CN116275306A - Simulation calculation method for honing force of internal-meshing powerful honing tooth processing - Google Patents
Simulation calculation method for honing force of internal-meshing powerful honing tooth processing Download PDFInfo
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- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F19/00—Finishing gear teeth by other tools than those used for manufacturing gear teeth
- B23F19/05—Honing gear teeth
- B23F19/057—Honing gear teeth by making use of a tool in the shape of an internal gear
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- B—PERFORMING OPERATIONS; TRANSPORTING
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Abstract
The invention relates to a simulation calculation method and a system for internal engagement powerful honing tooth processing honing force, and belongs to the technical field of gear processing. According to the honing machine, a honing wheel and a honing tooth kinematic model of a workpiece to be machined are built, a working face three-dimensional model of the honing wheel and a honing tooth groove three-dimensional model of the workpiece to be machined are built respectively, penetrating calculation is conducted on the two three-dimensional models to obtain an undeformed chip model and a honing tooth groove model respectively, a plurality of planes perpendicular to the cutting speed direction and intersecting with the undeformed chip model are built according to the undeformed cutting model, overlapping faces of each plane and the undeformed chip model are extracted, and then honing force of each overlapping face is calculated. The method effectively reduces the honing force estimation difficulty in the internal-meshing strong honing process, realizes the analysis of the association relationship between the honing force and the radial feeding amount of the honing wheel in the internal-meshing strong honing process, and provides a theoretical basis for optimizing the structure and the technological parameters of the internal-meshing strong honing machine tool.
Description
Technical Field
The invention belongs to the technical field of gear machining, and particularly relates to a simulation calculation method and a simulation calculation system for honing force of internal-meshing powerful honing machining.
Background
Gear transmission is one of the most important transmission modes in mechanical transmission, and is widely applied to various fields of mechanical engineering. With the progress and development of industrial technology, the requirements on the transmission performance of gears are continuously improved, and the requirements on the performances such as the gear precision, the hardness, the tooth surface quality and the like are correspondingly continuously improved, so that in many cases, the gears must be subjected to hard finish machining to correct the deviation caused by heat treatment. The honing tooth is used as a process for finishing the hard tooth surface gear, can better finish the tooth surface texture, and is the most common finishing process for the high-speed low-noise transmission gear.
The honing gear is a gear finishing mode of meshing and rolling the honing wheel and the workpiece gear at a certain axial intersection angle, and removing the material allowance by the pressure and relative sliding of the abrasive particles of the honing gear tooth surface to the workpiece tooth surface. In the gear honing process, the gear tooth of the honing wheel and the workpiece gear always have a process from the engaged state to the engaged state, so that the contact state of the honing wheel and the workpiece gear always changes, the magnitude and the direction of honing force in the gear honing process are different, and the alternating honing force can cause the generation of self-excited vibration so as to influence the processing precision of the gear.
Disclosure of Invention
The invention provides a simulation calculation method and a simulation calculation system for internal-meshing powerful honing force, which aim to solve the technical problems that the honing force in the internal-meshing powerful honing process is difficult to estimate and the optimization of the structure and the technological parameters of an internal-meshing powerful honing machine tool is limited in the prior art.
A simulation calculation method of internal engagement powerful honing machining honing force is based on geometric penetration calculation, adopts Solidworks2018 three-dimensional simulation software to simulate the honing process of a honing wheel of a honing machine tool on a workpiece to be machined, calculates honing force simulated in the honing machining process, and comprises the following operation steps:
(1) Establishing a honing wheel and a honing kinematic model of a workpiece to be machined
Establishing a honing kinematic model for representing the relative pose of a honing wheel and a workpiece to be machined in the honing process, and obtaining a coordinate mapping function reflecting the coordinate conversion relation between a honing wheel coordinate system and the workpiece to be machined, namely the honing kinematic model:
M＝T a R zwn M hg R zw R ｚ E……(1)
in the formula (1), E represents homogeneous coordinates of any point on the honing wheel coordinate system, and M represents homogeneous coordinates of the point mapped to the coordinate system of the workpiece to be machined; r is R z Representing a rotation motion change matrix of the honing wheel; r is R zw Representing a parallel motion change matrix of the X axis of the honing wheel and the X axis of the workpiece to be machined; m is M hg Expressing an axile angular motion change matrix of a honing wheel coordinate system and a workpiece coordinate system; r is R zwn Indicating that the honing wheel coordinate system returns to the autorotation state movement change matrix; t (T) a Representing a revolution motion change matrix of the honing wheel around a coordinate system of a workpiece to be machined;
(2) Establishing a three-dimensional model of a working surface of a honing wheel
Establishing a three-dimensional model of one working surface of the honing wheel according to the coordinate mapping function;
(3) Obtaining a three-dimensional model of a tooth slot to be honing and cut of a workpiece to be machined
Acquiring tooth surface point cloud data on a working surface of a to-be-machined workpiece through Matlab202la mathematical calculation software, generating a three-dimensional curved surface II through a Solidwoks2018 ScanTo3D grid processing function, and adding honing allowance on the three-dimensional curved surface II to obtain one to-be-honed tooth slot three-dimensional model of the to-be-machined workpiece;
(4) Establishing an undeformed chip model and a honing tooth groove model with mutually matched structures
According to the honing kinematic model, the three-dimensional model of the working face of the honing wheel is utilized to simulate honing the three-dimensional model of the tooth slot of the workpiece to be machined, and an undeformed chip model and a honing tooth slot model with mutually matched structures are respectively obtained through penetration calculation;
taking the honing tooth groove model as a workpiece tooth groove of the to-be-machined piece in the next simulation process;
(5) Calculating honing force according to undeformed chip model
Creating a plurality of planes perpendicular to the cutting speed direction and intersecting the undeformed chip model according to the undeformed chip model, extracting the overlapping surfaces of each plane and the undeformed chip model, and further calculating honing force F of each overlapping surface nh ：
In the formula (2), K h Honing force per unit area; a is that cuh An area of the overlapping surface; l (L) h For honing the free contact length of the undeformed chip l s Is l h An upper integral limit of (2); n (N) dynh (l h ) Free contact length l of undeformed chip for honing h Dynamic honing edge number in the upper range.
The further technical scheme is as follows:
in the step (1), a coordinate system S (O) of a workpiece to be machined is established according to the structure of the internal meshing strong gear honing machine tool and the gear honing principle w -X w ，Y w ，Z w ) Fixed coordinate system of honing wheel S (O Σ -X ∑ ，Y ∑ ，Z ∑ ) Self-rotation coordinate system S (O) h，1 -X h，1 ，Y h，1 ，Z h，1 ) Orbital coordinate system of honing wheel S (O h，2 -X h，2 ，Y h，2 ，Z h，2 )；
Wherein the coordinate system of the workpiece is used for representing the position of the workpiece, is fixedly connected with the workpiece, and is Z w The shaft is coincident with the axis of the workpiece to be processed; the fixed coordinate system of the honing wheel is wound around X relative to the coordinate system of the workpiece to be machined w The axis rotates through an angle of intersection sigma, and the two coordinate systems are separated by a center distance l, X ∑ And Y is equal to w Collinear, Z ∑ Is coincident with the axis of the honing wheel; the rotation coordinate system of the honing wheel winds Z relative to the fixed coordinate system of the honing wheel ∑ Rotate, Z h，1 And Z is ∑ Overlapping; the coordinate system of the revolution coordinate system of the honing wheel is O with respect to the rotation coordinate system of the honing wheel w As the center of a circle, O w O h，1 For radius rotation, X h，2 、Y h，2 、Z h，2 Respectively with X h，1 、Y h，1 、Z h，1 Parallel.
In step (1), T a ’R zwn ，M hg ，R zw And R is z The transformation matrices of (a) are represented as:
in (3), sigma is the intersection angle of the honing wheel and the workpiece gear, θ is the rotation angle of the honing wheel,
is the angle by which the honing wheel rotates about the workpiece gear.
The specific operation steps of the step (2) are as follows:
(2.1) according to the coordinate mapping function, respectively acquiring: the gear tooth top midpoint and the gear tooth top endpoint of the honing wheel and the mapping point of the gear tooth top midpoint on the gear axis of the honing wheel at any moment are respectively connected with coordinate values of a coordinate system on the workpiece fixedly, and a datum plane is created by the three points;
(2.2) determining the position of the gear tooth profile of the honing wheel on the reference surface by utilizing the honing wheel and the coordinates of each point on the honing wheel, and inserting an established section-tooth profile block into the position, so as to establish a first gear tooth profile of the honing wheel at one position;
the method for establishing the gear tooth profile sketch of the honing wheel at other positions on the gear tooth of the honing wheel is analogized according to the method for establishing the gear tooth profile sketch of the honing wheel;
and (2.3) setting a plurality of sampling points on the gear teeth of the honing wheel, establishing a three-dimensional spline curve according to the sampling points, and further lofting according to the gear tooth profile sketch of the honing wheel at each position of the gear teeth of the honing wheel to form a three-dimensional curved surface I, namely the working surface three-dimensional model.
In the step (5), before the honing force of each overlapping surface is calculated, the undeformed chip model is amplified, and then the amplified undeformed chip model is divided into a plurality of approximate rectangular microelements with equal thickness.
In the step (5), the dynamic grinding edge number N of the internal meshing strong honing tooth honing contact arc within the range of any contact length 1 dynh (l h ) The method comprises the following steps:
in the formula (4), A g Is a proportionality coefficient; c 1 Is the density of abrasive particles; v w And v h The linear speed of the workpiece gear and the linear speed of the honing wheel are respectively; a, a p Is the depth of cut; d, d eh Is the equivalent honing wheel diameter; l (L) h Is the undeformed chip length;
length of the undeformed chip cross-section position; the pseudo and tail are indices that characterize the distribution of abrasive particles on the working surface of the honing wheel.
For internal engagement powerful honing gear honing, the equivalent honing wheel diameter d eh The calculation formula of (2) is as follows:
in the formula (5), d w Diameter d of workpiece gear h For honing wheel diameter, Σ is the angle of intersection between the honing wheel and the workpiece gear.
Compared with the prior art, the invention has the beneficial technical effects that:
1. according to the simulation calculation method of honing force, through establishing a honing wheel and a honing tooth kinematic model of a workpiece to be machined, then respectively establishing a working surface three-dimensional model of the honing wheel and a honing tooth groove three-dimensional model of the workpiece to be machined, so that two three-dimensional models are subjected to penetration calculation to respectively obtain an undeformed chip model and a honing tooth groove model with mutually matched structures, finally, a plurality of planes which are perpendicular to the cutting speed direction and intersect with the undeformed chip model are created according to the undeformed chip model, overlapping surfaces of each plane and the undeformed chip model are extracted, and honing force of each overlapping surface is calculated. The simulation calculation method can simulate the internal engagement powerful honing process and calculate the honing force, effectively reduce the honing force estimation difficulty in the internal engagement powerful honing process, and can analyze the association relation between the honing force and the radial feeding amount of the honing wheel in the internal engagement powerful honing process, thereby providing a theoretical basis for optimizing the structure and technological parameters of the internal engagement powerful honing machine tool.
2. The simulation calculation method of honing force can amplify the undeformed chip model, and then divide the amplified undeformed chip model into a plurality of approximate rectangular infinitesimal units with equal thickness, so as to calculate honing force of each overlapped surface, namely honing force of a single working surface of the honing wheel, and accordingly honing force of the whole honing wheel can be obtained.
3. According to the simulation calculation method of honing force, the undeformed chip model is obtained through simulation cutting, so that the defect that the chip is deformed to different degrees due to the fact that a large amount of heat is generated in the actual cutting process is overcome, and the more accurate cross-sectional area of the chip can be obtained through multiple simulation training.
4. According to the simulation calculation method of the honing force, the number of the dynamic grinding edges is calculated, and the number of abrasive particles participating in cutting is calculated, so that a calculation model of the honing force has better applicability in different honing processes.
5. The simulation calculation method of the honing force solves the defect that only average honing force is considered in the past, and the calculation of the honing force of the workpiece state with respect to time and space changes in the honing process is completed.
Drawings
FIG. 1 is a flow chart of a simulation calculation method of the present invention;
FIG. 2 is a schematic illustration of a honing kinematic model according to the invention;
figure 3 is a process schematic diagram of a method of creating a three-dimensional model of one of the working surfaces of the honing wheel of the invention;
FIG. 4 is a schematic process diagram of a method for obtaining a three-dimensional model of one of tooth slots to be honing;
FIG. 5 is a graph showing honing force on a single tooth surface of a first turn of a first workpiece to be machined as a function of radial feed of the honing wheel;
FIG. 6 is a graph showing honing force on a single tooth surface of a first workpiece to be machined rotated 1 to 8 turns as a function of radial feed amount of a honing wheel;
FIG. 7 is a graph showing honing force and honing force as a function of radial feed of the honing wheel for a first revolution of the first workpiece to be machined over the entire tooth surface;
FIG. 8 is a graph showing honing force as a function of radial feed of the honing wheel for all tooth surfaces of 1 to 8 turns of the first workpiece to be machined;
fig. 9 is a graph showing the honing force as a function of the radial feed amount of the honing wheel during the whole honing process of the first workpiece to be machined.
FIG. 10 is a graph showing honing force on a single tooth surface of a first turn of a second workpiece as a function of radial feed of a honing wheel;
FIG. 11 is a graph showing honing force on a single tooth surface of a second workpiece to be machined rotated 1 to 8 turns as a function of radial feed of the honing wheel;
FIG. 12 is a graph showing honing force as a function of radial feed of the honing wheel for all tooth surfaces of a first turn of a second workpiece;
FIG. 13 is a graph showing honing force as a function of radial feed of the honing wheel for all tooth surfaces of 1 to 8 turns of the second workpiece;
fig. 14 is a graph showing honing force as a function of radial feed amount of the honing wheel during the whole honing process of the second workpiece.
FIG. 15 is a graph showing honing force on a single tooth surface as a function of radial feed of the honing wheel for a first turn of a third workpiece;
FIG. 16 is a graph showing honing force on a single tooth surface of a third workpiece to be machined rotated 1 to 8 turns as a function of radial feed of the honing wheel;
FIG. 17 is a chart showing honing force and honing force as a function of radial feed of the honing wheel for all tooth surfaces of a first turn of a third workpiece to be machined;
FIG. 18 is a graph showing honing force as a function of radial feed of the honing wheel for all tooth surfaces of the third workpiece to be machined rotated 1 to 8 turns;
fig. 19 is a graph showing the honing force as a function of the radial feed amount of the honing wheel during the whole honing process of the third workpiece to be machined.
Detailed Description
The present invention will be described in further detail with reference to examples.
Example 1
Referring to fig. 1, the present embodiment provides a simulation calculation method for internal engagement powerful gear honing process honing force, based on geometric penetration calculation, using Solidworks2018 three-dimensional simulation software to simulate a gear honing process of a honing wheel of a gear honing machine tool on a workpiece to be machined, and calculating the honing force in the gear honing process simulation stage.
Because each tooth slot of the gear processed by the generating method has the same enveloping process, the formation of the tooth slot of only one workpiece is simulated, and the whole stress of the honing wheel can be calculated by enveloping the stress of all parts of the honing wheel of the tooth slot of one workpiece.
The basic parameters of the first workpiece to be machined adopted in this embodiment are: number of teeth z １ =67, modulus m n =2.25, pressure angle α n =17.5°, gear helix angle β 1 =33°. Basic parameters of the honing wheel are: number of teeth z=123, modulus m n =2.25, pressForce angle alpha n =17.5°, gear helix angle β 2 ＝41.722°。
The operation steps of the simulation calculation are as follows:
(1) Establishing a honing wheel and a honing kinematic model of a workpiece to be machined
Establishing a honing kinematic model for representing the relative pose of the honing wheel and the workpiece to be machined in the honing process in three-dimensional simulation software, and obtaining a coordinate mapping function reflecting the coordinate conversion relation between a honing wheel coordinate system and a workpiece coordinate system:
M＝T a R zwn M hg R zw R z E (1)
in the formula (1), E represents the homogeneous coordinate of any point on the honing wheel coordinate system, and M represents the homogeneous coordinate of the point mapped to the workpiece coordinate system; r is R z Representing a rotation motion change matrix of the honing wheel; r is R zw Representing a parallel motion change matrix of the X axis of the honing wheel and the X axis of the workpiece gear; m is M hg Expressing an axisymmetric angular motion change matrix of the honing wheel coordinate system and the workpiece coordinate system; r is R zwn Indicating that the honing wheel coordinate system returns to the autorotation state movement change matrix; t (T) a And the revolution motion change matrix of the honing wheel around the workpiece coordinate system is represented.
Referring to fig. 2, a coordinate system S (O) of a workpiece to be machined is established according to the structure of the internal engagement powerful honing machine tool and the honing principle 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 )。
Wherein the coordinate system of the workpiece is used for representing the position of the workpiece, is fixedly connected with the workpiece, and is Z w The shaft is coincident with the axis of the workpiece to be processed; the fixed coordinate system of the honing wheel is wound around X relative to the coordinate system of the workpiece to be machined w The axis rotates through an angle of intersection sigma, and the two coordinate systems are separated by oneCenter distance l, X ∑ And Y is equal to w Collinear, Z ∑ Is coincident with the axis of the honing wheel; the rotation coordinate system of the honing wheel winds Z relative to the fixed coordinate system of the honing wheel ∑ Rotate, Z h，1 And Z is ∑ Overlapping; the coordinate system of the revolution coordinate system of the honing wheel is O with respect to the rotation coordinate system of the honing wheel w As the center of a circle, O w O h，1 For radius rotation, xh ，2 、Y h，2 、Z h，2 Respectively with X h，1 、Y h，1 、Z h，1 Parallel.
In this embodiment 1, assuming that the workpiece to be machined remains in a stationary state during machining, the movements of the respective axes of the honing machine tool are transferred to the honing wheel by homogeneous coordinate conversion, and in the honing process, the conversion matrix can be represented by the intersection angle of the honing wheel with the gear to be machined, the rotation angle of the honing wheel, and the rotation angle of the honing wheel around the gear to be machined. T (T) a ，R zwn ，M hg ，R zw And R is z The transformation matrices of (a) are represented as:
in (2), sigma is the axial angle of the honing wheel and the gear of the workpiece to be machined, θ is the rotation angle of the honing wheel,
is the angle by which the honing wheel rotates about the workpiece gear.
(2) Establishing a three-dimensional model of a working surface of a honing wheel
Establishing a three-dimensional model of one working surface of the honing wheel according to the coordinate mapping function;
referring to fig. 3, the working process of the method for creating a three-dimensional model of the working surface of the honing wheel is as follows:
(2.1) referring to a in fig. 3, according to the coordinate mapping function, respectively: the gear tooth top midpoint and the gear tooth top endpoint of the honing wheel and the mapping point of the gear tooth top midpoint on the gear axis of the honing wheel at any moment are fixedly connected with coordinate values of a coordinate system on a workpiece to be machined, and a datum plane is created by the three points;
(2.2) referring to B in fig. 3, determining the position of the tooth profile of the honing wheel on the reference plane by using the coordinates of the honing wheel and each point on the honing wheel, and inserting an established section profile block into the position, thereby establishing a tooth profile sketch of the honing wheel at one of the positions;
(2.3) referring to C in fig. 3, the method of creating the gear tooth profile sketch of the honing wheel at other positions on the gear tooth of the honing wheel is analogized to the method of creating the gear tooth profile sketch one of the honing wheel;
(2.4) referring to D in fig. 3, a plurality of sampling points are set on the gear teeth of the honing wheel, a three-dimensional spline curve is established according to the sampling points, and then a three-dimensional curved surface i.e. the working surface three-dimensional model is formed by lofting according to the gear tooth profile sketch of the honing wheel at each position of the gear teeth of the honing wheel.
(3) Obtaining a three-dimensional model of a tooth slot to be honing and cut of a workpiece to be machined
Referring to A in FIG. 4, firstly, acquiring tooth surface point cloud data on a working surface of a to-be-machined piece through Matlab2021a mathematical calculation software; referring to B in FIG. 4, generating a three-dimensional curved surface II through the grid processing function of Solidwoks2018 ScanTo 3D; referring to C in fig. 4, a honing allowance is added on the three-dimensional curved surface two; referring to D in fig. 4, a three-dimensional model of the tooth slot to be honing is obtained.
(4) Establishing an undeformed chip model and a honing tooth groove model with mutually matched structures
According to the honing kinematic model, performing simulated honing on a tooth groove three-dimensional model of a to-be-machined workpiece by utilizing a working surface three-dimensional model of the honing wheel, and respectively obtaining an undeformed chip model and a honing tooth groove model with mutually matched structures through penetration calculation;
referring to FIG. 5, the purpose of simulated honing is to find undeformed chips, so that a penetration calculation (i.e., boolean operation) is required, which is performed by cutting out the body through a curved surface. And (3) utilizing the curved surface of the working track of the honing wheel to cut off the entity of the workpiece to be machined, and cutting off the undeformed chip.
In addition, the honing tooth groove model obtained after the penetration calculation can be used as a workpiece tooth groove of a workpiece to be machined in the next simulation process.
(5) Calculating honing force according to undeformed chip model
Creating a plurality of planes which are along the length direction of the chip and intersect with the undeformed chip model according to the undeformed chip model, extracting the overlapped surfaces of each plane and the undeformed chip model, and further calculating honing force F of each overlapped surface nh ：
In the formula (3), K h Honing force per unit area; a is that cuh An area of the overlapping surface; l (L) h For honing the free contact length of the undeformed chip l s Is l h An upper integral limit of (2); n (N) dynh (l h ) Free contact length l of undeformed chip for honing h Dynamic honing edge number in the upper range.
In example 1, the undeformed chip model may be first subjected to the enlarging process, and then the enlarged undeformed chip model may be divided into a plurality of approximately rectangular microelements having the same thickness. The plurality of approximate rectangular microelements can respectively correspond to the plurality of overlapped surfaces, and then honing force of each overlapped surface is calculated according to each approximate rectangular microelement.
In addition, in the honing process, not all abrasive grains participate in cutting, and the abrasive grains participating in cutting are calculated. Internal engagement powerful honing tooth honing contact arc arbitraryDynamic number of grinding edges N in the range of contact length 1 dynh (l h ) The method comprises the following steps:
in the formula (4), A g Is a proportionality coefficient; c 1 Is the density of abrasive particles; v w And v h The linear speed of the workpiece gear and the linear speed of the honing wheel are respectively; a, a p Is the depth of cut; d, d eh Is the equivalent honing wheel diameter; l (L) h Is the undeformed chip length;
length of the undeformed chip cross-section position; alpha and beta are indices that characterize the distribution of abrasive particles on the working surface of the honing wheel. Equivalent honing wheel diameter d eh The calculation formula of (2) is as follows:
in the formula (5), d w Diameter d of workpiece gear h For honing wheel diameter, Σ is the angle of intersection between the honing wheel and the workpiece gear.
Referring to fig. 5 and 6, in the present embodiment 1, by calculating the honing force of each overlapping surface and according to the position at each overlapping surface, the correlation between the honing force on the tooth surface and the honing wheel radial feed amount can be analyzed. As can be seen from fig. 5, the honing force on the single tooth surface of the first round of rotation of the first workpiece to be machined increases with the radial feeding amount of the honing wheel, and the honing force shows a change that gradually increases and then rapidly decreases, reflecting the meshing-in and meshing-out process of the honing wheel and the first workpiece to be machined in the honing process. As can be seen from FIG. 6, the first workpiece to be machined is rotated 1 to 8 times respectively, and the honing force change condition of each circle of rotation of the single tooth surface is generally consistent, and the honing force change condition is gradually increased and then rapidly decreased.
Referring to fig. 7 and 8, in the present embodiment 1, in order to calculate honing force variation on all tooth surfaces. And superposing the forces on each tooth surface according to the superposition principle to obtain the association relation between honing force on all tooth surfaces and radial feeding amount of the honing wheel when the first workpiece to be machined rotates each circle. As can be seen from fig. 7, when the first workpiece rotates for the first turn, the honing force is changed at a certain frequency, and the changed frequency is related to the number of teeth of the first workpiece. As can be seen from fig. 8, when the first workpiece to be machined rotates for 1 to 8 turns, the honing force varies similarly with the radial feed amount of the honing wheel for each turn, and for the whole, the amplitude of the honing force gradually increases when the first workpiece to be machined rotates for 1 to 6 turns, and gradually decreases when the first workpiece to be machined rotates for 6 to 8 turns.
Referring to fig. 9, in embodiment 1, in order to calculate the honing force variation condition of the whole honing process of the first workpiece to be machined, the maximum value of the honing force during each rotation of the first workpiece to be machined is extracted and fitted, so as to obtain the association relationship between the honing force and the radial feeding amount of the honing wheel during the whole honing process. As can be seen from fig. 9, the honing force tends to gradually increase and then more rapidly decrease with the increase of the radial feeding amount of the honing wheel in the whole honing process. The honing force was gradually increased when the feed amount of the honing wheel was increased from 0 μm to 0.01449 μm, the maximum honing force was 217N, and the honing force was gradually decreased when the feed amount of the honing wheel was increased from 0.1449 μm to 0.021 μm. The prediction of honing force in the honing process according to embodiment 1 provides a theoretical basis for optimizing the honing process.
Example 2
The basic parameters of the second to-be-machined piece adopted in this embodiment are as follows: number of teeth z 2 =67, modulus m ｎ =2.25, pressure angle α n =17.5°, gear helix angle β 1 =33°. Basic parameters of the honing wheel are: number of teeth z=123, modulus m n =2.25, pressure angle α n =17.5°, gear helix angle β 2 ＝41.722°。
The procedure of the simulation calculation was the same as in example 1.
Referring to fig. 10 and 11, in the present embodiment 2, by calculating the honing force of each overlapping surface and according to the position at each overlapping surface, the correlation between the honing force on the tooth surface and the honing wheel radial feed amount can be analyzed. As can be seen from fig. 10, the honing force on the single tooth surface of the first turn of the second workpiece increases with the radial feeding amount of the honing wheel, and the honing force shows a change that gradually increases and then rapidly decreases, reflecting the meshing-in and meshing-out process of the honing wheel and the second workpiece during the honing process. As can be seen from FIG. 11, the second workpiece is rotated 1-8 turns, and the honing force change of each turn of the single tooth surface is substantially consistent, and the honing force change is gradually increased and then rapidly decreased.
Referring to fig. 12 and 13, in the present embodiment 2, in order to calculate honing force variation on all tooth surfaces. And superposing the forces on each tooth surface according to the superposition principle to obtain the association relation between honing force on all tooth surfaces and radial feeding amount of the honing wheel when the second workpiece to be machined rotates each circle. As can be seen from fig. 12, when the second workpiece rotates for the first turn, the honing force is changed at a certain frequency, and the changed frequency is related to the number of teeth of the first workpiece. As can be seen from fig. 13, when the second workpiece rotates 1 to 8 turns, the honing force varies similarly with the radial feed amount of the honing wheel for each turn, and for the whole, the amplitude of the honing force gradually increases when the second workpiece rotates 1 to 6 turns, and gradually decreases when the second workpiece rotates 6 to 8 turns.
Referring to fig. 14, in embodiment 2, in order to calculate the honing force variation condition of the whole honing process of the second workpiece, the maximum value of the honing force during each rotation of the second workpiece is extracted and fitted, so as to obtain the association relationship between the honing force and the radial feeding amount of the honing wheel during the whole honing process. As can be seen from fig. 14, the honing force tends to gradually increase and then more rapidly decrease with the increase of the radial feed amount of the honing wheel in the whole honing process. When the feed amount of the honing wheel is increased from 0 μm to 0.01394 μm, the honing force is gradually increased, the maximum honing force is 194N, and when the feed amount of the honing wheel is increased from 0.01394 μm to 0.021 μm, the honing force is gradually decreased. The present embodiment 2 provides a theoretical basis for the optimization of the gear honing process by predicting the gear honing force in the gear honing process.
Example 3
The basic parameters of the third to-be-machined part adopted in the embodiment are as follows: number of teeth z 3 =67, modulus m n =2.25, pressure angle α n =17.5°, gear helix angle β 1 =33°. Basic parameters of the honing wheel are: number of teeth z=123, modulus m n =2.25, pressure angle α n =17.5°, gear helix angle β 2 ＝41.722°。
The procedure of the simulation calculation was the same as in example 1.
Referring to fig. 15 and 16, in the present embodiment 3, by calculating the honing force of each overlapping surface and according to the position at each overlapping surface, the correlation between the honing force on the tooth surface and the honing wheel radial feed amount can be analyzed. As can be seen from fig. 15, the honing force on the single tooth surface of the first turn of the third workpiece to be machined increases with the radial feeding amount of the honing wheel, and the honing force shows a change that gradually increases and then rapidly decreases, reflecting the engagement and disengagement process of the honing wheel and the third workpiece to be machined in the honing process. As can be seen from FIG. 16, the third workpiece is rotated 1-8 turns, and the honing force change of each turn of the single tooth surface is substantially consistent, and the honing force change is gradually increased and then rapidly decreased.
Referring to fig. 17 and 18, in the present embodiment 3, in order to calculate honing force variation on all tooth surfaces. And superposing the forces on each tooth surface according to the superposition principle to obtain the association relation between honing force on all tooth surfaces and radial feeding amount of the honing wheel when the third to-be-machined piece rotates each circle. As can be seen from fig. 17, when the third workpiece rotates for the first turn, the honing force is changed at a certain frequency, and the changed frequency is related to the number of teeth of the first workpiece. As can be seen from fig. 18, when the third workpiece to be machined rotates for 1 to 8 circles, the honing force varies similarly with the radial feed amount of the honing wheel for each circle, and for the whole, the amplitude of the honing force gradually increases when the third workpiece to be machined rotates for 1 to 6 circles, and the amplitude of the honing force gradually decreases when the third workpiece to be machined rotates for 6 to 8 circles.
Referring to fig. 19, in embodiment 3, in order to calculate the honing force variation condition of the whole honing process of the third workpiece, the maximum value of the honing force during each rotation of the third workpiece is extracted and fitted, so as to obtain the association relationship between the honing force and the radial feeding amount of the honing wheel during the whole honing process. As can be seen from fig. 19, the honing force tends to gradually increase and then more rapidly decrease with the increase of the radial feed amount of the honing wheel in the whole honing process. When the feed amount of the honing wheel is increased from 0 μm to 0.01423 μm, the honing force is gradually increased, the maximum honing force is 224N, and when the feed amount of the honing wheel is increased from 0.01423 μm to 0.021 μm, the honing force is gradually decreased. The present embodiment 3 predicts the honing force in the honing process, and provides a theoretical basis for optimizing the honing process.
Example 4
The embodiment provides a simulation calculation device for internal engagement powerful honing tooth machining honing force, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor. The steps of the simulation calculation method of the internal gear honing force as in example 1, example 2 and example 3 were realized when the processor executed the program.
The simulation computing device may be a smart phone, a tablet computer, a notebook computer, a desktop computer, a rack-mounted server, a blade server, a tower server, or a cabinet server (including an independent server or a server cluster formed by a plurality of servers) for executing programs, and the like. The simulation computing device of the present embodiment includes at least but is not limited to: a memory, a processor, and the like, which may be communicatively coupled to each other via a system bus.
In this embodiment, the memory (i.e., readable storage medium) includes flash memory, hard disk, multimedia card, card memory (e.g., SD or DX memory, etc.), 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 memory, magnetic disk, optical disk, etc. In some embodiments, the memory may be an internal storage unit of a computer device, such as a hard disk or memory of the computer device. In other embodiments, the memory may also be an external storage device of a computer device, such as a plug-in hard disk, smart Media Card (SMC), secure Digital (SD) Card, flash Card (Flash Card) or the like, which are provided on the computer device. Of course, the memory may also include both internal storage units of the computer device and external storage devices. In this embodiment, the memory is typically used to store an operating system and various application software installed on the computer device. In addition, the memory can be used to temporarily store various types of data that have been output or are to be output.
The processor may be a central processing unit (Central Processing Unit, CPU), controller, microcontroller, microprocessor, or other data processing chip in some embodiments. The processor is typically used to control the overall operation of the computer device. In this embodiment, the processor is configured to run the program code or process data stored in the memory, so as to implement the processing procedure of the simulation calculation method for the internal gear honing force in the foregoing embodiments 1, 2 and 3, thereby simulating the internal gear honing process and calculating the honing force, which is beneficial to researching the honing contact process of the honing wheel and providing a theoretical basis for optimizing the internal gear honing machine structure and the technological parameters.
The embodiment provides a simulation calculation system for internal engagement powerful gear honing machining honing force, which can apply the simulation calculation methods for internal engagement powerful gear honing machining honing force described in embodiment 1, embodiment 2 and embodiment 3, further realize the gear honing process of a gear honing machine honing wheel on a workpiece to be machined, and calculate the honing force simulated in the gear honing machining process. The simulated computing system includes: the honing tool comprises a model generating component, a simulated honing component and a honing force calculating component.
The model generation component comprises a first generation module, a second generation module and a third generation module; the first generation module is used for establishing a honing kinematic model in three-dimensional simulation software and also used for obtaining a coordinate mapping function reflecting the coordinate conversion relation between a honing wheel coordinate system and a coordinate system of a workpiece to be machined; the second generation module is used for establishing a three-dimensional model of one working surface of the honing wheel according to the coordinate mapping function; the third generation module is used for acquiring one of the tooth slot three-dimensional model to be honing of the workpiece to be machined;
the simulated honing assembly is used for performing simulated honing on the tooth space three-dimensional model to be honed by utilizing the working surface three-dimensional model according to the honing kinematic model, and respectively obtaining an undeformed chip model and a honing tooth space model with mutually matched structures through geometric penetration calculation.
The honing force calculating assembly is used for creating a plurality of planes which are perpendicular to the cutting speed direction and intersect with the undeformed chip model according to the undeformed chip model, extracting the overlapped surfaces of each plane and the undeformed chip model, and further calculating the honing force at each overlapped surface.
It will be readily appreciated by those skilled in the art that the above embodiments 1-3 are only preferred embodiments of the present invention, and are not intended to limit the present invention, but any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of the present invention.
Claims (7)
1. A simulation calculation method of internal engagement powerful honing tooth processing honing force is based on geometric penetration calculation, adopts Solidworks2018 three-dimensional simulation software, and is characterized in that: the honing process of a honing wheel pair of a honing machine tool to be machined is simulated, honing force simulated in the honing process is calculated, and the operation steps are as follows:
(1) Establishing a honing wheel and a honing kinematic model of a workpiece to be machined
Establishing a honing kinematic model for representing the relative pose of a honing wheel and a workpiece to be machined in the honing process, and obtaining a coordinate mapping function reflecting the coordinate conversion relation between a honing wheel coordinate system and the workpiece to be machined, namely the honing kinematic model:
M＝T a R zwn M hg R zw R z E……(1)
in the formula (1), E represents the coordinate of any point on the honing wheelThe homogeneous coordinate on the system, M represents the homogeneous coordinate of the point mapped to the coordinate system of the workpiece to be processed; r is R z Representing a rotation motion change matrix of the honing wheel; r is R zw Representing a parallel motion change matrix of the X axis of the honing wheel and the X axis of the workpiece to be machined; m is M hg Expressing an axile angular motion change matrix of a honing wheel coordinate system and a workpiece coordinate system; r is R zwn Indicating that the honing wheel coordinate system returns to the autorotation state movement change matrix; t (T) a Representing a revolution motion change matrix of the honing wheel around a coordinate system of a workpiece to be machined;
(2) Establishing a three-dimensional model of a working surface of a honing wheel
Establishing a three-dimensional model of one working surface of the honing wheel according to the coordinate mapping function;
(3) Obtaining a three-dimensional model of a tooth slot to be honing and cut of a workpiece to be machined
Acquiring tooth surface point cloud data on a working surface of a to-be-machined workpiece through Matlab2021a mathematical calculation software, generating a three-dimensional curved surface II through a Solidwoks2018 ScanTo3D grid processing function, and adding honing allowance on the three-dimensional curved surface II to obtain one to-be-honed tooth slot three-dimensional model of the to-be-machined workpiece;
(4) Establishing an undeformed chip model and a honing tooth groove model with mutually matched structures
According to the honing kinematic model, the three-dimensional model of the working face of the honing wheel is utilized to simulate honing the three-dimensional model of the tooth slot of the workpiece to be machined, and an undeformed chip model and a honing tooth slot model with mutually matched structures are respectively obtained through penetration calculation;
taking the honing tooth groove model as a workpiece tooth groove of the to-be-machined piece in the next simulation process;
(5) Calculating honing force according to undeformed chip model
Creating a plurality of planes perpendicular to the cutting speed direction and intersecting the undeformed chip model according to the undeformed chip model, extracting the overlapping surfaces of each plane and the undeformed chip model, and further calculating honing force F of each overlapping surface nh ：
In the formula (2), K h Honing force per unit area; a is that cuh An area of the overlapping surface; l (L) h For honing the free contact length of the undeformed chip l s Is l h An upper integral limit of (2); n (N) dynh (l h ) Free contact length l of undeformed chip for honing h Dynamic honing edge number in the upper range.
2. The simulation calculation method of the honing force for machining the internal gear honing force according to claim 1, characterized by comprising the following steps: in the step (1), the step of (a),
according to the structure of the internal-meshing powerful honing machine tool and the honing principle, a coordinate system S (O) of a workpiece to be machined is established w -X w ，Y w ，Z w ) Fixed coordinate system of honing wheel S (O ∑ -X ∑ ，Y ∑ ，Z ∑ ) Self-rotation coordinate system S (O) h，1 -X h，1 ，Y h，1 ，Z h，1 ) Orbital coordinate system of honing wheel S (O h，2 -X h，2 ，Y h，2 ，Z h，2 )；
Wherein the coordinate system of the workpiece is used for representing the position of the workpiece, is fixedly connected with the workpiece, and is Z w The shaft is coincident with the axis of the workpiece to be processed; the fixed coordinate system of the honing wheel is wound around X relative to the coordinate system of the workpiece to be machined w The axis rotates through an angle of intersection sigma, and the two coordinate systems are separated by a center distance l, X ∑ And Y is equal to w Collinear, Z ∑ Is coincident with the axis of the honing wheel; the rotation coordinate system of the honing wheel winds Z relative to the fixed coordinate system of the honing wheel ∑ Rotate, Z h，1 And Z is ∑ Overlapping; the coordinate system of the revolution coordinate system of the honing wheel is O with respect to the rotation coordinate system of the honing wheel w As the center of a circle, O w O h，1 For radius rotation, X h，2 、Y h，2 、Z h，2 Respectively with X h，1 、Y h，1 、Z h，1 Parallel.
3. The simulation calculation method of the honing force for machining the internal gear honing force according to claim 1, characterized by comprising the following steps:
in step (1), T a ，R zwn ，M hg ，R zw And R is z The transformation matrices of (a) are represented as:
in (3), sigma is the intersection angle of the honing wheel and the workpiece gear, θ is the rotation angle of the honing wheel,
is the angle by which the honing wheel rotates about the workpiece gear.
4. The simulation calculation method of the honing force for machining the internal gear honing force according to claim 1, characterized by comprising the following steps: the specific operation steps of the step (2) are as follows:
(2.1) according to the coordinate mapping function, respectively acquiring: the gear tooth top midpoint and the gear tooth top endpoint of the honing wheel and the mapping point of the gear tooth top midpoint on the gear axis of the honing wheel at any moment are respectively connected with coordinate values of a coordinate system on the workpiece fixedly, and a datum plane is created by the three points;
(2.2) determining the position of the gear tooth profile of the honing wheel on the reference surface by utilizing the honing wheel and the coordinates of each point on the honing wheel, and inserting an established section-tooth profile block into the position, so as to establish a first gear tooth profile of the honing wheel at one position;
the method for establishing the gear tooth profile sketch of the honing wheel at other positions on the gear tooth of the honing wheel is analogized according to the method for establishing the gear tooth profile sketch of the honing wheel;
and (2.3) setting a plurality of sampling points on the gear teeth of the honing wheel, establishing a three-dimensional spline curve according to the sampling points, and further lofting according to the gear tooth profile sketch of the honing wheel at each position of the gear teeth of the honing wheel to form a three-dimensional curved surface I, namely the working surface three-dimensional model.
5. The simulation calculation method of the honing force for machining the internal gear honing force according to claim 1, characterized by comprising the following steps: in the step (5), before the honing force of each overlapping surface is calculated, the undeformed chip model is amplified, and then the amplified undeformed chip model is divided into a plurality of approximate rectangular microelements with equal thickness.
6. The simulation calculation method of the honing force for machining the internal gear honing force according to claim 1, characterized by comprising the following steps: in the step (5), the dynamic grinding edge number N of the internal meshing strong honing tooth honing contact arc within the range of any contact length 1 dynh (l h ) The method comprises the following steps:
N dynh (l h )＝A g [c 1 ] β [υ w /υ h ] α [a p /d eh ] α/2 [l` h /l h ] (4)
in the formula (4), A g Is a proportionality coefficient; c 1 Is the density of abrasive particles; upsilon (v) w And v h The linear speed of the workpiece gear and the linear speed of the honing wheel are respectively; a, a p Is the depth of cut; d, d eh Is the equivalent honing wheel diameter; l (L) h Is the undeformed chip length; l h Length of the undeformed chip cross-section position; alpha and beta are indices that characterize the distribution of abrasive particles on the working surface of the honing wheel.
7. The simulation calculation method of the honing force for machining the internal gear honing force according to claim 6, characterized by comprising the following steps: for internal engagement powerful honing gear honing, the equivalent honing wheel diameter d eh The calculation formula of (2) is as follows:
in the formula (5), d w Diameter d of workpiece gear h For honing wheel diameter, Σ is the angle of intersection between the honing wheel and the workpiece gear.
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