A method for optimizing sliding ratio of a hypoid gear

Abstract

The application provides a sliding rate optimization method of a hypoid gear, comprising the following steps: obtaining geometric parameters of the hypoid gear pair, obtaining range values of optimization variables by experience design, and then obtaining specific values; obtaining machining parameters; checking gear pair contact conditions by tooth surface contact analysis; calculating pinion tooth surface sliding rate, changing the values of the optimization variables in the experience range until the pinion tooth surface sliding rate is minimum; comparing the minimum values of the pinion tooth surface sliding rate under different cutter disc radii, and the cutter disc radius and the optimization variables when the minimum value is minimum are the values after optimization design. The application can greatly reduce the pinion tooth surface sliding rate, thereby significantly reducing the wear of the pinion and improving the service life of the entire gear pair; in addition, the pinion sliding rate is reduced, the friction heat generated by the mutual meshing of the tooth surfaces is reduced, thereby reducing the risk of tooth surface pitting failure and improving the transmission efficiency of the gear pair.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hypoid gear, in particular to a sliding rate optimization method of hypoid gear. BACKGROUND

[0002] Hypoid gear pair is widely used in automobile drive axle, since the small wheel offset distance was introduced into bevel gear in the 1920s, the original plane gear became space gear, that is, hypoid gear, which brings the following advantages:

[0003] Small wheel offset distance can increase the helix angle of small wheel, so as to increase the end face modulus of gear, and the outer diameter is also significantly increased, so that the strength of small wheel can be significantly improved without increasing the overall space of gear pair;

[0004] Under the same conditions, the number of small wheel teeth can be reduced, and the coincidence degree can be increased;

[0005] The existence of small wheel offset distance can improve the flexibility of automobile design, and the height of automobile chassis can be flexibly adjusted by upward or downward offset of small wheel, so as to change the off-road performance and stability of automobile.

[0006] However, the disadvantages caused by this are that the sliding rate and relative sliding speed of tooth surface are increased, which is easy to cause wear and fatigue pitting and other failure conditions.

[0007] The existing method for solving the wear of hypoid gear mainly improves the hardness and reduces the roughness of tooth surface in the gear manufacturing process, and mainly reduces the wear by adding additives in the lubricating oil during use, and mainly studies the formation of oil film based on the elastic lubrication theory to reduce wear and pitting and other aspects. At present, the research on sliding rate optimization of hypoid gear is still rare. SUMMARY

[0008] The purpose of the present application is to provide a method for reducing the failure risk of hypoid gear, a key part of automobile drive axle, such as tooth surface wear and pitting, by reducing the sliding rate to improve the service life and efficiency of gear pair, and to provide a new way for the design of long-life and high-efficiency hypoid gear.

[0009] In order to achieve the above purpose, the present application provides a sliding rate optimization method of hypoid gear, comprising the following steps:

[0010] S1, obtaining the geometric parameters of the hypoid gear pair according to the basic design parameters of the hypoid gear pair, the geometric parameters including the optimization variables to be optimized, obtaining the range value of the optimization variables by experience design, and then taking a specific value;

[0011] S2, obtaining the machining parameters according to the curvature and unit normal vector of the two meshing tooth surfaces of the hypoid gear at the reference point satisfying the preset condition and the geometric parameters determined in S1;

[0012] S3, checking the contact condition of the gear pair through tooth surface contact analysis, and returning to S1 to adjust the geometric parameters if the contact condition is not ideal;

[0013] S4, calculating the sliding rate of the pinion tooth surface, changing the value of the optimization variable within the experience range until the sliding rate of the pinion tooth surface is minimum, and the value of the optimization variable at this time is the optimal value under different cutter disc radii;

[0014] S5, comparing the minimum values of the sliding rates of the pinion tooth surface under different cutter disc radii, and the cutter disc radius and the optimization variable when the minimum value is minimum are the values after optimization design.

[0015] Further, the sliding rate model of the hypoid gear is: the coordinate system S1 {X1, Y1, Z1} is fixed with the pinion, the coordinate system S2 {X2, Y2, Z2} is fixed with the gear, and the installation coordinate system of the gear pair is S {X, Y, Z} and is fixed in space; the pinion and the gear rotate around Z1 and Z2 respectively, and the angular velocity vectors are ω (1) and ω (2) ; the two meshing tooth surfaces of the gear pair contact at M point, the position vectors of the pinion and the gear are r (1) and r (2) , and the shortest distance between the two axes, i.e. the offset distance, is E.

[0016] Further, the preset condition in S2 includes:

[0017] The unit normal vectors are equal, i.e. n1=n2;

[0018] The position vectors coincide, i.e. r1=r2+O1O2;

[0019] The normal curvatures in the tooth length direction are equal, i.e. A1=A2;

[0020] The normal curvatures in the tooth height direction are equal, i.e. B1=B2;

[0021] The short-term flexibilities in the tooth length direction are equal, i.e. C1=C2.

[0022] Further, the contact condition of the gear pair checked in S3 includes the contact area, the transmission error and the tooth surface topology.

[0023] Further, the sliding rate calculation formula of the pinion σ1 and the gear σ2 in S4 is:

[0024]

[0025] Wherein, n is the common unit normal vector of the two meshing tooth surfaces at M point, v (12)and ω (12) It is the relative velocity and relative angular velocity of the two meshing tooth surfaces at point M, k v (1) It is point M on the small gear tooth surface at v (12) The normal curvature in the direction of curvature, q, is a vector and can be expressed by the following formula:

[0026]

[0027] Furthermore, in S4, N meshing points are selected on the tooth surface contact trajectory, and N points are selected on both the working surface and the non-working surface. For different cutter head radii, the minimum value among the sum of the absolute values ​​of the sliding rates of the working and non-working surfaces of the small gear at each meshing point is the optimal value.

[0028]

[0029] Where σ 1d (i) and σ 1c (i) These refer to the sliding ratios of the working and non-working surfaces of the small wheel, respectively. The superscript i indicates the meshing point number from 1 to N. μ1 and μ2 are the sliding ratio weighting coefficients of the working and non-working surfaces, respectively. μ1 + μ2 = 1, and their values ​​range from 0 to 1.

[0030] The above-described solution of the present invention has the following beneficial effects:

[0031] The sliding ratio optimization design method for quasi-hyperboloid gears provided by this invention has considerable practical engineering significance. It can significantly reduce the sliding ratio of the pinion tooth surface, thereby significantly reducing the wear of the pinion and improving the life of the entire gear pair. In addition, the reduced sliding ratio of the pinion reduces the frictional heat generated by the meshing of the tooth surfaces, thereby reducing the risk of pitting failure and improving the transmission efficiency of the gear pair.

[0032] Other beneficial effects of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0033] Figure 1 This is a flowchart of the steps of the present invention;

[0034] Figure 2 This is the quasi-hyperboloid gear coordinate system in this invention;

[0035] Figure 3 The selection of the tooth surface meshing point in this invention;

[0036] Figure 4 This is a comparison chart of the small wheel slip ratio before and after optimization in this invention;

[0037] Figure 5 This is a comparison chart of the transmission efficiency of the gear pair before and after optimization in this invention. Detailed Implementation

[0038] To make the technical problems, solutions, and advantages of this invention clearer, a detailed description will be provided below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. Furthermore, the technical features involved in the different embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0039] In the description of this invention, for the sake of simplicity, the method or rule is depicted or described as a series of operations, not as an exhaustive list of experimental operations, nor as a restriction on the order of the experimental operations. For example, experimental operations may be performed in various orders and / or simultaneously, and include other experimental operations not described again. Furthermore, not all of the steps described herein are essential to the methods and algorithms described herein. Those skilled in the art will recognize and understand that these methods and algorithms can be represented by a series of unrelated states through state diagrams or items.

[0040] This invention relates to the field of quasi-hyperboloid gear technology, such as... Figure 2 As shown, a slip ratio model for a quasi-hyperboloid gear is established: coordinate system S1{X1,Y1,Z1} is fixed to the pinion, coordinate system S2{X2,Y2,Z2} is fixed to the gear, and the installation coordinate system of the gear pair is S{X,Y,Z}, which is fixed in space. The pinion and gear rotate about Z1 and Z2 respectively, with angular velocities ω and ω, respectively. (1) and ω (2) The two meshing tooth surfaces of the gear pair contact at point M, and the position vectors of the pinion and gear are r and r, respectively. (1) and r (2) The shortest distance between the two axes, i.e., the offset distance, is E. The formulas for calculating the slip ratios of the small wheel σ1 and the large wheel σ2 are:

[0041]

[0042] Where n is the common unit normal vector of the two meshing tooth surfaces at point M, and v (12) and ω (12) It is the relative velocity and relative angular velocity of the two meshing tooth surfaces at point M, k v (1) It is point M on the small gear tooth surface at v (12) The normal curvature in the direction, q is a vector, and they can be expressed by the following formula:

[0043]

[0044] According to the gear meshing principle, the slip ratio is the limiting value of the ratio of the arc length traversed by the relative sliding profiles of two teeth to the total arc length traversed by the tooth surface. Under the same conditions, the larger the absolute value of the slip ratio, the greater the wear on the tooth surface. Therefore, it is an important indicator for measuring the quality of gear transmission.

[0045] Several points are selected on the tooth surface contact trajectory; in this embodiment, 17 meshing points are used as examples to examine the tooth surface sliding rate. Each meshing point is equidistant from the others. Seventeen points are selected on both the working and non-working surfaces, and their positional order is as follows: Figure 3 As shown in Table 1, to clearly compare the effectiveness of this solution, a pair of hypoid gears is used as an example, and its geometric parameters are shown in Table 1:

[0046] Table 1. Geometric parameters of the hypoid gear example.

[0047]

[0048] In the design of quasi-hypoid gears, the basic design parameters include the number of teeth, module, offset, tooth width (B), helix angle (β), pressure angle (α), cutter head radius (r0), and offset coefficient (η). Among these, the number of teeth, module, and offset are difficult to change once determined due to limitations such as design dimensions, making them unsuitable as optimization variables. Based on the actual design situation, this embodiment selects tooth width (B), helix angle (β), pressure angle (α), cutter head radius (r0), and offset coefficient (η) as optimization variables. A preliminary design is completed based on engineering experience to determine the range of these optimization variables. For example, B∈[38,42], α∈[21.5,23.5], β∈[45,50], η∈[20,60], and r0 takes one of the discrete values ​​107.95, 114.3, and 120.65.

[0049] Figure 1 The flowchart shown is for the slip ratio optimization design of a quasi-hypoid gear. First, the geometric parameters are obtained from the basic design parameters of the quasi-hypoid gear. Then, based on the fact that the curvature and unit normal vector of the two meshing tooth surfaces at the reference point meet the preset conditions, a set of machining parameters is obtained by solving a system of multivariate nonlinear equations. The gear pair contact condition is first checked through tooth surface contact analysis (TCA), including the contact area, transmission error, and tooth surface topology. If the contact condition is not ideal, the geometric parameters are adjusted until the requirements are met. The slip ratio of the pinion tooth surface is calculated, and the values ​​of the optimization variables are changed within the empirical design range until the slip ratio of the pinion tooth surface is minimized; at this point, the optimization variable value is considered optimal.

[0050] Among them, the curvature and unit normal of the two meshing tooth surfaces at the reference point satisfy the following preset conditions:

[0051] The unit normal vectors are equal, i.e., n1 = n2;

[0052] The position vectors coincide, i.e., r1 = r2 + O1O2;

[0053] The normal curvatures along the tooth length direction are equal, i.e., A1 = A2;

[0054] The curvatures in the tooth height direction are equal, i.e., B1 = B2;

[0055] The short-range deflections along the tooth length are equal, i.e., C1 = C2.

[0056] When there are 17 meshing points, the minimum value among the sum of the absolute values ​​of the sliding ratios of the working surface (concave surface) and non-working surface (convex surface) of the pinion at each meshing point is the optimal value:

[0057]

[0058] Where σ 1d (i) and σ 1c (i) These refer to the slip ratios of the working and non-working surfaces of the small wheel, respectively, with the superscript i indicating the engagement point number from 1 to 17. Since each parameter significantly affects the slip ratio of the small wheel, and given that the driving habit of a car is such that the working time on the forward-facing surface is much longer than the reverse-facing surface, the slip ratio of the small wheel is selected as the optimization target. Slip ratio weighting coefficients are set, with μ1 and μ2 representing the slip ratio weighting coefficients of the working and non-working surfaces, respectively. μ1 + μ2 = 1, and their values ​​range from 0 to 1. μ2 < μ1 to reduce the weight of the non-working surface.

[0059] According to the Gleason standard, to reduce the number of cutter heads and manufacturing costs, the cutter heads for quasi-hypoid gears cannot be arbitrarily set; only a limited number of sets can be selected. Based on the actual situation of the gear pair in this example, the cutter head radius is selected from the aforementioned three discrete values. Therefore, the final step of the optimization method is to compare the sum of the sliding rates calculated for the three cutter heads and take the smallest one as the design value for the cutter head radius, thereby obtaining the optimized variables (geometric parameters). The optimized geometric parameters of the gear pair are shown in Table 2.

[0060] Table 2. Geometric parameters of the optimized hypoid gear pair

[0061]

[0062] Comparison before and after optimization:

[0063] The slip ratio of the example was optimized using the above-described optimization design method. Figure 4 To optimize the slip ratio curves of the concave and convex surfaces of the front and rear small wheels, a comparison of the figures shows that:

[0064] On the concave working surface of the small wheel, at the selected 17 meshing points, the optimized slip ratio was significantly lower than the unoptimized slip ratio. The maximum decrease in slip ratio on the concave surface reached 38.43. At meshing point 1, which is also the point where the absolute value of the concave slip ratio is the largest, the minimum decrease still reached 30.34, with a reduction percentage between 64% and 68.6%, which is very significant.

[0065] On the non-working surface (convex surface) of the small wheel, at the selected 17 meshing points, the optimized slip ratio is much smaller than the unoptimized slip ratio, with the maximum decrease occurring at meshing point 1, reaching 58.57. The decrease ranges from 11.4% to 29.58%, which is quite significant.

[0066] According to Gleason's efficiency calculation method, the efficiency e of a hypoid gear is calculated using the following formula:

[0067]

[0068] Among them, T max The maximum torque of the large wheel is given by β1; T is the torque of the large wheel at the desired efficiency; β1 and β2 are the midpoint helix angles of the small and large wheels, respectively; D is the pitch circle radius of the large end of the large wheel; λ is the friction coefficient between the teeth, typically taken as 0.05; α d It is the normal pressure angle of the front surface.

[0069] Based on the above formula for calculating the pinion gear, the efficiency of the two gear pairs before and after optimization was compared, and their efficiency curves are shown below. Figure 5 As shown in the figure, the efficiency of the optimized gear pair is higher than that of the unoptimized gear pair at all loads, with the efficiency increase reaching a maximum of 0.47%. This indirectly proves that the heat loss generated by sliding is effectively reduced after optimization, thus demonstrating the effectiveness of optimization in reducing tooth surface wear.

[0070] In summary, as the preceding analysis shows, the slip ratios of both the working surface (concave) and non-working surface (convex) of the pinion are significantly greater than those of the large gear. Furthermore, the design parameters are insensitive to the slip ratio of the large gear. Therefore, the slip ratio of the pinion determines the lifespan of the entire gear pair, which aligns with engineering practice (the pinion is prone to failure). To address this, optimization using the slip ratio optimization model proposed in this application significantly reduces the slip ratio of the pinion teeth, thereby substantially reducing pinion wear and increasing the lifespan of the entire gear pair. Additionally, the reduced slip ratio of the pinion decreases the frictional heat generated by tooth meshing, thus reducing the risk of pitting failure and improving the transmission efficiency of the gear pair.

[0071] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the slip ratio of a quasi-hyperboloid gear, characterized in that, Includes the following steps: S1. Obtain the geometric parameters of the hypoid gear pair based on the basic design parameters of the hypoid gear pair. The geometric parameters include the optimization variables to be optimized. Obtain the range of the optimization variables based on empirical design, and then take specific values. S2, based on the curvature of the two meshing tooth surfaces of the quasi-hyperboloid gear at the reference point and the unit normal vector satisfying the preset conditions, and the geometric parameters determined by S1, the machining parameters are obtained; S3, check the contact condition of the gear pair through tooth surface contact analysis. If the contact condition is not ideal, return to S1 to adjust the geometric parameters. S4. Calculate the sliding rate of the pinion tooth surface. Change the value of the optimization variable within the empirical range until the sliding rate of the pinion tooth surface is minimized. At this time, the value of the optimization variable is the optimal value under different cutter head radii. S5, compare the minimum value of the sliding rate of the small gear tooth surface under different cutter head radii, and the cutter head radius and optimization variables when the minimum value is reached are the values ​​after optimization design; The slip ratio model of the quasi-hyperboloid gear is as follows: coordinate system S1{X1,Y1,Z1} is fixed to the small gear, coordinate system S2{X2,Y2,Z2} is fixed to the large gear, and the installation coordinate system of the gear pair is S{X,Y,Z}, which is fixed in space; the small gear and the large gear rotate about Z1 and Z2 respectively, and their angular velocity vectors are ω (1) and ω (2) The two meshing tooth surfaces of the gear pair contact at point M, and the position vectors of the pinion and gear are r and r, respectively. (1) and r (2) The shortest distance between the two axes, i.e., the offset distance, is E; The formulas for calculating the slip ratios of the small wheel σ1 and the large wheel σ2 in S4 are as follows: Where n is the common unit normal vector of the two meshing tooth surfaces at point M, and v (12) and ω (12) It is the relative velocity and relative angular velocity of the two meshing tooth surfaces at point M, k v (1) It is point M on the small gear tooth surface at v (12) The normal curvature in the direction of curvature, q, is a vector and can be expressed by the following formula: In S4, tooth width, helix angle, pressure angle, cutter head radius, and offset coefficient are selected as optimization variables. N meshing points are chosen on both the working and non-working surfaces of the tooth surface contact trajectory. For different cutter head radii, the minimum value among the sum of the absolute values ​​of the sliding rates of the working and non-working surfaces of the pinion at each meshing point is the optimal value. Where σ 1d (i) and σ 1c (i) These refer to the sliding rates of the working and non-working surfaces of the small wheel, respectively. The superscript i indicates the meshing point number from 1 to N. μ1 and μ2 are the sliding rate weighting coefficients of the working and non-working surfaces, respectively. μ2 + μ2 = 1, and their values ​​range from 0 to 1. If μ2 < μ2, the weight of the non-working surface is reduced.

2. The method for optimizing the slip ratio of a quasi-hyperboloid gear according to claim 1, characterized in that, The preset conditions in S2 include: The unit normal vectors are equal, i.e., n1 = n2; The position vectors coincide, i.e., r1 = r2 + O1O2; The normal curvatures along the tooth length direction are equal, i.e., A1 = A2; The curvatures in the tooth height direction are equal, i.e., B1 = B2; The short-range deflections along the tooth length are equal, i.e., C1 = C2.

3. The method for optimizing the slip ratio of a quasi-hyperboloid gear according to claim 1, characterized in that, The gear pair contact condition checked in S3 includes the contact area, transmission error, and tooth surface topology.

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