A small-angle cross-axis transmission internal meshing bevel gear structure and its design method

Abstract

A small-angle cross-axis transmission internal meshing bevel gear structure and its design method, the bevel gear structure includes an internal gear and an external gear with conical tooth profiles, the meshing mode of the internal gear and the external gear is a spatial cycloid meshing, and the axial lines of the internal gear and the external gear intersect at a set angle; the meshing surface of the internal gear and the external gear is a continuous closed spatial curved surface, and the internal gear rotates and revolves simultaneously when meshing around the external gear. The meshing surface of the internal gear is a rolling cone surface, and the meshing surface of the external gear is a fixed cone surface. The independent variables in the gear profile solution process are: the transmission ratio i HV , shape parameter c, and the independent variables of the coordinate system (the radius R1 of the bottom surface of the inner gear pitch cone and the large end pitch cone angle δ1). Therefore, in the specific design process of the present invention, the above independent variables can be adjusted according to different working conditions. The gear of the present invention has higher rotation stability during the precession process and better transmission effect.

Description

Technical Field

[0001] The invention belongs to the technical field of bevel gear processing, and in particular relates to a small-angle cross-axis transmission internal meshing bevel gear structure and a design method thereof. Background Art

[0002] Bevel gears are used to transmit motion and power between two intersecting shafts. In general machinery, they are similar to cylindrical gears and can change the direction of transmission. Bevel gears are widely used in printing equipment, automobile differentials and reducers. They can also be used in locomotives, aviation, ships, power plants, steel mills, and railway transportation. Compared with other types of gears, bevel gears are economical, wear-resistant, and have a long life. They are simple to manufacture and install, have smooth transmission operation, high gear load capacity, and low noise. They are suitable for high-speed and heavy-load occasions. However, the application of bevel gears currently has limitations. Since the axial angle between the two teeth of the bevel gear cannot be maintained at a small angle, it cannot meet the requirements of some transmission mechanisms under small angles. For example, in the field of machinery, the transmission angle range of the intersecting shafts of the bevel screw compressor is within 3°~15°, and traditional bevel gears cannot change the direction of rotation at such a small angle. In order to further improve the working performance of bevel gears in changing the transmission of intersecting shafts, it is necessary to enable them to meet the requirements of intersecting shafts with small angles. However, there are certain requirements for the profile that meets this meshing method, and it is also difficult to solve its conjugate surface and obtain an analytical solution. This brings difficulties to the design and manufacture of internal meshing bevel gears. Summary of the invention

[0003] The purpose of the present invention is to address the problems in the above-mentioned prior art and provide a small-angle cross-axis transmission internal meshing bevel gear structure and a design method thereof, which adopts a conical structure in which the external gear and the internal gear are internally meshed. The profiles of the internal and external gears are both combined curves of the spatial epicycloid and the spatial hypocycloid, and the inner and outer rotors can achieve a meshing relationship without interfering with each other.

[0004] In order to achieve the above object, the present invention has the following technical solutions:

[0005] A small-angle cross-axis transmission internal meshing bevel gear structure includes an internal gear and an external gear whose tooth profiles are both conical structures. The meshing mode of the internal gear and the external gear is spatial cycloid meshing, and the axial lines of the internal gear and the external gear intersect at a set angle; the meshing surfaces of the internal gear and the external gear are continuous closed spatial curved surfaces, and the internal gear simultaneously rotates and revolves when meshing around the external gear.

[0006] As a preferred solution, the meshing surface of the internal gear is a rolling cone surface, and the meshing surface of the external gear is a fixed cone surface.

[0007] As a preferred solution, the pitch cone space coordinate systems OX1Y1Z1 and OX2Y2Z2 of the internal gear and the external gear are established. When the rolling cone surface of the internal gear performs a non-slip rolling motion on the outside of the fixed cone surface of the external gear, the trajectory of a point C1 on the upper edge of the generatrix of the rolling cone surface of the internal gear is a spatial epicycloid. When the rolling cone surface of the internal gear performs a non-slip rolling motion on the inside of the fixed cone surface of the external gear, the trajectory of a point C2 on the upper edge of the generatrix of the rolling cone surface of the internal gear is a spatial hypocycloid. Then:

[0008] The equation of the space epicycloid is:

[0009]

[0010] The equation of the cycloid in space is:

[0011]

[0012] In the formula, δ represents the cone angle of the fixed cone, q h and q e They respectively represent the cone angles of the rolling cone that generates the spatial inner cycloid and the spatial outer cycloid. When the internal gear and the external gear move relative to each other, the distance between each point on the tooth surface and the pitch cone vertex O remains unchanged, that is, they move on the spherical surface. R is the radius of the sphere where the spherical cycloid is located. The conical structure of the gear is formed by the change in the size of R.

[0013] As a preferred solution, the radius R of the sphere where the spherical cycloid is located is changed proportionally to generate tooth profile curves of different sizes, the tapers of the internal gear and the external gear are generated by the tooth profile curves of different sizes, and the tooth profile surfaces of the internal gear and the external gear are obtained by spatial lofting.

[0014] As a preferred solution, the end with the smaller cycloid area of ​​the internal gear and the external gear is the small end, and the end with the larger cycloid area is the large end. The tooth profile curve of the small end and the tooth profile curve of the large end have the same pitch cone angle, forming the same number of teeth and different pitch cone radii, which are selected according to the required tooth thickness.

[0015] As a preferred solution, the radius of the internal gear large end dividing cone is set to r1, the pitch cone angle is δ1, the internal gear large end dividing cone is used as the fixed cone, the number of teeth is Z1, and after the rolling cone rolls 360°, a spatial epicycloid C is generated. 11 and the cycloid C in space 12 The combined space curve is the tooth profile curve of the large end of the internal gear;

[0016] Set the outer gear large end indexing cone radius r2, the pitch cone angle δ2, the outer gear large end indexing cone as the fixed cone, the number of teeth is Z2, and after the rolling cone rolls 360°, the generated spatial epicycloid C 21 and the cycloid C in space 22 The combined space curve is the tooth profile curve of the large end of the external gear;

[0017] In the same way, generate the small end tooth profile curves of the internal gear and the external gear.

[0018] As a preferred solution, the pitch cone radii of the internal gear and the external gear satisfy the following relationship:

[0019]

[0020] The intersection angle of the indexing cone axis of the internal gear and the external gear is:

[0021] φ=δ1+δ2

[0022] In the internal gear transmission, in order to form a full tooth, the rolling cone rolls over the base circle at a certain cone angle, and the profile shape parameters are c, q h The cone angle of the rolling cone that generates the inner cycloid in space is expressed. The number of teeth of the internal gear is calculated as follows:

[0023]

[0024] A design method for the small-angle cross-axis transmission internal meshing bevel gear structure comprises the following steps:

[0025] Given transmission ratio i HV , the number of teeth of the internal gear z1=-i HV , where the transmission ratio is an integer;

[0026] Given the spatial cycloid shape parameter c, the internal gear indexing cone angle δ′1, and the large end cone radius r1;

[0027] The tooth profile curve E1 of the large end of the internal gear is obtained by the following formula:

[0028]

[0029]

[0030] Select the tooth thickness, obtain the base circle radius of the small end tooth profile according to tanδ1, and obtain the small end tooth profile curve E2 in the same way. Loft the tooth profiles at both ends to obtain the tooth profile surface, and perform gear model design and physical processing in the actual installation environment;

[0031] The external gear parameters are obtained according to the number of teeth, and the external gear tooth profile surface and the corresponding object are obtained by the same method.

[0032] Compared with the prior art, the present invention has at least the following beneficial effects:

[0033] The internal meshing bevel gear with the combined curve of the spatial epicycloid and the spatial hypocycloid as the tooth profile can satisfy the change of the rotation direction of the intersecting shaft transmission while being able to combine the function of the planetary gear set and can be applied to the mechanical precession process. Compared with the traditional planetary gear set, the spatial cycloid internal meshing method can increase the meshing area between the teeth, and the gear meshing can be in close contact, so that the gear has higher rotation stability during the precession process and better transmission effect. And the cone angle of the bevel gear proposed in the present invention is equal to the cone angle of the spatial cycloid roll, which can be changed according to different situations when designing the profile, so the present invention is applicable to the rotation of intersecting axes in a wider angle range. The gear tooth profile profile proposed in the present invention has a specific parameter equation, and it is a relatively simple cycloid equation. Under the control of the specific equation, the design of the complex three-dimensional model of the gear is simplified. The tooth profile of the internal meshing bevel gear of the present invention is a continuous closed spatial curved surface without a tooth top surface, which greatly simplifies the forming of the gear model and the processing process of the actual scheme. The number of gear teeth in the present invention is controlled by the spatial cycloid, which is convenient for optimizing the gear model under specific requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the meshing principle of the internal meshing bevel gear structure of the small-angle cross-axis transmission of the present invention;

[0035] Figure 2 Schematic diagram of spherical cycloid of the structural profile design of the internal meshing bevel gear of the small-angle cross-axis transmission of the present invention;

[0036] FIG3( a ) is a schematic diagram of the internal gear profile lofting of the present invention;

[0037] FIG3( b ) is a schematic diagram of the external gear profile lofting of the present invention;

[0038] FIG. 4( a ) is a three-dimensional model diagram of the structure of the internal meshing bevel gear of the small-angle cross-axis transmission according to an embodiment of the present invention;

[0039] FIG. 4( b ) is a schematic cross-sectional view of the structure of the internally meshing bevel gears in the small-angle cross-axis transmission according to an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0041] In order to further improve the working performance of the bevel gear in changing the transmission of intersecting axes so that it can meet the requirements of intersecting axes with small angles, the present invention proposes a small-angle cross-axis transmission internal meshing bevel gear structure, the meshing mode of the bevel gear is internal meshing, and the component structure is divided into an external gear 2 and an internal gear 1. The tooth profiles of the two gears are both conical structures, and the two gear shafts intersect at a certain angle in space, and the angle is small and can be adjusted according to the required requirements. The internal meshing bevel gear of the present invention can change the transmission direction of the intersecting axes with the characteristics of its own structure, and at the same time meet the characteristics of the internal meshing gear, so that the internal gear 1 can mesh around the external gear 2 to achieve the purpose of self-rotation and revolution. Since the meshing mode of the small-angle cross-axis transmission internal meshing bevel gear structure of the present invention is a spatial cycloid internal meshing, it has the characteristics of a cycloid gear with a compact structure, small size, light weight, large transmission ratio, high efficiency, and stable transmission, but there are certain requirements for the profile that meets the gear meshing mode, and it is also difficult to solve its conjugate surface, and it is difficult to obtain an analytical solution, which brings difficulties to the design and manufacture of the internal meshing bevel gear. Therefore, the present invention also proposes a design method for the small-angle cross-axis transmission internal meshing bevel gear structure.

[0042] The process of meshing of the internal bevel gear of the present invention is as follows: Figure 1 As shown, a spatial coordinate system is established. When a rolling cone with a smaller taper performs a non-slip tangential rolling motion on the outside of a fixed cone with a larger taper, the trajectory of a point M1 on its generatrix is ​​called a spatial epicycloid; when another rolling cone with a smaller taper performs a non-slip tangential rolling motion on the inside of the fixed cone, the trajectory of a point M2 on its generatrix is ​​called a spatial hypocycloid. In the internally meshing bevel gear proposed in the present invention, the two pitch cones δ1 and δ2 of the internal gear and the external gear roll against each other without sliding. Since the distance between each point on the tooth surface and the vertex O of the pitch cone remains unchanged when the two gears move relative to each other, that is, they move on a sphere, the tooth profile curve of the bevel gear is designed with a spherical curve. Like the cycloid on a plane, if the fixed cone happens to be the pitch cone of any one of the two rotors, then the conjugate curve of the spherical cycloid is the spherical cycloid generated based on the pitch cone of the other rotor, and the rolling cone is the same. As shown in FIG. Figure 2 As shown, for external gears, the spherical quasi-cycloid and the spherical cycloid are a pair of conjugate curves, and the meshing line is the base circle of their common rolling cone.

[0043] The coordinate system OX1Y1Z1 and the coordinate system OX2Y2Z2 in the figure are the coordinate systems of the inner and outer gear pitch cones of the present invention, respectively. As shown in the figure, when the rolling cone performs a non-slip rolling motion on the outside of the fixed cone, the trajectory of a point C1 on the upper edge of its generatrix is ​​a spatial epicycloid, and when the rolling cone 2 performs a non-slip rolling motion on the inside of the fixed cone 3, the trajectory of a point C2 on the upper edge of its generatrix is ​​a spatial hypocycloid. According to the properties of the cycloid, the spatial epicycloid and the spatial hypocycloid naturally satisfy the meshing relationship.

[0044] Then the cycloid l formed by C1 in space hyp The equation is:

[0045]

[0046] The spatial epicycloid l formed by C2 epi The equation is:

[0047]

[0048] In the formula, δ represents the cone angle of the fixed cone, q h and q e They represent the rolling cone angles that generate the inner and outer cycloids respectively, and R is the radius of the sphere where the spherical cycloid is located. The conical structure of the gear is formed by changing the size of R.

[0049] According to the above formula, by changing the spherical radius R, spherical cycloids of different sizes can be obtained. Please refer to Figure 3 (a) and Figure 3 (b). The curves shown in the figure are the gear tooth profiles of the present invention, which are obtained by proportionally changing the spherical radius R. The taper of the gear is generated by tooth profile curves of different sizes, and the tooth profile surface of the gear is obtained by spatial lofting. The end with the smaller area of ​​the spherical cycloid is the small end of the bevel gear, and the end with the larger area of ​​the spherical cycloid is the large end of the bevel gear. The tooth profile curve of the small end has the same pitch cone angle as the tooth profile curve of the large end, forming the same number of teeth, but different pitch cone radii, which can be optimized according to the required tooth thickness.

[0050] Set the radius of the internal gear large end indexing cone r1, the pitch cone angle δ1, and the internal gear large end indexing cone as the fixed cone, the number of teeth is Z1, and after the rolling cone rolls 360°, a spatial epicycloid C is generated. 11 and the cycloid C in space 12 The combined space curve is the tooth profile curve of the large end of the internal gear; the radius of the dividing cone of the large end of the external gear is set to r2, the pitch cone angle is δ2, the dividing cone of the large end of the external gear is set to be the fixed cone, the number of teeth is Z2, and after the rolling cone rolls 360°, the space epicycloid C is generated. 21 and the cycloid C in space 22 The combined space curve is the tooth profile curve of the large end of the outer gear. Similarly, the tooth profile curves of the small ends of the two gears. The radius of the two gear pitch cones satisfies:

[0051]

[0052] The intersection angle of the two gear indexing cone axes is:

[0053] φ=δ1+δ2

[0054] In the internal gear transmission, in order to form a full tooth, the rolling cone must roll over the base circle at a certain cone angle. Taking the profile shape parameter c, the number of teeth can be obtained as:

[0055]

[0056] The independent variables in the above solution process are: transmission ratio i HV , shape parameter c, and the independent variables of the coordinate system (internal gear pitch cone bottom radius R1 and large end pitch cone angle δ1). Therefore, in the specific design process of the small-angle cross-axis transmission internal meshing bevel gear structure of the present invention, the above-mentioned independent variables can be adjusted according to different working conditions.

[0057] The tooth profiles of the inner and outer gears of the space cycloid internal meshing bevel gear of the present invention are respectively the combined curves of the space inner cycloid and the space outer cycloid. Please refer to Figures 4(a) and 4(b), which are an embodiment of the present invention, where the inner gear 1 and the outer gear 2 are space cycloid meshing, wherein the axial lines of the inner gear 1 and the outer gear 2 intersect at a certain angle. The design idea is as follows:

[0058] 1. Given transmission ratio i HV , the number of teeth of internal gear 1 is z1=-i HV , where the transmission ratio is an integer.

[0059] 2. Given the spatial cycloid shape parameter c, the internal gear 1-division cone angle δ1′, and the large end cone radius r1.

[0060] 3. Use the formula:

[0061]

[0062]

[0063] Obtain the tooth profile curve E1 of the large end of the internal gear 1.

[0064] 4. Select the tooth thickness. According to tanδ1, the base circle radius of the small end tooth profile can be obtained. Similarly, the small end tooth profile curve E2 can be obtained. The tooth profiles at both ends are surface lofted to obtain the tooth profile surface shown in Figure 3(a). The gear model design and physical processing are carried out through the actual installation environment.

[0065] 5. The parameters of external gear 2 can be obtained according to the number of teeth, and the tooth profile surface and corresponding model of external gear 2 can be obtained by the same method.

[0066] The physical model of the two gears is obtained by matching the inner and outer gears, as shown in Figure 4(a) and Figure 4(b).

[0067] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A small-angle cross-axis transmission internal meshing bevel gear structure, characterized in that: The invention comprises an internal gear (1) and an external gear (2) both of which have conical tooth profiles, wherein the meshing mode of the internal gear (1) and the external gear (2) is a spatial cycloid meshing mode, and the axial lines of the internal gear (1) and the external gear (2) intersect at a set angle; the meshing surfaces of the internal gear (1) and the external gear (2) are continuous closed spatial curved surfaces, and the internal gear (1) simultaneously rotates and revolves around the external gear (2) when performing meshing motion; The meshing surface of the internal gear (1) is a rolling cone surface, and the meshing surface of the external gear (2) is a fixed cone surface; Establishing the pitch cone space coordinate system of the internal gear (1) and the external gear (2) OX 1 Y 1 Z 1 and OX 2 Y 2 Z 2. When the rolling cone surface of the internal gear (1) rolls on the outside of the fixed cone surface of the external gear (2) without slipping, a point on the upper edge of the generatrix of the rolling cone surface of the internal gear (1) C 1 is a spatial epicycloid. When the rolling cone surface of the internal gear (1) rolls on the inner side of the fixed cone surface of the external gear (2) without slipping, a point on the upper edge of the generatrix of the rolling cone surface of the internal gear (1) C The trajectory of 2 is a cycloid in space, then: The equation of the space epicycloid is: The equation of the cycloid in space is: In the formula, δ represents the cone angle of a given cone, q h and q e They represent the cone angles of the rolling cone that generate the spatial inner cycloid and the spatial outer cycloid respectively. When the internal gear (1) and the external gear (2) move relative to each other, the distance between each point on the tooth surface and the apex O of the pitch cone remains unchanged, that is, they move on the spherical surface. R is the radius of the sphere where the spherical cycloid lies, through R The change in size creates the conical structure of the gear; The radius R of the sphere where the spherical cycloid is located is changed proportionally to generate tooth profile curves of different sizes, the tapers of the internal gear (1) and the external gear (2) are generated through the tooth profile curves of different sizes, and the tooth profile surfaces of the internal gear (1) and the external gear (2) are obtained by spatial lofting.

2. The small-angle cross-axis transmission internal meshing bevel gear structure according to claim 1, characterized in that: The end of the internal gear (1) and the external gear (2) with a smaller cycloid area is the small end, and the end with a larger cycloid area is the large end. The tooth profile curve of the small end and the tooth profile curve of the large end have the same pitch cone angle, the same number of teeth, and different pitch cone radii, which are selected according to the required tooth thickness.

3. According to claim 2, the small-angle cross-axis transmission internal meshing bevel gear structure is characterized in that: Set the radius of the large end indexing cone of the internal gear (1) r 1. Pitch cone angle , the dividing cone at the large end of the internal gear (1) is the fixed cone, and the number of teeth is Z 1. After the rolling cone rolls 360°, a spatial epicycloid is generated C 11 and the space hypocycloid C 12 The combined space curve is the large end tooth profile curve of the internal gear (1); Set the radius of the outer gear (2) large end indexing cone r2 and the pitch cone angle , the outer gear (2) has a large end dividing cone as a fixed cone, and the number of teeth is Z 2. The spatial epicycloid generated by the rolling cone rolling 360° C 21 and the space hypocycloid C 22 The combined space curve is the tooth profile curve of the large end of the external gear; In the same way, generate the small end tooth profile curves of the internal gear (1) and the external gear (2).

4. The small-angle cross-axis transmission internal meshing bevel gear structure according to claim 3, characterized in that: The dividing cone radii of the internal gear (1) and the external gear (2) satisfy the following relationship: The intersection angle of the indexing cone axes of the internal gear (1) and the external gear (2) is: In the internal gear transmission, in order to form a full tooth, the rolling cone rolls over the base circle at a certain cone angle, and the profile shape parameters are c , q h The cone angle of the rolling cone that generates the inner cycloid in space is expressed as follows: The number of teeth of the internal gear (1) is calculated as follows: 。 5. A design method for a small-angle cross-axis transmission internal meshing bevel gear structure as claimed in any one of claims 1 to 4, characterized in that: The following steps are involved: Given transmission ratio , number of teeth of the internal gear (1) , where the transmission ratio is an integer; Given the shape parameters of the space cycloid c , internal gear (1) indexing cone angle , radius of the large end cone r 1; The large end tooth profile curve of the internal gear (1) is obtained by the following formula E 1: Select tooth thickness according to Get the base circle radius of the small end tooth profile, and get the small end tooth profile curve in the same way E 2. Loft the tooth profiles at both ends to obtain the tooth profile surface, and perform gear model design and physical processing in the actual installation environment; The parameters of the external gear (2) are obtained according to the number of teeth, and the tooth profile surface of the external gear (2) and the corresponding object are obtained by the same method.

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