Tooth surface shape analysis device and tooth surface shape analysis method

Abstract

This invention provides a tooth surface shape analysis device that can analyze tooth surface deformation when gears are assembled with high precision, thereby shortening the development period for tooth surface shapes. [Solution] The gear tooth shape analysis device 1, which analyzes the amount of displacement of the gear tooth surface shape before and after assembly, includes a gear model storage unit 11 that stores a 3D model of the gear, an approximate 2D tooth surface creation unit 12 that creates an approximate 2D tooth surface consisting of a plurality of 2D planar elements that approximate the tooth surface in the gear model, a normal direction vector calculation unit 13 that calculates the normal direction vector of the evaluation point on the approximate 2D tooth surface, a local coordinate system definition unit 14 that defines the local coordinate system of the evaluation point on the approximate 2D tooth surface from the normal direction vector, and a displacement amount calculation unit 15 that calculates the amount of displacement in the normal direction of the evaluation point before and after assembly of the gear in the local coordinate system.

Description

Technical Field

[0001] The present invention relates to a tooth surface shape analysis device and a tooth surface shape analysis method.

Background Art

[0002] In order for gears to mesh accurately, the shape accuracy of the gears is important. Therefore, the shape of the tooth surface is measured using a measuring machine to measure the error with respect to the design value. For example, in Patent Document 1, the three-dimensional tooth surface shape created from the measured data obtained by measuring a plurality of measurement points on the tooth surface and the three-dimensional design value are offset so that the error between them is minimized, and a configuration for accurately calculating the error amount is disclosed. In addition, by quantifying the shape error, the influence of the axial force of the tightening bolt for assembling the gear on the tooth surface deformation is also qualitatively evaluated.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] By comparing and verifying the measured data of tooth surface deformation obtained when the gears are assembled with the results of tooth surface deformation analysis, it becomes possible to evaluate the effectiveness of subsequent improved designs without the need for prototypes. To analyze tooth surface deformation when gears are assembled, one might consider analyzing the displacement in the direction of the normal to the tooth surface. However, with the configuration disclosed in Patent Document 1 and general-purpose structural analysis devices, when the tooth trace is a twisted curved surface such as in ring gears, it is difficult to calculate the normal direction at measurement points on the tooth surface, which is a three-dimensional curved surface, using a three-dimensional analysis model. Furthermore, even if the normal direction can be calculated, it must be calculated at all evaluation points across the entire tooth surface, which is extremely complicated and leads to a prolonged development period for the tooth surface shape. Therefore, there is room for improvement in order to analyze tooth surface deformation when gears are assembled with high accuracy and shorten the development period.

[0005] The present invention aims to provide a tooth surface shape analysis device and a tooth surface shape analysis method that can analyze tooth surface deformation when gears are assembled with high precision and shorten the development period for tooth surface shapes. [Means for solving the problem]

[0006] One aspect of the present invention is, A gear tooth shape analysis device for analyzing the amount of displacement of the tooth surface shape of a gear before and after assembly, A gear model storage unit that stores a three-dimensional model of the gear, An approximate 2D tooth surface creation unit that creates an approximate 2D tooth surface consisting of a plurality of 2D planar elements that approximate the tooth surface in the 3D model, A normal direction vector calculation unit calculates the normal direction vector of the evaluation point in the approximate two-dimensional tooth surface, A local coordinate system definition unit defines a local coordinate system for evaluation points on the approximate two-dimensional tooth surface based on the normal direction vector, A displacement calculation unit that calculates the normal displacement amount of the evaluation point before and after the assembly of the gear in the local coordinate system, It is included in tooth surface shape analysis equipment.

[0007] Other aspects of the present invention include: A gear tooth shape analysis method for analyzing the amount of displacement of the tooth surface shape before and after assembly, A gear model creation process for creating a three-dimensional model of the gear, A process for creating an approximate two-dimensional tooth surface, comprising creating an approximate two-dimensional tooth surface consisting of multiple two-dimensional planar elements that approximate the tooth surface in the aforementioned three-dimensional model, A normal direction vector calculation step for calculating the normal direction vector of the evaluation point in the approximate two-dimensional tooth surface, A local coordinate system definition step, which defines the local coordinate system of the evaluation points on the approximate two-dimensional tooth surface from the normal direction vector, A displacement calculation step for calculating the normal displacement of the evaluation point before and after the assembly of the gear in the local coordinate system, This includes tooth surface shape analysis methods. [Effects of the Invention]

[0008] According to one embodiment of the present invention, a tooth surface shape analysis device is generated, consisting of a plurality of 2D planar elements that approximate the tooth surface in a 3D model of a gear. Then, the normal direction vector of the evaluation points on the approximate 2D tooth surface is calculated, and a local coordinate system for the evaluation points on the approximate 2D tooth surface is defined from the normal direction vector. Subsequently, the normal direction displacement of the evaluation points before and after the assembly of the gear in the local coordinate system is calculated. By approximating the tooth surface with an approximate 2D tooth surface, the normal direction vector at the evaluation points on the tooth surface can be easily calculated even if the tooth surface is curved. Furthermore, since the amount of computation is reduced, the normal direction vector can be easily calculated for all evaluation points across the entire tooth surface. As a result, tooth surface deformation when a gear is assembled can be analyzed with high accuracy, and the development period for tooth surface shapes can be shortened.

[0009] Furthermore, according to another embodiment of the tooth surface shape analysis method of the present invention, an approximate two-dimensional tooth surface is generated consisting of a plurality of two-dimensional planar elements that approximate the tooth surface in the gear model. Then, the normal direction vector of the evaluation point on the approximate two-dimensional tooth surface is calculated, and the local coordinate system of the evaluation point on the approximate two-dimensional tooth surface is defined from the normal direction vector. Subsequently, the normal direction displacement of the evaluation point is calculated based on the local coordinate system before and after the assembly of the gear. In this way, by approximating the tooth surface with an approximate two-dimensional tooth surface, the normal direction vector at the evaluation point on the tooth surface can be easily calculated even if the tooth surface is a curved surface. In addition, since the amount of computation is reduced, the normal direction vector can be easily calculated for all evaluation points across the entire tooth surface. As a result, tooth surface deformation when the gear is assembled can be analyzed with high accuracy, and the development period for tooth surface shapes can be shortened.

[0010] As described above, according to the above embodiment, it is possible to provide a tooth surface shape analysis device and a tooth surface shape analysis method that can analyze tooth surface deformation when gears are assembled with high precision. [Brief explanation of the drawing]

[0011] [Figure 1] Functional block diagram of the tooth surface shape analysis device in Embodiment 1. [Figure 2] A perspective view of the gear model in Embodiment 1. [Figure 3] A top view of the gear model in Embodiment 1. [Figure 4] Cross-sectional view of the position of the arrow along line IV-IV in Figure 3. [Figure 5] This is a conceptual perspective view showing the tooth surface of the gear model in Embodiment 1. [Figure 6] Front view of an approximate two-dimensional tooth surface in Embodiment 1. [Figure 7] A flowchart illustrating the tooth surface shape analysis method in Embodiment 1. [Figure 8] A figure showing the first verification results of the verification test in Embodiment 1, including (a) measured data and (b) analysis results. [Figure 9]Figure showing the second verification result of (a) measured data and (b) analysis result in the verification test in Embodiment 1.

Mode for Carrying Out the Invention

[0012] (Embodiment 1) 1. Overview of the tooth surface shape analysis device 1 An embodiment of the tooth surface shape analysis device 1 will be described with reference to FIGS. 1 to 7. The tooth surface shape analysis device 1 analyzes the displacement amount before and after assembly in the tooth surface shape of a gear. As shown in FIG. 1, the tooth surface shape analysis device 1 includes a gear model storage unit 11, an approximate two-dimensional tooth surface creation unit 12, a normal direction vector calculation unit 13, a local coordinate system definition unit 14, and a displacement amount calculation unit 15. The tooth surface shape analysis device 1 is composed of an arithmetic device that executes a program for performing the processing of each component, a storage device that stores the program and the like, and an interface that inputs and outputs information related to each processing. Each component will be described in detail below.

[0013] 1-1. Gear model storage unit 11 The gear model storage unit 11 shown in FIG. 1 stores a gear model obtained by three-dimensionally modeling a gear to be analyzed. The form of the gear is not limited, and it may be an external gear or an internal gear, and may be a helical gear or a spur gear. In this embodiment, the gear to be analyzed is a ring gear, which is an external helical gear indicated by reference numeral 20 in FIG. 2.

[0014] As shown in FIGS. 2 and 3, the ring gear 20, which is the gear to be analyzed, has an annular shape and is assembled to a differential case 30, which is the mating member for assembly. The differential case 30 has a cylindrical portion 31 and a flange portion 32. The ring gear 20 is located on the outer peripheral side of the cylindrical portion 31, and is fastened and assembled to the flange portion 32 by screwing a bolt 33 that penetrates the flange portion 32 into the back surface of the ring gear 20, as shown in FIG. 4. In FIG. 4, the illustration of the tooth surface is omitted.

[0015] As shown in Figure 3, the bolts 33 are arranged in the circumferential direction. Instead of fastening with bolts 33, the ring gear 20 may be assembled by press-fitting it into the cylindrical portion 31. The ring gear 20 has teeth that are curved in the radial direction, and as shown in Figure 5, the tooth surface 21 of each tooth is a twisted curved surface.

[0016] The form of the 3D model of the gear to be analyzed is not limited, but in this embodiment, it is formed as a 3D mesh, as shown in Figures 2 and 5. It is preferable that the 3D mesh is formed so that the nodes of the mesh are located along the measurement path when measuring the amount of deformation on the tooth surface to be analyzed.

[0017] 1-2. Approximate 2D tooth surface creation unit 12 The approximate two-dimensional tooth surface creation unit 12 shown in Figure 1 creates an approximate two-dimensional tooth surface 22 (see Figure 6) consisting of a plurality of two-dimensional planar elements that approximate the tooth surface 21 in the three-dimensional model 20 of the gear shown in Figure 5. The two-dimensional planar elements in the approximate two-dimensional tooth surface 22 are assumed to have a thickness of 0 and a rigidity of 0 so as not to affect the analysis. In this embodiment, the approximate two-dimensional tooth surface 22 includes nodes that coincide with the nodes that appear on the tooth surface 21 of the three-dimensional model 20 of the gear. Note that the nodes that appear on the tooth surface of the three-dimensional mesh include secondary nodes between primary nodes, and some or all of the nodes of the approximate two-dimensional tooth surface 22 may coincide with the secondary nodes that appear on the tooth surface of the three-dimensional mesh.

[0018] In this embodiment, as shown in Figure 6, the multiple two-dimensional planar elements constituting the approximate two-dimensional tooth surface 22 are each represented as triangular planes, and the vertices of each triangular plane become nodes in the approximate two-dimensional tooth surface 22. The nodes in the approximate two-dimensional tooth surface 22 are arranged along the tooth profile direction P of the tooth surface 21 and along the tooth trace direction Q of the tooth surface 21.

[0019] 1-3. Normal Direction Vector Calculation Unit The normal direction vector calculation unit 13 shown in Figure 1 calculates the normal direction vector of the evaluation point on the approximate 2D tooth surface 22. As shown in Figure 6, the evaluation point on the approximate 2D tooth surface 22 can be appropriately selected from the nodes constituting the approximate 2D tooth surface 22, and in this embodiment, all nodes are used. To calculate the normal direction vector of the evaluation point 22a, first, 2D planar elements that include the node that will become the evaluation point 22a as constituent points are extracted. In this embodiment, as shown in Figure 6, six 2D planar elements 221, 222, 223, 224, 225, and 226 are extracted. Then, the direction cosines cosα, cosβ, and cosγ of the 2D planar elements 221 to 226 for each of the x, y, and z directions of the coordinate system in the 3D model are calculated. These direction cosines become the normal vectors (cosα, cosβ, cosγ) of each 2D planar element 221 to 226. Subsequently, the average of each component of the normal vector for each 2D planar element 221-226 is calculated, and the vector whose components are the average of each component is calculated as the normal direction vector, which is the vector indicating the normal direction of the evaluation point.

[0020] 1-4. Local Coordinate System Definition Section 14 The local coordinate system definition unit 14 shown in Figure 1 defines the local coordinate system of the evaluation point 22a on the approximate two-dimensional tooth surface 22 based on the normal direction vector of the evaluation point 22a. The local coordinate system of the evaluation point 22a is defined as a coordinate system in which the evaluation point 22a is the origin, the plane whose normal direction vector is the normal direction vector of the evaluation point 22a is the xy plane of the local coordinate system, and the direction of the normal direction vector of the evaluation point 22a is the local z axis.

[0021] 1-5. Displacement amount calculation unit 15 The displacement calculation unit 15 in Figure 1 calculates the normal displacement of the evaluation point before and after gear assembly in the local coordinate system of the evaluation point. In this embodiment, all nodes of the approximate two-dimensional tooth surface 22 are used as evaluation points, and the normal displacement of each evaluation point is calculated by automatic processing.

[0022] 2. Tooth surface shape analysis method The calculation of tooth surface displacement before and after gear assembly using the tooth surface shape analysis method in this embodiment 1 will be described in detail using the flowchart shown in Figure 7. As shown in Figure 7, the tooth surface shape analysis method in this embodiment 1 first creates a 3D mesh as a 3D model 20 of the gear in step S1 (gear model creation step). The created 3D model 20 of the gear is stored in the gear model storage unit 11.

[0023] Subsequently, in step S2, the approximate two-dimensional tooth surface creation unit 12 creates an approximate two-dimensional tooth surface 22 consisting of a plurality of two-dimensional planar elements that approximate the tooth surface 21 in the three-dimensional model 20 of the gear (approximate two-dimensional tooth surface creation step). In this embodiment, the approximate two-dimensional tooth surface 22 is assumed to coincide with all nodes that appear on the tooth surface 21 of the three-dimensional mesh constituting the three-dimensional model 20 of the gear.

[0024] Next, in step S3, the normal direction vector calculation unit 13 calculates the normal direction vector of the evaluation point on the approximate two-dimensional tooth surface 22 (normal direction vector calculation step). In the normal direction vector calculation step, two-dimensional planar elements 221 to 226 that include the node which becomes the evaluation point 22a as constituent points are extracted, and the direction cosines cosα, cosβ, and cosγ of the two-dimensional planar elements 221 to 226 for each of the x, y, and z directions of the coordinate system in the three-dimensional model are calculated. These direction cosines are used as the normal vectors (cosα, cosβ, cosγ) of each two-dimensional planar element 221 to 226, and the average of each component of the normal vector of each two-dimensional planar element 221 to 226 is calculated, and the normal direction vector of the evaluation point is calculated by using the average value of each component as the component of the vector.

[0025] Subsequently, in step S4, the local coordinate system definition unit 14 defines the local coordinate system of the evaluation point on the approximate two-dimensional tooth surface 22 from the normal direction vector of the evaluation point (local coordinate system definition step). Then, in step S5, the displacement amount calculation unit 15 calculates the normal direction displacement of the evaluation point before and after gear assembly in the local coordinate system of the evaluation point (displacement amount calculation step). Then, the flow ends. The calculated normal direction displacement of the evaluation point can be used in the design of improved gear shapes, allowing for accurate evaluation of the effects of shape changes without creating prototypes.

[0026] 3. Verification test of analysis accuracy Next, a verification test was conducted to confirm the analysis accuracy of the tooth surface shape analysis device 1 of this embodiment 1. In this verification test, the measured data of tooth surface displacement was compared with the analysis results of the displacement obtained by the tooth surface shape analysis device 1. The measurement points for the measured displacement data were set to the tooth profile direction and tooth trace direction on the tooth surface 21, and the evaluation points for the displacement obtained by the tooth surface shape analysis device 1 were also set to the same positions.

[0027] The measured data in the tooth profile direction shown in Figure 8(a) and the analysis results in the tooth profile direction shown in Figure 8(b) showed generally similar displacement trends. Similarly, the measured data in the tooth trace direction shown in Figure 9(a) and the analysis results in the tooth trace direction shown in Figure 9(b) also showed generally similar displacement trends. These verification results confirmed that the analysis performed by the tooth surface shape analysis device 1 was sufficiently accurate.

[0028] 4. Effects According to the tooth surface shape analysis device 1 of Embodiment 1, an approximate two-dimensional tooth surface 22 is generated, consisting of multiple two-dimensional planar elements that approximate the tooth surface 21 in the gear model. Then, the normal direction vector of the evaluation point on the approximate two-dimensional tooth surface 22 is calculated, and the local coordinate system of the evaluation point on the approximate two-dimensional tooth surface 22 is defined from this normal direction vector. Subsequently, the normal direction displacement of the evaluation point is calculated based on the local coordinate system before and after the gear assembly. In this way, by approximating the tooth surface with an approximate two-dimensional tooth surface, the normal direction vector at the evaluation point on the tooth surface can be easily calculated even if the tooth surface is a curved surface. Furthermore, since the amount of computation is reduced, the normal direction vector can be easily calculated for all evaluation points across the entire tooth surface. As a result, tooth surface deformation when the gear is assembled can be analyzed with high accuracy, and the development period for tooth surface shapes can be shortened.

[0029] Furthermore, in this embodiment 1, the gear model is constructed using a three-dimensional mesh. This allows for the formation of the gear model with higher precision and improves the accuracy of the tooth surface shape analysis.

[0030] Furthermore, in this embodiment 1, the nodes in the approximate two-dimensional tooth surface 22 are included in the nodes that appear on the tooth surface 21 of the three-dimensional mesh in the three-dimensional model 20 of the gear. This makes it easy to set the two-dimensional planar elements that constitute the approximate two-dimensional tooth surface 22.

[0031] Furthermore, in this embodiment 1, the evaluation points on the approximate two-dimensional tooth surface 22 are selected from the nodes on the approximate two-dimensional tooth surface 22. This allows for more accurate calculation of the displacement at the evaluation points, thereby improving the accuracy of the tooth surface shape analysis.

[0032] Furthermore, in this embodiment 1, the normal direction vector calculation unit 13 calculates the direction cosines for each axis direction in the orthogonal three-axis coordinate system of a plurality of two-dimensional planar elements 221 to 226 including the evaluation point, and calculates a vector whose components in the orthogonal three-axis coordinate system are the average values ​​of the direction cosines for each axis direction. As a result, the local coordinate system definition unit 14 can easily define the local coordinate system of each evaluation point based on the normal direction vector.

[0033] Furthermore, according to the tooth surface shape analysis method of this embodiment 1, an approximate 2D tooth surface 22 is generated, consisting of multiple 2D planar elements that approximate the tooth surface 21 in the 3D model 20 of the gear. Then, the normal direction vector of the evaluation point on the approximate 2D tooth surface 22 is calculated, and a local coordinate system for the evaluation point on the approximate 2D tooth surface 22 is defined from this normal direction vector. Subsequently, the normal direction displacement amount of the evaluation point before the gear is assembled in the local coordinate system is calculated. In this way, by approximating the tooth surface with the approximate 2D tooth surface 22, the normal direction vector at the evaluation point on the tooth surface can be easily calculated even if the tooth surface is a curved surface. In addition, since the amount of calculation is reduced, the normal direction vector can be easily calculated for all evaluation points across the entire tooth surface. As a result, tooth surface deformation when the gear is assembled can be analyzed with high accuracy, and the development period for tooth surface shapes can be shortened.

[0034] As described above, according to the above embodiment, it is possible to provide a tooth surface shape analysis device and a tooth surface shape analysis method that can analyze tooth surface deformation when gears are assembled with high precision and shorten the development period for tooth surface shapes. [Explanation of symbols]

[0035] 1. Tooth surface shape analysis device 11 Gear Model Memory Unit 12 Approximate 2D tooth surface creation section 13. Normal Direction Vector Calculation Unit 14. Local Coordinate System Definition 15 Displacement Amount Calculation Unit 20 3D Models 21 Tooth surface 22 Approximate 2D tooth surface 22a Rating 30 Differential Case 31 Cylindrical part 32 Guard section 33 volts 221~226 2D plane element

Claims

1. A gear tooth shape analysis device for analyzing the amount of displacement of the tooth surface shape of a gear before and after assembly, A gear model storage unit that stores a three-dimensional model of the gear, An approximate two-dimensional tooth surface creation unit that creates an approximate two-dimensional tooth surface consisting of a plurality of two-dimensional planar elements that approximate the tooth surface in the three-dimensional model, A normal direction vector calculation unit calculates the normal direction vector of the evaluation point in the approximate two-dimensional tooth surface, A local coordinate system definition unit defines a local coordinate system for evaluation points on the approximate two-dimensional tooth surface based on the normal direction vector, A displacement calculation unit that calculates the normal displacement amount of the evaluation point before and after the assembly of the gear in the local coordinate system, A tooth surface shape analysis device, including a tooth surface shape analysis device.

2. The tooth surface shape analysis apparatus according to claim 1, wherein the three-dimensional model is composed of a three-dimensional mesh.

3. The tooth surface shape analysis apparatus according to claim 2, wherein the nodes in the approximate two-dimensional tooth surface are included in the nodes that appear on the tooth surface of the three-dimensional mesh in the three-dimensional model.

4. The tooth surface shape analysis apparatus according to claim 3, wherein the evaluation points on the approximate two-dimensional tooth surface are selected from the nodes on the approximate two-dimensional tooth surface.

5. The tooth surface shape analysis apparatus according to any one of claims 1 to 4, wherein the normal direction vector calculation unit calculates the direction cosines in each axis direction in the orthogonal three-axis coordinate system of the plurality of two-dimensional planar elements including the evaluation point, and calculates a vector whose components in the orthogonal three-axis coordinate system are the average values ​​of the direction cosines in each axis direction.

6. A gear tooth shape analysis method for analyzing the amount of displacement of the tooth surface shape before and after assembly, A gear model creation process for creating a three-dimensional model of the gear, A process for creating an approximate two-dimensional tooth surface, comprising creating an approximate two-dimensional tooth surface consisting of a plurality of two-dimensional planar elements that approximate the tooth surface in the three-dimensional model, A normal direction vector calculation step for calculating the normal direction vector of the evaluation point in the approximate two-dimensional tooth surface, A local coordinate system definition step, which defines the local coordinate system of the evaluation points on the approximate two-dimensional tooth surface from the normal direction vector, A displacement calculation step for calculating the normal displacement of the evaluation point before and after the assembly of the gear in the local coordinate system, A tooth surface shape analysis method, including the above.

Images