Method for calculating contact stress of ball cage type constant velocity universal joint

Abstract

The invention discloses a ball cage type constant velocity universal joint contact stress calculation method, and belongs to the technical field of constant velocity universal joints, and the method comprises the following steps: obtaining a pre-constructed raceway geometric model; geometric parameters of the steel balls are obtained according to the raceway geometric model and the geometric relation; according to the raceway geometric model and the geometric parameters of the steel balls, the curvature sum of contact points of the steel balls and the raceway is obtained; and according to the Hertz contact theory and the curvature sum, the maximum contact stress of the ball cage type constant velocity universal joint in contact with the raceway is calculated. The method can solve the problems that an existing calculation method is large in calculation amount, time-consuming and high in requirement for calculation resources.

Description

Technical Field

[0001] The invention relates to the technical field of constant velocity universal joints, in particular to a contact stress calculation method for a ball cage type constant velocity universal joint. Background Art

[0002] Ball-cage constant velocity joints are commonly used in automotive transmission systems, especially front-wheel drive vehicles. Their function is to transmit power at different angles while maintaining constant speed rotation. Contact stress refers to the stress in the contact area between the steel balls inside the joint and the raceways of the spider and bell housing. Excessive contact stress can cause wear and fatigue in the ball-cage constant velocity joint, affecting its life and reliability. Therefore, the contact stress must be accurately verified during design and optimization. Existing methods usually use numerical simulations such as finite element analysis to calculate the contact stress, but finite element analysis is often computationally intensive, time-consuming, and requires high computing resources. Summary of the Invention

[0003] The present invention aims to provide a method for calculating contact stress in a constant velocity joint. The method uses the corresponding curvature sums obtained based on different raceway models and the geometric parameters of the steel balls on the inner and outer raceways of the different raceway models. The method then calculates the maximum contact stress between the constant velocity joint and the raceway using the corresponding curvature sums. This method allows for rapid calculation of the contact stress of the constant velocity joint while ensuring accurate contact stress calculation. The present invention is achieved through the following technical solutions.

[0004] In a first aspect, the present invention provides a method for calculating contact stress of a ball cage type constant velocity universal joint, comprising:

[0005] Get the pre-built raceway geometry model;

[0006] Obtaining geometric parameters of the steel ball according to the raceway geometric model and geometric relationship;

[0007] The curvature and the contact point between the steel ball and the raceway are obtained according to the raceway geometric model and the geometric parameters of the steel ball. ;

[0008] According to Hertz contact theory and the curvature and Calculate the maximum contact stress between the ball cage constant velocity joint and the raceway.

[0009] Optionally, the raceway geometric model includes an arc-shaped raceway geometric model and an elliptical raceway geometric model; the arc-shaped raceway includes an arc-shaped inner raceway and an arc-shaped outer raceway, and the elliptical raceway includes an elliptical inner raceway and an elliptical outer raceway;

[0010] The geometric parameters of the steel ball include the center O of the steel ball, the diameter D of the steel ball w , steel ball rotation diameter D;

[0011] The center of the arc raceway O1, the contact point C between the steel ball and the arc inner and outer raceways, the rotation center of the steel ball on the arc inner raceway O2, the rotation center of the steel ball on the arc outer raceway O3,

[0012] Elliptical raceway center O1 ′ , the contact point C between the steel ball and the inner and outer raceways of the elliptical raceway ′ , the center of rotation of the steel ball on the elliptical inner raceway O2 ′ , the steel ball rotation center O3 on the elliptical outer raceway ′ .

[0013] Optionally, the curvature of the contact point between the steel ball and the raceway and Including the curvature of the contact point between the steel ball and the arc inner raceway and , the curvature of the contact point between the steel ball and the arc outer raceway and , the curvature of the contact point between the steel ball and the elliptical inner raceway and , the curvature of the contact point between the steel ball and the elliptical outer raceway and .

[0014] Optionally, the curvature of the contact point between the steel ball and the arc-shaped inner raceway is Calculated by the following formula:

[0015] ;

[0016] Where, is the curvature coefficient of the arc raceway, and D is the rotation diameter of the steel ball.

[0017] Optionally, the curvature of the contact point between the steel ball and the arc-shaped outer raceway is Calculated by the following formula:

[0018] .

[0019] Optionally, the curvature of the contact point between the steel ball and the elliptical inner raceway is Calculated by the following formula:

[0020] ;

[0021] Where, is the curvature coefficient of the elliptical raceway, It is the angle between the line connecting the center O of the steel ball and the contact point C' of the elliptical raceway and the radial plane perpendicular to the axis of rotation of the steel ball.

[0022] Optionally, the curvature of the contact point between the steel ball and the elliptical outer raceway and Calculated by the following formula:

[0023] ;

[0024] Where, is the curvature coefficient of the elliptical raceway, It is the angle between the line connecting the center O of the steel ball and the contact point C' of the elliptical raceway and the radial plane perpendicular to the axis of rotation of the steel ball around the center of rotation.

[0025] Optionally, the maximum contact stress between the ball cage constant velocity joint and the raceway Calculated by the following formula:

[0026] ;

[0027] In the formula, the contact between the arc-shaped raceway and the elliptical raceway and the steel ball is point contact, and point contact will form an elliptical contact area; a* and b* are the major and minor axes of the elliptical contact area formed under point contact according to Hertz contact theory, respectively; P is the contact load between the steel ball and the raceway, which is calculated by the following formula:

[0028] ;

[0029] Where T is the torque applied to the steel balls, Z is the number of steel balls, and L is the distance from the contact point between the steel ball center O and the raceway to the steel ball's rotation center.

[0030] Optionally, the distance L between the steel ball center O and the contact point of the raceway to the steel ball rotation center includes:

[0031] The distance L between the steel ball center O and the contact point C of the arc inner raceway to the steel ball rotation center O2 i ; The distance L between the steel ball center O and the contact point C of the arc-shaped outer raceway to the steel ball rotation center O3 e ; The distance L between the steel ball center O and the contact point C' of the elliptical inner raceway to the steel ball rotation center O2' i '; The distance L between the steel ball center O and the contact point C' of the elliptical inner raceway to the steel ball rotation center O3' e ′; where L i , L e , L i ′ and L e ' are calculated by the following formulas:

[0032] ;

[0033] ;

[0034] ;

[0035] .

[0036] In a second aspect, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon, characterized in that when the computer program / instruction is executed by a processor, the steps of the method for calculating the contact stress of a ball cage type constant velocity universal joint described in the first aspect are implemented.

[0037] Beneficial effects:

[0038] The contact stress calculation method of the ball cage type constant velocity universal joint proposed in the present invention can first calculate the structural parameters of the raceway through the geometric model and geometric relationship of the raceway, thereby uniquely determining the structure of the raceway, thereby improving the accuracy of subsequent contact stress calculation; secondly, the present invention comprehensively considers and calculates the maximum contact stress to which the steel ball is subjected when moving in two different types of arc-shaped and elliptical raceways, so that in practical applications, the maximum contact stress between the steel ball and the raceway can be controlled according to actual needs, thereby improving the service life of the ball cage type constant velocity universal joint; finally, the maximum contact stress is calculated using the formula designed by the present invention for the process of calculating the maximum contact stress, thereby improving the speed of the calculation process while ensuring the accuracy of the calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The figure shows a flow chart of the contact stress calculation method of the ball cage type constant velocity universal joint of the present invention;

[0040] Figure 2 The figure shows a schematic diagram of the geometric model of the arc-shaped raceway of the present invention;

[0041] Figure 3 Shown is a schematic diagram of the geometric model of the elliptical raceway of the present invention;

[0042] Figure 4 Shown is a schematic diagram of a ball cage type constant velocity universal joint (arc-shaped raceway) model of the present invention;

[0043] Figure 5 Shown is a simplified model schematic diagram of the ball cage type constant velocity universal joint (arc-shaped raceway) of the present invention;

[0044] Figure 6 The figure shows a schematic diagram of simulation results of an arc-shaped ball cage constant velocity universal joint according to the present invention;

[0045] Figure 7 Shown is a schematic diagram of simulation results of an elliptical roller ball cage type constant velocity universal joint of the present invention. DETAILED DESCRIPTION

[0046] The following is a further description with reference to the accompanying drawings and specific embodiments. It should be understood that in the description of the present invention, the terms "first," "second," etc. are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Therefore, a feature designated "first," "second," etc. may explicitly or implicitly include one or more of the features.

[0047] Example 1

[0048] This embodiment introduces a method for calculating contact stress of a ball-and-cage constant velocity universal joint, including:

[0049] Get the pre-built raceway geometry model;

[0050] Obtaining geometric parameters of the steel ball according to the raceway geometric model and geometric relationship;

[0051] The curvature and the contact point between the steel ball and the raceway are obtained according to the raceway geometric model and the geometric parameters of the steel ball. ;

[0052] According to Hertz contact theory and the curvature and Calculate the maximum contact stress between the ball cage constant velocity joint and the raceway.

[0053] Example 2

[0054] Based on Example 1, this example introduces a specific implementation process of a method for calculating contact stress of a ball cage type constant velocity universal joint, such as Figure 1 As shown, specifically including the following:

[0055] In a specific implementation of the embodiment of the present invention, the raceway geometric model includes an arc raceway geometric model such as Figure 2 As shown, and the elliptical raceway geometry model is as follows Figure 3 As shown; the arc-shaped raceway includes an arc-shaped inner raceway and an arc-shaped outer raceway, and the elliptical raceway includes an elliptical inner raceway and an elliptical outer raceway. Figure 4 Schematic diagram of the ball cage constant velocity universal joint (arc raceway) model. Figure 4 The inner raceway is the raceway between the steel ball and the planetary sleeve, and the outer raceway is the raceway between the steel ball and the bell housing.

[0056] 1. Construct the raceway geometry model and determine the raceway geometry parameters

[0057] In a specific implementation of the embodiment of the present invention, Figure 2 and Figure 3 The geometric parameters of the raceway include the center of the ball O, the diameter of the ball D w , steel ball rotation diameter D;

[0058] The center of the arc-shaped raceway O1, the contact point C between the steel ball and the arc-shaped inner and outer raceways, the rotation center of the steel ball on the arc-shaped inner raceway O2, and the rotation center of the steel ball on the arc-shaped outer raceway O3.

[0059] Elliptical raceway center O1 ′ , the contact point C between the steel ball and the inner and outer raceways of the elliptical raceway ′ , the center of rotation of the steel ball on the elliptical inner raceway O2 ′ , the steel ball rotation center O3 on the elliptical outer raceway ′ .

[0060] exist Figure 1 In the figure, the distance between OO1 is: , (1)

[0061] Where f1 is the curvature coefficient of the arc raceway, .

[0062] exist Figure 2 Where β is the contact angle, which is the angle between the line connecting the center O of the steel ball and the contact point C′ of the elliptical raceway and the radial plane perpendicular to the axis of rotation of the steel ball around the center of rotation, and a and b are the major and minor semi-axes of the ellipse, respectively.

[0063] The contact point C between the steel ball and the raceway ′ Substitute (x0,y0) into the elliptic equation and its first-order and second-order derivatives are:

[0064] ; (2)

[0065] ; (3)

[0066] ;(4)

[0067] Let C ′ The instantaneous curvature at the point is , is the instantaneous curvature radius, then C ′ The second-order derivative of a point on the ellipse can also be expressed as:

[0068] ; (5)

[0069] Where,

[0070] Combining formula (4) and formula (5), we can get:

[0071] ; (6)

[0072] Combining equations (2), (3), and (6) we can get a and b:

[0073] ; (7)

[0074] Introducing the raceway curvature coefficient have:

[0075] (8)

[0076] Where, It is the angle between the line connecting the center O of the steel ball and the contact point C' of the elliptical raceway and the radial plane perpendicular to the axis of rotation of the steel ball.

[0077] Substituting formula (8) into formula (7) yields:

[0078] ; (9)

[0079] In practical applications, after obtaining the above parameters, the structures of the two raceways can be uniquely determined.

[0080] 2. Calculate the curvature and

[0081] In a specific embodiment of the present invention, the curvature of the contact point between the steel ball and the raceway is Including the curvature of the contact point between the steel ball and the arc inner raceway and , the curvature of the contact point between the steel ball and the arc outer raceway and , the curvature of the contact point between the steel ball and the elliptical inner raceway and , the curvature of the contact point between the steel ball and the elliptical outer raceway and .

[0082] (1) For the contact between the steel ball and the arc-shaped inner raceway, the steel ball is pre-set as contact body 1, the inner raceway is pre-set as contact body 2, the axial plane of the contact tangent point C is pre-set as principal plane I, and the other plane orthogonal to principal plane I is pre-set as principal plane II. The convex surface of the two contact planes is positive, and the concave surface is negative.

[0083] (2) For the contact between the steel ball and the arc-shaped outer raceway, the steel ball is pre-set as contact body 1, the outer raceway is pre-set as contact body 3, the axial plane of the contact tangent point C is pre-set as principal plane III, and the other plane orthogonal to principal plane III is pre-set as principal plane IV. The convex surface of the two contact planes is positive, and the concave surface is negative.

[0084] (3) For the contact between the steel ball and the elliptical inner raceway, the steel ball is pre-set as contact body 1, the inner raceway is pre-set as contact body 2, and the contact tangent point C is pre-set as ′ The axial plane is the main plane I ′ , and the main plane Ⅰ ′ The other orthogonal plane is the principal plane Ⅱ ′ The convex surface of the two contact planes is positive and the concave surface is negative.

[0085] (4) For the contact between the steel ball and the elliptical outer raceway, the steel ball is pre-set as contact body 1, the inner raceway is pre-set as contact body 3, and the contact tangent point C is pre-set as ′ The axial plane is the main plane III ′ , and the main plane III ′ The other orthogonal plane is the principal plane Ⅳ ′ The convex surface of the two contact planes is positive and the concave surface is negative.

[0086] 2.1 Calculate the curvature and

[0087] In a specific embodiment of the present invention, the curvature of the steel ball and the arc-shaped inner raceway is Calculated by the following formula:

[0088] ;(10)

[0089] Where, is the equivalent curvature radius of the contact point C between the steel ball and the arc-shaped inner raceway on the main plane I, is the equivalent radius of curvature of the contact point C between the steel ball and the arc-shaped inner raceway on the main plane II, and is calculated by the following formulas:

[0090] ;(11)

[0091] Where, and They are respectively the curvature radius of the steel ball on the main plane I, the curvature radius of the steel ball on the main plane II, the curvature radius of the arc-shaped inner raceway on the main plane I, and the curvature radius of the arc-shaped inner raceway on the main plane II, and are calculated by the following formulas:

[0092] ;(12)

[0093] Substituting formula (11) and formula (12) into formula (10) yields:

[0094] ; (13)

[0095] 2.2 Calculate the curvature and

[0096] In a specific implementation of the embodiment of the present invention, the curvature of the steel ball and the arc-shaped outer raceway is Calculated by the following formula:

[0097] ;(14)

[0098] Where, is the equivalent curvature radius of the contact point C between the steel ball and the arc-shaped outer raceway on the main plane III, is the equivalent radius of curvature of the contact point C between the steel ball and the arc-shaped outer raceway on the main plane IV, and is calculated by the following formulas:

[0099] ;(15)

[0100] Where, and They are respectively the curvature radius of the steel ball on the main plane III, the curvature radius of the steel ball on the main plane IV, the curvature radius of the arc-shaped outer raceway on the main plane III, and the curvature radius of the arc-shaped outer raceway on the main plane IV, and are calculated by the following formulas:

[0101] ; (16)

[0102] Substituting equations (15) and (16) into equation (14), we can obtain:

[0103] (17)

[0104] 2.3 Calculate the curvature and

[0105] In a specific embodiment of the present invention, the curvature of the steel ball and the elliptical inner raceway is Calculated by the following formula:

[0106] ; (18)

[0107] Where, C is the contact point between the steel ball and the elliptical inner raceway ′ In the main plane I ′ The equivalent radius of curvature on C is the contact point between the steel ball and the elliptical inner raceway ′ In the main plane II ′ The equivalent radius of curvature on the y-axis is calculated by the following formulas:

[0108] ;(19)

[0109] Where, and The steel ball is on the main plane Ⅰ ′ The radius of curvature on the main plane II ′ The curvature radius on the main plane I ′ The curvature radius and the elliptical inner raceway on the main plane II ′The curvature radius on the y-axis is calculated by the following formula:

[0110] ; (20)

[0111] Substituting formula (19) and formula (20) into formula (18) yields:

[0112] .(twenty one)

[0113] 2.4 Calculate the curvature and

[0114] In a specific embodiment of the present invention, the curvature of the steel ball and the elliptical outer raceway is Calculated by the following formula:

[0115] ;(twenty two)

[0116] Where, C is the contact point between the steel ball and the elliptical outer raceway ′ In the main plane III ′ The equivalent radius of curvature on C is the contact point between the steel ball and the arc outer raceway ′ Point on the principal plane IV ′ The equivalent radius of curvature on the y-axis is calculated by the following formulas:

[0117] ;(twenty three)

[0118] Where, and The contact points C of the steel ball and the elliptical outer raceway are ′ In the main plane III ′ The radius of curvature on the main plane IV ′ The curvature radius on the main plane III ′ The curvature radius and the elliptical outer raceway on the main plane IV ′ The curvature radius on the y-axis is calculated by the following formula:

[0119] ;(twenty four)

[0120] Substituting equation (23) and equation (24) into equation (22), we can obtain:

[0121] (25)

[0122] 3. Calculate the maximum contact stress

[0123] In a specific implementation of the embodiment of the present invention, the maximum contact stress between the ball cage constant velocity universal joint and the raceway is Calculated by the following formula:

[0124] ; (26)

[0125] Where, the contact between the steel ball and the raceway of the ball cage constant velocity universal joint is a point contact type. Point contact will form an elliptical contact area. a* and b* are the major and minor semi-axes of the elliptical contact area formed under point contact according to Hertz contact theory. P is the contact load between the steel ball and the raceway, which is calculated by the following formulas:

[0126] ; (27)

[0127] ; (28)

[0128] Substituting formulas (27)-(28) into formula (26) yields the final maximum contact stress: .

[0129] In formula (27) and formula (28), T is the torque applied to the steel ball, Z is the number of steel balls, L is the distance from the contact point between the steel ball center O and the raceway to the steel ball rotation center, κ is the elliptic coefficient of the elliptical area formed by the contact between the steel ball and the raceway, ε is the second kind of elliptic integral, E1 is the equivalent elastic modulus,

[0130] (29)

[0131] (30)

[0132] (31)

[0133] In the above formula, R' is the ratio of the equivalent principal curvatures of the two principal planes at the contact point, μ a 、μ b and E a 、E b are the Poisson's ratio and elastic modulus of the two contacting objects, respectively.

[0134] In formula (28), the distance L between the steel ball center O and the contact point of the raceway to the steel ball rotation center includes the following four cases:

[0135] The distance L between the steel ball center O and the contact point C of the arc inner raceway to the steel ball rotation center O2 i ; The distance L between the steel ball center O and the contact point C of the arc-shaped outer raceway to the steel ball rotation center O3 e; The distance L between the steel ball center O and the contact point C' of the elliptical inner raceway to the steel ball rotation center O2' i '; The distance L between the steel ball center O and the contact point C' of the elliptical inner raceway to the steel ball rotation center O3' e ′; where L i , L e , L i ′ and L e ' are calculated by the following formulas:

[0136] ;

[0137] ;

[0138] ;

[0139] .

[0140] In formula (29) and formula (30), the ratio R' of the equivalent principal curvatures of the two principal planes at the contact tangent point includes the following four cases: R1', the ratio of the equivalent principal curvature of principal plane I to principal plane II at the contact tangent point C between the center of the steel ball O and the arc-shaped inner raceway; R2', the ratio of the equivalent principal curvature of principal plane III to principal plane IV at the contact tangent point C between the center of the steel ball O and the arc-shaped inner raceway; R3', the ratio of the equivalent principal curvature of principal plane ⅠⅠ' to principal plane ⅡⅠ' at the contact tangent point C' between the center of the steel ball O and the arc-shaped inner raceway; R4', the ratio of the equivalent principal curvature of principal plane ⅠⅠ' to principal plane ⅡⅠ' at the contact tangent point C' between the center of the steel ball O and the arc-shaped inner raceway; and they are calculated by the following formulas respectively:

[0141] ;

[0142] ;

[0143] ;

[0144] .

[0145] 4. Simulation Experiment

[0146] As shown in Tables 1 and 2, the specific structural parameters of the arc-shaped and elliptical ball cage constant velocity universal joints are provided respectively. The materials of the two types of universal joints are the same. The elastic modulus of the bell housing is 2.01×1011N / m2 and the Poisson's ratio is 0.3; the elastic modulus of the steel ball, star-shaped sleeve, and cage is 2.06×1011N / m2 and the Poisson's ratio is 0.29. Before performing finite element simulation, the universal joint model needs to be simplified, ignoring the structure that does not affect the internal contact stress of the universal joint. The model before simplification is as follows: Figure 4 , the simplified model is as follows Figure 5 .

[0147] Figure 6 and Figure 7 Tables 1 and 2 show the experimental results of finite element analysis of the universal joints shown in Tables 1 and 2. Table 3 compares the numerical solution calculated using the above formula with the simulation results. Maximum contact stress result 1 is calculated using the method introduced in this invention, while maximum contact stress result 2 is obtained through conventional finite element method experiments.

[0148] As can be seen from Table 3, the errors between the calculation results of the present invention and the experimental results are all less than 10%, that is, all within the error tolerance range, which proves the correctness of the results. At the same time, due to the large amount of calculation, time-consuming and high requirements for computing resources of finite element analysis, if the models of ellipses, circular arcs, and different numbers of steel balls calculated by finite element method need to be modeled one by one, the modeling is complicated and the calculation time is long. However, the formula designed by the present invention is used for calculation, and the program is already compiled. It is applicable to the models of circular arcs, ellipses, and various numbers of steel balls. Direct input parameters can be quickly calculated, and the calculation is convenient and fast. While ensuring the accuracy of the calculation results, the efficiency is higher than the calculation rate of the finite element method experiment.

[0149] Table 1 Structural parameters of ball cage constant velocity universal joint 1

[0150] Table 2 Structural parameters of ball cage constant velocity universal joint 2

[0151] Table 3 Comparison of calculation results of ball cage constant velocity universal joints 1 and 2 (MPa)

[0152] Example 3

[0153] This embodiment introduces a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the method for calculating contact stress of a ball-cage constant velocity universal joint as described in Embodiment 1 or 2 are implemented.

[0154] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0155] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0156] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0157] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0158] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which are all protected by the present invention.

Claims

1. A method for calculating contact stress of a ball cage type constant velocity universal joint, characterized in that: include: Get the pre-built raceway geometry model; Obtaining geometric parameters of the steel ball according to the raceway geometric model and geometric relationship; The curvature and the contact point between the steel ball and the raceway are obtained according to the raceway geometric model and the geometric parameters of the steel ball. ; According to Hertz contact theory and the curvature and Calculate the maximum contact stress between the ball cage constant velocity joint and the raceway.

2. The contact stress calculation method of a ball cage type constant velocity universal joint according to claim 1 is characterized in that: The raceway geometric model includes an arc-shaped raceway geometric model and an elliptical raceway geometric model; the arc-shaped raceway includes an arc-shaped inner raceway and an arc-shaped outer raceway, and the elliptical raceway includes an elliptical inner raceway and an elliptical outer raceway; The geometric parameters of the steel ball include the center O of the steel ball, the diameter D of the steel ball w , steel ball rotation diameter D; The center of the arc raceway O1, the contact point C between the steel ball and the arc inner and outer raceways, the rotation center of the steel ball on the arc inner raceway O2, the rotation center of the steel ball on the arc outer raceway O3, Elliptical raceway center O1 ′ , the contact point C between the steel ball and the inner and outer raceways of the elliptical raceway ′ , the center of rotation of the steel ball on the elliptical inner raceway O2 ′ , the steel ball rotation center O3 on the elliptical outer raceway ′ .

3. The contact stress calculation method of a ball cage type constant velocity universal joint according to claim 2, characterized in that: The curvature of the contact point between the steel ball and the raceway and Including the curvature of the contact point between the steel ball and the arc inner raceway and , the curvature of the contact point between the steel ball and the arc outer raceway and , the curvature of the contact point between the steel ball and the elliptical inner raceway and , the curvature of the contact point between the steel ball and the elliptical outer raceway and .

4. The method for calculating contact stress of a ball cage type constant velocity universal joint according to claim 3, wherein: The curvature of the contact point between the steel ball and the arc-shaped inner raceway and Calculated by the following formula: ； Where, is the curvature coefficient of the arc raceway.

5. The method for calculating contact stress of a ball cage type constant velocity universal joint according to claim 3, wherein: The curvature of the contact point between the steel ball and the arc-shaped outer raceway and Calculated by the following formula: ； Where, is the curvature coefficient of the arc raceway.

6. The method for calculating contact stress of a ball cage type constant velocity universal joint according to claim 3, wherein: The curvature of the contact point between the steel ball and the elliptical inner raceway and Calculated by the following formula: ； Where, is the curvature coefficient of the elliptical raceway, It is the angle between the line connecting the center O of the steel ball and the contact point C' of the elliptical raceway and the radial plane perpendicular to the axis of rotation of the steel ball.

7. The contact stress calculation method of a ball cage type constant velocity universal joint according to claim 3, characterized in that: The curvature and Calculated by the following formula: ； Where, is the curvature coefficient of the elliptical raceway, It is the angle between the line connecting the center O of the steel ball and the contact point C' of the elliptical raceway and the radial plane perpendicular to the axis of rotation of the steel ball.

8. The method for calculating contact stress of a ball cage type constant velocity universal joint according to any one of claims 4 to 7, wherein: The maximum contact stress between the ball cage type constant velocity universal joint and the raceway Calculated by the following formula: ； Where a* and b* are the major and minor axes of the ellipse contact area formed under point contact according to Hertz contact theory, respectively. P is the contact load between the steel ball and the raceway, which is calculated using the following formula: ； Where T is the torque applied to the steel balls, Z is the number of steel balls, and L is the distance from the contact point between the steel ball center O and the raceway to the steel ball's rotation center.

9. The method for calculating contact stress of a ball cage type constant velocity universal joint according to claim 8, wherein: The distance L between the steel ball center O and the contact point between the raceway and the steel ball rotation center includes: The distance L between the steel ball center O and the contact point C of the arc inner raceway to the steel ball rotation center O2 i ; The distance L between the steel ball center O and the contact point C of the arc-shaped outer raceway to the steel ball rotation center O3 e ; The distance L between the steel ball center O and the contact point C' of the elliptical inner raceway to the steel ball rotation center O2' i '; The distance L between the steel ball center O and the contact point C' of the elliptical inner raceway to the steel ball rotation center O3' e ′; where L i 、L e 、L i ′ and L e ' are calculated by the following formulas: ； ； ； 。 10. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the steps of the method for calculating contact stress of a ball cage type constant velocity universal joint according to any one of claims 1 to 9 are implemented.

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