CN112283318A

CN112283318A - High-strength bevel gear tooth form design method

Info

Publication number: CN112283318A
Application number: CN202010944576.9A
Authority: CN
Inventors: 贾巨民; 詹隽青; 高波; 马雅丽; 刘文开; 张淼
Original assignee: Army Military Transportation University
Current assignee: Army Military Transportation University
Priority date: 2020-09-10
Filing date: 2020-09-10
Publication date: 2021-01-29

Abstract

The invention discloses a tooth profile design method of a high-strength bevel gear, which covers a conical gear and a non-conical gear. The high-strength bevel gear adopts a LogoX tooth form, the part (tooth top) above a pitch line (the conical gear is degraded into a pitch circle) is convex, the part (tooth root) below the pitch line is concave, and a pair of gear teeth can realize convex-concave meshing in the transmission process; the tooth profile is formed by connecting a series of characteristic points, the curvature centers of the characteristic points are on a pitch curve (pitch circle), when a pair of tooth profiles are meshed at the corresponding characteristic points, the curvature centers are superposed and fall at the nodes, and the instantaneous pure rolling condition is met; compared with an involute tooth profile, the tooth surface contact stress and the slip rate of the involute tooth profile are greatly reduced, the friction is reduced, the transmission with fewer teeth can be realized, and the strength and the efficiency are obviously improved.

Description

High-strength bevel gear tooth form design method

Technical Field

The invention belongs to the field of mechanical design, and particularly relates to a tooth profile design method of a high-strength bevel gear, which covers a conical gear and a non-conical gear.

Technical Field

Bevel gears are used for crossed-axis transmission, and strength is one of the most important performance indexes. At present, the bevel gear generally adopts an involute tooth profile, and the theoretical tooth profile of the bevel gear is a spherical involute. The involute has many excellent properties, but has many defects, firstly, because the shape is convex, a pair of bevel gears are in convex-convex meshing, the contact stress is large, and the contact strength is limited; secondly, except that two tooth surfaces on the pitch cone are in pure rolling contact, other parts all have sliding, and the farther away from the pitch cone, the larger the slip rate is, so that the friction and the abrasion are serious; furthermore, due to the shape and undercut of the involute, the number of gear teeth cannot be too small, the root of the gear teeth is not wide enough, and the bending strength is weak. The weakness of the method is particularly obvious in the application fields of high speed, heavy load and the like.

In recent years, noncircular bevel gear transmission is widely applied in some fields, the tooth profile design is more complex, and the involute is difficult to meet the performance requirement.

In 1990, t.komori et al (a New gear Profile Having Zero Relative current Profile), Transactions of the ASME, vol.112, separator, 1990) proposed a New Tooth Profile, named Logix Tooth Profile, mainly for cylindrical Gears, belonging to a planar mesh, whose Profile is of a convex-concave combination type, with a pitch circle as a dividing point, a Tooth Profile above (addendum) the pitch circle being convex and below (dedendum) the pitch circle being concave, and a pair of gear transmissions, constituting a convex-concave mesh, with a greatly reduced Contact stress; furthermore, because the logIX tooth profile is formed by connecting a series of characteristic points, the curvature centers of the characteristic points are on a pitch circle, when a pair of tooth profiles are meshed with the corresponding characteristic points, the curvature centers are superposed and fall on the nodes, so that the instantaneous pure rolling condition is met, although relative sliding exists in the transition between the adjacent connecting points, the connecting points (pure rolling meshing points) can be designed to be enough, the slip ratio value is not too large, the friction is reduced, and the contact strength and the transmission efficiency of the gear teeth are obviously improved. In addition, compared with an involute tooth form, the root of the gear tooth of the LogoX tooth form is thicker, and the bending strength can be improved to a certain extent. Further, by adopting the LogiX tooth form, the number of the gear teeth can be designed to be less, and the bending strength can be further improved.

By extension, for planar non-cylindrical gears, the pitch circle becomes a non-circular pitch line, and the above LogiX principle is still valid.

How to apply the above LogiX tooth form principle to bevel gears is the main content of the present invention. Because bevel gear transmission belongs to space meshing, theoretical calculation and design of the bevel gear transmission are carried out on a spherical surface, and the LogiX tooth profile design method suitable for plane gear meshing cannot be directly transplanted to the spherical surface.

Disclosure of Invention

The invention provides a tooth form design method of a high-strength bevel gear, which covers the tooth form design of a bevel gear and a non-bevel gear.

A bevel gear tooth form design method based on a LogiX tooth form principle comprises the steps of mapping a spherical pitch curve to a plane, constructing a plane tooth form and reversely mapping the plane tooth form to a spherical surface; the mapping from the spherical pitch curve to the plane and the reverse mapping from the plane tooth form to the spherical surface both adopt a method of geodesic curvature preservation, namely, the geodesic curvature of the spherical curve is ensured to be equal to the relative curvature of the plane curve; the plane tooth profile structure adopts a LogiX tooth profile principle: the tooth profile consists of a convex part and a concave part, wherein the part (tooth top) above a pitch curve is convex, the part (tooth root) below the pitch curve is concave, and the tooth profiles of a pair of gear teeth can realize convex-concave meshing in the transmission process; the tooth profile is formed by connecting a series of characteristic points, the curvature centers of the characteristic points are on a pitch curve, when a pair of tooth profiles are meshed at the corresponding characteristic points, the curvature centers are superposed and fall on the pitch curve, and the instantaneous pure rolling condition is met.

Bevel gears encompass bevel gears and non-bevel gears, a special case of which is bevel gear.

The invention has the following beneficial effects: according to the method, the plane LogoX tooth form principle can be applied to a spherical surface to complete the tooth form design of the bevel gear, and the designed bevel gear has the characteristics of high strength, low slip rate, small friction, high transmission efficiency and the like. And because the bevel gear generally adopts forging or extrusion molding, compared with the common involute bevel gear, the manufacturing process difficulty and the cost of the high-strength bevel gear designed according to the invention are not increased, and the high-strength bevel gear is very easy to popularize and apply.

Drawings

FIG. 1 is a schematic view of a bevel gear drive;

FIG. 2 is a schematic diagram of a fixed ratio power transmission pitch cone rolling only;

FIG. 3 is a schematic pure rolling cone diagram of the variator ratio drive pitch;

FIG. 4 is a plan view pitch graph illustration;

FIG. 5 is a schematic view of a rack tooth profile and a normal thereto;

FIG. 6 is a schematic view of a tooth form and its normal, pitch lines;

FIG. 7 is a schematic view of a spherical tooth profile and pitch curve;

FIG. 8 is a schematic view of an involute planetary bevel gear;

FIG. 9 is a schematic view of an involute half-shaft bevel gear;

FIG. 10 is a schematic view of a spherical tooth profile

FIG. 11 is a schematic illustration of a planetary bevel gear based on a LogiX tooth profile;

FIG. 12 is a schematic illustration of a half shaft bevel gear based on a LogiX tooth profile;

FIG. 13 is a schematic view of a bevel gear drive pair based on the LogoX tooth profile

FIG. 14 is a schematic of the differential gearing;

FIG. 15 is a schematic view of a low tooth count high strength bevel gear pair;

FIG. 16 is a schematic view of a non-conical gear drive.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

The invention provides a tooth profile design method of a high-strength bevel gear, which comprises the steps of mapping a spherical pitch curve to a plane, constructing a plane LogiX tooth profile and reversely mapping the plane tooth profile to the spherical surface, and comprises the following specific steps:

1. spherical pitch curve mapping

Fig. 1 is a schematic diagram of a pair of bevel gear transmission structures.

∑＝δ₁+δ₂

The transmission ratio is as follows:

in the formula (I), the compound is shown in the specification,

angle of rotation of two gears, delta₁,δ₂Two-gear pitch angle, ω₁,ω₂-two gear speeds.

For fixed ratio transmissions, δ₁,δ₂All are constant values and their motion corresponds to a pure rolling of a pair of pitch cones as shown in fig. 2. And for variable ratio transmissions, δ₁,δ₂Become into

(or

) The motion of which corresponds to a pure rolling of a pair of non-circular pitch cones, as shown in fig. 3. The intersection line of the pitch cone and the sphere is called a spherical pitch curve, and the equation can be expressed as:

in the formula, r₀Spherical radius, in the latter embodiment, r is taken₀=45.1。

Spherical equation:

the geodesic curvature of one curve is as follows:

in the formula, the intersection angle of the gamma-spherical curve and the meridian line, and the s-arc length.

A curve is constructed on a plane:

the following steps are performed:

κ_r＝κ_g

κ_r-relative curvature of the plane curve and having:

the planar curve is formed by mapping the spherical curve onto the plane.

The planar pitch curve shown in fig. 4 can be obtained by applying the above method to the spherical pitch curve shown in fig. 3.

Obviously, the calculation principle of the bevel gear transmission is similar to that of the non-bevel gear transmission, but the bevel gear transmission is simpler, and a pair of pure rolling circular pitch curves of a spherical surface are mapped onto a plane to form two pure rolling circular arcs, as shown in fig. 6, wherein only a pair of corresponding gear tooth meshing tooth profiles are shown.

2. Plane LogiX tooth-shaped structure

Based on the plane pitch curve, a tooth profile curve is constructed according to the LogiX tooth profile principle, and the tooth profile of the medium rack is firstly constructed, as shown in fig. 5. The tooth profile is composed of two parts, wherein the part above the pitch line (tooth top) is convex, the part below the pitch line (tooth bottom) is concave, each part is formed by connecting a series of characteristic points, and the curvature center of the characteristic points is on the pitch line.

For involute tooth profile, it is known that a medium rack tooth profile is a segment of a pressure angle α_nStraight line of (a)_n-pressure angle at the pitch line.

The gear tooth profile can be conjugated (created, generated) using the rack shown in fig. 5 as a medium, as shown in fig. 6. The tooth profile is also composed of convex-concave parts, convex above the pitch line (tooth top) and concave below the pitch line (tooth root), the center of curvature of the characteristic point being on the pitch curve. When a pair of gears are used for transmission, convex-concave meshing can be realized, and when the corresponding tooth profiles are in contact with characteristic points, the curvature centers of the corresponding tooth profiles are superposed and just fall on a node, so that the instantaneous pure rolling condition is met.

3. Spherical tooth form calculation

After the tooth profile design is finished on the plane, the reverse mapping is carried out by adopting the mapping principle provided in the previous step, namely, the geodesic curvature of the spherical curve is ensured to be equal to the relative curvature of the plane curve

κ_g＝κ_r

The spherical tooth profile can be obtained, in the mapping process, the points on the plane pitch curve and the spherical pitch curve correspond one to one, and the normal line of the plane tooth profile is mapped into a spherical large arc. The mapping results are shown in fig. 7.

4. Examples of the embodiments

Example 1:

the bevel gear transmission of some automobile differential consists of two planetary gears and two half-shaft gears, 10 teeth of the planetary gears and 16 teeth of the half-shaft gears.

Originally, the involute tooth profile is adopted, and bevel gears are shown in figures 8 and 9.

Now, the tooth profile is changed into the LogoX tooth profile, the design is carried out according to the method provided by the invention, firstly, a spherical pitch curve is obtained, as shown in figure 2, then, the spherical pitch curve is mapped on a plane, on the basis of the plane LogoX tooth profile, as shown in figures 5 and 6, then, the spherical tooth profile is obtained by adopting reverse mapping, as shown in figure 10, and finally, the structural design is carried out, so that gears are formed, as shown in figures 11 and 12, and a transmission pair and a differential mechanism are formed, as shown in figures 13 and 14.

Compared with the original involute bevel gear transmission, the tooth surface contact stress and the slip rate of the involute bevel gear transmission are greatly reduced, the friction is reduced, the tooth root thickness is also increased to a certain extent, and the strength and the efficiency are obviously improved.

Example 2:

7/10 the high-strength bevel gear pair is of involute tooth form, affected by undercut and tooth top sharpening, and has not too few teeth to meet the requirement of contact ratio greater than 1. By using the invention, the transmission pair with less teeth can be designed, so that the gear teeth become stronger and the bending strength is higher. Fig. 15 shows an 7/10 high-strength bevel gear pair used in a differential of a certain type, in which the number of planet gears is 7 and the number of half-shaft gears is 10, and on the premise of meeting various performance requirements, the bending strength of the gear teeth can be further improved by more than 30% compared with the gear pair shown in fig. 13.

EXAMPLE 3A Limited slip differential of variable Transmission ratio of a certain type, using non-conical gears for transmission, the transmission ratio law is as follows

Setting, wherein: i.e. i₂₁Is the transmission ratio of the side gear 2 to the planetary gear 1, z₁、z₂The number of teeth of the planet gear 1 and the half axle gear 2,

the rotation angle of the planetary gear 1 is c-0.5, n-1, and 3 is a constant. The curve of the spherical pitch and the tooth profile are shown in FIG. 7, and the finally formed gear pair is shown in FIG. 16, wherein z₁＝9，z₂＝18，c＝0.4，n＝1。

Claims

1. A tooth profile design method for a high-strength bevel gear is characterized by comprising the steps of mapping a spherical pitch curve to a plane, constructing a plane tooth profile and reversely mapping the plane tooth profile to a spherical surface; the mapping from the spherical pitch curve to the plane and the reverse mapping from the plane tooth form to the spherical surface both adopt a method of geodesic curvature preservation, namely, the geodesic curvature of the spherical curve is ensured to be equal to the relative curvature of the plane curve; the plane tooth profile is constructed by adopting a LogiX principle and consists of a convex part and a concave part, wherein the part above a pitch curve, namely the tooth top, is convex, the part below the pitch curve, namely the tooth root, is concave, and in the transmission process, the tooth profiles of a pair of gear teeth can realize convex-concave meshing; the plane tooth profile is formed by connecting a series of characteristic points, the curvature centers of the characteristic points are on a pitch curve, when a pair of tooth profiles are meshed at the corresponding characteristic points, the curvature centers are superposed, and instantaneous pure rolling conditions are met on the pitch.

2. The method for designing a tooth profile of a high-strength bevel gear according to claim 1, wherein the bevel gear includes a bevel gear and a non-bevel gear, and the bevel gear is a special case of the non-bevel gear.