A simulation calculation method for honing force in internal meshing high-power honing process

Abstract

The present invention relates to a simulation calculation method and system for the honing force of internal meshing power honing, and belongs to the technical field of gear processing. The present invention establishes a honing kinematic model of the honing wheel and the workpiece to be processed, and then respectively establishes a three-dimensional model of the working surface of the honing wheel and a three-dimensional model of the tooth groove to be honed of the workpiece to be processed, and performs penetration calculation on the two three-dimensional models to obtain an undeformed chip model and a honing tooth groove model respectively. According to the undeformed cutting model, multiple planes perpendicular to the cutting speed direction and intersecting with the undeformed chip model are created, and the overlapping surface of each plane and the undeformed chip model is extracted, and then the honing force of each overlapping surface is calculated. The method of the present invention effectively reduces the difficulty of estimating the honing force during the internal meshing power honing process, realizes the analysis of the correlation between the honing force during the internal meshing power honing process and the radial feed of the honing wheel, and provides a theoretical basis for the optimization of the structure and process parameters of the internal meshing power honing machine tool.

Description

Technical Field

[0001] The invention belongs to the technical field of gear processing, and in particular relates to a simulation calculation method and system for honing force in internal meshing high-force honing processing. Background Art

[0002] Gear transmission is one of the most important transmission methods in mechanical transmission and is widely used in various fields of mechanical engineering. With the advancement and development of industrial technology, the requirements for gear transmission performance continue to increase, and the requirements for gear accuracy, hardness, and tooth surface quality are also increasing accordingly. In many cases, gears must be hard-finished to correct deviations caused by heat treatment. Gear honing, as a finishing process for hardened gears, can effectively modify the tooth surface texture and is the most commonly used finishing process for high-speed, low-noise transmission gears.

[0003] Gear honing is a gear finishing method in which a honing wheel and a workpiece gear mesh at a fixed axial angle, with the pressure and relative sliding of the abrasive grains on the honing wheel teeth removing excess material. During the honing process, the contact state between the honing wheel teeth and the workpiece gear constantly changes, as the honing wheel teeth and the workpiece gear constantly engage and disengage. As a result, the honing forces vary in magnitude and direction. These alternating honing forces can cause self-excited vibrations, which in turn affect gear machining accuracy. Summary of the Invention

[0004] In order to solve the technical problems in the prior art that the honing force estimation in the internal meshing power honing process is difficult and limits the optimization of the internal meshing power honing machine tool structure and process parameters, the present invention provides a simulation calculation method and system for the honing force of internal meshing power honing processing.

[0005] A simulation calculation method for the honing force of internal meshing high-power honing is based on geometric penetration calculation and uses Solidworks 2018 3D simulation software to simulate the honing process of a honing wheel on a workpiece to be machined. The honing force of the simulated honing process is calculated. The operation steps are as follows:

[0006] (1) Establish the kinematic model of the honing wheel and the workpiece to be processed

[0007] A honing kinematic model is established to characterize the relative posture of the honing wheel and the workpiece during the honing process. A coordinate mapping function that reflects the coordinate transformation relationship between the honing wheel coordinate system and the workpiece coordinate system is obtained, namely the honing kinematic model:

[0008] M=T a R zwn M hg R zw R ｚ E……(1)

[0009] In formula (1), E represents the homogeneous coordinate of any point in the honing wheel coordinate system, and M represents the homogeneous coordinate of the point mapped to the workpiece coordinate system; R z Represents the rotational motion change matrix of the honing wheel; R zw M represents the parallel motion change matrix between the X-axis of the honing wheel and the X-axis of the workpiece to be processed; hg R represents the motion change matrix of the intersection angle between the honing wheel coordinate system and the workpiece coordinate system; zwn T represents the motion change matrix when the honing wheel coordinate system returns to the rotation state; a The matrix representing the revolution motion change of the honing wheel around the coordinate system of the workpiece to be processed;

[0010] (2) Establish a three-dimensional model of the working surface of the honing wheel

[0011] Establishing a three-dimensional model of one of the working surfaces of the honing wheel according to the coordinate mapping function;

[0012] (3) Obtain a three-dimensional model of the tooth groove to be honed in the workpiece

[0013] The tooth surface point cloud data on one working surface of the workpiece to be machined is obtained by using Matlab2021a mathematical calculation software, and a three-dimensional curved surface 2 is generated by the mesh processing function of Solidworks2018 ScanTo3D. A honing allowance is added to the three-dimensional curved surface 2 to obtain a three-dimensional model of one of the tooth grooves to be honed of the workpiece to be machined;

[0014] (4) Establishing a structurally matched undeformed chip model and honing tooth groove model

[0015] According to the honing kinematic model, the three-dimensional model of the working surface of the honing wheel is used to simulate honing the three-dimensional model of the tooth groove of the workpiece to be processed, and an undeformed chip model and a honing tooth groove model with mutually matching structures are obtained through penetration calculation;

[0016] Using the honing tooth groove model as the workpiece tooth groove of the workpiece to be machined in the next simulation process;

[0017] (5) Calculation of honing force based on the undeformed chip model

[0018] According to the undeformed chip model, multiple planes perpendicular to the cutting speed direction and intersecting with the undeformed chip model are created, and the overlapping surface between each plane and the undeformed chip model is extracted, and then the honing force F of each overlapping surface is calculated. nh :

[0019]

[0020] In formula (2), Kh A is the honing force per unit area; cuh is the area of ​​the overlapping surface; l h is the arbitrary contact length of the undeformed chip during honing, l s for l h The upper limit of the integral; N dynh (l h ) is the arbitrary contact length l of the undeformed chips during honing h Number of dynamic honing edges in the upper range.

[0021] Further technical solutions are as follows:

[0022] In step (1), according to the structure of the internal meshing power honing machine tool and the honing principle, a coordinate system S(O) of the workpiece to be processed is established. w -X w , Y w , Z w ), the fixed coordinate system S(O Σ -X ∑ , Y ∑ , Z ∑ ), the rotation coordinate system of the honing wheel S(O h，1 -X h，1 , Y h，1 , Z h，1 ), the revolution coordinate system of the honing wheel S(O h，2 -X h，2 , Y h，2 , Z h，2 );

[0023] Among them, the coordinate system of the workpiece to be processed is used to represent the position of the workpiece to be processed and is fixedly connected to the workpiece to be processed. w The axis coincides with the axis of the workpiece to be processed; the fixed coordinate system of the honing wheel is relative to the coordinate system of the workpiece to be processed around X w The axis rotates through an axis intersection angle ∑, and the two coordinate systems are separated by a center distance l, X ∑ With Y w Collinear, Z ∑ Coincident with the axis of the honing wheel; the rotation coordinate system of the honing wheel is relative to the fixed coordinate system of the honing wheel around Z ∑ Rotate, Z h，1 With Z ∑ The revolution coordinate system of the honing wheel is relative to the rotation coordinate system of the honing wheel with O w is the center of the circle, O w O h，1 is the radius of rotation, X h，2 、Y h，2 、Z h，2 Respectively with X h，1 、Y h，1 、Z h，1parallel.

[0024] In step (1), T a 'R zwn , M hg , R zw and R z The transformation matrices are expressed as:

[0025]

[0026]

[0027]

[0028] In formula (3), ∑ is the axial intersection angle between the honing wheel and the workpiece gear, θ is the rotation angle of the honing wheel, It is the angle that the honing wheel rotates around the workpiece gear.

[0029] The specific operation steps of step (2) are as follows:

[0030] (2.1) According to the coordinate mapping function, respectively obtain: the coordinate values ​​of the tooth top midpoint, the tooth top point, and the mapping point of the tooth top midpoint on the honing wheel axis at any time in the workpiece fixed coordinate system, and create a reference plane with these three points;

[0031] (2.2) Using the coordinates of the honing wheel and each point on the honing wheel, determine the position of the honing wheel tooth profile on the reference plane and insert a created cross-section tooth profile sketch block at the position, thereby creating a honing wheel tooth profile sketch at one of the positions. Figure 1 ;

[0032] The method for establishing the tooth profile sketch of the honing wheel teeth at other positions on the honing wheel teeth is in accordance with the method for establishing the tooth profile sketch of the honing wheel teeth. Figure 1 The establishment method is analogous;

[0033] (2.3) A plurality of sampling points are set on the honing wheel teeth and a three-dimensional spline curve is established based on the sampling points, and then a three-dimensional surface is formed by lofting according to the honing wheel tooth profile sketch at each position of the honing wheel teeth, namely, the three-dimensional model of the working surface.

[0034] In step (5), before calculating the honing force of each overlapping surface, the undeformed chip model is firstly magnified, and then the magnified undeformed chip model is divided into a plurality of approximately rectangular microelements of equal thickness.

[0035] In step (5), the number of dynamic grinding edges N within the range of any contact length 1 of the internal meshing power honing contact arc is dynh (lh )for:

[0036]

[0037] In formula (4), A g is the proportional coefficient; c1 is the abrasive density; v w and v h are the linear speed of the workpiece gear and the linear speed of the honing wheel respectively; a p is the cutting depth; d eh is the equivalent honing wheel diameter; l h is the undeformed chip length; is the length of the undeformed chip cross section; pseudo and tail are indices that characterize the distribution state of abrasive particles on the working surface of the honing wheel.

[0038] For internal gear honing, the equivalent honing wheel diameter d eh The calculation formula is:

[0039]

[0040] In formula (5), d w is the diameter of the workpiece gear, d h is the diameter of the honing wheel, and ∑ is the axial angle between the honing wheel and the workpiece gear.

[0041] Compared with the prior art, the beneficial technical effects of the present invention are embodied in the following aspects:

[0042] 1. The honing force simulation calculation method of the present invention establishes a honing kinematic model of the honing wheel and the workpiece to be machined, and then separately establishes a three-dimensional model of a working surface of the honing wheel and a three-dimensional model of a tooth groove to be honed in the workpiece to be machined. The two three-dimensional models are then subjected to penetration calculation to obtain an undeformed chip model and a honing tooth groove model with mutually matching structures. Finally, based on the undeformed chip model, multiple planes perpendicular to the cutting speed direction and intersecting with the undeformed chip model are created, and the overlapping surfaces of each plane and the undeformed chip model are extracted to calculate the honing force of each overlapping surface. This simulation calculation method can simulate the internal meshing power honing process and calculate the honing force, effectively reducing the difficulty of estimating the honing force during the internal meshing power honing process. It can also analyze the correlation between the honing force and the radial feed rate of the honing wheel during the internal meshing power honing process, thereby providing a theoretical basis for the optimization of the structure and process parameters of the internal meshing power honing machine tool.

[0043] 2. The simulation calculation method of the honing force of the present invention can first enlarge the undeformed chip model, and then divide the enlarged undeformed chip model into multiple approximately rectangular elements of equal thickness, so as to calculate the honing force of each overlapping surface, that is, the honing force exerted on a single working surface of the honing wheel, and thus obtain the honing force exerted on the honing wheel as a whole.

[0044] 3. The simulation calculation method of the honing force of the present invention obtains an undeformed chip model by simulating cutting, thereby overcoming the large amount of heat generated in the actual cutting process and causing the chips to produce different degrees of deformation. Through multiple simulation training, a more accurate chip cross-sectional area can be obtained.

[0045] 4. The simulation calculation method of the honing force of the present invention also calculates the number of abrasive grains involved in cutting by calculating the number of dynamic grinding edges, so that the calculation model of the honing force has better applicability in different honing processes.

[0046] 5. The simulation calculation method of the honing force of the present invention solves the deficiency of only considering the average honing force in the past, and completes the calculation of the honing force with respect to the time and space changes of the workpiece state during the honing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Flowchart of the simulation calculation method of the present invention;

[0048] Figure 2 Schematic diagram of the kinematic model of gear honing according to the present invention;

[0049] Figure 3 A schematic diagram of the process of establishing a three-dimensional model of one working surface of a honing wheel according to the present invention;

[0050] Figure 4 Schematic diagram of the process of obtaining a three-dimensional model of a tooth groove to be honed in a workpiece according to the present invention;

[0051] Figure 5 This is a graph showing the variation of the honing force on a single tooth surface of the first workpiece during the first rotation as a function of the radial feed of the honing wheel;

[0052] Figure 6 This is a graph showing the variation of the honing force on a single tooth surface of the first workpiece with the radial feed of the honing wheel when the workpiece rotates 1 to 8 circles;

[0053] Figure 7 The honing force on all tooth surfaces of the first workpiece during the first rotation is a graph showing the variation of the honing force with the radial feed of the honing wheel;

[0054] Figure 8 This is a graph showing the variation of the honing force on all tooth surfaces of the first workpiece as a function of the radial feed of the honing wheel when the workpiece rotates 1 to 8 circles;

[0055] Figure 9 This is a graph showing the change in honing force versus the radial feed of the honing wheel during the entire honing process of the first workpiece.

[0056] Figure 10 This is a graph showing the variation of the honing force on a single tooth surface of the second workpiece during the first rotation as a function of the radial feed of the honing wheel;

[0057] Figure 11 This is a graph showing the variation of the honing force on a single tooth surface of the second workpiece with the radial feed of the honing wheel when the workpiece rotates 1 to 8 times;

[0058] Figure 12 This is a graph showing the variation of the honing force on all tooth surfaces of the second workpiece during the first rotation with the radial feed of the honing wheel;

[0059] Figure 13 This is a graph showing the variation of the honing force on all tooth surfaces of the second workpiece as a function of the radial feed of the honing wheel when the workpiece rotates 1 to 8 circles;

[0060] Figure 14 This is a graph showing the change in honing force versus the radial feed of the honing wheel during the entire honing process of the second workpiece.

[0061] Figure 15 This is a graph showing the variation of the honing force on a single tooth surface of the third workpiece with the radial feed of the honing wheel during the first rotation;

[0062] Figure 16 This is a graph showing the variation of the honing force on a single tooth surface of the third workpiece with the radial feed of the honing wheel when the workpiece rotates 1 to 8 circles;

[0063] Figure 17 This is the graph showing the honing force on all tooth surfaces of the third workpiece during the first rotation as a function of the radial feed of the honing wheel;

[0064] Figure 18 This is a graph showing the variation of the honing force on all tooth surfaces of the third workpiece as a function of the radial feed of the honing wheel when the workpiece rotates 1 to 8 circles;

[0065] Figure 19 This is a graph showing the change in honing force versus the radial feed of the honing wheel during the entire honing process of the third workpiece. DETAILED DESCRIPTION

[0066] The present invention is described in further detail below with reference to the embodiments.

[0067] Example 1

[0068] See also Figure 1This embodiment provides a simulation calculation method for the honing force of internal meshing high-power honing processing. Based on geometric penetration calculation, Solidworks2018 three-dimensional simulation software is used to simulate the honing process of a workpiece to be processed by the honing wheel of a honing machine tool, and calculate the honing force in the honing process simulation stage.

[0069] Since each tooth groove of the gear machined by the generating method has the same enveloping process, it is possible to simulate the formation of only one workpiece tooth groove. The forces acting on the honing wheel as a whole can be calculated by enveloping all parts of the honing wheel of a workpiece tooth groove.

[0070] The basic parameters of the first workpiece to be processed used in this embodiment are: number of teeth z １ =67, modulus m n =2.25, pressure angle α n =17.5°, gear helix angle β1 = 33°. The basic parameters of the honing wheel are: number of teeth z = 123, module m n =2.25, pressure angle α n =17.5°, gear helix angle β2 = 41.722°.

[0071] The simulation calculation steps are as follows:

[0072] (1) Establish the kinematic model of the honing wheel and the workpiece to be processed

[0073] A honing kinematic model is established in the three-dimensional simulation software to characterize the relative position of the honing wheel and the workpiece during the honing process, and a coordinate mapping function reflecting the coordinate transformation relationship between a honing wheel coordinate system and a workpiece coordinate system is obtained:

[0074] M=T a R zwn M hg R zw R z E (1)

[0075] In formula (1), E represents the homogeneous coordinate of any point in the honing wheel coordinate system, M represents the homogeneous coordinate of the point mapped to the workpiece coordinate system; R z Represents the rotational motion change matrix of the honing wheel; R zw M represents the parallel motion change matrix between the X-axis of the honing wheel and the X-axis of the workpiece gear; hg R represents the motion change matrix of the intersection angle between the honing wheel coordinate system and the workpiece coordinate system; zwn T represents the motion change matrix when the honing wheel coordinate system returns to the rotation state; a Represents the revolution motion change matrix of the honing wheel around the workpiece coordinate system.

[0076] See also Figure 2According to the structure of the internal meshing power honing machine and the principle of honing, the coordinate system S(O w -X w , Y w , Z w ), honing wheel fixed coordinate system S(O ∑ -X ∑ , Y ∑ , Z ∑ ), honing wheel rotation coordinate system S(O h，1 -X h，1 , Y h，1 , Z h，1 ), honing wheel revolution coordinate system S(O h，2 -X h，2 , Y h，2 , Z h，2 ).

[0077] Among them, the coordinate system of the workpiece to be processed is used to represent the position of the workpiece to be processed and is fixedly connected to the workpiece to be processed. w The axis coincides with the axis of the workpiece to be processed; the fixed coordinate system of the honing wheel is relative to the coordinate system of the workpiece to be processed around X w The axis rotates through an axis intersection angle ∑, and the two coordinate systems are separated by a center distance l, X ∑ With Y w Collinear, Z ∑ Coincident with the axis of the honing wheel; the rotation coordinate system of the honing wheel is relative to the fixed coordinate system of the honing wheel around Z ∑ Rotate, Z h，1 With Z ∑ The revolution coordinate system of the honing wheel is relative to the rotation coordinate system of the honing wheel with O w is the center of the circle, O w O h，1 is the radius rotation, Xh ，2 、Y h，2 、Z h，2 Respectively with X h，1 、Y h，1 、Z h，1 parallel.

[0078] In this first embodiment, it is assumed that the workpiece remains stationary during the machining process, and the motion of each axis of the gear honing machine is transferred to the honing wheel through homogeneous coordinate transformation. During the honing process, the transformation matrix can be represented by the axial angle between the honing wheel and the gear of the workpiece, the rotation angle of the honing wheel, and the angle of rotation of the honing wheel around the gear of the workpiece. a , R zwn , M hg , R zw and R z The transformation matrices are expressed as:

[0079]

[0080]

[0081]

[0082] In formula (2), ∑ is the axial intersection angle between the honing wheel and the gear to be machined, θ is the rotation angle of the honing wheel, It is the angle that the honing wheel rotates around the workpiece gear.

[0083] (2) Establish a three-dimensional model of the working surface of the honing wheel

[0084] Establishing a three-dimensional model of one of the working surfaces of the honing wheel according to the coordinate mapping function;

[0085] See also Figure 3 The operating steps of the method for establishing the three-dimensional model of the working surface of the honing wheel are as follows:

[0086] (2.1) See Figure 3 A in the figure is used to obtain, according to the coordinate mapping function, the coordinate values ​​of the tooth top midpoint, the tooth tip point, and the mapping point of the tooth top midpoint on the honing wheel axis at any time in the fixed coordinate system of the workpiece, and to create a reference plane using the three points.

[0087] (2.2) See Figure 3 In step B, the coordinates of the honing wheel and each point on the honing wheel are used to determine the position of the honing wheel tooth profile on the reference plane, and a cross-section tooth profile sketch block is inserted at the position to thereby establish the honing wheel tooth profile sketch at one of the positions. Figure 1 ;

[0088] (2.3) See Figure 3 In C, the method for establishing the tooth profile sketch of the honing wheel at other positions on the honing wheel teeth is based on the tooth profile sketch of the honing wheel. Figure 1 The establishment method is analogous;

[0089] (2.4) See Figure 3 In D, multiple sampling points are set on the teeth of the honing wheel, and a three-dimensional spline curve is established based on the sampling points. Then, a three-dimensional surface is formed by lofting the tooth profile sketch of the honing wheel at each position of the honing wheel teeth, that is, the three-dimensional model of the working surface.

[0090] (3) Obtain a three-dimensional model of the tooth groove to be honed in the workpiece

[0091] See also Figure 4In A, first use Matlab2021a mathematical calculation software to obtain the tooth surface point cloud data on a working surface of the workpiece to be processed; see Figure 4 B in the figure is processed by the mesh processing function of Solidworks2018 ScanTo3D to generate the three-dimensional surface 2; see Figure 4 C in , add honing allowance to 3D surface 2; see Figure 4 D in the figure is used to obtain the three-dimensional model of the tooth groove to be honed.

[0092] (4) Establishing a structurally matched undeformed chip model and honing tooth groove model

[0093] According to the honing kinematic model, the three-dimensional model of the working surface of the honing wheel is used to simulate the honing of the three-dimensional model of the tooth groove of the workpiece, and through penetration calculation, an undeformed chip model and a honing tooth groove model with mutually matched structures are obtained respectively;

[0094] See also Figure 5 The goal of simulated honing is to obtain undeformed chips, which requires penetration calculations (i.e., Boolean operations). The specific implementation method is to cut solid objects through curved surfaces. The curved surface of the honing wheel's working path is used to cut away the solid object to be machined, and the removed chips are undeformed chips.

[0095] In addition, the honing tooth groove model obtained after penetration calculation can be used as the workpiece tooth groove of the workpiece to be processed in the next simulation process.

[0096] (5) Calculation of honing force based on the undeformed chip model

[0097] According to the undeformed chip model, multiple planes are created along the chip length direction and intersecting with the undeformed chip model, and the overlapping surface between each plane and the undeformed chip model is extracted, and then the honing force F of each overlapping surface is calculated. nh :

[0098]

[0099] In formula (3), K h A is the honing force per unit area; cuh is the area of ​​the overlapping surface; l h is the arbitrary contact length of honing undeformed chips, l s l h The upper limit of the integral; N dynh (l h ) is the arbitrary contact length l of the undeformed chips during honing h Number of dynamic honing edges in the upper range.

[0100] In this first embodiment, the undeformed chip model can be enlarged and then divided into a plurality of approximately rectangular microelements of equal thickness. The plurality of approximately rectangular microelements can correspond to a plurality of overlapping surfaces, and the honing force of each overlapping surface can be calculated based on each of the approximately rectangular microelements.

[0101] In addition, during the honing process, not all abrasive particles will participate in cutting, so the abrasive particles that participate in cutting must be calculated. dynh (l h )for:

[0102]

[0103] In formula (4), A g is the proportional coefficient; c1 is the abrasive density; v w and v h are the linear speed of the workpiece gear and the linear speed of the honing wheel respectively; a p is the cutting depth; d eh is the equivalent honing wheel diameter; l h is the undeformed chip length; is the length of the undeformed chip section; α and β are indices that characterize the distribution of abrasive particles on the working surface of the honing wheel. eh The calculation formula is:

[0104]

[0105] In formula (5), d w is the diameter of the workpiece gear, d h is the diameter of the honing wheel, and ∑ is the axial angle between the honing wheel and the workpiece gear.

[0106] See also Figure 5 and Figure 6 In this embodiment 1, the honing force of each overlapping surface is calculated, and according to the position of each overlapping surface, the correlation between the honing force on the tooth surface and the radial feed of the honing wheel can be analyzed. Figure 5 It can be seen that the honing force on a single tooth surface of the first workpiece during the first rotation increases gradually and then decreases rapidly as the radial feed of the honing wheel increases, reflecting the meshing process between the honing wheel and the first workpiece during the honing process. Figure 6 It can be seen that when the first workpiece rotates 1 to 8 circles respectively, the honing force changes of a single tooth surface in each circle are generally consistent, that is, they gradually increase first and then decrease rapidly.

[0107] See also Figure 7 and Figure 8In this embodiment 1, in order to calculate the change of the honing force on all tooth surfaces, the forces on each tooth surface are superimposed according to the principle of overlap, and the correlation between the honing force on all tooth surfaces and the radial feed of the honing wheel when the first workpiece rotates one circle is obtained. Figure 7 It can be seen that when the first workpiece rotates the first circle, the honing force changes at a certain frequency, and the frequency of change is related to the number of teeth of the first workpiece. Figure 8 It can be seen that when the first workpiece rotates 1 to 8 circles respectively, the change of the honing force with the radial feed of the honing wheel in each circle is similar. As a whole, when the first workpiece rotates 1 to 6 circles, the amplitude of the honing force gradually increases, and when it rotates 6 to 8 circles, the amplitude of the honing force gradually decreases.

[0108] See also Figure 9 In this embodiment 1, in order to calculate the honing force variation of the first workpiece during the entire honing process, the maximum value of the honing force during each rotation of the first workpiece is extracted and fitted, thereby obtaining the correlation between the honing force and the radial feed of the honing wheel during the entire honing process. Figure 9 It can be seen that throughout the honing process, the honing force gradually increases with the increase in the radial feed of the honing wheel, then decreases rapidly. When the honing wheel feed increases from 0 μm to 0.01449 μm, the honing force gradually increases, reaching a maximum of 217 N. When the honing wheel feed increases from 0.1449 μm to 0.021 μm, the honing force gradually decreases. This Example 1 predicts the honing force during the honing process, providing a theoretical basis for optimizing the honing process.

[0109] Example 2

[0110] The basic parameters of the second workpiece used in this embodiment are: number of teeth z2 = 67, module m ｎ =2.25, pressure angle α n =17.5°, gear helix angle β1 = 33°. The basic parameters of the honing wheel are: number of teeth z = 123, module m n =2.25, pressure angle α n =17.5°, gear helix angle β2 = 41.722°.

[0111] The operation steps of the simulation calculation are the same as those in Example 1.

[0112] See also Figure 10 and Figure 11 In this embodiment 2, the honing force of each overlapping surface is calculated, and according to the position of each overlapping surface, the correlation between the honing force on the tooth surface and the radial feed of the honing wheel can be analyzed. Figure 10It can be seen that the honing force on a single tooth surface of the second workpiece during the first rotation increases gradually and then decreases rapidly with the increase of the radial feed of the honing wheel, reflecting the meshing process between the honing wheel and the second workpiece during the honing process. Figure 11 It can be seen that the honing force changes of a single tooth surface in each rotation of the second workpiece are generally consistent when the workpiece rotates 1 to 8 times, that is, they gradually increase at first and then decrease rapidly.

[0113] See also Figure 12 and Figure 13 In this embodiment 2, in order to calculate the change of the honing force on all tooth surfaces, the forces on each tooth surface are superimposed according to the principle of overlap, and the correlation between the honing force on all tooth surfaces and the radial feed of the honing wheel when the second workpiece rotates one circle is obtained. Figure 12 It can be seen that when the second workpiece rotates the first circle, the honing force changes at a certain frequency, and the frequency of change is related to the number of teeth of the first workpiece. Figure 13 It can be seen that when the second workpiece rotates 1 to 8 circles respectively, the change of the honing force with the radial feed of the honing wheel in each circle is similar. As a whole, when the second workpiece rotates the 1st to 6th circle, the amplitude of the honing force gradually increases, and when it rotates the 6th to 8th circle, the amplitude of the honing force gradually decreases.

[0114] See also Figure 14 In this embodiment 2, in order to calculate the honing force variation of the second workpiece during the entire honing process, the maximum value of the honing force during each rotation of the second workpiece is extracted and fitted, thereby obtaining the correlation between the honing force and the radial feed of the honing wheel during the entire honing process. Figure 14 It can be seen that throughout the honing process, the honing force gradually increases with the increase in the radial feed of the honing wheel, then decreases rapidly. When the honing wheel feed increases from 0 μm to 0.01394 μm, the honing force gradually increases, reaching a maximum honing force of 194 N. When the honing wheel feed increases from 0.01394 μm to 0.021 μm, the honing force gradually decreases. This Example 2 predicts the honing force during the honing process, providing a theoretical basis for optimizing the honing process.

[0115] Example 3

[0116] The basic parameters of the third workpiece used in this embodiment are: number of teeth z3 = 67, module m n =2.25, pressure angle α n =17.5°, gear helix angle β1 = 33°. The basic parameters of the honing wheel are: number of teeth z = 123, module m n =2.25, pressure angle α n=17.5°, gear helix angle β2 = 41.722°.

[0117] The operation steps of the simulation calculation are the same as those in Example 1.

[0118] See also Figure 15 and Figure 16 In this embodiment 3, the honing force of each overlapping surface is calculated, and according to the position of each overlapping surface, the correlation between the honing force on the tooth surface and the radial feed of the honing wheel can be analyzed. Figure 15 It can be seen that the honing force on a single tooth surface of the third workpiece during the first rotation increases gradually and then decreases rapidly with the increase of the radial feed of the honing wheel, reflecting the meshing process between the honing wheel and the third workpiece during the honing process. Figure 16 It can be seen that the honing force changes of a single tooth surface in each rotation of the third workpiece are generally consistent when the workpiece rotates 1 to 8 times, which is gradually increasing at first and then rapidly decreasing.

[0119] See also Figure 17 and Figure 18 In this embodiment 3, in order to calculate the change of the honing force on all tooth surfaces, the forces on each tooth surface are superimposed according to the principle of overlap, and the correlation between the honing force on all tooth surfaces and the radial feed of the honing wheel when the third workpiece rotates one circle is obtained. Figure 17 It can be seen that when the third workpiece rotates the first circle, the honing force changes at a certain frequency, and the frequency of change is related to the number of teeth of the first workpiece. Figure 18 It can be seen that when the third workpiece rotates 1 to 8 circles respectively, the change of the honing force with the radial feed of the honing wheel in each circle is similar. As a whole, when the third workpiece rotates the 1st to 6th circle, the amplitude of the honing force gradually increases, and when it rotates the 6th to 8th circle, the amplitude of the honing force gradually decreases.

[0120] See also Figure 19 In this embodiment 3, in order to calculate the honing force variation of the third workpiece during the entire honing process, the maximum value of the honing force during each rotation of the third workpiece is extracted and fitted, thereby obtaining the correlation between the honing force and the radial feed of the honing wheel during the entire honing process. Figure 19 It can be seen that throughout the honing process, the honing force gradually increases with the increase in the radial feed of the honing wheel, then decreases rapidly. When the honing wheel feed increases from 0 μm to 0.01423 μm, the honing force gradually increases, reaching a maximum of 224 N. When the honing wheel feed increases from 0.01423 μm to 0.021 μm, the honing force gradually decreases. This Example 3 predicts the honing force during the honing process, providing a theoretical basis for optimizing the honing process.

[0121] Example 4

[0122] This embodiment provides a device for simulating and calculating the honing force of an internal meshing high-force gear honing process, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the method for simulating and calculating the honing force of an internal meshing high-force gear honing process described in Examples 1, 2, and 3 are implemented.

[0123] The simulation computing device can be a smartphone, tablet computer, laptop computer, desktop computer, rack server, blade server, tower server, or cabinet server (including a standalone server or a server cluster composed of multiple servers) that executes the program. The simulation computing device of this embodiment includes at least but is not limited to: a memory and a processor that can be interconnected via a system bus.

[0124] In this embodiment, the memory (i.e., readable storage medium) includes flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, magnetic disk, optical disk, etc. In some embodiments, the memory may be an internal storage unit of a computer device, such as the hard disk or internal memory of the computer device. In other embodiments, the memory may also be an external storage device of the computer device, such as a plug-in hard disk equipped with the computer device, a smart media card (SMC), a secure digital (SD) card, a flash memory card, etc. Of course, the memory may also include both the internal storage unit of the computer device and its external storage device. In this embodiment, the memory is generally used to store the operating system and various application software installed on the computer device. In addition, the memory may also be used to temporarily store various types of data that have been output or are about to be output.

[0125] In some embodiments, the processor can be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip. The processor is generally used to control the overall operation of the computer device. In this embodiment, the processor is used to run the program code stored in the memory or process data to implement the processing process of the simulation calculation method of the honing force of the internal meshing power honing process in the aforementioned embodiments 1, 2, and 3, thereby simulating the internal meshing power honing process and calculating the honing force, which is beneficial to studying the honing contact process of the honing wheel and providing a theoretical basis for the optimization of the structure and process parameters of the internal meshing power honing machine tool.

[0126] This embodiment provides a system for simulating and calculating the honing force of an internal meshing high-force gear honing process. The system can apply the methods for simulating and calculating the honing force of an internal meshing high-force gear honing process described in Examples 1, 2, and 3 to simulate the honing process of a workpiece being honed by a honing wheel on a honing machine tool and calculate the honing force of the simulated honing process. The system includes a model generation component, a honing simulation component, and a honing force calculation component.

[0127] The model generation component includes a first generation module, a second generation module, and a third generation module; the first generation module is used to establish a honing kinematic model in a three-dimensional simulation software, and is also used to obtain a coordinate mapping function that reflects the coordinate transformation relationship between a honing wheel coordinate system and a workpiece coordinate system; the second generation module is used to establish a three-dimensional model of one of the working surfaces of the honing wheel according to the coordinate mapping function; and the third generation module is used to obtain a three-dimensional model of one of the tooth grooves to be honed of the workpiece;

[0128] The simulated honing component is used to simulate the honing of the three-dimensional model of the tooth groove to be honed using the three-dimensional model of the working surface according to the honing kinematic model, and obtain the undeformed chip model and the honing tooth groove model with mutually matched structures through geometric penetration calculation.

[0129] The honing force calculation component is used to create multiple planes perpendicular to the cutting speed direction and intersecting with the undeformed chip model according to the undeformed chip model, and extract the overlapping surface between each plane and the undeformed chip model, and then calculate the honing force at each overlapping surface.

[0130] It is easy for those skilled in the art to understand that the above embodiments 1-3 are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A simulation calculation method for the honing force of internal meshing high-power honing is based on geometric penetration calculation and uses Solidworks 2018 3D simulation software. The characteristics are: To simulate the honing process of a workpiece being machined by the honing wheel of a gear honing machine and calculate the honing force during the honing process, follow these steps: (1) Establish the kinematic model of the honing wheel and the workpiece to be processed A honing kinematic model is established to characterize the relative posture of the honing wheel and the workpiece during the honing process. A coordinate mapping function that reflects the coordinate transformation relationship between the honing wheel coordinate system and the workpiece coordinate system is obtained, namely the honing kinematic model: M=T a R zwn M hg R zw R z E……(1) In formula (1), E represents the homogeneous coordinate of any point in the honing wheel coordinate system, and M represents the homogeneous coordinate of the point mapped to the workpiece coordinate system; R z Represents the rotational motion change matrix of the honing wheel; R zw M represents the parallel motion change matrix between the X-axis of the honing wheel and the X-axis of the workpiece to be processed; hg R represents the motion change matrix of the intersection angle between the honing wheel coordinate system and the workpiece coordinate system; zwn T represents the motion change matrix when the honing wheel coordinate system returns to the rotation state; a The matrix representing the revolution motion change of the honing wheel around the coordinate system of the workpiece to be processed; (2) Establish a three-dimensional model of the working surface of the honing wheel Establishing a three-dimensional model of one of the working surfaces of the honing wheel according to the coordinate mapping function; (3) Obtain a three-dimensional model of the tooth groove to be honed in the workpiece The tooth surface point cloud data on one working surface of the workpiece to be machined is obtained by using Matlab2021a mathematical calculation software. The mesh processing function of Solidwoks2018 ScanTo3D is used to generate a second three-dimensional curved surface. A honing allowance is added to the second three-dimensional curved surface to obtain a three-dimensional model of one of the tooth grooves to be honed of the workpiece to be machined. (4) Establishing a structurally matched undeformed chip model and honing tooth groove model According to the honing kinematic model, the three-dimensional model of the working surface of the honing wheel is used to simulate honing the three-dimensional model of the tooth groove of the workpiece to be processed, and an undeformed chip model and a honing tooth groove model with mutually matching structures are obtained through penetration calculation; Using the honing tooth groove model as the workpiece tooth groove of the workpiece to be machined in the next simulation process; (5) Calculation of honing force based on the undeformed chip model According to the undeformed chip model, multiple planes perpendicular to the cutting speed direction and intersecting with the undeformed chip model are created, and the overlapping surface between each plane and the undeformed chip model is extracted, and then the honing force F of each overlapping surface is calculated. nh : In formula (2), K h A is the honing force per unit area; cuh is the area of ​​the overlapping surface; l h is the arbitrary contact length of the undeformed chip during honing, l s l h The upper limit of points; N dynh (l h ) is the arbitrary contact length l of the undeformed chips during honing h Number of dynamic honing edges in the upper range.

2. The method for simulating and calculating the honing force of internal meshing power honing according to claim 1, characterized in that: In step (1), According to the structure of the internal meshing power honing machine tool and the honing principle, the coordinate system S(O) of the workpiece to be processed is established. w -X w , Y w , Z w ), the fixed coordinate system S(O ∑ -X ∑ , Y ∑ , Z ∑ ), the rotation coordinate system of the honing wheel S(O h，1 -X h，1 , Y h，1 , Z h，1 ), the revolution coordinate system of the honing wheel S(O h，2 -X h，2 , Y h，2 , Z h，2 ); Among them, the coordinate system of the workpiece to be processed is used to represent the position of the workpiece to be processed and is fixedly connected to the workpiece to be processed. w The axis coincides with the axis of the workpiece to be processed; the fixed coordinate system of the honing wheel is relative to the coordinate system of the workpiece to be processed around X w The axis rotates through an axis intersection angle ∑, and the two coordinate systems are separated by a center distance l, X ∑ With Y w Collinear, Z ∑ Coincident with the axis of the honing wheel; the rotation coordinate system of the honing wheel is relative to the fixed coordinate system of the honing wheel around Z ∑ Rotate, Z h，1 With Z ∑ The revolution coordinate system of the honing wheel is relative to the rotation coordinate system of the honing wheel with O w is the center of the circle, O w O h，1 is the radius of rotation, X h，2 、Y h，2 、Z h，2 Respectively with X h，1 、Y h，1 、Z h，1 parallel.

3. The method for simulating and calculating the honing force of internal meshing power honing according to claim 1, characterized in that: In step (1), T a , R zwn , M hg , R zw and R z The transformation matrices are expressed as: In formula (3), ∑ is the axial intersection angle between the honing wheel and the workpiece gear, θ is the rotation angle of the honing wheel, It is the angle that the honing wheel rotates around the workpiece gear.

4. The method for simulating and calculating the honing force of internal meshing power honing according to claim 1, characterized in that: The specific operation steps of step (2) are as follows: (2.1) According to the coordinate mapping function, respectively obtain: the coordinate values ​​of the tooth top midpoint, the tooth top point, and the mapping point of the tooth top midpoint on the honing wheel axis at any time in the workpiece fixed coordinate system, and create a reference plane with these three points; (2.2) using the coordinates of the honing wheel and each point on the honing wheel, determining the position of the honing wheel tooth profile on the reference plane and inserting a created cross-section tooth profile sketch block at the position, thereby creating a first honing wheel tooth profile sketch at one of the positions; Wherein, the method for establishing the honing wheel tooth profile sketches at other positions on the honing wheel teeth is analogous to the method for establishing the honing wheel tooth profile sketch 1; (2.3) A plurality of sampling points are set on the honing wheel teeth and a three-dimensional spline curve is established based on the sampling points, and then a three-dimensional surface is formed by lofting according to the honing wheel tooth profile sketch at each position of the honing wheel teeth, namely, the three-dimensional model of the working surface.

5. The method for simulating and calculating the honing force of internal meshing power honing according to claim 1, characterized in that: In step (5), before calculating the honing force of each overlapping surface, the undeformed chip model is firstly magnified, and then the magnified undeformed chip model is divided into a plurality of approximately rectangular microelements of equal thickness.

6. The method for simulating and calculating the honing force of internal meshing power honing according to claim 1, characterized in that: In step (5), the number of dynamic grinding edges N within the range of any contact length 1 of the internal meshing power honing contact arc is dynh (l h )for: N dynh (l h )=A g [c1] β [υ w / υ h ] α [a p / d eh ] α / 2 [l` h / l h ] (4) In formula (4), A g is the proportional coefficient; c1 is the abrasive density; υ w and υ h are the linear speed of the workpiece gear and the linear speed of the honing wheel respectively; a p is the cutting depth; d eh is the equivalent honing wheel diameter; l h is the length of undeformed chip; l` h is the length of the undeformed chip cross section; α and β are indices that characterize the distribution of abrasive particles on the working surface of the honing wheel.

7. The method for simulating and calculating the honing force of internal meshing power honing according to claim 6, characterized in that: For internal gear honing, the equivalent honing wheel diameter d eh The calculation formula is: In formula (5), d w is the diameter of the workpiece gear, d h is the diameter of the honing wheel, and ∑ is the axial angle between the honing wheel and the workpiece gear.

Images