Differential straight bevel gear structure and design method thereof

Abstract

The present application belongs to the technical field of gear machining, and particularly relates to a straight-toothed bevel gear structure and a design method thereof. The differential straight-toothed bevel gear structure comprises mutually meshed straight-toothed bevel gears, the tooth root fillet of the straight-toothed bevel gears is designed with a full circular arc, the tooth root angle of the straight-toothed bevel gears is provided with a tooth root angle increment, and the tooth root angle increment should make the coincidence degree of the straight-toothed bevel gears at the position of two-thirds of the tooth width from the large end to the small end greater than or equal to 1. The present application adopts a double shrinkage tooth design, further increases the tooth root fillet, and adopts a full circular arc design for the tooth root fillets of the half shaft gears and the planetary gears, and meanwhile, reinforcing ribs are arranged at the large and small ends of the planetary gears and the half shaft gears. The tooth root bending strength of the half shaft gears and the planetary gears is improved, and meanwhile, the present application can meet the demand of lightweight and high strength of new energy vehicles.

Description

Technical Field

[0001] This invention belongs to the field of gear processing technology, and specifically relates to a straight bevel gear structure and its design method. Background Technology

[0002] A car differential is a mechanism that allows the left and right (or front and rear) drive wheels to rotate at different speeds. A typical passenger car differential mainly consists of a differential housing, planetary gears, half-shaft gears, and a planetary shaft. It is the most common type of differential on the market, with both the planetary gears and half-shaft gears using straight bevel gears. During operation, power is output from the engine or electric motor, and after multiple speed reductions and torque increases, it is transmitted to the differential. It is the component in the transmission that transmits the largest amount of torque, requiring very high strength, often at the cost of increased size. The planetary gears and half-shaft gears are the bottleneck components of the overall load-bearing capacity of the differential system, determining the upper limit of the entire differential system's strength. To achieve a smaller differential size and adapt to increasingly smaller installation space requirements, a design with fewer teeth and a larger module is usually chosen. This reduces the size of the bevel gears while giving them higher bending strength. Currently, the commonly used designs for planetary gears and half-shaft gears in differentials can be divided into two types: unequal clearance shrinkage gears and equal clearance shrinkage gears. The characteristic of unequal clearance shrinkage gears is that the clearance of the gear pair gradually decreases from the large end to the small end, the root fillet is small, and the strength is weak. The characteristic of equal clearance shrinkage gears is that the generatrix of the top cone of the gear is always parallel to the generatrix of the root cone of the mating gear, and the clearance of the gear pair is equal at both the large and small ends. Compared with unequal clearance shrinkage gears, the root fillet is larger and the strength is improved, but the size of the root fillet is still limited by the small end, and the improvement in gear strength is limited.

[0003] In existing differentials, the design of planetary gears and half-shaft gears, regardless of whether they employ unequal or equal clearance shrinkage gears, has limited improvement in the root radius, preventing further enhancement of the bevel gear's strength. This fails to meet the lightweight and high-strength requirements of new energy vehicles. Summary of the Invention

[0004] To address the aforementioned problems, this invention discloses a differential spur bevel gear structure, which includes meshing spur bevel gears, wherein the root fillet of the spur bevel gears adopts a full circular arc design.

[0005] The spur bevel gear has a root angle increment, which should ensure that the contact ratio at the meshing position (two-thirds of the tooth width from the large end to the small end) is greater than or equal to 1.

[0006] Furthermore, the spur bevel gear includes a half-shaft gear and a planetary gear;

[0007] The half-shaft gear is provided with a half-shaft gear disk, and the half-shaft gear disk is provided with half-shaft gear teeth distributed in a circumferential array. There are half-shaft gear tooth roots between adjacent half-shaft gear teeth, and the tooth root fillet at the half-shaft gear tooth root adopts a full arc design.

[0008] The planetary gear is provided with a planetary gear disk, and planetary gear teeth are arranged in a circumferential array on the planetary gear disk. Planetary gear roots are provided between the planetary gear teeth, and the root fillet of the planetary gear teeth adopts a full arc design.

[0009] Furthermore, the half-shaft gear includes a large end and a small end, the large end of the half-shaft gear is provided with a large end reinforcing rib, and the small end of the half-shaft gear is provided with a small end reinforcing rib.

[0010] The planetary gear includes a large end and a small end. The large end of the planetary gear is provided with a planetary gear large end reinforcing rib, and the small end of the planetary gear is provided with a planetary gear small end reinforcing rib.

[0011] On the other hand, the present invention discloses a differential spur bevel gear structure design method, the design method including: using a full circular arc structure to design the tooth root fillet of the meshing spur bevel gears;

[0012] Set the root angle increment of the spur bevel gear. The root angle increment should make the contact ratio of the spur bevel gear at the two-thirds meshing position from the large end to the small end greater than or equal to 1. Based on the number of teeth, root height of the large end, outer cone distance, pitch cone angle, tooth width, tip circle diameter of the large end, pitch circle diameter of the large end, and base circle diameter of the large end, obtain the contact ratio of the spur bevel gear at the two-thirds meshing position from the large end to the small end.

[0013] Based on the overlap at the two-thirds meshing position of the tooth width from the large end to the small end of the straight bevel gear, determine whether the tooth root angle increment design is reasonable.

[0014] Furthermore, the spur bevel gear includes a half-shaft gear and a planetary gear;

[0015] Before setting the root angle increment of the straight bevel gear, the spherical radius coefficient of the straight bevel gear and the calculated torque of the differential are set, and the outer cone distance of the straight bevel gear is obtained based on the spherical radius coefficient of the straight bevel gear and the calculated torque of the differential.

[0016] Set the number of teeth on the planetary gears, and obtain the cone angles of the half-shaft gear and the planetary gears based on the number of teeth on the planetary gears;

[0017] The large-end module of the straight bevel gear is obtained based on the cone angle, number of teeth, and outer cone distance of the straight bevel gear.

[0018] Set the pressure angle, radial displacement coefficient, tooth addendum coefficient, and clearance coefficient of the spur bevel gear. Based on the pressure angle, radial displacement coefficient, tooth addendum coefficient, clearance coefficient, large end module, and cone angle of the spur bevel gear, obtain the large end tooth addendum, large end tooth dedendum, large end tooth tip circle diameter, large end tooth dedendum circle diameter, and large end base circle diameter of the spur bevel gear.

[0019] Furthermore, obtaining the overlap ratio at the two-thirds meshing position of the straight bevel gear from the large end to the small end specifically includes:

[0020] Set the tooth width of the spur bevel gear, and based on the tooth width, the large end addendum circle diameter, the addendum cone angle, the tooth tip angle, the outer cone distance, the pitch cone angle, the large end base circle diameter, and the base circle angle, obtain the meshing addendum circle diameter, the meshing pitch circle diameter, and the meshing base circle diameter at the meshing position where the tooth width is two-thirds from the large end to the small end of the spur bevel gear.

[0021] Based on the addendum circle diameter, cone angle, pitch circle diameter, and base circle diameter, obtain the equivalent addendum circle diameter, pitch circle diameter, base circle diameter, and meshing length of the spur bevel gear at the meshing position where the tooth width is two-thirds from the large end to the small end.

[0022] Based on the number of teeth, cone angle, equivalent pitch circle diameter, equivalent meshing length, and pressure angle of the spur bevel gear, obtain the equivalent number of teeth, equivalent module, and contact ratio at the meshing position where the tooth width is two-thirds from the large end to the small end.

[0023] Furthermore, obtaining the addendum circle diameter, pitch circle diameter, and base circle diameter of the spur bevel gear at the two-thirds meshing position from the large end to the small end specifically includes:

[0024] Based on the tooth width W and the large end addendum circle diameter d of the straight bevel gear a δ, the angle of the apex cone a and tooth tip angle θ a The diameter of the addendum circle of the meshing teeth is calculated using the following formula:

[0025]

[0026] In the formula, d' a The tip circle diameter of the meshing teeth of the spur bevel gear;

[0027] The pitch circle diameter is calculated based on the tooth width W, outer cone distance Re, and pitch cone angle δ of the spur bevel gear; the calculation formula is as follows:

[0028]

[0029] In the formula, d e ' is the pitch circle diameter of the spur bevel gear;

[0030] Based on the tooth width W and the base circle diameter d of the spur bevel gear b Cone angle δ and base radius θ b The diameter of the meshing base circle is calculated using the following formula:

[0031]

[0032] In the formula, d b ' is the meshing base circle diameter of the spur bevel gear.

[0033] Furthermore, obtaining the equivalent tip circle diameter, equivalent pitch circle diameter, equivalent base circle diameter, and equivalent meshing length at the two-thirds meshing position of the straight bevel gear from the large end to the small end specifically includes:

[0034] Based on the tip circle diameter d' of the meshing teeth a The equivalent tip circle diameter at the meshing position is obtained by calculating the cone angle δ; the calculation formula is as follows:

[0035]

[0036] In the formula, d av This is the equivalent tooth tip circle diameter at the meshing position;

[0037] The equivalent addendum circle diameter d at the meshing position of the planetary gear can be obtained from the above formula. av2 The equivalent tip circle diameter d at the meshing position of the half-shaft gear av1 ;

[0038] According to the pitch circle diameter d e The equivalent pitch circle diameter at the meshing position is obtained by calculating the cone angle δ; the calculation formula is as follows:

[0039]

[0040] In the formula, d ev This is the equivalent pitch circle diameter at the meshing position;

[0041] Based on the meshing base circle diameter d b The equivalent base circle diameter at the meshing position is calculated using the cone angle δ; the calculation formula is as follows:

[0042]

[0043] In the formula, d bv This is the equivalent base circle diameter at the meshing position;

[0044] The equivalent base circle diameter d at the meshing position of the planetary gear can be obtained from the above formula. bv2 The equivalent base circle diameter d at the meshing position of the half-shaft gear bv1 ;

[0045] Based on the equivalent tooth tip circle diameter d at the meshing position of the half-shaft gear av2 The equivalent tip circle diameter d at the meshing position of the planetary gear av2 The equivalent base circle diameter d at the meshing position of the half-shaft gear bv1 The equivalent base circle diameter d at the meshing position of the planetary gear bv2 The equivalent engagement length at the engagement position is calculated using the pressure angle α; the calculation formula is as follows:

[0046]

[0047] In the formula, g av This is the equivalent engagement length at the engagement position.

[0048] Furthermore, obtaining the equivalent number of teeth, equivalent module, and contact ratio at the two-thirds meshing position of the straight bevel gear from the large end to the small end specifically includes:

[0049] The equivalent number of teeth Z at the meshing position is calculated based on the number of teeth Z and the cone angle δ of the spur bevel gear. v The calculation formula is as follows:

[0050]

[0051] In the formula, Z v This represents the equivalent number of teeth at the meshing position;

[0052] Based on the equivalent pitch circle diameter d at the meshing position ev and equivalent number of teeth Z v The equivalent modulus m at the meshing position was calculated. v The calculation formula is as follows:

[0053]

[0054] In the formula, m v This is the equivalent modulus at the meshing position;

[0055] Based on the equivalent meshing length g av Equivalent modulus m v The overlap ratio ε at two-thirds of the meshing position is calculated using the pressure angle α; the calculation formula is as follows:

[0056]

[0057] In the formula, ε represents the degree of overlap at the meshing position.

[0058] Furthermore, the determination of the rationality of the tooth root angle increment Δf design based on the overlap ε at the two-thirds meshing position of the straight bevel gear from the large end to the small end specifically includes:

[0059] ε < 1; the tooth root angle increment Δf is poorly designed;

[0060] ε≥1; the tooth root angle increment Δf is reasonably designed.

[0061] This invention adopts a double shrinking tooth design to further increase the tooth root radius; and the tooth root arc of the half shaft gear and planetary gear adopts a full arc design, while reinforcing ribs are provided at both the large and small ends of the planetary gear and half shaft gear; while improving the tooth root bending strength of the half shaft gear and planetary gear, it can meet the requirements of lightweight and high strength of new energy vehicles.

[0062] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures pointed out in the description, claims and drawings. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 A front view schematic diagram of an embodiment of the spur bevel gear structure of the present invention is shown;

[0065] Figure 2 A schematic diagram of the overall structure of an embodiment of the spur bevel gear structure of the present invention is shown;

[0066] Figure 3 A bottom view schematic diagram of an embodiment of the straight bevel gear structure of the present invention is shown;

[0067] In the diagram: 1-Half-shaft gear, 2-Planetary gear, 3-Large end of half-shaft gear, 4-Small end of half-shaft gear, 5-Large end of planetary gear, 6-Small end of planetary gear, 7-Small end reinforcing rib of half-shaft gear, 8-Small end reinforcing rib of planetary gear, 9-Root angle of half-shaft gear, 10-Root angle of planetary gear, 11-Toe tip of half-shaft gear, 12-Root of half-shaft gear, 13-Large end reinforcing rib of half-shaft gear, 14-Spline of half-shaft gear, 15-Root of planetary gear, 16-Toe tip of planetary gear, 17-Large end reinforcing rib of planetary gear, 18-Inner hole of planetary gear. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] This invention proposes a differential spur bevel gear structure, aiming to improve spur bevel gears by significantly increasing their bending strength without changing the size of the large and small bevel gears, thus better meeting the lightweight and high-strength requirements of new energy vehicles. The differential spur bevel gear structure includes meshing half-shaft gear 1 and planetary gear 2. Half-shaft gear 1 and planetary gear 2, based on an equal clearance shrinkage tooth design, incorporate a root angle increment Δf. This increased root angle achieves double shrinkage teeth, while maintaining equal clearance at both ends of the gear pair. The root fillet is further enhanced, and both half-shaft gear 1 and planetary gear 2 employ a full-circle design. Furthermore, reinforcing ribs are provided at both ends of half-shaft gear 1 and planetary gear 2 to further improve the bending strength of the bevel gear system.

[0070] like Figure 1 As shown, the half-shaft gear 1 includes the large end 3, the small end 4, the reinforcing rib 7 at the small end, and the tooth root angle 9. Planetary gear 2 includes the large end 5 of the planetary gear, the small end 6 of the planetary gear, the small end reinforcing rib 8 of the planetary gear, and the root angle 10° of the planetary gear. Half-shaft gear tooth root angle 9 The half-shaft gear tooth root angle increment Δf1 is provided, and the planetary gear tooth root angle is 10°. The planetary gear tooth root angle increment Δf2 is provided at the location; the settings of Δf1 and Δf2 should ensure that the overlap ratio ε of the spur bevel gear structure at the meshing position of two-thirds of the tooth width from the large end to the small end is greater than or equal to 1.

[0071] A half-shaft gear 1 is fixedly provided with a half-shaft gear disk, and half-shaft gear teeth are fixedly provided in a circumferential array on the half-shaft gear disk. The large end 3 of the half-shaft gear is located on the side of the half-shaft gear disk away from the gear axis; the small end 4 of the half-shaft gear is located on the side of the half-shaft gear disk closer to the gear axis, and a small end reinforcing rib 7 is fixedly provided on the small end 4; such as Figure 2 As shown, a reinforcing rib 13 is fixedly provided on the large end 3 of the half-shaft gear. The reinforcing rib 7 at the small end of the half-shaft gear and the reinforcing rib 13 at the large end of the half-shaft gear are used to improve the bending resistance of the half-shaft gear 1.

[0072] like Figure 2As shown, the half-shaft gear 1 has a through hole, and the through hole has a circumferentially arrayed half-shaft gear splines 14. The half-shaft gear splines 14 are used to complete the assembly between the half-shaft gear 1 and the half-shaft. The half-shaft gear tooth tip 11 is fixedly set at one end of the half-shaft gear tooth. The half-shaft gear tooth root 12 is provided between two adjacent half-shaft gear teeth. The tooth root fillet at the half-shaft gear tooth root 12 adopts a full arc design to enhance the bending resistance of the half-shaft gear 1.

[0073] A planetary gear disk is fixedly mounted on planetary gear 2. Planetary gear teeth are fixedly arranged in a circumferential array on the planetary gear disk. The large end 5 of the planetary gear is located on the side of the planetary gear disk away from the gear axis, and the small end 6 of the planetary gear is located on the side of the planetary gear disk closer to the gear axis. A planetary gear small end reinforcing rib 8 is fixedly mounted on the small end 6. Figure 3 As shown, a planetary gear large end reinforcing rib 17 is fixedly provided on the planetary gear large end 5. The planetary gear small end reinforcing rib 8 and the planetary gear large end reinforcing rib 17 are used to enhance the bending resistance of the planetary gear 2.

[0074] like Figure 3 As shown, planetary gear 2 is provided with planetary gear inner hole 18. Planetary gear 2 is connected to external power through inner hole 18 and receives the transmitted torque. Planetary gear tooth tip 16 is fixedly set at one end of planetary gear tooth. Planetary gear disk is also provided with planetary gear tooth roots 15 distributed in a circumferential array. Planetary gear tooth roots 15 are located between planetary gear teeth. The tooth root fillet at planetary gear tooth root 15 adopts a full arc design to enhance the bending resistance of planetary gear 2.

[0075] The half-shaft gear 1 and planetary gear 2 of this invention are first based on an equal clearance shrinking tooth design, and then the root angle 9 of the half-shaft gear and the root angle 10 of the planetary gear are increased to achieve a double shrinking tooth transformation. This makes the width of the tooth tip 11 of the half-shaft gear equal or gradually decreasing from the large end to the small end, and the width of the tooth tip of the planetary gear gradually increasing from the large end to the small end, thereby further increasing the root fillet of the bevel gear system and further enhancing the gear strength. The root fillets of both the half-shaft gear 1 and the planetary gear 2 adopt a full arc design to improve the bending strength of the gears. Both the large and small ends of the half-shaft gear 1 and the planetary gear 2 are provided with reinforcing ribs to improve the bending strength of the gears. This invention can ensure that the gear system achieves a greater strength improvement under the premise of the same volume, and can better meet the requirements of lightweight and high strength of new energy vehicles.

[0076] This invention proposes a design method for a spur bevel gear structure in a differential. This method first designs the half-shaft gear 1 and planetary gear 2 based on equal-clearance contracted teeth. Then, it increases the root angle 9 of the half-shaft gear and the root angle 10 of the planetary gear to achieve a double-contracted tooth transformation, further increasing the root fillet of the bevel gear system and thus improving gear strength. The spur bevel gear design method includes:

[0077] The tooth root fillet of the meshing straight bevel gears adopts a full circular arc structure design;

[0078] Set the root angle increment of the spur bevel gear. The root angle increment should make the contact ratio of the spur bevel gear at the two-thirds meshing position from the large end to the small end greater than or equal to 1. Based on the number of teeth, root height of the large end, outer cone distance, pitch cone angle, tooth width, tip circle diameter of the large end, pitch circle diameter of the large end, and base circle diameter of the large end, obtain the contact ratio of the spur bevel gear at the two-thirds meshing position from the large end to the small end.

[0079] Based on the overlap at the two-thirds meshing position of the tooth width from the large end to the small end of the straight bevel gear, determine whether the tooth root angle increment design is reasonable.

[0080] The specific steps include:

[0081] S1. Obtain the outer cone distance of the straight bevel gear.

[0082] Set the spherical radius coefficient K of the straight bevel gear b And differential torque calculation T d The spherical radius coefficient K of straight bevel gears b The value range is 2.52-2.99. In this embodiment, K is set to... b =2.69, T d =410 Nm;

[0083] According to the spherical radius coefficient K of straight bevel gears b And differential torque calculation T d The spherical radius R of the straight bevel gear is calculated. b The formula for the spherical radius of a straight bevel gear is as follows:

[0084]

[0085] In the formula, the differential calculation torque T d The unit is Nm; the spherical radius R of a straight bevel gear b The unit is mm;

[0086] Based on the spherical radius R of the straight bevel gear b The outer cone distance Re of the straight bevel gear is obtained by rounding down the value to an integer or 0.5. Specifically, this rounding principle means taking the larger value and avoiding the smaller one. For example, the calculated result R... b =48.2, rounded to 48.5, the formula calculation result R b =48.6, rounded to 49; the outer cone distances Re1 and Re2 of the half-shaft gear 1 and planetary gear 2 in this embodiment are obtained by the above method; in this embodiment, Re1 = Re2 = 53.

[0087] S2. Obtain the cone angle of half-shaft gear 1 and planetary gear 2.

[0088] The number of teeth Z1 of the half-shaft gear 1 and the number of teeth Z2 of the planetary gear 2 are set. The value range of the number of teeth Z2 of the planetary gear 2 used in the passenger car differential is 9-11. The value range of the number of teeth Z1 of the half-shaft gear 1 is obtained based on the number of teeth Z2 of the planetary gear 2 and the speed ratio of the differential (speed ratio range is 1.3-1.6). In this embodiment, Z2 = 10 and Z1 = 16 are set.

[0089] The cone angles of half-shaft gear 1 and planetary gear 2 are calculated based on the number of teeth Z1 of half-shaft gear 1 and the number of teeth Z2 of planetary gear 2, using the following formula:

[0090] δ2=arctan(Z2 / Z1)

[0091] δ1=90°-δ2

[0092] In the formula, δ2 is the cone angle of planetary gear 2, in degrees; δ1 is the cone angle of half-shaft gear 1, in degrees.

[0093] S3. Obtain the large-end module of half-shaft gear 1 and planetary gear 2.

[0094] The pitch circle diameter of the spur bevel gear is calculated based on the pitch cone angle and the outer cone distance Re; the calculation formula is as follows:

[0095] d e = 2 * Re * sin(δ)

[0096] In the formula, d e δ is the pitch circle diameter of the large end of the spur bevel gear; δ is the cone angle of the spur bevel gear.

[0097] Substituting the cone angle and outer cone distance Re of half-shaft gear 1 and planetary gear 2 into the above formula, the large end pitch circle diameter d of planetary gear 2 can be obtained. e2 The pitch circle diameter d of the large end of the half-shaft gear 1 e1 In this embodiment, d e2 =56.18; d e1 =89.888.

[0098] The large-end module of a straight bevel gear is calculated based on its large-end pitch circle diameter and the number of teeth. The calculation formula is as follows:

[0099]

[0100] In the formula, m e Z is the large-end module of the spur bevel gear; Z is the number of teeth of the spur bevel gear.

[0101] Substituting the pitch circle diameter and number of teeth of the half-shaft gear 1 and planetary gear 2 into the above formula, we obtain the module m of the half-shaft gear 1 and planetary gear 2. e1 and m e2 In this embodiment, m e1 =m e2 =5.618.

[0102] S4. Obtain the large end addendum, large end dedendum, large end addendum circle diameter, large end dedendum circle diameter, and large end base circle diameter of half-shaft gear 1 and planetary gear 2.

[0103] The pressure angle α of the spur bevel gear is set, and the value of the pressure angle α is in the range of 22.5°-25°. In this embodiment, α is set to 22.5°.

[0104] Based on the differential speed ratio and the fatigue strength calculated by simulation of the straight bevel gear, and combined with the height change method, the radial displacement coefficient x of the straight bevel gear is set; in this embodiment, the radial displacement coefficient x2 of the planetary gear 2 is set to 0.173, and the radial displacement coefficient x1 of the half shaft gear 1 is equal in magnitude and opposite in sign to x2, that is, x1 = -0.173.

[0105] Set the addendum coefficient h of the spur bevel gear a * and the porosity coefficient c*, ha* range from 0.85 to 1.15, h a * A larger value results in a larger tooth tip diameter and a narrower tooth tip width, to prevent the tooth tip from being too sharp; c* is usually greater than or equal to 0.2. A larger value results in a smaller tooth root, which leads to reduced gear strength. c* needs to be set according to the gear strength requirements and differential lubrication requirements; in this embodiment, h is set... a * = 0.92, and the porosity coefficient c* = 0.2.

[0106] According to the tooth tip height coefficient h of spur bevel gears a * Radial displacement coefficient x and large-end module m e The tooth tip height h of the spur bevel gear is calculated. a The calculation formula is as follows:

[0107]

[0108] The large end addendum h of planetary gear 2 in this embodiment is obtained from the above formula. a2 =6.14; Large end tooth tip height h of half-shaft gear 1 a1 =5.36;

[0109] According to the tooth tip height coefficient h of spur bevel gears a *, Clearance coefficient c*, Radial displacement coefficient x, and Large-end module m e The root height h of the large end of the spur bevel gear is calculated. fThe calculation formula is as follows:

[0110]

[0111] The root height h of the large end of planetary gear 2 in this embodiment is obtained from the above formula. f2 =5.36; the root height h of the large end of the half-shaft gear 1 f1 =7.3.

[0112] According to the pitch circle diameter d of the large end of the spur bevel gear e Tooth tip height h a The diameter d of the large end addendum circle of the straight bevel gear is calculated from the cone angle δ. a The calculation formula is as follows:

[0113] d a =d e +2*h a *cosδ

[0114] The large end addendum circle diameter d of planetary gear 2 in this embodiment is obtained from the above formula. a2 =66.59; Large end addendum circle diameter d of half-shaft gear 1 a1 =94.34.

[0115] According to the pitch circle diameter d of the large end of the spur bevel gear e Large end tooth root height h f The diameter d of the large end root circle of the straight bevel gear is calculated from the cone angle δ. f The calculation formula is as follows:

[0116] d f =d e -2*h f *cosδ

[0117] The large end root circle diameter d of planetary gear 2 in this embodiment is obtained from the above formula. f2 =47.09; d, the diameter of the root circle of the large end of the half-shaft gear 1 f1 =82.13.

[0118] According to the pitch circle diameter d of the large end of the spur bevel gear e The base circle diameter d of the large end of the spur bevel gear is calculated using the pressure angle α. b The calculation formula is as follows:

[0119] d b =d e *cosα

[0120] The base circle diameter d of the planetary gear 2 in this embodiment is obtained from the above formula. b2 =51.9; the base circle diameter d of the large end of half-shaft gear 1 b1=83.

[0121] S5. Obtain the tooth tip angle, tooth root angle, tip cone angle, root cone angle, and base fillet of half-shaft gear 1 and planetary gear 2.

[0122] To further enhance the strength of the root fillet, this invention sets a root angle increment Δf. Increasing the root angle of planetary gear 2 leads to an increase in the root circle of the small end 6 of the planetary gear at the same tooth width, while decreasing the addendum circle of the small end 4 of the axle gear, ensuring that the tooth tip clearance from the large end to the small end remains constant. Similarly, increasing the root angle 9 of the axle gear leads to an increase in the root circle of the small end 4 of the axle gear at the same tooth width, while decreasing the addendum circle of the small end 6 of the planetary gear. Since the base circles at the same tooth width are equal in size, increasing the root angle will cause the overlap of the meshing section from the large end to the small end to gradually decrease, resulting in a decline in the NVH performance of the bevel gear system. Therefore, in addition to considering strength improvement, the NVH performance of the differential should also be taken into account during the design. Thus, the root angle increment Δf cannot be too large. When designing the root angle increment Δf of planetary gear 2 and axle gear 1, the overlap of the meshing position at two-thirds of the tooth width from the large end to the small end should be greater than or equal to 1.

[0123] Set the tooth root angle increment Δf; in this embodiment, the tooth root angle increment Δf1 of the half-shaft gear 1 is set to 0.02 rad, and the tooth root angle increment Δf2 of the planetary gear 2 is set to 0.065 rad;

[0124] Based on the root height h of the large end of the straight bevel gear f The root angle θ of the spur bevel gear is obtained by calculating the external cone distance Re and the root angle increment Δf. f The calculation formula is as follows:

[0125]

[0126] The root angle θ of the planetary gear in this embodiment is obtained from the above formula. f2 = 5.36; Half-shaft gear tooth root angle θ f1 =7.3.

[0127] According to the root angle θ of a straight bevel gear f Obtain the tooth tip angle θ of the straight bevel gear. a ;

[0128] Planetary gear tooth tip angle θ a2 =θ f1 Half-shaft gear tooth tip angle θ a1 =θ f2 ;

[0129] Based on the cone angle δ and the tip angle θ of the straight bevel gear a The tip cone angle δ of the spur bevel gear is calculated. aThe calculation formula is as follows:

[0130] δ a =δ+θ a

[0131] The planetary gear cone angle δ in this embodiment is obtained from the above formula. a2 =5.36; Half-shaft gear tip cone angle δ a1 =6.14.

[0132] Based on the cone angle δ and root angle θ of a straight bevel gear f The root cone angle δ of the spur bevel gear is calculated. f The calculation formula is as follows:

[0133] δ f =δ-θ f

[0134] The root cone angle δ of the planetary gear in this embodiment is obtained from the above formula. f2 =7.3; Half-shaft gear root cone angle δ f1 =4.2.

[0135] According to the pitch circle diameter d of the large end of the spur bevel gear e d, the base circle diameter of the large end b The base fillet angle θ of the spur bevel gear is obtained by calculating the outer cone distance Re and the cone angle δ. b The calculation formula is as follows:

[0136]

[0137] The base fillet angle θ of the planetary gear in this embodiment is obtained from the above formula. b2 = 2.723°; half-shaft gear base fillet θ b1 =6.944°.

[0138] S6. Obtain the addendum circle diameter, pitch circle diameter, and base circle diameter of the half-shaft gear 1 and planetary gear 2 at the meshing position where the tooth width is two-thirds from the large end to the small end.

[0139] The tooth width of the bevel gear in a passenger car differential usually varies with the load torque, which ranges from 1500 Nm to 4500 Nm, and the tooth width ranges from 14 mm to 20 mm. In this embodiment, the design process is described with a tooth width of 18 mm, that is, the tooth width W1 of the half shaft gear 1 = the tooth width W2 of the planetary gear 2 = 18 mm, and the overlap ratio at the 12 mm meshing section at two-thirds of the tooth width is calculated.

[0140] Based on the tooth width W and the large end addendum circle diameter d of the straight bevel gear a δ, the angle of the apex cone a and tooth tip angle θ aThe calculated addendum diameter d' of the meshing teeth a The calculation formula is as follows:

[0141]

[0142] The planetary gear meshing tooth tip circle diameter d' in this embodiment is obtained from the above formula. a2 =49.7; Diameter of the addendum circle of the meshing teeth of the half-shaft gear d' a1 =72.44;

[0143] The pitch circle diameter d of the spur bevel gear is calculated based on the tooth width W, outer cone distance Re, and pitch cone angle δ. e The calculation formula is as follows:

[0144]

[0145] The pitch circle diameter d of the planetary gear meshing circle in this embodiment is obtained from the above formula. e '2=43.36; pitch circle diameter of the half-shaft gear meshing circle d e '1 = 69.535;

[0146] Based on the tooth width W and the base circle diameter d of the spur bevel gear b Cone angle δ and base radius θ b The meshing base circle diameter d was calculated. b The calculation formula is as follows:

[0147]

[0148] The diameter d of the planetary gear meshing base circle in this embodiment can be obtained from the above formula. b '2=40.15; half-shaft gear meshing base circle diameter d b '1=64.242.'

[0149] S7. Obtain the equivalent addendum circle diameter, equivalent pitch circle diameter, equivalent base circle diameter, and equivalent meshing length of the half-shaft gear 1 and planetary gear 2 at the two-thirds meshing position from the large end to the small end.

[0150] Based on the tip circle diameter d' of the meshing teeth a The equivalent tip circle diameter d at the meshing position is calculated from the cone angle δ. av The calculation formula is as follows:

[0151]

[0152] The equivalent pitch circle diameter d of planetary gear 2 in this embodiment is obtained from the above formula. av2 =58.611; Equivalent pitch circle diameter d of half-shaft gear 1 av1 =136.686;

[0153] According to the pitch circle diameter d e The equivalent pitch circle diameter d at the meshing position is obtained by calculating the cone angle δ. ev The calculation formula is as follows:

[0154]

[0155] The equivalent pitch circle diameter d of planetary gear 2 in this embodiment is obtained from the above formula. ev2 =51.25; Equivalent pitch circle diameter d of half-shaft gear 1 ev1 =131.2;

[0156] Based on the meshing base circle diameter d b The equivalent base circle diameter d at the meshing position is calculated from the cone angle δ. bv The calculation formula is as follows:

[0157]

[0158] The equivalent base circle diameter d of planetary gear 2 in this embodiment is obtained from the above formula. bv2 =47.349; Equivalent base circle diameter d of half-shaft gear 1 bv1 =121.213;

[0159] Based on the equivalent tip circle diameter d of half-shaft gear 1 av1 The equivalent pitch circle diameter d of planetary gear 2 av2 The equivalent base circle diameter d of half-shaft gear 1 bv1 The equivalent base circle diameter d of planetary gear 2 bv2 The equivalent meshing length g at the meshing position is calculated using the pressure angle α. av The calculation formula is as follows:

[0160]

[0161] Based on the above formula, the equivalent meshing length g of the half-shaft gear 1 and planetary gear 2 at the two-thirds meshing position from the large end to the small end in this embodiment is obtained. av1 and g av2 g av1 =g av2 =13.9467.

[0162] S8. Obtain the equivalent number of teeth, equivalent module, and overlap ratio of the half-shaft gear 1 and planetary gear 2 at the two-thirds meshing position from the large end to the small end.

[0163] The equivalent number of teeth Z at the meshing position is calculated based on the number of teeth Z and the cone angle δ of the spur bevel gear. v The calculation formula is as follows:

[0164]

[0165] Based on the above formula, the equivalent number of teeth Z at the two-thirds meshing position of the half-shaft gear 1 in this embodiment can be obtained. v1 =30.189; Equivalent number of teeth Z at the two-thirds meshing position of planetary gear 2 v2 =11.792.

[0166] Based on the equivalent pitch circle diameter d at the meshing position ev and equivalent number of teeth Z v The equivalent modulus m at the meshing position was calculated. v The calculation formula is as follows:

[0167]

[0168] Based on the above formula, the equivalent modulus m at the two-thirds meshing position of the half-shaft gear 1 in this embodiment is obtained. v1 The equivalent module m of the planetary gear at two-thirds meshing position v2 m v1 =m v2 =4.346.

[0169] Based on the equivalent meshing length g av Equivalent modulus m v The overlap ratio ε at two-thirds of the meshing position is calculated using the pressure angle α; the calculation formula is as follows:

[0170]

[0171] The overlap ratio ε1 at the two-thirds meshing position of the half-shaft gear 1 and the overlap ratio ε2 at the two-thirds meshing position of the planetary gear 2 are obtained according to the above formula; ε1=ε2=1.1.

[0172] S9. Based on the calculated overlap ε at two-thirds of the meshing position, determine whether the tooth root angle increment Δf design is reasonable.

[0173] ε < 1; the tooth root angle increment Δf is poorly designed;

[0174] ε=1; the tooth root angle increment Δf is reasonably designed, and the tooth root angle increment Δf reaches its maximum value;

[0175] ε>1; the tooth root angle increment Δf is reasonably designed and can be adjusted according to the strength of gear bending.

[0176] For example, taking a half-shaft gear as an example; the strength of a double-retracting toothed gear and a constant clearance retracting toothed gear are compared and analyzed; the comparison and analysis process is as follows:

[0177] Under the premise that the tooth profile parameters of the bevel gear, such as module, number of teeth, pressure angle, tooth width, addendum, dedendum, and material, are kept the same, the maximum root fillet coefficient of the half-shaft gear obtained by the equal clearance shrinkage tooth design is 0.5, and it is still a double arc when the maximum fillet is used; while the design of this case results in a maximum root fillet coefficient of 0.6 for the half-shaft gear, and it is a full arc when the maximum fillet is used; according to the ISO10300:2014 verification standard, the strength verification was carried out, and the bending stress at the root of the half-shaft gear with equal clearance shrinkage tooth design was SF=1742Mpa, while the bending stress at the root of the half-shaft gear obtained by the design of this case was SF'=1587Mpa; under the premise of transmitting the same amount of torque, the bending stress at the root of the half-shaft gear obtained by the design of this case is less than that of the half-shaft gear obtained by the equal clearance shrinkage tooth design; that is, the bending resistance of the half-shaft gear obtained by the design of this case is improved by 8.9%, which is close to the strength improvement level of the strong spraying process. The parameters and simulation results of the half-shaft gear are shown in Table 1:

[0178] Table 1. Parameters and simulation results of the half-shaft gear.

[0179]

[0180] This invention achieves the transformation of straight bevel gears into double-contraction gears by setting the root angle increment Δf; in addition, the further increase of the root radius allows straight bevel gears to achieve a full-circle arc design; thus, the differential straight bevel gear system achieves a greater strength improvement in the same volume, which can better meet the lightweight and high-strength requirements of new energy vehicles.

[0181] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A differential spur bevel gear structure, characterized in that, Including meshing straight bevel gears, the tooth root fillet of the straight bevel gears adopts a full arc design; The tooth root angle of the straight bevel gear is provided with a tooth root angle increment, and the tooth root angle increment should make the overlap ratio of the straight bevel gear at the meshing position of two-thirds of the tooth width from the large end to the small end greater than or equal to 1. Obtaining the overlap ratio of a straight bevel gear at the two-thirds meshing position from the large end to the small end specifically includes: Set the tooth width of the spur bevel gear, and based on the tooth width, the large end addendum circle diameter, the addendum cone angle, the tooth tip angle, the outer cone distance, the pitch cone angle, the large end base circle diameter, and the base circle angle, obtain the meshing addendum circle diameter, the meshing pitch circle diameter, and the meshing base circle diameter at the meshing position where the tooth width is two-thirds from the large end to the small end of the spur bevel gear. Based on the addendum circle diameter, cone angle, pitch circle diameter, and base circle diameter, obtain the equivalent addendum circle diameter, pitch circle diameter, base circle diameter, and meshing length of the spur bevel gear at the meshing position where the tooth width is two-thirds from the large end to the small end. Based on the number of teeth, cone angle, equivalent pitch circle diameter, equivalent meshing length, and pressure angle of the spur bevel gear, obtain the equivalent number of teeth, equivalent module, and contact ratio at the meshing position where the tooth width is two-thirds from the large end to the small end.

2. The differential spur bevel gear structure according to claim 1, characterized in that, The straight bevel gear includes a half-shaft gear (1) and a planetary gear (2); The half-shaft gear (1) is provided with a half-shaft gear disk, and the half-shaft gear disk is provided with half-shaft gear teeth distributed in a circular array. A half-shaft gear tooth root (12) is provided between adjacent half-shaft gear teeth, and the tooth root fillet at the half-shaft gear tooth root (12) adopts a full arc design. The planetary gear (2) is provided with a planetary gear disk, and the planetary gear disk is provided with a circumferential array of planetary gear teeth. Planetary gear tooth roots (15) are provided between the planetary gear teeth, and the tooth root fillet at the planetary gear tooth root (15) adopts a full arc design.

3. A differential spur bevel gear structure according to claim 2, characterized in that, The half-shaft gear (1) includes a large end (3) and a small end (4). The large end (3) of the half-shaft gear is provided with a large end reinforcing rib (13), and the small end (4) of the half-shaft gear is provided with a small end reinforcing rib (7). The planetary gear (2) includes a large end (5) and a small end (6). The large end (5) of the planetary gear is provided with a large end reinforcing rib (17), and the small end (6) of the planetary gear is provided with a small end reinforcing rib (8).

4. A method for designing a differential spur bevel gear structure, used in the differential spur bevel gear structure described in any one of claims 1-3, characterized in that, The design method includes: using a full circular arc structure to design the root fillet of meshing straight bevel gears; Set the root angle increment of the spur bevel gear. The root angle increment should make the contact ratio of the spur bevel gear at the two-thirds meshing position from the large end to the small end greater than or equal to 1. Based on the number of teeth, root height of the large end, outer cone distance, pitch cone angle, tooth width, addendum circle diameter of the large end, pitch circle diameter of the large end, and base circle diameter of the large end, obtain the contact ratio of the spur bevel gear at the two-thirds meshing position from the large end to the small end. Based on the overlap at the two-thirds meshing position of the tooth width from the large end to the small end of the straight bevel gear, determine whether the tooth root angle increment design is reasonable.

5. The structural design method according to claim 4, characterized in that, The straight bevel gear includes a half-shaft gear (1) and a planetary gear (2); Before setting the root angle increment of the straight bevel gear, the spherical radius coefficient of the straight bevel gear and the calculated torque of the differential are set, and the outer cone distance of the straight bevel gear is obtained based on the spherical radius coefficient of the straight bevel gear and the calculated torque of the differential. Set the number of teeth of the planetary gear (2), and obtain the cone angle of the half shaft gear (1) and the planetary gear (2) based on the number of teeth of the planetary gear (2); The large-end module of the straight bevel gear is obtained based on the cone angle, number of teeth, and outer cone distance of the straight bevel gear. Set the pressure angle, radial displacement coefficient, tooth addendum coefficient, and clearance coefficient of the spur bevel gear. Based on the pressure angle, radial displacement coefficient, tooth addendum coefficient, clearance coefficient, large end module, and cone angle of the spur bevel gear, obtain the large end tooth addendum, large end tooth dedendum, large end tooth tip circle diameter, large end tooth dedendum circle diameter, and large end base circle diameter of the spur bevel gear.

6. The structural design method according to claim 4, characterized in that, The specific steps for obtaining the addendum circle diameter, pitch circle diameter, and base circle diameter of the spur bevel gear at the two-thirds meshing position from the large end to the small end include: Based on the tooth width of the spur bevel gear W Large end tooth tip circle diameter d a , vertex angle and tooth tip angle θ a The diameter of the addendum circle of the meshing teeth is calculated using the following formula: In the formula, The tip circle diameter of the meshing teeth of the spur bevel gear; Based on the tooth width of the spur bevel gear W , outer cone distance Re and cone angle The pitch circle diameter is calculated using the following formula: In the formula, The pitch circle diameter of the spur bevel gear; Based on the tooth width of the spur bevel gear W Large end base circle diameter d b Cone angle and base fillet θ b The diameter of the meshing base circle is calculated using the following formula: In the formula, The base circle diameter of the spur bevel gear.

7. The structural design method according to claim 4, characterized in that, The specific steps for obtaining the equivalent tip circle diameter, equivalent pitch circle diameter, equivalent base circle diameter, and equivalent meshing length of the spur bevel gear at the two-thirds meshing position from the large end to the small end specifically include: Based on the tip circle diameter of the meshing teeth and cone angle The equivalent tip circle diameter at the meshing position is calculated using the following formula: In the formula, d av This is the equivalent tooth tip circle diameter at the meshing position; The equivalent tip circle diameter of the planetary gear (2) at the meshing position is obtained from the above formula. d av2 The equivalent tip circle diameter of the half-shaft gear (1) at the meshing position d av1 ; According to the pitch circle diameter and cone angle The equivalent pitch circle diameter at the meshing position is calculated using the following formula: In the formula, d ev This is the equivalent pitch circle diameter at the meshing position; Based on the meshing base circle diameter and cone angle The equivalent base circle diameter at the meshing position is calculated using the following formula: In the formula, d bv This is the equivalent base circle diameter at the meshing position; The equivalent base circle diameter at the meshing position of the planetary gear (2) can be obtained from the above formula. d bv2 ; Equivalent base circle diameter at the meshing position of the half-shaft gear (1) d bv1 ; Based on the equivalent tooth tip circle diameter at the meshing position of the half-shaft gear (1) d av2 The equivalent tip circle diameter of the planetary gear (2) at the meshing position d av2 ; Equivalent base circle diameter at the meshing position of the half-shaft gear (1) d bv1 The equivalent base circle diameter at the meshing position of the planetary gear (2) d bv2 and pressure angle α The equivalent engagement length at the engagement position is calculated using the following formula: In the formula, g av This is the equivalent engagement length at the engagement position.

8. The structural design method according to claim 4, characterized in that, The specific steps for obtaining the equivalent number of teeth, equivalent module, and contact ratio at the two-thirds meshing position of the straight bevel gear from the large end to the small end include: Based on the number of teeth of a straight bevel gear Z and cone angle The equivalent number of teeth at the meshing position is calculated. Z v The calculation formula is as follows: In the formula, Z v This represents the equivalent number of teeth at the meshing position; Based on the equivalent pitch circle diameter at the meshing position d ev and equivalent number of teeth Z v The equivalent modulus at the meshing position was calculated. m v The calculation formula is as follows: In the formula, m v This is the equivalent modulus at the meshing position; Based on equivalent meshing length g av Equivalent Modulus m v and pressure angle α The overlap ratio at the two-thirds meshing position was calculated. The calculation formula is as follows: In the formula, This represents the degree of overlap at the meshing position.

9. The structural design method according to claim 4, characterized in that, The overlap ratio at the two-thirds meshing position of the straight bevel gear from the large end to the small end. Determine the tooth root angle increment Δ f Whether a design is reasonable specifically includes: <1; Tooth root angle increment Δ f The design is flawed; ≥1; Tooth root angle increment Δ f The design is reasonable.

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