A non-vertical staggered axis gear and its modeling method

Abstract

The present invention relates to a non-vertical staggered axis gear and a modeling method thereof. The non-vertical staggered axis gear comprises a first straight bevel gear and a second straight bevel gear meshing with each other, wherein the rotation axes of the first straight bevel gear and the second straight bevel gear do not intersect, the rotation axes of the first straight bevel gear and the second straight bevel gear are neither parallel nor perpendicular, and the tooth lines of the first straight bevel gear and the second straight bevel gear are both straight lines. The three-dimensional modeling of the non-vertical staggered axis hyperboloid straight bevel gear constructed by the present invention provides a physical basis for studying the machining of non-vertical staggered axis hyperboloid straight bevel gears. The gear can be used as a transmission gear in a gear reducer to transmit the rotation and speed change of a prime mover and an actuator in any position relationship.

Description

Technical Field

[0001] The present invention relates to the technical field of gear manufacturing, and in particular to a non-vertical staggered axis gear and a modeling method thereof. Background Art

[0002] In currently used gear transmissions, the two gear axes are either parallel or perpendicular. This requires that the prime mover and actuator must conform to a specific positional relationship. If the prime mover and actuator axes are not parallel, intersecting, or perpendicular, but rather have an arbitrary relationship, there is currently no gear assembly that can transmit rotational motion and achieve speed change or direction reversal. Summary of the Invention

[0003] In order to solve the above problems, the present invention proposes a non-vertical staggered axis gear and a modeling method thereof.

[0004] The specific plan is as follows:

[0005] A non-vertical staggered axis gear comprises a first straight bevel gear and a second straight bevel gear meshing with each other, wherein the rotation axes of the first straight bevel gear and the second straight bevel gear do not intersect, the rotation axes of the first straight bevel gear and the second straight bevel gear are neither parallel nor perpendicular, and the tooth lines of the first straight bevel gear and the second straight bevel gear are both straight lines.

[0006] A method for modeling a gear with non-vertical staggered axes comprises the following steps:

[0007] S1: Calculate the tooth line equations of the first straight bevel gear and the second straight bevel gear;

[0008] S2: Calculate the tooth profile equations of the first straight bevel gear and the second straight bevel gear;

[0009] S3: According to the tooth line equations of the first straight bevel gear and the second straight bevel gear and the tooth profile line equations of the first straight bevel gear and the second straight bevel gear, models of the first straight bevel gear and the second straight bevel gear are created and assembled using 3D software.

[0010] Furthermore, the tooth line equation is calculated based on the shortest distance between the rotation axes of the first straight bevel gear and the second straight bevel gear, the number of teeth of the first straight bevel gear and the second straight bevel gear, the spatial angle between the rotation axes of the first straight bevel gear and the second straight bevel gear, and the length of the tooth line.

[0011] Furthermore, the calculation formula of the tooth line equation of the first straight bevel gear is:

[0012]

[0013] The calculation formula of the tooth line equation of the second straight bevel gear is:

[0014]

[0015] Among them, x1 and y1 represent the coordinates of the point on the tooth line of the first straight bevel gear, x2 and y2 represent the coordinates of the point on the tooth line of the second straight bevel gear, w1 and w2 represent the rotation axes of the first and second straight bevel gears, a represents the shortest distance between the rotation axes of the first and second straight bevel gears, z1 and z2 represent the number of teeth of the first and second straight bevel gears, Σ represents the spatial angle between w1 and w2, and t represents the length of the tooth line.

[0016] Furthermore, the tooth profile equation of the first straight bevel gear is:

[0017]

[0018] Among them, the intermediate variable Q 1x , Q 1y and Q 1w The calculation formula is:

[0019]

[0020]

[0021]

[0022] The tooth profile equation of the second straight bevel gear is:

[0023]

[0024] Among them, the intermediate variable Q 2x , Q 2y and Q 2w The calculation formula is:

[0025]

[0026]

[0027]

[0028] In the formula, α represents the meshing angle, x1 and y1 represent the coordinates of the points on the tooth profile line of the first straight bevel gear respectively, x2 and y2 represent the coordinates of the points on the tooth profile line of the second straight bevel gear respectively, w1 and w2 represent the rotation axes of the first and second straight bevel gears respectively, t represents the length of the tooth line, and the positional relationship between the two gears in space is set as follows: the first straight bevel gear is fixedly connected to the coordinate system O1, and the second straight bevel gear is fixedly connected to the coordinate system O2. The instantaneous axis of the gear passes through the x-axis point O of the shortest distance connecting the two gear axes, then a1 represents the length of the straight line OO1, a2 represents the length of the straight line OO2, γ1 represents the angle between the instantaneous axis and w1, γ2 represents the angle between the instantaneous axis and w2, ρ(θ) represents the common normal length, and θ represents the rotation angle of the gear.

[0029] Furthermore, the method for creating the gear model in step S3 is: calculating the coordinates of each discrete point on the tooth line according to the tooth profile equation, creating the meshing point of the tooth profile for each discrete point on the tooth line by three-dimensional software, connecting the meshing points to obtain the tooth profile, creating the tooth surface from the tooth profile, creating the tooth profile from the two tooth surfaces, and finally generating the gear from the tooth profile array.

[0030] The present invention adopts the above technical solution, and the rotating axes of the two meshing gears are neither intersecting nor parallel. The spatial angle between the rotating axes of the two gears can be any angle greater than zero degrees and less than 90 degrees, so that the gear transmission is not restricted by the positional relationship between the prime mover and the actuator, and can transmit rotation in any positional relationship to achieve speed change or steering. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Shown is a flow chart of embodiment 1 of the present invention.

[0032] Figure 2 Shown is a schematic diagram of the coordinate system position connected to the gear according to the first embodiment of the present invention.

[0033] Figure 3 Shown is a schematic diagram of derivation of a gear tooth profile equation according to an embodiment of the present invention.

[0034] Figure 4 Shown is a schematic diagram of a gear tooth profile according to an embodiment of the present invention.

[0035] Figure 5 The diagram shows the creation of a tooth profile and generation of a gear from a tooth surface in accordance with the first embodiment of the present invention.

[0036] Figure 6 Shown is an isometric view of intermeshing hypoid spur gears with non-perpendicular staggered axes.

[0037] Figure 7 Shown is a front view of intermeshing hypoid spur gears with non-perpendicular staggered axes.

[0038] Figure 8Shown is a side view of intermeshing hypoid spur gears with non-perpendicular staggered axes.

[0039] Figure 9 Shown is a top view of intermeshing hypoid spur gears with non-perpendicular staggered axes. DETAILED DESCRIPTION

[0040] To further illustrate the embodiments, the present invention is provided with accompanying drawings. These drawings form part of the disclosure and are primarily used to illustrate the embodiments and, in conjunction with the relevant description in the specification, to explain the operating principles of the embodiments. By referring to these drawings, those skilled in the art will be able to understand other possible embodiments and the advantages of the present invention.

[0041] The present invention will now be further described with reference to the accompanying drawings and specific embodiments.

[0042] An embodiment of the present invention provides a non-vertical staggered axis gear, comprising a first straight bevel gear and a second straight bevel gear meshing with each other, wherein the rotation axes of the first straight bevel gear and the second straight bevel gear do not intersect, the rotation axes of the first straight bevel gear and the second straight bevel gear are neither parallel nor perpendicular, and the tooth lines of the first straight bevel gear and the second straight bevel gear are both straight lines.

[0043] like Figure 1 As shown, assume that the positional relationship between the two gears in space is: the first straight bevel gear is fixedly connected to the coordinate system O1, and the rotation axis is w1; the second straight bevel gear is fixedly connected to the coordinate system O2, and the rotation axis is w2. The spatial angle between w1 and w2 is Σ, Σ is any value greater than zero and less than 90 degrees, and the closest distance between the two straight bevel gear axes is a.

[0044] The embodiment of the present invention also provides a method for modeling non-vertical staggered axis gears, such as Figure 2 As shown, the method includes the following steps:

[0045] S1: Calculate the tooth line equations of the first and second straight bevel gears.

[0046] At a given instant, when two tooth surfaces mesh, the contact line between the pitch surfaces is a straight line K. This line K is called the instantaneous rotation axis-sliding axis, or simply the instantaneous axis. Existing data (Wu Xutang, Principles of Gear Meshing [M]. Beijing: Machinery Industry Press, 1982) demonstrates that the instantaneous axis K of a gear passes through point O on the x-axis, the line connecting the two gear axes at the shortest distance, and is perpendicular to the x-axis. Let OO1 = a1 and OO2 = a2. The angle between K and w1 is γ1, and the angle between K and w2 is γ2. The discrete points of the tooth line are calculated using the parametric equations for the instantaneous axis K in coordinate systems O1 and O2.

[0047] In coordinate system O1, the tooth line equation of the first straight bevel gear is:

[0048]

[0049] In the coordinate system O2, the tooth line equation of the second straight bevel gear is:

[0050]

[0051] Among them, x1 and y1 represent the coordinates of the point on the tooth line of the first straight bevel gear, x2 and y2 represent the coordinates of the point on the tooth line of the second straight bevel gear, w1 and w2 represent the rotation axes of the first and second straight bevel gears, a represents the shortest distance between the rotation axes of the first and second straight bevel gears, z1 and z2 represent the number of teeth of the first and second straight bevel gears, Σ represents the spatial angle between w1 and w2, and t is a parameter representing the length OT of the tooth line. Since the tooth line is a straight line, the tooth profile of the gear is determined to be a spur gear.

[0052] S2: Calculate the tooth profile equations of the first straight bevel gear and the second straight bevel gear.

[0053] Since the tooth lines of two meshing gears are collinear and therefore necessarily parallel and tangent, a pair of fully meshing conjugate tooth surfaces can theoretically be obtained by obtaining another pair of tangent tooth profile curves, K1 and K2, that do not overlap with the tooth lines. A series of tooth profile groups are constructed on the tooth lines, and the tooth surfaces are approximated using 3D CAD software.

[0054] In this embodiment, when the first straight bevel gear and the second straight bevel gear are meshed, there is a pair of tangent tooth profile curves M1 and M2. When the tooth profile of the first straight bevel gear rotates by an angle θ, the tooth profile of the second straight bevel gear rotates in the opposite direction. Angle, so that the two gear tooth profiles are tangent at the meshing point M, such as Figure 3 Show.

[0055] In the coordinate system O1, the equation of the straight bevel gear tooth profile M1 is:

[0056]

[0057] in:

[0058]

[0059]

[0060]

[0061] Where α is the engagement angle.

[0062] Based on different points on the tooth line, the tooth profile equation (3) is used to calculate a set of meshing point coordinates. The discrete meshing point coordinates are connected into a curve, which is the tooth profile set of one tooth surface of the first straight bevel gear. Taking the meshing angle as -α, the meshing point coordinates of the tooth profile of one tooth surface are calculated to obtain the tooth profile set of the other tooth surface of the first straight bevel gear.

[0063] In the coordinate system O2, the tooth profile M2 equation of the second straight bevel gear is:

[0064]

[0065] in:

[0066]

[0067]

[0068]

[0069] Where α is the engagement angle.

[0070] Based on different points on the tooth line, the tooth profile equation (4) is used to calculate a set of meshing point coordinates. The discrete meshing point coordinates are connected to form a curve, which is the tooth profile set of the second straight bevel gear. Taking the meshing angle as -α, the meshing point coordinates of the tooth profile of the first tooth surface are calculated to obtain the tooth profile set of the other tooth surface of the first straight bevel gear.

[0071] ρ(θ) represents the common normal length. The tooth shape is determined by the common normal length ρ(θ). Different tooth shapes have different functions of the common normal length ρ(θ). If there are no special requirements, it is basically an involute tooth shape. In this case, the common normal length of a fixed point on the tooth line is proportional to the rotation angle θ, that is:

[0072] ρ(θ)=λθ (5)

[0073] Where λ is the proportional coefficient, which is a constant when the tooth profile is an involute.

[0074] The function of the common normal length ρ(θ) is related to the parameter t, that is, the length of the tooth line OT. The function of the common normal length ρ(θ) varies at different points along the tooth line, changing with the parameter t. To ensure that the common normal lengths of the tooth surface equations of the two gears are consistent, the parameter θ is set to the rotation angle of the first straight bevel gear.

[0075] S3: According to the tooth line equations of the first straight bevel gear and the second straight bevel gear and the tooth profile line equations of the first straight bevel gear and the second straight bevel gear, models of the first straight bevel gear and the second straight bevel gear are created and assembled using 3D software.

[0076] The creation methods of the two gear models are: calculate the coordinates of each discrete point on the tooth line according to the tooth profile equation, create the meshing point of the tooth profile at each discrete point on the tooth line by 3D CAD software, and connect the meshing points to obtain the tooth profile as shown in the figure. Figure 4 As shown. Create the tooth surface from the tooth profile, create the tooth shape from the two tooth surfaces, and finally generate the gear from the tooth shape array, as shown Figure 5 shown.

[0077] After assembly, a pair of meshing, non-vertical staggered shaft transmission devices are obtained, which transmit the rotation of any position relationship to achieve speed change or steering, such as Figure 6 shown.

[0078] refer to Figure 7 、 Figure 8 and Figure 9 From the front view, side view and top view of the mutually meshing non-vertical staggered axis hyperbolic straight bevel gears, it can be concluded that the axes of the non-vertical staggered axis hyperbolic straight bevel gears are not perpendicular or intersecting in space.

[0079] Based on the gear model created above, third-party CAM software generates CNC machining code, and a CNC machine tool processes the blank into shape, resulting in a physical hyperbolic straight bevel gear with non-perpendicular staggered axes. Specialized tooling can also be developed, and specialized machine tools can be used for machining.

[0080] The specific examples of the process in this embodiment are as follows:

[0081] 1. Tooth line parameters

[0082] Assume that the number of teeth of the first straight bevel gear is z1 = 29, the number of teeth of the second straight bevel gear is z2 = 17, the offset distance of the staggered axis is a = 100 mm, and the normal pressure angle α = ±22°. Then the tooth line parameter equation of the first straight bevel gear is:

[0083]

[0084] The tooth line parameter equation of the second straight bevel gear is:

[0085]

[0086] 2. Tooth profile parameter equation

[0087] Set z1 = 29, z2 = 17, a = 100 mm, α = ± 22°, and set the tooth profile to involute teeth. The value of the common normal length ρ (θ) can be obtained by calculation:

[0088]

[0089] Substituting t = {190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330} into Equations (3), (4), and (8) yields the involute tooth profile equations for the left and right tooth surfaces of the two gears at each point with parameter t. The density of parameter t values ​​is determined by the design error; smaller errors lead to denser values ​​of t. By trying to find appropriate values ​​for parameter θ, the tooth profile can be calculated. The tooth surface is generated from the meshing of the tooth profile, and the tooth shape is calculated from the tooth surface, completing the 3D CAD design of the gear.

[0090] In this embodiment, the two gears constructed are named non-perpendicular staggered axis hyperbolic straight bevel gears. Since the rotation axes are neither intersecting nor parallel, the pitch surfaces generated by their instantaneous axes around the gear rotation axes are hyperbolic surfaces; since the spatial angle between the rotation axes of a pair of meshing gears can be any angle greater than zero and less than 90 degrees, and the tooth shape is a straight bevel gear, they are called non-perpendicular staggered axis hyperbolic straight bevel gears.

[0091] The three-dimensional modeling of non-perpendicularly staggered axis hyperboloid straight bevel gears constructed in this embodiment provides a physical basis for studying the machining of non-perpendicularly staggered axis hyperboloid straight bevel gears. These gears can be used as transfer gears in gear reducers, transmitting the rotation and speed change of prime movers and actuators in arbitrary positional relationships. This embodiment has the following scientific research and practical application value:

[0092] 1. It can be used as a transfer gear in a reducer, transmitting rotation at any position to achieve speed change or steering. The tooth profile of this gear is straight, making it insensitive to axial assembly errors of the pinion in high-ratio transmissions. It can tolerate certain assembly errors or axial deformation during operation, making it particularly suitable for transmitting low-speed, heavy-load rotation at any position.

[0093] 2. Provide accurate 3D models for designing transmissions with arbitrary position relationships, and provide accurate CAE simulation data for designing non-vertical staggered axis hyperbolic straight bevel gears.

[0094] 3. Provide a physical basis for the research and design of machining tools and methods for non-vertical staggered axis hyperbolic straight bevel gears.

[0095] 4. When certain parameters of non-vertical staggered axis hyperboloid straight bevel gears are changed, cylindrical gears, bevel gears and vertical staggered axis hyperboloid straight bevel gears can be obtained, providing theoretical and physical basis for studying the relationship between various gears and optimizing tooth surface design.

[0096] Although the present invention has been particularly shown and described in conjunction with preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made to the present invention without departing from the spirit and scope of the invention as defined in the appended claims, and all such changes are within the scope of protection of the present invention.

Claims

1. A method for modeling non-vertical staggered axis gears, characterized in that: The following steps are involved: S1: Calculate the tooth line equations of the first straight bevel gear and the second straight bevel gear; The tooth line equation is calculated based on the shortest distance between the rotation axes of the first straight bevel gear and the second straight bevel gear, the number of teeth of the first straight bevel gear and the second straight bevel gear, the spatial angle between the rotation axes of the first straight bevel gear and the second straight bevel gear, and the length of the tooth line; S2: Calculate the tooth profile equations of the first straight bevel gear and the second straight bevel gear; S3: According to the tooth line equations of the first straight bevel gear and the second straight bevel gear and the tooth profile line equations of the first straight bevel gear and the second straight bevel gear, models of the first straight bevel gear and the second straight bevel gear are created and assembled using 3D software.

2. The method for modeling non-vertical staggered axis gears according to claim 1, wherein: The calculation formula of the tooth line equation of the first straight bevel gear is: The calculation formula of the tooth line equation of the second straight bevel gear is: Among them, x1 and y1 respectively represent the coordinates of the point on the tooth line of the first straight bevel gear, x2 and y2 respectively represent the coordinates of the point on the tooth line of the second straight bevel gear, w1 and w2 respectively represent the rotation axes of the first and second straight bevel gears, a represents the shortest distance between the rotation axes of the first and second straight bevel gears, z1 and z2 respectively represent the number of teeth of the first and second straight bevel gears, Σ represents the spatial angle between w1 and w2, and t represents the length of the tooth line.

3. The method for modeling non-vertical staggered axis gears according to claim 1, wherein: The tooth profile equation of the first straight bevel gear is: Among them, the intermediate variable Q 1x , Q 1y and Q 1w The calculation formula is: The tooth profile equation of the second straight bevel gear is: Among them, the intermediate variable Q 2x , Q 2y and Q 2w The calculation formula is: In the formula, α represents the meshing angle, x1 and y1 represent the coordinates of the points on the tooth profile line of the first straight bevel gear respectively, x2 and y2 represent the coordinates of the points on the tooth profile line of the second straight bevel gear respectively, w1 and w2 represent the rotation axes of the first straight bevel gear and the second straight bevel gear respectively, t represents the length of the tooth line, and the positional relationship between the two gears in space is set as follows: the first straight bevel gear is fixedly connected to the coordinate system O1, and the second straight bevel gear is fixedly connected to the coordinate system O2. The instantaneous axis of the gear passes through the x-axis point O of the shortest distance connecting the two gear axes, then a1 represents the length of the straight line OO1, a2 represents the length of the straight line OO2, γ1 represents the angle between the instantaneous axis and w1, γ2 represents the angle between the instantaneous axis and w2, ρ(θ) represents the common normal length, θ represents the rotation angle of the gear, z1 and z2 represent the number of teeth of the first straight bevel gear and the second straight bevel gear respectively.

4. The method for modeling non-vertical staggered axis gears according to claim 1, wherein: The method for creating the gear model in step S3 is as follows: the coordinates of each discrete point on the tooth line are calculated according to the tooth profile equation, the meshing point of the tooth profile of each discrete point on the tooth line is created by three-dimensional software, the meshing points are connected to obtain the tooth profile, the tooth surface is created from the tooth profile, the tooth profile is created from the two tooth surfaces, and finally the tooth profile array is used to generate the gear.

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