gear turning. Summary of the Invention

[0003] Ultrasonic vibration-assisted machining primarily involves introducing a periodic excitation signal in both the cutting and depth directions, causing the tool's trajectory to assume an elliptical shape. However, due to the complex curved surface of face gear teeth, machining them requires planning a tool contact trajectory that envelops the gear tooth surface. Therefore, if ultrasonic vibration-assisted machining is simply applied to face gear turning, there are the following drawbacks: First, the coupling effect of the elliptical trajectory and the tool contact trajectory results in additional residual height along the cutting direction on the face gear tooth surface, significantly increasing the tooth surface roughness. Second, under the influence of the elliptical trajectory, an unreasonable tool contact trajectory prevents the tool and workpiece from separating properly, rendering ultrasonic vibration-assisted turning akin to conventional turning.

[0004] In view of this, in order to solve the shortcomings of ultrasonic vibration-assisted machining when applied to gear turning, the purpose of the present invention is to provide an ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for gear surface turning, which achieves the goal of efficiently and accurately machining all tooth surfaces on a spiral path through tool contact trajectory planning and control.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning of face gears, using ultrasonic vibration-assisted machining, five-axis linkage turning, and ultra-precision single-point diamond turning technology, includes the following steps:

[0007] Step 1: Plan the initial tool contact path of the envelope gear tooth surface: Based on the NURBS inversion algorithm, use the discrete points on the tooth surface as the shape value points, combine the centripetal parameterization method to determine the node vector, and project the Archimedean spiral into the NURBS parameter space to generate the initial tool contact point of the envelope tooth surface;

[0008] Step 2: Determine the machining conditions for minimum residual height: Calculate the tool's elliptical trajectory in the cutting and cutting depth directions based on ultrasonic vibration parameters, analyze the coincidence conditions of the initial contact points between the tool and the workpiece, and optimize the machine tool G code running speed to ensure that the number of spiral trajectories between adjacent tool contact points meets the time synchronization relationship;

[0009] Step 3: Adjust the tool contact point distribution to achieve normal separation between the tool and the workpiece: Use the golden section method to adjust the initial tool contact point path to ensure that the cutting speed is less than the vibration speed of the tool along the cutting direction, so as to achieve periodic separation between the tool and the workpiece.

[0010] Furthermore, in step 1, the method steps for planning the initial knife contact path of the tooth surface of the envelope gear are:

[0011] 11) Establish a single tooth surface 3D model of the left or right tooth surface of the face gear, evenly select discrete points on the single tooth surface to form point cloud data; rotate the point cloud data array around the gear axis to generate a set of discrete points corresponding to all single tooth surfaces;

[0012] 12) Using the discrete points as the shape value points, perform inversion calculation based on the NURBS algorithm to determine the control points that characterize the geometric characteristics of the tooth surface;

[0013] 13) To address the node vector error problem caused by the sudden change in the distance between discrete points on adjacent tooth surfaces, a centripetal parameterization method is used to optimize the node distribution;

[0014] 14) Project the Archimedean spiral into the NURBS parameter space to generate the initial tool contact path of the envelope tooth surface, including:

[0015] 141) The Archimedean spiral is discretized in the polar coordinate system using the equal arc length discretization method;

[0016] 142) Perform parameterization and normalization processing on discrete points to improve the interpolation accuracy of tool contact points;

[0017] 15) The type value point corresponding to the node vector is calculated by the NURBS algorithm, which is the tool contact point; the initial tool contact point path of the envelope gear tooth surface is formed. This path is projected by spiral lines and parameterized optimization to achieve a single spiral trajectory covering all tooth surfaces.

[0018] Furthermore, in step 12), the method for performing inversion calculation based on the NURBS algorithm is:

[0019]

[0020] Where: (x k,l ,y k,l ,z k,l ) is the coordinate value of the discrete point; For nodes The corresponding i-th p-th basis function; For nodes The corresponding l-th q-th basis function; and They are the control points corresponding to the x, y, and z directions respectively; is the control point; is the node value of the kth u direction; is the node value of the kth v direction, m + and n + are the number of discrete points in the u and v directions respectively.

[0021] Furthermore, in step 13), the method of optimizing node distribution using the centripetal parameterization method is:

[0022]

[0023] Among them: Among them: d l is the sum of the chord lengths of adjacent type value points; is the i-th node under the l-th latitude; Q i,l is the (i,j)th type value point.

[0024] Compute node vector and The corresponding basis functions transform the above equation into a one-dimensional linear equation system, the unique solution of which is the characteristic point characterizing the tooth surface of the face gear.

[0025] Furthermore, in step 141), the method of discretizing the Archimedean spiral in the polar coordinate system using the equal arc length discretization method is:

[0026]

[0027] Where: r is the pole diameter; k is the distance between two discrete points; j is the distance between two spiral lines; n is the nth knife contact point; N + is the total number of knife contacts;

[0028] In step 142), the method for performing parameterization and normalization processing on the discrete points is:

[0029]

[0030] Where: floor(·) is the floor rounding function.

[0031] Furthermore, in step 2, the method steps for determining the processing conditions for the minimum residual height are:

[0032] 21) Based on the ultrasonic vibration parameters, define the periodic elliptical trajectory equation of the tool in the cutting direction and cutting depth direction plane;

[0033] 22) In the elliptical trajectory, the initial contact point A1 where the tool first contacts the workpiece must coincide with the tool contact point position in the NC program;

[0034] 23) Synchronize machine tool G code running speed and vibration cycle

[0035] 231) Calculate the time t1 when the tool reaches the initial contact point A1;

[0036] 232) Synchronize the machine tool G code running speed S to obtain the corresponding relationship between the execution time interval of two adjacent lines of NC code and the ultrasonic vibration period;

[0037] 233) When the ultrasonic vibration frequency is high, there may be multiple spiral tracks between adjacent knife contacts. The corresponding relationship is optimized so that the number of spiral tracks between adjacent knife contacts satisfies the time synchronization relationship.

[0038] Furthermore, in step 21), the periodic elliptical trajectory equation of the tool in the cutting direction and cutting depth direction plane is:

[0039]

[0040] Where: P c and P d are the coordinates of the tool along the cutting direction and cutting depth direction respectively; A c and A d are the amplitude of the excitation signal; ω is the angular frequency of the tool; t is the processing time; is the angular phase shift.

[0041] Furthermore, in step 231), the time t1 when the tool reaches the initial contact point A1 is:

[0042]

[0043] Among them: A d is the amplitude of the excitation signal; h is the residual height of the tool produced by the movement of the tool along the tool contact trajectory under the action of ultrasonic vibration; ω is the angular frequency of the tool; is the angular phase displacement; f is the vibration frequency;

[0044] In step 232), the corresponding relationship between the execution time interval of two adjacent lines of numerical control code and the ultrasonic vibration period is:

[0045]

[0046] Where: S is the G code running speed;

[0047] In step 233), the corresponding relationship optimization expression is:

[0048]

[0049] Where: k′ is the number of spiral tracks between adjacent knife contacts.

[0050] Furthermore, in step three, the method steps for regulating the distribution of the tool contact points to achieve normal separation of the tool and the workpiece are as follows:

[0051] 31) Calculate the vibration speed v of the tool along the cutting direction c and machine cutting speed v a , establish the relationship model between cutting speed and vibration speed;

[0052] 32) The normal separation condition between the tool and the workpiece is defined as: the absolute value of the cutting speed |v a | is less than the absolute value of the vibration velocity of the tool along the cutting direction |v c |;

[0053] 33) The golden section method is used to optimize the knife contact point distribution and obtain the optimized knife contact point path.

[0054] Furthermore, in step 31), the vibration speed v of the tool along the cutting direction is c for:

[0055]

[0056] in: is the time derivative of the tool position along the cutting direction; A c is the amplitude of the excitation signal; ω is the angular frequency of the tool;

[0057] Machine cutting speed v a for:

[0058]

[0059] Where: ‖C n ,C n+1 ‖ is the knife contact C n Movement to C n+1 The norm distance of Knife contact C n Coordinate value of (Cx_n+1 ,C y_n+1 ,C z_n+1 ) is the knife contact C n+1 The coordinate value of

[0060] The method of optimizing the distribution of knife contact points using the golden section method is:

[0061]

[0062] in: The optimized knife contact path.

[0063] The beneficial effects of the present invention are:

[0064] The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears of the present invention first discretely selects points on all right tooth surfaces. Based on the NURBS (Non-Uniform Rational B-Splines) algorithm, the discrete points are used as form value points to determine the control points of the tooth surface features. The centripetal parameterization method is used to reduce the influence of the sudden change in the node distance between adjacent tooth surfaces on the accuracy of the interpolation point. The initial tool contact point of the right tooth surface of the envelope gear is obtained by projecting the Archimedean spiral into the NURBS parameter space. Then, the motion trajectory of the tool in the cutting direction and the cutting depth direction after considering the ultrasonic vibration assistance is determined, the change law of the tool position in a single cycle is analyzed, and the judgment condition when the initial contact point between the tool and the workpiece in the elliptical trajectory and the tool contact point on the tooth surface of the envelope gear coincide with each other is given, thereby determining the G code reading speed of the machine tool at the minimum residual height. Finally, the conditions satisfied when the ultrasonic elliptical trajectory is normally separated from the workpiece are revealed by combining the cutting speed and the vibration speed, and the initial tool contact point is regulated based on the golden section optimization method. The present invention has the following outstanding effects:

[0065] The present invention combines the advantages of ultrasonic vibration assistance, five-axis linkage turning, and ultra-precision single-point diamond turning to solve the problem that existing face gear machining methods cannot meet the required contour accuracy and surface quality due to the difficulty in tool manufacturing and the easy wear of the tool.

[0066] In response to the new difficulties arising from the combination of the three, the present invention realizes the simultaneous processing of all tooth surfaces through a single spiral path through tool contact planning and regulation, greatly improving the processing efficiency of face gears while ensuring processing accuracy, providing technical guarantees for high-precision manufacturing of face gears, and is conducive to promoting the development of a new generation of helicopter main reducers. This method also provides a solution for other difficult-to-process materials with complex surfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0068] Figure 1 This is a flow chart of an embodiment of the ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears of the present invention;

[0069] Figure 2 is the change of the distance between adjacent nodes on the tooth surface;

[0070] Figure 3 is the initial knife contact path on the envelope gear tooth surface;

[0071] Figure 4 The machining principle of ultrasonic vibration-assisted five-axis ultra-precision turning of face gears. DETAILED DESCRIPTION

[0072] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0073] like Figure 1 As shown, the ultrasonic vibration assisted five-axis ultra-precision single-point diamond turning method for face gears of this embodiment adopts ultrasonic vibration assisted processing, five-axis linkage turning and ultra-precision single-point diamond turning technology, and includes the following steps.

[0074] Step 1: Plan the initial tool contact path of the envelope gear tooth surface: Based on the NURBS inversion algorithm, use the discrete points on the tooth surface as the shape value points, combine the centripetal parameterization method to determine the node vector, and project the Archimedean spiral into the NURBS parameter space to generate the initial tool contact point of the envelope tooth surface.

[0075] In this embodiment, the method steps for planning the initial knife contact path of the tooth surface of the envelope gear are as follows:

[0076] 11) Establish a single tooth surface three-dimensional model of the left or right tooth surface of the face gear, evenly select discrete points on the single tooth surface to form point cloud data; rotate the point cloud data array around the gear axis to generate a set of discrete points corresponding to all single tooth surfaces.

[0077] 12) The discrete points (x k,l ,y k,l ,z k,l ) as the type value point {Q k.l}, perform inverse calculation based on the NURBS algorithm to determine the control points that characterize the geometric features of the tooth surface.

[0078] In this embodiment, the method for performing inversion calculation based on the NURBS algorithm is:

[0079]

[0080] Among them: Among them: (xk,l ,y k,l ,z k,l ) is the coordinate value of the discrete point; For nodes The corresponding i-th p-th basis function; For nodes The corresponding l-th q-th basis function; and They are the control points corresponding to the x, y, and z directions respectively; is the control point; is the node value of the kth u direction; is the node value of the kth v direction, m + and n + are the number of discrete points in the u and v directions respectively.

[0081] 13) Aiming at the node vector error problem caused by the sudden change of the distance between discrete points on adjacent tooth surfaces, the centripetal parameterization method is used to optimize the node distribution.

[0082] In particular, by the type value point {Q k.l}Confirmed It will directly affect the interpolation accuracy of the free-form surface. Since the distance corresponding to the discrete points between adjacent tooth surfaces increases suddenly, such as Figure 2 As shown, and A sudden change in the distance between the nodes will result in a node vector The error increases significantly.

[0083] In this embodiment, in order to process local irregular data points and ensure the interpolation accuracy of the free-form surface, a centripetal parameterization method is used to optimize the node distribution. The method is:

[0084]

[0085] Where: d l is the sum of the chord lengths of adjacent type value points; is the i-th node under the l-th latitude; Q i,l is the (i,j)th type value point.

[0086] Node Vector The same principle can be applied to calculate the node vector. and The corresponding basis functions and the calculation method of the basis functions are prior art and will not be elaborated in detail in this embodiment. The above formula is converted into a one-dimensional linear equation system, which has a unique solution, and the unique solution is the characteristic point that characterizes the tooth surface of the face gear.

[0087] 14) Project the Archimedean spiral into the NURBS parameter space to generate the initial tool contact path of the envelope tooth surface.

[0088] Specifically, due to the large size and hollow center of the spiral disk, the equal-angle discretization method cannot be used to discretize the helix of the face gear tooth surface. Therefore, this embodiment uses the equal-arc-length discretization method, which ensures that the distances between adjacent discrete points are equal without considering the loss of feature information in the center of the surface.

[0089] 141) The Archimedean spiral is discretized in the polar coordinate system using the equal arc length discretization method. The method is:

[0090]

[0091] Where: r is the pole diameter; k is the distance between two discrete points; j is the distance between two spiral lines; n is the nth knife contact point; N + is the total number of knife contacts.

[0092] 142) The discrete points obtained by discretizing the Archimedean spiral are parameterized and normalized to improve the interpolation accuracy of the tool contact point. The method is as follows:

[0093]

[0094] Where: floor(·) is the floor rounding function.

[0095] 15) Calculate node vectors using the NURBS algorithm The corresponding type value point Q(x t,t ,y t,t ,z t,t ), which is the knife contact:

[0096] C n =(C x_n ,C y_n ,C z_n )(n=0,1,…,M + )

[0097] like Figure 3 As shown in the figure, the initial knife contact path of the envelope gear tooth surface is formed. This path is optimized through spiral projection and parameterization to achieve a single spiral trajectory covering all tooth surfaces.

[0098] Step 2: Determine the processing conditions for the minimum residual height: Calculate the elliptical trajectory of the tool in the cutting direction and cutting depth direction based on the ultrasonic vibration parameters, analyze the coincidence conditions of the initial contact points between the tool and the workpiece, and optimize the machine tool G code running speed to ensure that the number of spiral trajectories between adjacent tool contact points meets the time synchronization relationship.

[0099] In this embodiment, the method steps for determining the processing conditions for the minimum residual height are as follows:

[0100] 21) Based on the ultrasonic vibration parameters, define the periodic elliptical trajectory equation of the tool in the cutting direction and cutting depth direction plane. Specifically, the periodic elliptical trajectory equation of the tool in the cutting direction and cutting depth direction plane is:

[0101]

[0102] Where: P c and P d are the coordinates of the tool along the cutting direction and cutting depth direction respectively; A c and A d are the amplitude of the excitation signal; ω is the angular frequency of the tool; t is the processing time; is the angular phase shift.

[0103] like Figure 4 As shown in the figure, the machining principle of ultrasonic vibration assisted five-axis ultra-precision turning of face gears is shown. Among them, the elliptical trajectory (marked in black) is the motion trajectory of the tool after applying periodic excitation signals in the cutting direction and cutting depth direction. Taking a vibration cycle as an example, A0 is the starting point of the tool, A1 is the initial contact point between the tool and the workpiece, A2 is the separation point between the tool and the workpiece, and A3 is the end point of the tool within the cycle. Figure 4 As shown in Figure 1, h is the residual height of the tool produced by the movement of the tool contact trajectory under the action of ultrasonic vibration. In the cutting direction and cutting depth direction plane, h is affected by the cutting speed, vibration frequency and amplitude, and h≤A d .

[0104] 22) In the elliptical trajectory, the initial contact point A1 where the tool first contacts the workpiece must coincide with the tool contact point position in the NC program.

[0105] 23) Synchronize machine tool G code running speed and vibration cycle

[0106] 231) Calculate the time t1 when the tool reaches the initial contact point A1 as:

[0107]

[0108] Among them: A d is the amplitude of the excitation signal; h is the residual height of the tool produced by the movement of the tool along the tool contact trajectory under the action of ultrasonic vibration; ω is the angular frequency of the tool; is the angular phase displacement; f is the vibration frequency.

[0109] 232) Synchronize the machine tool G code running speed S and obtain the corresponding relationship between the execution time interval of two adjacent lines of CNC code and the ultrasonic vibration period.

[0110] Specifically, in the five-axis ultra-precision turning process, each axis of the machine tool moves strictly according to the G code in the machine tool coordinate system, that is, each axis of the machine tool moves from the nth line of code to the position corresponding to the n+1th line of code in the same time. n =(C x_n ,C y_n ,C z_n ) to C n+1 =(C x_n+1 ,C y_n+1 ,C z_n+1 The running time between two adjacent lines of NC program is:

[0111]

[0112] In order to ensure that the residual height under the combined action of the tool spiral trajectory and the tool contact trajectory is minimum, it is necessary to ensure that the initial contact point between the tool and the workpiece at A1 and the tool contact C n =(C x_n ,C y_n ,C z_n ) coincides, time t n and t1 needs to satisfy t n = t1, the corresponding relationship between the execution time interval of two adjacent lines of NC code and the ultrasonic vibration period is obtained:

[0113]

[0114] Where: S is the G code running speed.

[0115] 233) When the ultrasonic vibration frequency is high, there may be multiple spiral tracks between adjacent knife contacts. The corresponding relationship is optimized so that the number of spiral tracks between adjacent knife contacts satisfies the time synchronization relationship. Specifically, the corresponding relationship optimization expression is:

[0116]

[0117] Where: k′ is the number of spiral tracks between adjacent knife contacts.

[0118] Step 3: Adjust the tool contact point distribution to achieve normal separation between the tool and the workpiece: Use the golden section method to adjust the initial tool contact point path to ensure that the cutting speed is less than the vibration speed of the tool along the cutting direction, so as to achieve periodic separation between the tool and the workpiece.

[0119] In this embodiment, the method steps for regulating the distribution of the tool contact points to achieve normal separation of the tool and the workpiece are as follows:

[0120] 31) Calculate the vibration speed v of the tool along the cutting direction c and machine cutting speed v a, establish the relationship model between cutting speed and vibration speed.

[0121] Specifically, the vibration speed v of the tool along the cutting direction c for:

[0122]

[0123] in: is the time derivative of the tool position along the cutting direction; A c is the amplitude of the excitation signal; ω is the angular frequency of the tool.

[0124] Machine cutting speed v a for:

[0125]

[0126] Where: ‖C n ,C n+1 ‖ is the knife contact C n Movement to C n+1 The norm distance of Knife contact C n Coordinate value of (C x_n+1 ,C y_n+1 ,C z_n+1 ) is the knife contact C n+1 The coordinate value of .

[0127] 32) The normal separation condition between the tool and the workpiece is defined as: the absolute value of the cutting speed |v a | is less than the absolute value of the vibration velocity of the tool along the cutting direction |v c |.

[0128] According to the vibration speed v of the tool along the cutting direction c and machine cutting speed v a From the calculation formula, we can see that in order to ensure |v a |<|v c |, on the one hand, you can adjust the G code running speed, on the other hand, you can adjust the tool contact C n =(C x_n ,C y_n ,C z_n )(n=0,1,…,M + ) distribution. In step 2, in order to ensure that the initial contact point between the tool and the workpiece is consistent with the tool contact point C n =(C x_n ,C y_n ,C z_n ) overlap, the G code running speed has been determined, therefore, in order to ensure the normal separation of the tool and the workpiece, it is necessary to further adjust the distribution of the initial tool contact points.

[0129] 33) The golden section method is used to optimize the knife contact point distribution and obtain the optimized knife contact point path.

[0130] The method of optimizing the distribution of knife contact points using the golden section method is:

[0131]

[0132] in: The optimized knife contact path.

[0133] The above embodiments are merely preferred embodiments for the purpose of fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention. The scope of protection of the present invention shall be subject to the claims.

Claims

1. A method for ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning of face gears, using ultrasonic vibration-assisted machining, five-axis linkage turning, and ultra-precision single-point diamond turning technology, characterized by: The steps include: Step 1: Plan the initial tool contact path of the envelope gear tooth surface: Based on the NURBS inversion algorithm, use the discrete points on the tooth surface as the shape value points, combine the centripetal parameterization method to determine the node vector, and project the Archimedean spiral into the NURBS parameter space to generate the initial tool contact point of the envelope tooth surface; Step 2: Determine the machining conditions for minimum residual height: Calculate the tool's elliptical trajectory in the cutting and cutting depth directions based on ultrasonic vibration parameters, analyze the coincidence conditions of the initial contact points between the tool and the workpiece, and optimize the machine tool G code running speed to ensure that the number of spiral trajectories between adjacent tool contact points meets the time synchronization relationship; Step 3: Adjust the tool contact point distribution to achieve normal separation between the tool and the workpiece: Use the golden section method to adjust the initial tool contact point path to ensure that the cutting speed is less than the vibration speed of the tool along the cutting direction, so as to achieve periodic separation between the tool and the workpiece.

2. The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears according to claim 1, characterized in that: In step 1, the method steps for planning the initial knife contact path of the tooth surface of the envelope gear are as follows: 11) Establish a single tooth surface 3D model of the left or right tooth surface of the face gear, evenly select discrete points on the single tooth surface to form point cloud data; rotate the point cloud data array around the gear axis to generate a set of discrete points corresponding to all single tooth surfaces; 12) Using the discrete points as the shape value points, perform inversion calculation based on the NURBS algorithm to determine the control points that characterize the geometric characteristics of the tooth surface; 13) To address the node vector error problem caused by the sudden change in the distance between discrete points on adjacent tooth surfaces, a centripetal parameterization method is used to optimize the node distribution; 14) Project the Archimedean spiral into the NURBS parameter space to generate the initial tool contact path of the envelope tooth surface, including: 141) The Archimedean spiral is discretized in the polar coordinate system using the equal arc length discretization method; 142) Perform parameterization and normalization processing on discrete points to improve the interpolation accuracy of tool contact points; 15) The type value point corresponding to the node vector is calculated by the NURBS algorithm, which is the tool contact point; the initial tool contact point path of the envelope gear tooth surface is formed. This path is projected by spiral lines and parameterized optimization to achieve a single spiral trajectory covering all tooth surfaces.

3. The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears according to claim 2, characterized in that: In step 12), the method for performing inversion calculation based on the NURBS algorithm is: Where: (x k,l ,y k,l ,z k,l ) is the coordinate value of the discrete point; For nodes The corresponding i-th p-th basis function; ) is a node The corresponding l-th q-th basis function; and They are the control points corresponding to the x, y, and z directions respectively; is the control point; is the node value of the kth u direction; is the node value of the kth v direction, m + and n + are the number of discrete points in the u and v directions respectively.

4. The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears according to claim 2, characterized in that: In step 13), the method of optimizing node distribution using the centripetal parameterization method is: Where: d l is the sum of the chord lengths of adjacent type value points; is the i-th node under the l-th latitude; Q i,l is the (i,j)th type value point; Compute node vector and The corresponding basis functions transform the above equation into a one-dimensional linear equation system, the unique solution of which is the characteristic point characterizing the tooth surface of the face gear.

5. The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears according to claim 2, characterized in that: In step 141), the method of discretizing the Archimedean spiral in the polar coordinate system using the equal arc length discretization method is: Where: r is the pole diameter; k is the distance between two discrete points; j is the distance between two spiral lines; n is the nth knife contact point; N + is the total number of knife contacts; In step 142), the method for performing parameterization and normalization processing on the discrete points is: Where: floor(·) is the floor rounding function.

6. The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears according to claim 1, characterized in that: In step 2, the method steps for determining the processing conditions for the minimum residual height are as follows: 21) Based on the ultrasonic vibration parameters, define the periodic elliptical trajectory equation of the tool in the cutting direction and cutting depth direction plane; 22) In the elliptical trajectory, the initial contact point A1 where the tool first contacts the workpiece must coincide with the tool contact point position in the NC program; 23) Synchronize machine tool G code running speed and vibration cycle 231) Calculate the time t1 when the tool reaches the initial contact point A1; 232) Synchronize the machine tool G code running speed S to obtain the corresponding relationship between the execution time interval of two adjacent lines of NC code and the ultrasonic vibration period; 233) When the ultrasonic vibration frequency is high, there may be multiple spiral tracks between adjacent knife contacts. The corresponding relationship is optimized so that the number of spiral tracks between adjacent knife contacts satisfies the time synchronization relationship.

7. The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears according to claim 6, characterized in that: In step 21), the periodic elliptical trajectory equation of the tool in the cutting direction and cutting depth direction plane is: Where: P c and P d are the coordinates of the tool along the cutting direction and cutting depth direction respectively; A c and A d are the amplitude of the excitation signal; ω is the angular frequency of the tool; t is the processing time; is the angular phase shift.

8. The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears according to claim 6, characterized in that: In step 231), the time t1 when the tool reaches the initial contact point A1 is: Among them: A d is the amplitude of the excitation signal; h is the residual height of the tool produced by the movement of the tool along the tool contact trajectory under the action of ultrasonic vibration; ω is the angular frequency of the tool; is the angular phase displacement; f is the vibration frequency; In step 232), the corresponding relationship between the execution time interval of two adjacent lines of numerical control code and the ultrasonic vibration period is: Where: S is the G code running speed; In step 233), the corresponding relationship optimization expression is: Where: k′ is the number of spiral tracks between adjacent knife contacts.

9. The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears according to claim 1, characterized in that: In step three, the method steps for regulating the distribution of the tool contact points to achieve normal separation of the tool and the workpiece are as follows: 31) Calculate the vibration speed v of the tool along the cutting direction c and machine cutting speed v a , establish the relationship model between cutting speed and vibration speed; 32) The normal separation condition between the tool and the workpiece is defined as: the absolute value of the cutting speed |v a | is less than the absolute value of the vibration velocity of the tool along the cutting direction |v c |; 33) The golden section method is used to optimize the knife contact point distribution and obtain the optimized knife contact point path.

10. The ultrasonic vibration-assisted five-axis ultra-precision single-point diamond turning method for face gears according to claim 1, characterized in that: In step 31), the vibration speed v of the tool along the cutting direction c for: in: is the time derivative of the tool position along the cutting direction; A c is the amplitude of the excitation signal; ω is the angular frequency of the tool; Machine cutting speed v a for: Where: ‖C n ,C n+1 ‖ is the knife contact C n Movement to C n+1 The norm distance of Knife contact C n Coordinate value of (C x_n+1 ,C y_n+1 ,C z_n+1 ) is the knife contact C n+1 The coordinate value of The method of optimizing the distribution of knife contact points using the golden section method is: in: This is the optimized knife contact path.

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