A method for analyzing forward and reverse engagement of a hypoid gear for a robot

Abstract

The application discloses a kind of hyperboloid gear positive and reverse meshing analysis method for robot, comprising the following steps: modeling to hyperboloid gear pair;Hyperboloid gear pair is respectively analyzed to positive and reverse, obtains positive and reverse tooth surface meshing trace, contact mark;The model obtained by modeling is imported into simulation software, actual working condition load is applied, and positive and reverse bearing contact simulation is carried out, and the meshing mark under the meshing simulation state of reverse engagement is obtained;The numerical model of hyperboloid gear tooth surface established by the modeling is compared with the result obtained by simulation software, and the positive and reverse transmission error curve of hyperboloid gear pair is obtained.The application realizes the system evaluation and optimization of the meshing performance of hyperboloid gear pair under positive and reverse working conditions, can comprehensively improve the transmission efficiency, meshing stability and service life of gear pair for robot joint under multiple working conditions and multiple load conditions, and has important engineering application value.

Description

Technical Field

[0001] This invention relates to the field of quasi-hyperboloid gear meshing analysis, and more particularly to a method for analyzing the forward and reverse meshing of quasi-hyperboloid gears for robots. Background Technology

[0002] Quasi-hyperboloid gears, see Figure 1 As a crucial mechanical transmission component widely used in automotive drive axles and marine power transmission systems, the hypoid gear has garnered significant attention due to its advantages such as large transmission ratio, compact structure, and high transmission efficiency. In traditional applications, hypoid gears operate primarily in a unidirectional forward rotation condition. Therefore, existing research on contact analysis and performance optimization of hypoid gears typically focuses on forward rotation conditions where the concave surface of the pinion and the convex surface of the gear are the main contact surfaces, performing gear contact analysis (TCA) and meshing performance optimization. This research method works well in unidirectional transmission applications such as automobiles and ships, but its limitation lies in neglecting the meshing performance under reverse rotation conditions.

[0003] However, with the development of science and technology, such as robotics, robot joints, as typical power transmission modules, often require frequent alternating forward and reverse rotation operations in practical work. Especially in articulated robots, the complex load conditions and varied motion patterns place higher demands on transmission accuracy and stability. Unlike commonly used symmetrical gear structures (such as harmonic reducers and RV reducers), quasi-hypoid gears have a natural asymmetry in their tooth surfaces; that is, the concave surface of the smaller gear and the convex surface of the larger gear differ significantly in geometry and contact characteristics. Therefore, under reverse rotation conditions, the meshing performance of quasi-hypoid gear pairs often differs from that under forward rotation conditions, manifesting as meshing imprint shift, changes in contact area, and increased transmission errors. If these performance differences are not effectively controlled, they will seriously affect the efficiency, accuracy, and lifespan of robot joint transmissions.

[0004] In the design and assembly of existing hypoid gear pairs, meshing adjustments and quality control are typically based solely on the forward rotation condition, with little attention paid to the meshing characteristics under reverse rotation conditions. This neglect leads to potential malfunctions in some high-performance transmission applications, such as robotics, where joint mechanisms may experience abnormal noises, jamming, or even premature tooth wear during reverse rotation, thus hindering the further application and promotion of hypoid gears in the robotics field.

[0005] Patent application CN119066814A discloses a method to improve the meshing state of gear pairs. Targeting general-purpose reducer gear pairs, it employs a closed-loop process: first, contact spot simulation; then, prototype contact spot testing; and finally, optimization and retesting based on the results to improve off-center loading and noise / vibration characteristics. However, it does not distinguish between forward and reverse rotation conditions, nor does it provide quantitative accuracy indicators such as transmission error (TE). The simulation toolchain and geometric reconstruction path are described in a rather abstract manner, making it more suitable for unidirectional automotive transmission scenarios. It lacks sufficient support for bidirectional consistency and lifespan evaluation of hyperboloids in reversing applications.

[0006] Patent application CN114519242B discloses a method for calculating point-line loads on tooth surface meshing based on transient simulation analysis results. This method belongs to a post-processing workflow that extracts pressure from transient finite element results and calculates point-line loads, focusing on the actual load distribution to serve elastohydrodynamic lubrication and strength verification. However, it is not limited to quasi-hypoid gears, does not address the differences between forward and reverse rotation and the output of transmission accuracy curves, and lacks a complete geometric accuracy modeling chain including point cloud, meshing coordinate system re-expression, 3D reconstruction, and load-bearing contact simulation. Furthermore, its verification prioritizes program correctness rather than system-level dual-condition performance.

[0007] Therefore, how to establish a quasi-hypoid gear meshing analysis and optimization method that can simultaneously take into account both forward and reverse rotation conditions has become a key technical problem that urgently needs to be solved in the design of high-performance transmission systems. Summary of the Invention

[0008] To address the aforementioned deficiencies in the existing technology, the present invention aims to provide a method for analyzing the forward and reverse meshing of quasi-hypoid gears for robots, thereby solving the problems of insufficient meshing performance, large transmission error, and difficulty in guaranteeing meshing quality of quasi-hypoid gear pairs under reverse working conditions in the existing technology.

[0009] This invention provides a method for analyzing the forward and reverse meshing of quasi-hyperboloid gears used in robots, characterized by the following steps:

[0010] Model the hyperboloid gear pair;

[0011] Perform forward and reverse rotation analysis on the hyperboloid gear pair to obtain the meshing traces and contact marks on the tooth surfaces in both directions.

[0012] The model obtained from modeling is imported into simulation software, actual working condition loads are applied, and forward and reverse bearing contact simulation is performed to obtain meshing imprints and meshing traces under forward and reverse meshing simulation conditions.

[0013] The numerical model of the quasi-hyperboloid gear tooth surface established by the modeling is compared with the results obtained by simulation software to obtain the forward and reverse transmission error curve of the quasi-hyperboloid gear pair.

[0014] Furthermore, the modeling of the aligning hyperboloid gear pair described in this invention includes:

[0015] Perform gear modeling to obtain three-dimensional spatial point cloud data of the small gear tooth surface and the large gear tooth surface;

[0016] The point cloud data is then re-expressed in the meshing coordinate system;

[0017] A three-dimensional solid model of the quasi-hyperboloid gear pair is reconstructed based on the point cloud data.

[0018] Furthermore, the present invention performs forward and reverse rotation analysis on the aligned hyperboloid gear pair to obtain the meshing traces and contact imprints of the forward and reverse gear surfaces, including:

[0019] When the hypoid gear pair rotates forward, the concave surface of the small gear contacts the convex surface of the large gear, forming a forward rotation meshing trace. Through gear contact analysis, the distribution of the meshing area and the characteristics of the contact imprint in the forward rotation state are obtained.

[0020] When a hypoid gear pair reverses direction, the convex surface of the small gear meshes with the concave surface of the large gear, forming a reverse meshing trace. Through gear contact analysis, the distribution of the meshing area and the characteristics of the contact imprint in the reverse state are obtained.

[0021] Furthermore, the present invention describes importing the model obtained from modeling into simulation software, applying actual working condition loads, performing forward and reverse rotation bearing contact simulation, and obtaining meshing imprints and meshing traces under forward and reverse rotation meshing simulation conditions, including:

[0022] Perform forward rotation load contact simulation to obtain the contact imprint distribution under forward rotation meshing simulation state;

[0023] Perform reverse load contact simulation to obtain the contact imprint distribution under reverse meshing simulation state;

[0024] The differences in meshing behavior between forward and reverse rotation under load conditions were analyzed.

[0025] Furthermore, the present invention compares the numerical model of the quasi-hyperboloid gear tooth surface established by modeling with the results obtained by simulation software to obtain the forward and reverse transmission error curves of the quasi-hyperboloid gear pair, including:

[0026] Under forward rotation meshing conditions, the forward rotation transmission error curve is obtained through simulation;

[0027] Under reverse meshing conditions, the reverse transmission error curve is obtained through simulation.

[0028] Furthermore, the transmission error function corresponding to the transmission error curve is:

[0029] ;

[0030] At the initial contact, the rotation angles of the small wheel and the large wheel are recorded as follows: , After the gear pair rotates by a certain angle, the rotation angles of the small gear and the large gear are respectively... , , and These represent the number of teeth on the small wheel and the large wheel, respectively.

[0031] Furthermore, when the transmission ratio is not constant, the transmission error function is:

[0032] ;

[0033] The transmission error curve is based on the large wheel rotation angle. Independent variable, transmission error The curve represents the functional relationship between the dependent variable and the dependent variable.

[0034] Furthermore, the method for obtaining the tooth surface meshing trace during forward rotation is as follows:

[0035] During forward rotation, the concave surface of the smaller wheel contacts the convex surface of the larger wheel; obtain the tooth surface reference point of the concave surface of the smaller wheel and the convex surface of the larger wheel, and the rotation angle of the larger and smaller wheels when the tooth surface reference point of the concave surface of the smaller wheel contacts the tooth surface reference point of the convex surface of the larger wheel. , and the installation distance of the small wheels Small wheel offset distance Large wheel installation distance ;

[0036] During forward rotation, the meshing coordinate system Position vector of concave surface of small and medium wheel sum normal vector equation It can be represented as:

[0037] ;

[0038] ;

[0039] Meshing coordinate system Position vector of the convex surface of the medium and large wheel sum normal vector equation It can be represented as:

[0040] ;

[0041] ;

[0042] , Representing the small wheel coordinate system The equations of the position vector and normal vector of the concave surface of the small wheel in the figure. , Representing the large wheel coordinate system Equations for the position vector and normal vector of the convex surface of the medium-to-large wheel;

[0043] When the gears are engaged in forward rotation, the following equation is satisfied:

[0044] ;

[0045] ;

[0046] Solving the above system of equations will yield the tooth surface meshing traces during forward rotation.

[0047] Furthermore, the method for obtaining the tooth surface meshing trace during the reversal is as follows:

[0048] When the wheels reverse, the convex surface of the smaller wheel engages with the concave surface of the larger wheel;

[0049] During reversal, the meshing coordinate system Position vector of the convex surface of the small and medium wheel sum normal vector equation It can be represented as:

[0050] ;

[0051] ;

[0052] Meshing coordinate system Position vector of the concave surface of the medium and large wheel sum normal vector equation It can be represented as:

[0053] ;

[0054] ;

[0055] in, and Representing the small wheel coordinate system The equations of the position vector and normal vector of the small wheel convex surface. and Representing the large wheel coordinate system Equations for the position vector and normal vector of the concave surface of the large wheel;

[0056] When the gears mesh in reverse, the following equation is satisfied:

[0057] ;

[0058] ;

[0059] Solving the above system of equations will yield the tooth surface meshing traces during the reverse rotation.

[0060] The technical solution provided by this invention has the following advantages compared with the prior art:

[0061] (1) By establishing a quasi-hyperboloid gear pair meshing model under both forward and reverse working conditions, and combining numerical analysis and finite element simulation verification, the meshing characteristics of the gear pair used in robot joints under various working conditions can be systematically and accurately evaluated, overcoming the limitation of traditional focus only on forward working conditions.

[0062] (2) A high-precision solid model of the gear pair was established by modeling the gear cutting process and combining Matlab numerical calculation with point cloud import into UG modeling. Subsequently, Abaqus finite element simulation was used to realistically reflect the performance indicators of the gear pair under load, such as meshing marks and transmission errors, and to verify the consistency and engineering applicability of the numerical model and the simulation model.

[0063] (3) The analysis and optimization method established by the present invention can optimize the forward and reverse meshing state in advance during the design stage, reduce the problems of abnormal wear of tooth surface and decrease of joint accuracy caused by the deterioration of reverse meshing, significantly improve the transmission efficiency, service life and overall reliability of robot joint modules, and has important engineering application value. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the overall structure of a quasi-hyperboloid gear pair in the prior art;

[0065] Figure 2 This is a schematic diagram of tooth surface point cloud modeling in the coordinate system of the quasi-hyperboloid gear pair of the present invention;

[0066] Figure 3 This is a schematic diagram of tooth surface point cloud modeling in the meshing coordinate system of the quasi-hyperboloid gear pair of the present invention;

[0067] Figure 4 This is a schematic diagram of the UG 3D model of the quasi-hyperboloid gear pair of the present invention;

[0068] Figure 5 This is a diagram showing the analysis results of the forward rotation meshing trace of the quasi-hyperboloid gear pair of the present invention;

[0069] Figure 6 This is a diagram showing the analysis results of the reverse meshing trace of the quasi-hyperboloid gear pair of the present invention;

[0070] Figure 7 This is a schematic diagram of the forward meshing coordinate system in this invention;

[0071] Figure 8 This is a schematic diagram of the reverse meshing coordinate system in this invention;

[0072] Figure 9 This is a distribution diagram of the contact marks from the forward rotation of the quasi-hyperboloid gear pair according to the present invention.

[0073] Figure 10 This is a distribution diagram of the contact marks from the reverse bearing of the quasi-hyperboloid gear pair according to the present invention;

[0074] Figure 11 This is a schematic diagram of a standard transmission error curve;

[0075] Figure 12 This is a graph showing the forward rotation transmission error of the quasi-hyperboloid gear pair of the present invention;

[0076] Figure 13 This is a diagram showing the reverse transmission error curve of the quasi-hyperboloid gear pair of the present invention;

[0077] Figure 14 This is a flowchart of the present invention. Detailed Implementation

[0078] The present invention will be further described in detail below with reference to the embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following embodiments.

[0079] Example 1

[0080] This embodiment discloses a method for analyzing the forward and reverse meshing of quasi-hyperboloid gears used in robots. (See also...) Figure 14 This includes the following steps:

[0081] S1. Model the hyperboloid gear pair.

[0082] S11. Perform gear modeling and obtain three-dimensional spatial point cloud data of the small gear tooth surface and the large gear tooth surface;

[0083] Point cloud data (PCD) in three-dimensional space is a collection of a large number of discrete three-dimensional coordinate points. Each point typically contains spatial location information (x, y, z), and in some scenarios, attributes such as color, normal vector, and intensity are also added. Essentially, a point cloud is a discrete sampling representation of the geometric shape of a real object or scene surface. The characteristic of point clouds is that they are non-continuous surfaces generated through mathematical modeling; each point contains three-dimensional spatial information and can completely describe the spatial shape of an object.

[0084] The hypoid gear is a spatially interlaced shaft gear transmission. Its tooth surface is a complex curved surface, and the tooth surfaces of the pinion and the large gear are conjugate through the principle of spatial meshing.

[0085] The key to generating its point cloud data is to establish a mathematical model of the tooth surface and obtain three-dimensional coordinate points through discrete sampling.

[0086] For details, see Figure 2In the gear coordinate system, three-dimensional point cloud data of the pinion and gear tooth surfaces can be obtained by using a tooth surface modeling program based on Matlab, which can accurately describe the tooth surface morphology formed by the actual cutting of the quasi-hyperboloid gear pair.

[0087] Figure 2 In the middle, the right side shows the dot cloud of the pinion tooth surface. The cyan dot cloud represents the convex surface of the pinion tooth, and the yellow dot cloud represents the concave surface of the pinion. Figure 2 The left side shows the dot cloud of the large gear tooth surface. The blue dot cloud represents the concave surface of the large gear tooth, and the green dot cloud represents the convex surface of the large gear tooth.

[0088] S12. Represent the point cloud data in the meshing coordinate system;

[0089] For details, see Figure 3 The gear pair point cloud data is re-expressed in the meshing coordinate system to generate tooth surface point clouds that meet the actual assembly posture requirements, providing a data basis for subsequent forward and reverse meshing analysis.

[0090] Figure 3 In the diagram, cyan dot clouds represent the convex surface of small gear teeth, yellow dot clouds represent the concave surface of small gear teeth, blue dot clouds represent the concave surface of large gear teeth, and green dot clouds represent the convex surface of large gear teeth.

[0091] S13. Reconstruct a three-dimensional solid model of the quasi-hyperboloid gear pair based on the point cloud data.

[0092] For details, see Figure 4 The point cloud data is imported into a modeling software, such as UG, to reconstruct a three-dimensional solid model of the quasi-hyperboloid gear pair, including the small gear solid and the large gear solid, thus establishing an accurate geometric basis for virtual assembly, contact analysis and finite element simulation.

[0093] S2. Perform forward and reverse rotation analysis on the hyperboloid gear pair to obtain the meshing traces and contact marks on the forward and reverse gear surfaces.

[0094] Because the axes of the hypoid gear pair are spatially intersecting, the meshing of the pinion and the gear is a relative motion of spatial conjugate surfaces. During forward and reverse rotation, the rotation direction of the pinion changes, resulting in significant changes in the relative sliding direction of the two tooth surfaces, the meshing trace, and the contact imprint.

[0095] The meshing trace, or the trajectory of the contact point between two gears, is the movement trajectory of the contact point on a fixed space (such as the tooth surface of the large or small gear) during the meshing process, reflecting the continuity and stability of the meshing.

[0096] Contact imprints refer to the distribution of the contact area on the tooth surface under actual load (usually manifested as two-dimensional patches). Their location, size, and shape directly affect the load-bearing capacity and lifespan of the gear.

[0097] See Figure 5Under forward rotation conditions, the concave surface of the small gear contacts the convex surface of the large gear. Through gear contact analysis (TCA), the forward rotation meshing trace under forward rotation conditions is obtained.

[0098] Specifically, the method for obtaining the tooth surface meshing trace during forward rotation is as follows:

[0099] During forward rotation, the concave surface of the smaller wheel contacts the convex surface of the larger wheel; obtain the tooth surface reference point of the concave surface of the smaller wheel and the convex surface of the larger wheel, and the rotation angle of the larger and smaller wheels when the tooth surface reference point of the concave surface of the smaller wheel contacts the tooth surface reference point of the convex surface of the larger wheel. , and the installation distance of the small wheels Small wheel offset distance Large wheel installation distance ;

[0100] See Figure 7 During forward rotation, the meshing coordinate system Position vector of concave surface of small and medium wheel sum normal vector equation It can be represented as:

[0101] ;

[0102] ;

[0103] Meshing coordinate system Position vector of the convex surface of the medium and large wheel sum normal vector equation It can be represented as:

[0104] ;

[0105] ;

[0106] , Representing the small wheel coordinate system The equations of the position vector and normal vector of the concave surface of the small wheel in the figure. , Representing the large wheel coordinate system Equations for the position vector and normal vector of the convex surface of the medium-to-large wheel;

[0107] When the gears are engaged in forward rotation, the following equation is satisfied:

[0108] ;

[0109] ;

[0110] Solving the above system of equations will yield the tooth surface meshing traces during forward rotation.

[0111] Figure 5In the diagram, yellow point clouds represent the concave surface of the small gear, green point clouds represent the convex surface of the large gear teeth, and red point clouds represent the meshing traces, which are mapped to the gear shaft section through coordinate transformation.

[0112] See Figure 6 In reverse rotation, the convex surface of the small gear meshes with the concave surface of the large gear. Through gear contact analysis, the reverse meshing trace in the reverse state is obtained. It shows contact characteristics different from those in forward rotation, including changes in the position of the contact area and differences in the contact shape.

[0113] Specifically, the method for obtaining the tooth surface meshing trace during reversal is as follows:

[0114] When the wheels reverse, the convex surface of the smaller wheel engages with the concave surface of the larger wheel;

[0115] See Figure 8 During reversal, the meshing coordinate system Position vector of the convex surface of the small and medium wheel sum normal vector equation It can be represented as:

[0116] ;

[0117] ;

[0118] Meshing coordinate system Position vector of the concave surface of the medium and large wheel sum normal vector equation It can be represented as:

[0119] ;

[0120] ;

[0121] in, and Representing the small wheel coordinate system The equations of the position vector and normal vector of the small wheel convex surface. and Representing the large wheel coordinate system Equations for the position vector and normal vector of the concave surface of the large wheel;

[0122] When the gears mesh in reverse, the following equation is satisfied:

[0123] ;

[0124] ;

[0125] Solving the above system of equations will yield the tooth surface meshing traces during the reverse rotation.

[0126] When performing reverse meshing analysis of the convex surface of the small wheel and the concave surface of the large wheel, the initial rotation angle of the large wheel should be maintained. Initial rotation angle of the small wheel Small wheel installation distance Small wheel offset distance and the installation distance of the large wheels Similar to the forward rotation scenario, this setting simulates the installation and adjustment process during actual assembly, using the forward rotation state as a reference, thereby analyzing the meshing performance under the same assembly conditions in the reverse rotation state. Following the forward rotation analysis process, the tooth surface meshing trajectory during the reverse rotation can be further obtained.

[0127] Figure 6 In the diagram, cyan dot clouds represent the convex surface of the small gear teeth, blue dot clouds represent the concave surface of the large gear teeth, and red dot clouds represent the meshing traces, which are mapped to the gear shaft section through coordinate transformation.

[0128] from Figure 5 and Figure 6 The meshing trace results show that, under forward rotation, the meshing trace between the convex surface of the large gear and the concave surface of the small gear is mainly distributed in the middle region of the tooth surface, indicating that the two tooth surfaces mesh stably and have uniform contact under this condition. However, under reverse rotation, the meshing trace is slightly biased towards the large end of the gear, meaning the contact between the concave surface of the large gear and the convex surface of the small gear is concentrated in the large end region. This change indicates that there is a certain difference in the meshing contact characteristics of the gears under forward and reverse rotation conditions, which may affect the load distribution and meshing stiffness of the gear pair.

[0129] S3. Import the model obtained from modeling into the simulation software, apply actual working condition loads, perform forward and reverse bearing contact simulation, and obtain meshing imprints and meshing traces under forward and reverse meshing simulation conditions.

[0130] Specifically, in this embodiment, the three-dimensional solid model of the quasi-hyperboloid gear pair is imported into the Abaqus finite element simulation software to establish a load contact analysis (LTCA) model, which simulates the meshing behavior of the gear pair under actual load conditions and obtains the meshing imprints and meshing traces under forward and reverse rotation conditions.

[0131] See Figure 9 Perform forward rotation load contact simulation to obtain the contact imprint distribution under forward rotation meshing simulation conditions; see [link / reference]. Figure 10 We conducted a reverse load contact simulation to obtain the contact imprint distribution under the reverse meshing simulation state; thereby further analyzing the difference in meshing behavior between forward and reverse rotation under load conditions.

[0132] By comparing the post-processed images, it can be seen that when rotating forward, the high stress is distributed on the tooth surface, while when rotating backward, the stress is concentrated at the root of the small end tooth.

[0133] S4. Compare the numerical model of the quasi-hyperboloid gear tooth surface established by modeling with the results obtained by simulation software to obtain the forward and reverse transmission error curve of the quasi-hyperboloid gear pair.

[0134] In actual meshing, the instantaneous transmission ratio often differs from the designed transmission ratio. To quantify the deviation between the actual transmission angle and the theoretical value, transmission error is introduced as an evaluation index.

[0135] At the initial contact, let the rotation angles of the small wheel and the large wheel be respectively... , After the gear pair rotates by a certain angle, the rotation angles of the small gear and the large gear are respectively... , , and These are the number of teeth on the pinion and gear, respectively. If the transmission ratio is constant, then:

[0136]

[0137] When the transmission ratio is not constant in practice, the transmission error function is defined as follows:

[0138]

[0139] To visualize the variation of transmission error with rotation angle, a system based on the rotation angle of the large wheel can be established. Independent variable, transmission error This is a functional relationship curve for the dependent variable. This curve visually reflects the transmission error fluctuation during the meshing process of a single pair of gears. This curve is then used as... By shifting the gear pair left and right once for each period, a complete transmission error curve is obtained.

[0140] like Figure 11 As shown, a typical standard transmission error curve has the following characteristics: except for the reference contact point where the transmission error value is zero, the transmission error values ​​at all other contact points are less than zero. This indicates that the actual rotational speed of the large gear is lower than the theoretical value at the beginning and end of the meshing cycle. Furthermore, the transmission error curve typically exhibits a downward curvature and intersects at both ends. The intersection point corresponds to the instant when the previous pair of meshing tooth surfaces just disengages and the next pair begins to contact. The existence of the intersection point ensures continuous and smooth power transmission and stable gear operation.

[0141] Following the above process, the transmission error curves for the forward and reverse rotation of the quasi-hyperboloid gear in this embodiment are as follows: Figure 12-13 As shown. Figure 12 To obtain the forward rotation transmission error curve through simulation under forward rotation meshing conditions; Figure 13 To obtain the reverse transmission error curve under reverse meshing conditions.

[0142] As can be seen, the transmission error curve during forward rotation basically meets the requirements of the standard transmission error curve, while the transmission error curves during reverse rotation do not intersect, which will lead to discontinuous transmission.

[0143] By comparing and analyzing, the differences in transmission accuracy under forward and reverse operating conditions are revealed, providing a reference for the design and optimization of quasi-hypoid gear pairs.

[0144] Through the aforementioned modeling, meshing analysis, and finite element simulation steps, this invention achieves a systematic evaluation and optimization of the meshing performance of quasi-hyperboloid gear pairs under both forward and reverse rotation conditions. Compared to existing technologies that only focus on unidirectional conditions, this invention can comprehensively improve the transmission efficiency, meshing stability, and service life of robot joint gear pairs under multiple working conditions and loads, and has significant engineering application value.

[0145] This invention targets quasi-hypoid gear pairs for robot joints, integrating both forward and reverse rotation conditions throughout the entire process of modeling, tooth surface contact analysis, and load-bearing contact simulation. A high-fidelity geometric model is constructed based on point cloud reconstruction and meshing coordinate system re-expression. Meshing traces and contact imprints are simultaneously acquired under both conditions, and forward and reverse rotation transmission error curves are output. Through comparison and optimization, considering bidirectional accuracy consistency, efficiency, and lifespan, a reproducible data and software chain and a quantitative criterion system are formed. The invention achieves a systematic evaluation and optimization of the meshing performance of quasi-hypoid gear pairs under forward and reverse rotation conditions from three aspects: commutation meshing differences, quantitative accuracy evaluation, and engineering implementation. By establishing a high-precision tooth surface modeling method under forward and reverse rotation conditions, combined with gear contact analysis (TCA) and load-bearing contact analysis (LTCA), accurate evaluation and optimized design of the meshing performance of quasi-hypoid gear pairs under bidirectional conditions are achieved, thereby improving the overall performance, reliability, and service life of the robot joint transmission system.

[0146] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method of analyzing engagement of a hypoid gear for forward and reverse rotation of a robot, characterized by, Includes the following steps: Model the hyperboloid gear pair; Perform forward and reverse rotation analysis on the hyperboloid gear pair to obtain the meshing traces and contact marks on the tooth surfaces in both directions. The model obtained from modeling is imported into simulation software, actual working condition loads are applied, and forward and reverse bearing contact simulation is performed to obtain meshing imprints and meshing traces under forward and reverse meshing simulation conditions. The numerical model of the quasi-hyperboloid gear tooth surface established by modeling is compared with the results obtained by simulation software to obtain the forward and reverse transmission error curves of the quasi-hyperboloid gear pair; The method for obtaining the tooth surface meshing trace during forward rotation is as follows: During forward rotation, the concave surface of the smaller wheel contacts the convex surface of the larger wheel; obtain the tooth surface reference point of the concave surface of the smaller wheel and the convex surface of the larger wheel, and the rotation angle of the larger and smaller wheels when the tooth surface reference point of the concave surface of the smaller wheel contacts the tooth surface reference point of the convex surface of the larger wheel. , and the installation distance of the small wheels Small wheel offset distance Large wheel installation distance ; During forward rotation, the meshing coordinate system Position vector of concave surface of small and medium wheel sum normal vector equation Represented as: ； ； Meshing coordinate system Position vector of the convex surface of the medium and large wheel sum normal vector equation Represented as: ； ； , Representing the small wheel coordinate system The equations of the position vector and normal vector of the concave surface of the small wheel in the figure. , Representing the large wheel coordinate system Equations for the position vector and normal vector of the convex surface of the medium-to-large wheel; When the gears are engaged in forward rotation, the following equation is satisfied: ； ； Solving the above system of equations yields the tooth surface meshing trace during forward rotation; The method for obtaining the tooth surface meshing trace during reversal is as follows: When the wheels reverse, the convex surface of the smaller wheel engages with the concave surface of the larger wheel; During reversal, the meshing coordinate system Position vector of the convex surface of the small and medium wheel sum normal vector equation Represented as: ； ； Meshing coordinate system Position vector of the concave surface of the medium and large wheel sum normal vector equation Represented as: ； ； in, and Representing the small wheel coordinate system The equations of the position vector and normal vector of the small wheel convex surface. and Representing the large wheel coordinate system Equations for the position vector and normal vector of the concave surface of the large wheel; When the gears mesh in reverse, the following equation is satisfied: ； ； Solving the above system of equations yields the tooth surface meshing traces during the reverse rotation.

2. The method for analyzing the forward and reverse meshing of quasi-hyperboloid gears for robots according to claim 1, characterized in that: The modeling of the aligned hyperboloid gear pair includes: Perform gear modeling to obtain three-dimensional spatial point cloud data of the small gear tooth surface and the large gear tooth surface; The point cloud data is then re-expressed in the meshing coordinate system; A three-dimensional solid model of the quasi-hyperboloid gear pair is reconstructed based on the point cloud data.

3. The method for analyzing the forward and reverse meshing of quasi-hyperboloid gears for robots according to claim 1, characterized in that: The alignment of the hyperboloid gear pair is analyzed in both forward and reverse directions to obtain the meshing traces and contact marks on the tooth surfaces in both directions, including: When the hypoid gear pair rotates forward, the concave surface of the small gear contacts the convex surface of the large gear, forming a forward rotation meshing trace. Through gear contact analysis, the distribution of the meshing area and the characteristics of the contact imprint in the forward rotation state are obtained. When a hypoid gear pair reverses direction, the convex surface of the small gear meshes with the concave surface of the large gear, forming a reverse meshing trace. Through gear contact analysis, the distribution of the meshing area and the characteristics of the contact imprint in the reverse state are obtained.

4. The method for analyzing the forward and reverse meshing of quasi-hyperboloid gears for robots according to claim 1, characterized in that: The process of importing the model obtained from modeling into simulation software, applying actual working condition loads, performing forward and reverse rotation bearing contact simulation, and obtaining meshing imprints and meshing traces under forward and reverse rotation meshing simulation conditions includes: Perform forward rotation load contact simulation to obtain the contact imprint distribution under forward rotation meshing simulation state; Perform reverse load contact simulation to obtain the contact imprint distribution under reverse meshing simulation state; The differences in meshing behavior between forward and reverse rotation under load conditions were analyzed.

5. The method for analyzing the forward and reverse meshing of quasi-hyperboloid gears for robots according to claim 1 or 4, characterized in that: The step of comparing the numerical model of the quasi-hyperboloid gear tooth surface established by modeling with the results obtained by simulation software to obtain the forward and reverse transmission error curves of the quasi-hyperboloid gear pair includes: Under forward rotation meshing conditions, the forward rotation transmission error curve is obtained through simulation; Under reverse meshing conditions, the reverse transmission error curve is obtained through simulation.

6. The method for analyzing the forward and reverse meshing of quasi-hyperboloid gears for robots according to claim 5, characterized in that: The transmission error function corresponding to the transmission error curve is: ； At the initial contact, the rotation angles of the small wheel and the large wheel are recorded as follows: , After the gear pair rotates by a certain angle, the rotation angles of the small gear and the large gear are respectively... , , and These represent the number of teeth on the small wheel and the large wheel, respectively.

7. The method for analyzing the forward and reverse meshing of quasi-hyperboloid gears for robots according to claim 6, characterized in that: When the transmission ratio is not constant, the transmission error function is: ； The transmission error curve is based on the large wheel rotation angle. Independent variable, transmission error The curve represents the functional relationship between the dependent variable and the dependent variable.

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