Design method of face gear with novel tooth profile curve and face gear

Abstract

The invention relates to the field of face gear pair mechanical transmission in a helicopter transmission system, in particular to a novel face gear tooth profile curve design method. The invention systematically provides a design method for the equiangular helix tooth profile of the face gear, a method for designing a novel face gear tooth profile curve and verifying the feasibility of the face gear tooth profile curve is defined, the equiangular helix tooth profile of the straight spur gear is designed, and the equiangular helix tooth profile of the straight spur gear is designed according to the tooth surface curve of the equiangular helix spur gear. The tooth surface curve of the equiangular helix tooth profile surface gear is designed, the designed equiangular helix tooth profile surface gear has better bearing performance, and the bearing capacity, the transmission efficiency and the reliability of surface gear transmission are improved; the service life of the face gear is prolonged; and the mass of the face gear pair is reduced, and the lightweight design is achieved.

Description

Technical Field

[0001] The invention relates to the field of mechanical transmission of face gear pairs in helicopter transmission systems, and in particular to a novel face gear tooth profile curve design method. Background Art

[0002] At present, the transmission system is developing towards high performance, high speed, high load and high power. The high-speed and heavy-load transmission conditions have put forward more stringent requirements on the structural form, transmission performance and service life of the gear transmission system, and promoted the exploration and research in the fields of new gear structure, new tooth shape and new transmission form. For example, the main reducer of the helicopter requires the transmission system to occupy a small space, transmit large power, work smoothly, have low noise and vibration, etc. The existing spiral bevel gears have the disadvantages of high installation accuracy and high sensitivity to load after the gear teeth are deformed under load, which can no longer meet the growing high-performance transmission requirements. However, the face gear transmission has broad application value in the field of intersecting axis power and motion transmission due to its simple structure, light weight, low vibration, low noise and insensitivity to installation errors. According to the characteristics of the tooth shape of the small gear involved in the meshing, the face gear transmission can be divided into spur face gear transmission, helical face gear transmission and arc face gear transmission. Among them, the spur face gear transmission is a transmission form in which the involute spur cylindrical gear meshes with the spur face gear. Compared with the other two types of face gear transmission, it has many unique advantages and has broad prospects for engineering application. At present, involute tooth profiles have been applied to various types of gears, such as cylindrical gears, bevel gears and worm gears. Arc tooth profiles, cycloid tooth profiles and parabolic tooth profiles have also been studied successively, and have shown excellent performance in their respective fields.

[0003] However, the load-bearing performance of the gears with the above-mentioned various tooth profile curves is still relatively limited in the field of mechanical transmission of the inner gear pair of the helicopter transmission system.

[0004] The existing technology is still unable to solve the problem of relatively limited load-bearing capacity of traditional face gear transmission under high-speed and heavy-load conditions. Summary of the invention

[0005] To this end, it is necessary to provide a design method for face gears with a new tooth profile curve. The equiangular helical tooth profile face gear designed by this method has better load-bearing performance, improves the load-bearing capacity, transmission efficiency and reliability of the face gear transmission; extends the service life of the face gear; reduces the mass of the face gear pair, and realizes a lightweight design.

[0006] To achieve the above objectives, the present application provides a design method for a gear with a novel tooth profile curve surface, comprising the following steps:

[0007] S1: Design a spur gear as a tool gear, the tooth profile curve of the spur gear is:

[0008]

[0009] Among them, r0 is the diameter of the circle of the equiangular helix, k is the constant of the equiangular helix, θ s is the parameter of the equiangular helix tooth profile, θ os The angle parameter from the vertical symmetry line to the starting point of the equiangular helix determines the tooth width of the gear shaping cutter on the base circle, θ os =π / 2N S , N S is the number of teeth of the gear shaping cutter, μ s It is the tooth width coefficient of the tool tooth profile changing along the tooth width direction.

[0010] S2: Take the spur gear as the tool gear, combine the tooth profile curve of the spur gear, and use the gear meshing principle and coordinate transformation to design the tooth surface equation of the face gear:

[0011]

[0012] Among them, φ θ =θ s +θ os +φ s ,φ2=m 2s φ s ,φ s is the rotation angle of the tool gear, φ2 is the rotation angle of the face gear, m 2s is the transmission ratio of the face gear and the cutter gear, m 2s =N s / N2, N2 is the number of teeth of the face gear.

[0013] Furthermore, the method further comprises the following steps:

[0014] S3: Also includes a pinion, the pinion meshes with the face gear, and the tooth profile curve formula of the pinion is:

[0015]

[0016] Among them, r0 is the diameter of the circle of the equiangular helix, k is the constant of the equiangular helix, θ s is the parameter of the equiangular helix tooth profile, θ os The angle parameter from the vertical symmetry line to the starting point of the equiangular helix determines the tooth width of the gear shaping cutter on the base circle, θ os =π / 2N S , N S is the number of teeth of the gear shaping cutter, μ s It is the tooth width coefficient of the tool tooth profile changing along the tooth width direction.

[0017] 1. Furthermore, a face gear is formed by machining the above-mentioned tool gear, and the pinion gear is meshed and assembled with the face gear, and the pinion gear drives the face gear.

[0018] Furthermore, the method also includes step S4: establishing a three-dimensional model of a spur face gear, performing Boolean processing on a spur cylindrical gear and a face gear blank in Solidworks to generate spur face gear teeth with processing marks, cutting out one of the teeth, performing a tooth surface finishing operation on the tooth to obtain a tooth with a smooth surface, and finally obtaining a complete spur face gear model through an array.

[0019] Furthermore, it also includes S5: establishing an assembly model of a face gear pair with few teeth meshing, for use in a workbench to perform static strength simulation, performing a gear cutting operation on the gear, retaining 3-5 pairs of gear teeth meshing, and finally assembling the face gear pair model with few teeth meshing.

[0020] Furthermore, it also includes S6: performing static strength simulation analysis of the face gear pair, and using Ansys Workbench simulation software to perform simulation analysis of contact stress and bending stress of the face gear pair.

[0021] Furthermore, it also includes S7: generating three-dimensional models of spur gears and spur face gears with involute tooth profiles, and performing simulation analysis of bending stress and contact stress of face gear pairs with involute tooth profiles.

[0022] Furthermore, it also includes S8: comparing the bending stress and contact stress of the gears with equiangular helical tooth profile and involute tooth profile, it is concluded that the gears with equiangular helical tooth profile have better load-bearing capacity.

[0023] A face gear is designed by adopting any of the above-mentioned design methods for the novel tooth profile curve face gear.

[0024] Different from the prior art, the above technical solution has the following technical effects:

[0025] 1) This invention provides a new tooth profile curve of face gear. The tooth surface equation of the face gear is derived based on the meshing principle and coordinate transformation, which promotes further exploration and research on the new tooth profile curve of face gear;

[0026] 2) Compared with the involute tooth profile face gear, the equiangular helical tooth profile face gear designed in the present invention has smaller bending stress and contact stress under the same working conditions, thereby improving the load-bearing capacity of the face gear pair transmission and extending its service life, while also achieving a lightweight design. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Equiangular helix cylindrical gear tooth profile;

[0028] Figure 2 Involute cylindrical gear tooth profile;

[0029] Figure 3 Face gear machining coordinate system;

[0030] Figure 4 Gear tooth surface with equiangular helix tooth profile;

[0031] Figure 5 Involute tooth profile gear tooth surface;

[0032] Figure 6 Spur gear model with equiangular helical tooth profile;

[0033] Figure 7 Spur gear model with involute tooth profile;

[0034] Figure 8 Model generated by machining equiangular helical tooth profile gear;

[0035] Fig. 9 Model generated by machining involute tooth profile gear;

[0036] Fig.10 Smoothing process of gears with equiangular helical tooth profile;

[0037] Fig.11 Smoothing process of involute tooth profile gear;

[0038] Fig.12 Assembly drawing of gear pair with few teeth in meshing with equiangular helical tooth profile;

[0039] Fig.13 Assembly drawing of involute tooth profile gear pair with few teeth meshing;

[0040] Fig.14 Bending stress simulation diagram of face gear;

[0041] Fig.15 Contact stress simulation diagram of face gear. DETAILED DESCRIPTION

[0042] In order to explain the technical content, structural features, achieved objectives and effects of the technical solution in detail, the following is a detailed description in conjunction with specific embodiments and accompanying drawings.

[0043] Reference to "embodiment" herein means that the specific features, structures or characteristics described in conjunction with the embodiment may be included in at least one embodiment of the present application. The term "embodiment" appearing in various places in the specification does not necessarily refer to the same embodiment, nor does it particularly limit its independence or association with other embodiments. In principle, in the present application, as long as there is no technical contradiction or conflict, the various technical features mentioned in the embodiments can be combined in any way to form a corresponding implementable technical solution.

[0044] Unless otherwise defined, the technical terms used in this document have the same meanings as those generally understood by those skilled in the art to which this application belongs; the use of relevant terms in this document is only for describing specific embodiments and is not intended to limit this application.

[0045] In the description of this application, the term "and / or" is an expression used to describe the logical relationship between objects, indicating that three relationships may exist, for example, A and / or B, which means: A exists, B exists, and A and B exist at the same time. In addition, the character " / " in this article generally indicates that the objects before and after are in an "or" logical relationship.

[0046] In the present application, terms such as “first” and “second” are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship of quantity, priority or sequence between these entities or operations.

[0047] Without further limitations, in this application, the words "include", "comprises", "has" or other similar expressions used in the sentences are intended to cover non-exclusive inclusion. These expressions do not exclude the presence of additional elements in the process, method or product including the elements, so that the process, method or product including a series of elements may include not only those limited elements, but also other elements not explicitly listed, or also include elements inherent to such process, method or product.

[0048] Similar to the understanding in the Examination Guidelines, in this application, expressions such as "greater than", "less than", "exceed" and the like are understood to exclude the number itself; expressions such as "above", "below", "within" and the like are understood to include the number itself. In addition, in the description of the embodiments of this application, "multiple" means more than two (including two), and similar expressions related to "multiple" are also understood in this way, such as "multiple groups", "multiple times", etc., unless otherwise clearly and specifically limited.

[0049] In the description of the embodiments of the present application, space-related expressions used, such as "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "vertical", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc., indicate the orientation or position relationship based on the orientation or position relationship shown in the specific embodiments or drawings, and are only for the convenience of describing the specific embodiments of the present application or facilitating the reader's understanding, and do not indicate or imply that the referred device or component must have a specific position, a specific orientation, or be constructed or operated in a specific orientation, and therefore cannot be understood as a limitation on the embodiments of the present application.

[0050] Unless otherwise expressly specified or limited, in the description of the embodiments of the present application, the terms such as "install", "connect", "connect", "fix", "set", etc. used should be understood in a broad sense. For example, the "connection" can be a fixed connection, a detachable connection, or an integrated setting; it can be a mechanical connection, an electrical connection, or a communication connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium; it can be the internal connection of two elements or the interaction relationship between two elements. For technicians in the technical field to which the present application belongs, the specific meanings of the above terms in the embodiments of the present application can be understood according to the specific circumstances.

[0051] Implementation Case 1

[0052] An embodiment of the present invention provides a design method for a gear having a novel tooth profile curve surface, comprising the following steps:

[0053] S1 designs the equiangular helical tooth profile of spur gears and derives the tooth surface equations of equiangular helical gears.

[0054] Referring to the polar coordinate equation of the equiangular helix and the involute tooth surface equation, the equiangular helix tooth surface equation that conforms to the cylindrical gear tooth profile curve is given as shown in formula (1), where r0 is the diameter of the equiangular helix generating circle; k is the constant of the equiangular helix; θ s is the parameter of the equiangular helix tooth profile; θ os is the angle parameter from the vertical symmetry line to the starting point of the equiangular helix, which determines the tooth width of the gear shaping cutter on the base circle. In this embodiment, θ os =π / 2N s , N s is the number of teeth of the gear shaping cutter; μ s It is the tooth width coefficient of the tool tooth profile changing along the tooth width direction.

[0055]

[0056] S1 According to the gear basic parameter table 1, enter the equiangular helix tooth surface equation of the cylindrical gear tooth profile curve in Matlab, and draw the left and right tooth profile curves of the equiangular helix cylindrical gear, as shown in Figure 1 As shown. By modifying the value of k, tooth profiles with different tooth thicknesses can be obtained. The smaller k is, the thicker the tooth at the tooth root and the thinner the tooth at the tooth top. The larger k is, the thinner the tooth at the tooth root and the thicker the tooth at the tooth top. Modify θ s The value of can define the starting point and end point of the equiangular helix. Enter the parametric equation of the involute tooth profile, select the appropriate parameters and draw the left and right tooth profiles of the involute cylindrical gear, such as Figure 2 Here, the basic parameters such as the module and number of teeth of the gear should be consistent, so that they can be compared in the static strength simulation later. In order to avoid the root cutting phenomenon of the equiangular helical tooth profile gear, h a * =0.8, c * =0.3, the tooth height is 1.9m, m is the module of the gear, that is, the cylindrical gear and face gear with short teeth. The cylindrical gear and face gear with involute tooth profile are normal teeth, h a * =1, c * =0.25, the tooth height is 2.25m. At the same time, in order to avoid the sharpening of the face gear teeth, the tooth width of the face gear should be reasonably selected.

[0057] Table 1 Basic parameters of gears

[0058]

[0059] S2 derives the tooth surface equations of equiangular helical tooth profile gears.

[0060] After S2-1 obtains the tooth surface equation of the tool gear, the unit normal vector of the tool gear is calculated according to the tooth surface equation, as shown in formula (3). Establish the face gear machining coordinate system, as shown in Figure 3 As shown. According to the face gear machining coordinate system, the transformation matrix M is obtained. 2s , M 2s =M 2p =M pm =M ms The transformation matrix M 2s The coordinate system S s Transform to coordinate system S2, and the other transformation matrices are similar. The calculated M 2s The result is shown in formula (4).

[0061]

[0062]

[0063] S2-2 Calculate the relative speed V at the contact point between the tool gear tooth surface and the processed gear tooth surface s (s2) , V s (s2) =V s (s) -V s (2) =(W s (s) -W s (2) )×r s , the final expression of relative velocity is shown in formula (5). Where: V s (s) and W s (s) In the coordinate system S s Speed ​​and angular velocity of the lower cutter gear, V s (2) and W s (2) In the coordinate system S s The speed and angular velocity of the gear below. γ m It is the intersection angle between the two axes of the cutter gear and the face gear, which is equal to 90°.

[0064]

[0065] S2-3 According to the gear meshing principle, the condition for any point on the tool gear to become a meshing point is that the relative motion velocity vector of the point is located within the common tangent plane passing through the point. Therefore, the condition for a point on the tool gear tooth surface to become a meshing point is: n·v=0.

[0066] In the coordinate system S s Under this condition, the meshing equation f(μ s ,θ s ,φ s )=0 can be determined by the following formula:

[0067]

[0068] Therefore, the tooth surface equation of the face gear can be expressed by the following set of equations:

[0069]

[0070] Finally, the tooth surface equation of the gear with equiangular helical tooth profile is shown in formula (6).

[0071]

[0072] Where φ θ =θ s +θ os +φs ,φ2=m 2s φ s ,φ s represents the rotation angle of the tool gear; φ2 represents the rotation angle of the face gear. m 2s is the transmission ratio of the face gear and the cutter gear, m 2s =N s / N2, N2 is the number of teeth of the face gear.

[0073] By writing a Matlab program to draw the tooth surface of the face gear, such as Figure 4 The figure shows the tooth surface of the gear with equiangular helical tooth profile. Figure 5 The tooth surface of the gear with involute tooth profile is shown in Figure 1. The visualization of the tooth surface proves the correctness of the derived tooth surface equation of the gear with equiangular helical tooth profile.

[0074] S3 establishes a three-dimensional model of a spur gear with an equiangular spiral tooth profile.

[0075] It is necessary to establish a small gear for meshing and assembling with the spur gear; secondly, establish a three-dimensional model of the spur gear for machining the spur gear as a tool gear.

[0076] S3 generates the left and right tooth profiles of the spur gear in Matlab and then exports the data points. In Solidworks, the left and right tooth profile curves of the spur gear are generated by inserting the curves passing through the XYZ points and solidifying them. Then, solid modeling operations are performed to generate a three-dimensional model. Here, the spur gear model for processing and the pinion for assembly need to be generated separately, such as Figure 6 The figure shows a spur gear model with an equiangular helical tooth profile. Figure 7 Shown is a spur gear model with an involute tooth profile.

[0077] S4 establishes a three-dimensional model of a spur gear with an equiangular helical tooth profile.

[0078] In Solidworks, Boolean machining is performed on the spur gear and face gear blanks to generate spur face gear teeth with machining marks. One of the teeth is cut out and the tooth surface is smoothed to obtain a smooth tooth. Finally, the array is used to obtain a complete spur face gear model.

[0079] When S4-1 is processing the face gear by Boolean, the tool gear and the face gear blank are assembled according to the assembly relationship, and the processing code is generated by secondary development of Solidworks, and the face gear with processing traces is generated by running. Figure 8 The model shown is generated by machining the equiangular helical tooth profile surface gear. Fig. 9The model shown is generated by machining the involute tooth profile face gear. Here, machining the equiangular helical tooth profile face gear will produce root undercutting and tooth tip sharpening, so it is necessary to design a suitable k value to reduce the root undercutting, and at the same time, the equiangular helical tooth profile spur gear is designed with short teeth to reduce the root undercutting and keep the undercutting within an acceptable range.

[0080] After the Boolean processing is completed, S4-2 cuts a complete single tooth from the generated face gear teeth, performs tooth surface finishing on this single tooth, removes the processing marks left by the processing, and finally generates a complete spur face gear with smooth tooth surface. Fig.10 The figure shows the smoothing process of the equiangular helical tooth profile gear. Fig.11 Shown is the smoothing process of the involute tooth profile gear.

[0081] S5 establishes an assembly model of a face gear pair with few teeth meshing, which is used for static strength simulation in Workbench.

[0082] Taking into account the length of simulation time and the accuracy of simulation results, this patent chooses to perform gear cutting operations on the gears, retaining 3-5 pairs of gear teeth in meshing, and finally assembling the face gear pair with less tooth meshing.

[0083] S5 cuts the generated cylindrical gear and face gear in Solidworks, and then assembles the model of the face gear pair with few teeth meshing. Fig.12 The figure shows the meshing assembly diagram of the gear pair with few teeth of the equiangular helical tooth profile surface. Fig.13 Shown is the assembly diagram of a gear pair with a small number of teeth in meshing with an involute tooth profile.

[0084] S6 performs static strength simulation analysis of face gear pairs.

[0085] Ansys Workbench simulation software is used to perform simulation analysis on contact stress and bending stress of face gear pairs.

[0086] S6 imports the few-tooth meshing assembly model of the face gear pair into Workbench for static structure simulation analysis, sets the same simulation parameters, sets the tooth surfaces of the cylindrical gear and the face gear to friction contact, fixes the cylindrical gear, and applies a certain torque to the face gear.

[0087] S7 generates three-dimensional models of spur gears and spur face gears with involute tooth profiles, and performs simulation analysis of bending stress and contact stress of face gear pairs with involute tooth profiles. Fig.14 Shown are the bending stress simulation diagrams of face gears. The left figure is the bending stress simulation diagram of the face gear with equiangular helical tooth profile, and the right figure is the bending stress simulation diagram of the face gear with involute tooth profile.

[0088] S8 compares the bending stress and contact stress of gears with equiangular helical tooth profile and involute tooth profile. Fig.15 The figure shows the contact stress simulation diagram of the face gear. The left figure shows the contact stress simulation diagram of the face gear with equiangular helical tooth profile, and the right figure shows the contact stress simulation diagram of the face gear with involute tooth profile. It is concluded that the bearing capacity of the face gear with equiangular helical tooth profile is better, which proves the feasibility of the design of the new face gear tooth profile curve.

[0089] From the simulation results, it can be seen that the bending stress and contact stress of the equiangular helical tooth profile face gear are smaller than those of the involute tooth profile face gear. The simulation results prove the feasibility of designing the face gear tooth profile curve into an equiangular helix, and it is concluded that the equiangular helical tooth profile face gear has better load-bearing capacity and also achieves lightweight design.

[0090] It should be noted that, although the above embodiments have been described in this article, the patent protection scope of the present invention is not limited thereby. Therefore, based on the innovative concept of the present invention, changes and modifications made to the embodiments described herein, or equivalent structures or equivalent process changes made using the contents of the present invention specification and drawings, directly or indirectly applying the above technical solutions to other related technical fields, are all included in the patent protection scope of the present invention.

Claims

1. A design method for a gear with a new tooth profile curve surface, characterized in that: The steps include: S1: Design a spur gear as a tool gear, the tooth profile curve of the spur gear is: Among them, r0 is the diameter of the circle of the equiangular helix, k is the constant of the equiangular helix, θ s is the parameter of the equiangular helix tooth profile, θ os The angle parameter from the vertical symmetry line to the starting point of the equiangular helix determines the tooth width of the gear shaping cutter on the base circle, θ os =π / 2N S , N S is the number of teeth of the gear shaping cutter, μ s It is the tooth width coefficient of the tool tooth profile changing along the tooth width direction. S2: Take the spur gear as the tool gear, combine the tooth profile curve of the spur gear, and use the gear meshing principle and coordinate transformation to design the tooth surface equation of the face gear: Among them, φ θ =θ s +θ os +φ s ,φ2=m 2s φ s ,φ s is the rotation angle of the tool gear, φ2 is the rotation angle of the face gear, m 2s is the transmission ratio of the face gear and the cutter gear, m 2s =N s / N2, N2 is the number of teeth of the face gear.

2. The design method of the new tooth profile curve surface gear according to claim 1 is characterized in that: The following steps are also included: S3: Also includes a pinion, the pinion meshes with the face gear, and the tooth profile curve formula of the pinion is: Among them, r0 is the diameter of the circle of the equiangular helix, k is the constant of the equiangular helix, θ s is the parameter of the equiangular helix tooth profile, θ os The angle parameter from the vertical symmetry line to the starting point of the equiangular helix determines the tooth width of the gear shaping cutter on the base circle, θ os =π / 2N S , N S is the number of teeth of the gear shaping cutter, μ s is the tooth width coefficient of the tool tooth profile changing along the tooth width direction.

3. The design method of the new tooth profile curve surface gear according to claim 2 is characterized in that: The face gear is formed by machining the tool gear, and the pinion gear is meshed and assembled with the face gear, and the pinion gear drives the face gear.

4. The design method of the new tooth profile curve surface gear according to claim 3 is characterized in that: The method also includes step S4: establishing a three-dimensional model of a spur face gear, performing Boolean processing on a spur cylindrical gear and a face gear blank in Solidworks to generate spur face gear teeth with processing marks, cutting out one of the teeth, performing a tooth surface finishing operation on the tooth to obtain a tooth with a smooth surface, and finally obtaining a complete spur face gear model through an array.

5. The design method of the new tooth profile curve surface gear according to claim 4 is characterized in that: It also includes S5: establishing an assembly model of a face gear pair with few teeth meshing, which is used for static strength simulation in the workbench, cutting the gears, and retaining 3-5 pairs of gear teeth meshing, and finally assembling the face gear pair model with few teeth meshing.

6. The design method of the new tooth profile curve surface gear according to claim 5 is characterized in that: It also includes S6: static strength simulation analysis of the face gear pair, and simulation analysis of contact stress and bending stress of the face gear pair using Ansys Workbench simulation software.

7. The design method of the new tooth profile curve surface gear according to claim 6 is characterized in that: Also included is S7: Generate 3D models of spur gears and spur face gears with involute tooth profiles, and perform simulation analysis of bending stress and contact stress of face gear pairs with involute tooth profiles.

8. The design method of the new tooth profile curve surface gear according to claim 7 is characterized in that: It also includes S8: Comparing the bending stress and contact stress of the equiangular helical tooth profile and the involute tooth profile surface gear, it is concluded that the load-bearing capacity of the equiangular helical tooth profile surface gear is better.

9. A face gear, characterized in that: The face gear is designed by using the design method of the novel tooth profile curve face gear described in any one of claims 1-8.

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