Design method suitable for inner and outer cone type blunt staggered angle hypoid gear

Abstract

The invention relates to a design method suitable for an inner and outer cone type blunt stagger angle hypoid gear, in particular to a general geometric design method suitable for an inner cone and outer cone type blunt stagger angle hypoid gear pair, and aims at a hypoid gear under a blunt stagger angle working condition. A conventional hypoid gear design method is difficult to meet the requirements of high bearing capacity and low error sensitivity under a blunt staggered angle working condition, so that undercutting and distortion of a tooth surface are often caused, and the meshing quality of a gear pair is influenced; according to the method, a geometric meshing model of the blunt staggered angle hypoid gear is established, meshing analysis and mechanical characteristics are combined, the tooth profile and machine tool parameters are optimized, it is ensured that flawless tooth surface design is achieved under the extreme working condition, the working performance and reliability of a gear pair are effectively improved, and the method is suitable for various high-load transmission systems.

Description

Technical Field

[0001] The present invention is a design technology for complex space transmission gear pairs, belongs to the field of transmission and drive, and relates to a design method for quasi-hyperid gears with obtuse staggered angles in the form of inner and outer cones, and in particular to a universal geometric design method for quasi-hyperid gear pairs with obtuse staggered angles in the form of inner and outer cones. Background Art

[0002] Due to the axial offset of the pinion and the unequal helix angles of the master and driven wheels, hypoid gears have significant advantages such as flexible spatial layout and smaller size at the same strength. This design effectively overcomes the low efficiency and high cost problems caused by complex mechanisms in the power transmission process at extreme scales, and also solves key problems such as narrow space and poor lubrication conditions caused by the adjustment of the installation angle of the power unit. Therefore, it has extremely high promotion and application value in the aerospace field. In helicopter transmission systems, there are a large number of obtuse-angle transmission forms, such as helicopter main reducer transmission and main reducer and splitter transmission. Obtuse-staggered-angle hypoid gears show significant application potential in these fields. Although many scholars have made significant progress in the design of orthogonal hypoid gears, existing methods still face the following problems in the design of obtuse-staggered-angle hypoid gears:

[0003] 1) The existing design method is not suitable for hypoid gears with obtuse staggered angles, and the solutions of the three major geometric relationships do not converge. Traditional methods are often based on conventional gear geometry models and fail to fully consider the complexity of obtuse staggered angles, resulting in instability during the solution process due to changes in contact conditions.

[0004] 2) The design parameter boundaries of blunt staggered hypoid gears are not clear, and tooth surface defects such as undercutting, sharpening, and tool interference exist. These defects are mainly caused by improper parameter selection during the design process and the lack of effective constraints, which leads to a mismatch between the tooth surface shape and the tool selection.

[0005] 3) The traditional meshing characteristic analysis method does not converge in the case of an obtuse staggered angle due to its special form. The surface distortion of the hypoid gear with an obtuse staggered angle is greater. When using finite element analysis, the quality of the meshing has a significant impact on the solution results.

[0006] Therefore, based on the shortcomings of existing orthogonal hypoid gear design methods and tooth surface defect avoidance technologies, researchers in this field should invent new design methods to overcome the above defects. Summary of the invention

[0007] In view of this, in order to solve the problem that the current manufacturing parameter calculation process of obtuse staggered angle quasi-curved gear pairs is incomplete, and the existing design methods are not fully applicable to the avoidance of tooth surface defects of obtuse staggered angle quasi-curved gears, resulting in root cutting and distortion of the tooth surface, and affecting the meshing quality of the gear pair, the present invention provides a design method for obtuse staggered angle quasi-curved gears suitable for internal and external cone forms and for internal and external cone forms.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] A design method for hypoid gears with blunt staggered angles in inner and outer cone forms, comprising the following steps:

[0010] Step S1: Establish a basic geometric parameter calculation process based on the three major spatial geometric relationships and the limiting normal curvature and the limiting pressure angle, and provide boundary conditions in the form of inner cone and outer cone;

[0011] The initial geometric parameters of the pitch cone are defined, and the three major geometric relationships between the two pitch cones when they are tangent in space at the tangent contact point M are derived. The two major conditions constraining the geometric characteristics of the obtuse staggered angle quasi-hyperbolic gear pair are obtained: the limiting normal curvature and the limiting pressure angle. By analyzing the relationship between the inner cone, outer cone, transmission ratio and shaft angle, the corresponding boundary conditions are established to ensure that the corresponding meshing requirements are met during the design process. This forms a pitch cone parameter calculation method that can effectively improve the design accuracy and processing efficiency of the gear pair and ensure the stable performance of the gear during use.

[0012] Step S2: Propose a machine tool processing parameter design method based on an improved local synthesis method taking contact behavior preset into consideration;

[0013] According to the tooth blank parameters of the hypoid gear with an obtuse staggered angle of the inner cone and the outer cone obtained in step S1, the contact characteristics are preset by using the improved local synthesis method, and the machine tool processing parameters are optimized, including the contact area size, the contact area direction and the transmission error, to ensure the appropriate contact state;

[0014] Step S3: establishing a method for avoiding tooth surface defects of hypoid gears with blunt staggered angles;

[0015] By calculating the position of the singular point in the tooth surface and adjusting the machine tool processing parameters inversely to avoid the singular point outside the tooth surface, root cutting is effectively avoided; the transmission ratio of the design is limited to be less than the maximum transmission ratio without tool interference, effectively avoiding tool interference; by adjusting the concave and convex machine tool root cone angles of the small wheel respectively, the uneven transition of the tooth root is avoided, thereby improving the performance of the gear;

[0016] Step S4: forming a meshing characteristic analysis method for blunt staggered angle hypoid gears in the form of inner cone and outer cone;

[0017] According to the machining parameters of the above-mentioned hypoid gear pair with obtuse staggered angles in the form of inner cone and outer cone, an accurate meshing model of hypoid gears with obtuse staggered angles in the form of inner cone and outer cone is established, and its meshing characteristics are analyzed.

[0018] Furthermore, in step S1, the three major geometric relationships of the two cone sections when they are tangent in space at the tangent contact point M are specifically:

[0019] The first geometric relationship is as follows:

[0020]

[0021] In the formula,

[0022]

[0023]

[0024] in and are the generatrix of the small wheel and large wheel pitch cone respectively, and are the rotation angles of the small wheel and large wheel pitch cone generatrix respectively, is the helix angle of the small wheel Helix angle with large wheel difference.

[0025] The second geometric relationship is the helix angle and transmission ratio of the small wheel and the large wheel at the reference point M. The relationship between:

[0026]

[0027] The third geometric relationship is as follows:

[0028]

[0029] After obtaining the above three geometric conditions, the limiting normal curvature and limiting pressure angle are used to constrain the geometric characteristics of the blunt staggered angle hypoid gear pair; according to the Wildhaber theory, the limiting pressure angle is expressed as follows:

[0030]

[0031] In the formula, the auxiliary coefficient , It is expressed as follows:

[0032]

[0033]

[0034] The limiting normal curvature is expressed as follows:

[0035]

[0036] In the formula, the auxiliary coefficient , It is expressed as follows:

[0037]

[0038]

[0039] By offset distance and the limiting normal curvature Two layers of iteration are performed for the iterative target to obtain the pitch cone data of the hypoid gear with an obtuse staggered angle.

[0040] Furthermore, in the preset contact characteristics of the local synthesis method in step S2, it is necessary to determine the position of the reference contact point P within the large gear tooth surface, as shown below:

[0041]

[0042] Three conditions are preset at the reference contact point P to control the contact characteristics, namely: (1) the semi-major axis length of the contact ellipse ; (2) Angle between the contact line and the tooth root direction and (3) the first-order derivative of the transmission error Based on the above preset conditions, the initial values ​​of the machine tool processing parameters of the large wheel and the small wheel are calculated, and the machine tool parameters are adjusted to avoid tooth surface defects in order to obtain a good tooth surface in the end.

[0043] Furthermore, in step S3, in order to avoid the influence of tool interference, at a specific axis angle, the selected transmission ratio cannot exceed the maximum transmission ratio determined by the following formula:

[0044]

[0045] Undercutting is predicted and avoided by using local singular points, which are defined by the following equation:

[0046]

[0047] In the formula, and In the coordinate system Tool speed and relative speed defined in;

[0048] When the concave and convex surfaces of the hypoid gear pinion are machined using the five-cut method, resulting in an uneven transition at the tooth root, in order to solve this defect, the machine tool root taper angles of the concave and convex surfaces need to be adjusted separately. and ; The initial value of the machine tool root taper angle is determined by the following formula:

[0049]

[0050] Through the above process, the machine tool parameters of the concave and convex surface of the hypoid gear pinion with obtuse staggered angles in the form of inner cone and outer cone are obtained to preset contact characteristics and avoid tooth surface defects.

[0051] Furthermore, step S4 uses the ABAQUS finite element gear tooth load contact analysis method to verify the consistency between the meshing characteristics and the preset contact behavior, compares the gear tooth load contact analysis results with the preset contact behavior, and optimizes the meshing characteristics analysis model.

[0052] It provides theoretical support for the design and manufacture of hypoid gears with obtuse staggered angles in the form of inner and outer cones, ensuring their reliability and performance stability in high-load applications.

[0053] The beneficial effects of the present invention are:

[0054] 1. The design method of the obtuse staggered angle hypoid gears with inner and outer cone forms disclosed in the present invention is based on the calculation process of basic geometric parameters of the obtuse staggered angle hypoid gears with three major spatial geometric relationships and the limiting normal curvature and the limiting pressure angle. According to the relationship between the initial value of the large wheel pitch cone angle and the transmission ratio and the shaft angle, the boundary conditions of the two configurations of the obtuse staggered angle hypoid gears with inner and outer cones are derived, and the reason why the large wheel pitch cone angle exceeds 90° and evolves into an inner cone form during the pitch cone design process is analyzed, which solves the problem that the traditional design method cannot take into account the calculation of basic geometric parameters of both the inner cone and the outer cone.

[0055] 2. The present invention discloses a design method for quasi-hyperbolic gears with obtuse staggered angles in the form of inner and outer cones. It is a machine tool processing parameter design method that takes into account contact behavior preset and tooth surface defect avoidance based on an improved local synthesis method, and forms a machine tool parameter calculation method for preset contact area position, contact area size, contact area direction, and transmission error size.

[0056] 3. The present invention discloses a design method for obtuse-staggered-angle quasi-hyperid gears with inner and outer cone forms, and a method for avoiding tooth surface defects of obtuse-staggered-angle quasi-hyperid gears. Aiming at the occurrence of tooth surface defects such as root cutting and tooth tip sharpening, a set of machine tool parameter design processes for quickly adjusting machine tool parameters to avoid tooth surface defects are formed, which provides a scientific basis for the high-quality manufacturing of obtuse-staggered-angle quasi-hyperid gears.

[0057] 4. The present invention discloses a design method for obtuse-staggered hypoid gears with inner and outer cone forms, and an analysis method for meshing characteristics of obtuse-staggered hypoid gears with inner and outer cone forms. The finite element gear tooth load contact analysis method is used to analyze the obtuse-staggered hypoid gears with inner and outer cone forms respectively. Based on the above analysis results, the meshing characteristic analysis model is optimized to achieve efficient control of the contact characteristics of obtuse-staggered hypoid gears.

[0058] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0060] Figure 1 is the geometric relationship diagram of the obtuse staggered angle hypoid gear of the present invention, wherein Figure 1 (a) is the relationship diagram of the inner cone and the pitch cone. Figure 1 (b) is the geometric relationship diagram of the inner cone;

[0061] Figure 2 It is a closed diagram of the inner and outer cone boundaries of the obtuse staggered angle hypoid gear of the present invention;

[0062] Figure 3 This is a flow chart of the improved local synthesis method in step S2 of the present invention;

[0063] Figure 4 The present invention is a diagram of the inner cone gear blank machining process and tool interference phenomenon, wherein Figure 4 (a) is the inner cone gear blank machining process. Figure 4 (b) Tool interference phenomenon;

[0064] Figure 5 The meshing model of the hypoid gear with an obtuse staggered angle of the inner cone and the outer cone of the present invention is shown in FIG. Figure 5 (a) is the meshing model of hypoid gears with blunt staggered angles in the form of external cones. Figure 5 (b) is the meshing model of hypoid gears with blunt staggered angles in the form of an inner cone;

[0065] Figure 6 is the finite element mesh model of the obtuse staggered angle hypoid gear of the present invention, wherein Figure 6 (a) is the mesh model of the hypoid gear with an inner cone configuration and an obtuse staggered angle. Figure 6(b) is the mesh model of hypoid gear with blunt staggered angle in external cone configuration;

[0066] Figure 7 The finite element analysis results of the two types of hypoid gears with obtuse staggered angles in the present invention are shown in Figure 2. Figure 7 (a) is the finite element analysis result of the hypoid gear with an inner cone configuration and an obtuse staggered angle. Figure 7 (b) is the finite element analysis result of the hypoid gear with an obtuse staggered angle in the external cone configuration; DETAILED DESCRIPTION

[0067] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0068] A method for designing a hypoid gear with an obtuse staggered angle and suitable for inner and outer cone forms, comprising the following steps:

[0069] Step S1: Establish a basic geometric parameter calculation process based on the three major spatial geometric relationships and the limiting normal curvature and limiting pressure angle, and provide boundary conditions in the form of inner cone and outer cone.

[0070] The initial geometric parameters of the pitch cone are defined, and the three major geometric relationships between the two pitch cones when they are tangent in space at the tangent contact point M are derived. The two major conditions constraining the geometric characteristics of the obtuse staggered angle quasi-hyperbolic gear pair are obtained: the limiting normal curvature and the limiting pressure angle. By analyzing the relationship between the inner cone, outer cone, transmission ratio and shaft angle, the corresponding boundary conditions are established to ensure that the corresponding meshing requirements are met during the design process. This forms a pitch cone parameter calculation method that can effectively improve the design accuracy and processing efficiency of the gear pair and ensure the stable performance of the gear during use.

[0071] Specifically: Obtuse staggered angle hypoid gears can be divided into two configurations: inner cone form and outer cone form. Figure 1 is the geometric relationship diagram of the obtuse staggered hypoid gear, where Figure 1 (a) is the relationship diagram of the inner cone and the pitch cone. Figure 1 (b) is the geometric relationship diagram of the inner cone form; the process of solving the geometric parameters of the blunt staggered angle hypoid gear applicable to both the inner cone and the outer cone configuration is to obtain the geometric parameters of the blunt staggered angle hypoid gear through (1) the pitch cone angle of the small wheel ; (2) Pitch angle of the large wheel ; (3) Axis angle These three known parameters are used to solve the small wheel. The large wheel satisfies all the design parameters of the spatial contact point M and eventually evolves into the following three geometric relationships.

[0072] The first geometric relationship is as follows:

[0073]

[0074] In the formula,

[0075]

[0076]

[0077] in and are the generatrix of the small wheel and large wheel pitch cone respectively, and are the rotation angles of the small wheel and large wheel pitch cone generatrix respectively, is the helix angle of the small wheel Helix angle with large wheel difference.

[0078] The second geometric relationship is the helix angle and transmission ratio of the small wheel and the large wheel at the reference point M. The relationship between:

[0079]

[0080] The third geometric relationship is as follows:

[0081]

[0082] After obtaining the above three geometric conditions, it is necessary to use the limiting normal curvature and limiting pressure angle to constrain the geometric characteristics of the obtuse staggered angle hypoid gear pair. According to Wildhaber theory, the limiting pressure angle can be expressed as follows:

[0083]

[0084] In the formula, the auxiliary coefficient , It can be expressed as follows:

[0085]

[0086]

[0087] The limiting normal curvature can be expressed as follows:

[0088]

[0089] In the formula, the auxiliary coefficient , It can be expressed as follows:

[0090]

[0091]

[0092] By offset distance and the limiting normal curvature Two-layer iteration for the iteration target can obtain the pitch cone data of the obtuse staggered angle hypoid gear. The geometric design process of the obtuse staggered angle hypoid gear is not sensitive to the choice of gear tooth shrinkage method. The tooth blank parameters of the obtuse staggered angle hypoid gear can be calculated by reasonably selecting one of them.

[0093] Figure 2 The closed boundary diagram of the inner and outer cones of the obtuse staggered angle hypoid gear is shown in Figure 1. The inner and outer cones of the obtuse staggered angle hypoid gear can be configured by the large pitch cone angle. Whether it exceeds 90°, when the large wheel pitch angle When the pitch angle exceeds 90°, it is an inner cone. If it does not exceed 90°, it is defined as an external cone. The initial value of the large pitch cone angle can be To approximately determine the initial value of the large wheel pitch cone angle It can be expressed as follows:

[0094]

[0095] The two configurations of inner and outer cones of blunt staggered hypoid gears can be obtained by the initial value of the large pitch cone angle. Whether it exceeds 90° is used to distinguish.

[0096] Step S2: Propose a machine tool processing parameter design method based on an improved local synthesis method that considers contact behavior presets.

[0097] After calculating the tooth blank data of the hypoid gear pair with obtuse staggered angles of the inner cone and outer cone according to the above content, it is necessary to calculate the tool machining parameters based on the improved local synthesis method and tooth surface defect avoidance method. Figure 3 The flowchart of the improved local synthesis method is shown below. First, the position of the reference contact point P in the large gear tooth surface needs to be determined, as shown below:

[0098]

[0099] Three conditions are preset at the reference contact point P to control the contact characteristics, namely: (1) the semi-major axis length of the contact ellipse ; (2) Angle between the contact line and the tooth root direction and (3) the first-order derivative of the transmission error Based on the above preset conditions, the initial values ​​of the machine tool processing parameters of the large wheel and the small wheel can be calculated. Through the meshing characteristic results, according to the contact position, whether the tooth root transition is smooth, the size of the contact area, the direction of the contact area, and the size of the transmission error, the position of the reference contact point P, the three preset conditions, and the machine tool root cone angle are reversed. After continuous iteration, the final machine tool parameters are calculated to avoid tooth surface defects and obtain the final good tooth surface.

[0100] Step S3: Establishing a method for avoiding the tooth surface defects of hypoid gears with obtuse staggered angles. Figure 4 (a) is the inner cone gear blank machining process. Figure 4 (b) Tool interference phenomenon; the shaft angle of the obtuse staggered hypoid gear transmission form is large, which often makes the large wheel pitch cone angle exceed 90°. At this time, the pitch cone is an inner cone. Although the impact on the performance of the gear pair is small, it has a certain impact on the processing and manufacturing process. In order to avoid the impact of tool interference, at a specific shaft angle, the selected transmission ratio cannot exceed the maximum transmission ratio determined by the following formula

[0101]

[0102] Due to the particularity of obtuse staggered angle transmission, undercutting is likely to occur on the pinion tooth surface of the obtuse staggered angle hypoid gear. Undercutting can be predicted and avoided by using local singular points. The singular points on the tooth surface can be defined by the following formula:

[0103]

[0104] In the formula, and In the coordinate system Tool speed and relative speed defined in .

[0105] The concave and convex surfaces of the hypoid gear pinion with staggered angles are machined using the five-cut method, which may result in an uneven transition at the tooth root. To solve this defect, the machine tool root taper angles of the concave and convex surfaces need to be adjusted separately. and The initial value of the machine tool root taper angle can be determined by the following formula:

[0106]

[0107] Through the above process, the machine tool parameters of the concave and convex surface of the hypoid gear pinion with obtuse staggered angles in the form of inner cone and outer cone that preset contact characteristics and avoid tooth surface defects can be obtained.

[0108] Step S4: Form an analysis method for the meshing characteristics of hypoid gears with blunt staggered angles suitable for inner and outer cones. After calculating the machine tool parameters according to the above process, the tooth surface point sets of the large and small wheels can be obtained by coordinate transformation and solving the meshing equations, and the following can be established: Figure 5 The meshing model of hypoid gears with two obtuse staggered angles, inner cone and outer cone, is shown in the figure. Figure 5 (a) is the meshing model of hypoid gears with blunt staggered angles in the form of external cones. Figure 5 (b) is the meshing model of hypoid gears with blunt staggered angles in the form of an inner cone.

[0109] The actual meshing characteristics of the meshing model obtained by the initial values ​​of the machine tool parameters obtained by the improved local synthesis method may not be consistent with the preset conditions. It is necessary to quickly adjust the machine tool parameters based on the results of the meshing characteristics analysis to obtain good meshing characteristics.

[0110] To perform finite element gear tooth contact analysis on the meshing model obtained above using ABAQUS, the geometric model must first be meshed. At this point, not only the quality of the mesh must be guaranteed, but also the overall number of meshes must be controlled to avoid inaccurate solution results and excessive calculations.

[0111] When meshing, since the finite element analysis of the entire gear is too laborious, we chose to cut out 7 teeth of the large gear for finite element analysis to reduce meshing and subsequent calculations. The contacting tooth surfaces of the two gears are meshed with 110×30 meshes, while the non-contact surfaces are meshed with sparse meshes, which can reduce the amount of calculations while ensuring the accuracy of the solution.

[0112] Figure 6 It is the finite element mesh model of the hypoid gear with an obtuse staggered angle between the inner cone and the outer cone, where Figure 6 (a) is the mesh model of the hypoid gear with an inner cone configuration and an obtuse staggered angle. Figure 6 (b) is the mesh model of the outer cone configuration obtuse staggered angle hypoid gear; the mesh type of the large wheel is C3D8R, and the mesh type of the small wheel is C3D10. The Young's modulus of the gear pairs of the two configurations is set to 210GPa, and the Poisson's ratio is set to 0.3. A torque load of 100NM is applied to the large wheels of the two configurations, and finite element analysis is performed. The results are shown in the figure. Figure 7 As shown, Figure 7 (a) is the finite element analysis result of the hypoid gear with an inner cone configuration and an obtuse staggered angle. Figure 7 (b) is the finite element analysis result of the hypoid gear with an obtuse staggered angle and an external cone configuration.

[0113] A series of meshing point positions and contact ellipses of the designed inner cone and outer cone blunt staggered angle quasi-hyperbolic gear pairs are obtained through the finite element analysis method. Based on this, the machine tool parameters are adjusted to effectively avoid the occurrence of poor contact behavior on the tooth surface.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A design method for hypoid gears with blunt staggered angles in inner and outer cone forms, characterized in that: The following steps are involved: Step S1: Establish a basic geometric parameter calculation process based on the three major spatial geometric relationships and the limiting normal curvature and the limiting pressure angle, and provide boundary conditions in the form of inner cone and outer cone; The initial geometric parameters of the pitch cone are defined, and the three major geometric relationships between the two pitch cones when they are tangent in space at the tangent contact point M are derived, and the two major conditions constraining the geometric characteristics of the blunt staggered angle quasi-hyperbolic gear pair are obtained: the limiting normal curvature and the limiting pressure angle; by analyzing the relationship between the inner cone, the outer cone, the transmission ratio and the shaft angle, the corresponding boundary conditions are established to ensure that the corresponding meshing requirements are met during the design process, forming a pitch cone parameter calculation method that can effectively improve the design accuracy and processing efficiency of the gear pair and ensure the stable performance of the gear in use; Step S2: Propose a machine tool processing parameter design method based on an improved local synthesis method taking contact behavior preset into consideration; According to the tooth blank parameters of the hypoid gear with an obtuse staggered angle of the inner cone and the outer cone obtained in step S1, the contact characteristics are preset by using the improved local synthesis method, and the machine tool processing parameters are optimized, including the contact area size, the contact area direction and the transmission error, to ensure the appropriate contact state; Step S3: establishing a method for avoiding tooth surface defects of hypoid gears with blunt staggered angles; By calculating the position of the singular point in the tooth surface and adjusting the machine tool processing parameters inversely to avoid the singular point outside the tooth surface, root cutting is effectively avoided; the transmission ratio of the design is limited to be less than the maximum transmission ratio without tool interference, effectively avoiding tool interference; by adjusting the concave and convex machine tool root cone angles of the small wheel respectively, the uneven transition of the tooth root is avoided, thereby improving the performance of the gear; Step S4: forming a meshing characteristic analysis method for blunt staggered angle hypoid gears in the form of inner cone and outer cone; According to the machining parameters of the above-mentioned hypoid gear pair with obtuse staggered angles in the form of inner cone and outer cone, an accurate meshing model of hypoid gears with obtuse staggered angles in the form of inner cone and outer cone is established, and its meshing characteristics are analyzed.

2. The design method for hypoid gears with blunt staggered angles in inner and outer cone forms as claimed in claim 1, characterized in that: In step S1, the three major geometric relationships of the two cone sections when they are tangent in space at the tangent contact point M are as follows: The first geometric relationship is as follows: In the formula, in and are the generatrix of the small wheel and large wheel pitch cone respectively, and are the rotation angles of the small wheel and large wheel pitch cone generatrix respectively, is the helix angle of the small wheel Helix angle with large wheel difference; The second geometric relationship is the helix angle and transmission ratio of the small wheel and the large wheel at the reference point M. The relationship between: The third geometric relationship is as follows: After obtaining the above three geometric conditions, the limiting normal curvature and limiting pressure angle are used to constrain the geometric characteristics of the blunt staggered angle hypoid gear pair; according to the Wildhaber theory, the limiting pressure angle is expressed as follows: In the formula, the auxiliary coefficient , It is expressed as follows: The limiting normal curvature is expressed as follows: In the formula, the auxiliary coefficient , It is expressed as follows: By offset distance and the limiting normal curvature Two layers of iteration are performed for the iterative target to obtain the pitch cone data of the hypoid gear with an obtuse staggered angle.

3. The design method for hypoid gears with blunt staggered angles in inner and outer cone forms as claimed in claim 2, characterized in that: In the local synthesis method preset contact characteristics in step S2, it is necessary to determine the position of the reference contact point P within the large gear tooth surface, as shown below: Three conditions are preset at the reference contact point P to control the contact characteristics, namely: (1) the semi-major axis length of the contact ellipse ; (2) Angle between the contact line and the tooth root direction and (3) the first-order derivative of the transmission error Based on the above preset conditions, the initial values ​​of the machine tool processing parameters of the large wheel and the small wheel are calculated, and the machine tool parameters are adjusted to avoid tooth surface defects in order to obtain a good tooth surface in the end.

4. The design method for hypoid gears with blunt staggered angles in inner and outer cone forms as claimed in claim 3, characterized in that: In step S3, in order to avoid the influence of tool interference, at a specific axis angle, the selected transmission ratio cannot exceed the maximum transmission ratio determined by the following formula: Undercutting is predicted and avoided by using local singular points, which are defined by the following equation: In the formula, and In the coordinate system Tool speed and relative speed defined in; When the concave and convex surfaces of the hypoid gear pinion are machined using the five-cut method, resulting in an uneven transition at the tooth root, in order to solve this defect, the machine tool root taper angles of the concave and convex surfaces need to be adjusted separately. and ; The initial value of the machine tool root taper angle is determined by the following formula: Through the above process, the machine tool parameters of the concave and convex surface of the hypoid gear pinion with obtuse staggered angles in the form of inner cone and outer cone are obtained to preset contact characteristics and avoid tooth surface defects.

5. The design method for hypoid gears with blunt staggered angles for inner and outer cones as claimed in claim 4, characterized in that: Step S4 uses the ABAQUS finite element gear tooth load contact analysis method to verify the consistency between the meshing characteristics and the preset contact behavior, compares the gear tooth load contact analysis results with the preset contact behavior, and optimizes the meshing characteristics analysis model.

Images