Bevel gear and bevel gear transmission system and axial force self-balancing design method

Abstract

The invention relates to an axial force self-balancing design method for a bevel gear and a helical gear in the technical field of gear transmission, which comprises the following steps: establishing a unified axial couple balance equation, and carrying out collaborative matching design on key geometric parameters of the bevel gear and the helical gear, so that the axial forces generated by the bevel gear and the helical gear during transmission are equal in magnitude and opposite in direction; therefore, the self-balancing of the axial couple in the system is realized, and the additional axial load on the bearing and the box body is fundamentally eliminated. According to the method, the net axial couple on the transmission shaft system is eliminated through accurate parameter matching, so that bearing model selection is not limited by huge axial load any more, a designer can select a bearing type (such as a deep groove ball bearing) which is relatively simple in structure and lower in friction loss, or select a bearing with a smaller size under the same load, and the design cost is reduced. Therefore, the shafting structure is obviously simplified, and the assembly cost is reduced.

Description

Technical Field

[0001] This invention relates to the field of gear transmission technology, and in particular to a bevel gear and helical gear transmission system and an axial force self-balancing design method. Background Technology

[0002] Bevel gear-cylindrical gear drives are commonly used in applications requiring motion transmission between intersecting shafts, such as power transmission devices in mining, automotive, and aerospace machinery. Compared to spur gears, helical gears offer advantages such as higher load capacity, smoother operation, and lower noise, making them particularly widely used in high-speed, heavy-duty transmission systems. However, while bevel gears and helical gears change the direction of motion and improve dynamic performance and load capacity, they inevitably introduce axial forces. Axial forces impose additional axial loads on bearings, leading to accelerated wear, reduced service life, and can also cause axial vibration or displacement, affecting the meshing transmission performance of the gears.

[0003] In existing designs, to reduce the adverse effects of axial forces, bearings capable of withstanding large axial forces (such as paired angular contact ball bearings or tapered roller bearings) are typically used to bear the load, and the structure is reinforced by measures such as increasing the thickness of the housing wall. However, using bearings capable of withstanding large axial forces inevitably leads to a complex shaft system structure and makes assembly and adjustment difficult; moreover, these methods do not fundamentally reduce axial forces, but only enhance the force-bearing capacity, which limits the selection of bearing type and size and is not conducive to the lightweight design of transmission devices.

[0004] In view of this, the present invention proposes a bevel gear and helical gear transmission system and an axial force self-balancing design method. The aim is to achieve equal and opposite cancellation of axial forces within the transmission system through the coordinated design of gear parameters, thereby eliminating or significantly reducing the net axial couple of the transmission shaft system from the source, thus improving the load-bearing capacity of the transmission system, making the selection of bearing type more flexible, and facilitating the lightweighting of gear transmission devices. Summary of the Invention

[0005] This invention aims to solve the technical problem in existing technologies where bevel gears and helical gears, when driven on the same axis, experience a large axial couple due to the superposition of axial forces generated by the two gears, or forces with opposite directions but unequal magnitudes. Specifically, this axial couple significantly increases the axial load on the bearings, accelerates bearing wear, and reduces the service life and reliability of the transmission system. Furthermore, to withstand this axial couple, it is often necessary to select bearings with greater load-bearing capacity and more complex structures (such as paired angular contact ball bearings or tapered roller bearings), and to strengthen the housing structure, resulting in a bulky, costly transmission device with limited design freedom.

[0006] To address the aforementioned technical problems, this invention provides a self-balancing design method for axial forces of bevel gears and helical gears, and a gear transmission system designed based thereon. The core of this method lies in establishing a unified axial couple balance equation and collaboratively matching the key geometric parameters of the bevel gears and helical gears. This ensures that the axial forces generated by the two gears during transmission are equal in magnitude and opposite in direction, thereby achieving self-balancing of the axial couple within the system and fundamentally eliminating additional axial loads on the bearings and housing.

[0007] A self-balancing design method for axial forces of bevel gears and helical gears includes the following steps: S1: Given or determine the initial geometric parameters of the coaxially arranged bevel gear and helical gear; the initial geometric parameters are the input basis for design matching and include at least: the pitch circle diameter d of the bevel gear at the midpoint of the tooth width. (m，锥) δ, the cone angle (锥) Helix angle β (锥) With normal pressure angle α (锥) The pitch circle diameter d of the cylindrical helical gear (斜) With helix angle β (斜) and the same torque T transmitted by both; S2: Establish the axial couple equilibrium equation, which describes the axial force F generated by the bevel gear. (a，锥) The axial force F generated by the cylindrical helical gear (a，斜) The conditions for achieving equilibrium and mutual cancellation. The equilibrium equation is specifically: tanβ (斜) / d (斜) =k a / d (m，锥) Where, k a The axial force coefficient of the bevel gear reflects the influence of the bevel gear's geometric parameters on its ability to generate axial force.

[0008] S3: Based on the axial couple balance equation, perform coordinated parameter matching design; this step involves matching the geometric parameters of the bevel gear with the helix angle β of the cylindrical helical gear. (锥) By performing systematic matching, the axial forces generated by the two gear pairs under the torque T are equal in magnitude and opposite in direction, thereby achieving self-balancing of the axial couple of the entire transmission shaft system.

[0009] Furthermore, the axial force coefficient k of the bevel gear a Calculated using the following formula: k a = (tanα) (锥) sinδ (锥) ) / cosβ (锥) ±tanβ (锥) cosδ(锥) The "±" sign in the formula is determined by the helix direction and rotation direction of the bevel gear pair. A positive sign is used when the axial force points towards the larger end, and a negative sign is used otherwise. This formula is universally applicable, especially when the bevel gear is a straight bevel gear with a helix angle β. (锥) =0, the axial force coefficient k a The calculation formula is simplified to: k a =tanα (锥) sinδ (锥) .

[0010] Furthermore, the collaborative parameter matching design in step S3 is a flexible bidirectional matching design, specifically including the following two reversible implementation paths: Path 1 (Forward Design): Preset the geometric parameters of the bevel gear (e.g., determine them based on strength or spatial constraints), and calculate its axial force coefficient k. a Then, according to the equilibrium equation tanβ (斜) / d (斜) =k a / d (m，锥) The helix angle β of the cylindrical helical gear required to achieve axial force balance can be directly solved. (斜) .

[0011] Path 2 (Reverse Design): Preset the helix angle β of the cylindrical helical gear. (斜) (If standard gears are selected or constrained by other transmission chains), the axial force coefficient k required to satisfy the balance at this time can be obtained by reverse calculation based on the balance equation. a The value relationship is determined by adjusting the helix angle β of the bevel gear. (斜) and / or normal pressure angle α (锥) The value of k makes the calculated value... a The value satisfies the aforementioned value relationship. When executing path two, adjust β. (锥) and α (锥) To satisfy target k a The value is a multi-solution optimization process, which allows designers to further optimize multiple performance indicators such as the overlap ratio, tooth root bending strength, or machinability of the gear pair while ensuring axial force balance.

[0012] Based on the above design method, the present invention also provides a gear transmission system. This system includes a bevel gear and a cylindrical helical gear rigidly coaxially connected via the same transmission shaft. The geometric parameters of the bevel gear and the cylindrical helical gear are determined through a coordinated matching design based on the axial force couple balance equation. Therefore, under rated operating conditions, the axial force generated by the bevel gear is equal in magnitude and opposite in direction to the axial force generated by the cylindrical helical gear, thereby preventing the bearings at both ends of the transmission shaft from bearing a net axial load. In a preferred embodiment, the driven gear of the bevel gear and the driving gear of the cylindrical helical gear are fixed on the same transmission shaft. Thanks to the self-balancing of the axial force, the bearings supporting the transmission shaft can be of a simpler and lower-cost type, such as deep groove ball bearings.

[0013] Compared with the prior art, the beneficial effects of the present invention are: 1. Significantly reduces bearing axial load requirements and simplifies shaft system structure: This invention achieves self-balancing of the net axial couple on the transmission shaft system through precise parameter matching. This eliminates the constraint of huge axial loads when selecting bearings. Therefore, designers can choose bearing types with lower axial load requirements, simpler structures, and lower friction losses (such as deep groove ball bearings), or select smaller bearings to meet the same radial and axial working conditions, thereby significantly simplifying the shaft system structure and reducing assembly and manufacturing costs.

[0014] 2. Improve the load-bearing capacity and design flexibility of the transmission system: This invention provides a two-way matching balance design method, which breaks the limitations of unidirectional design. It can balance bevel gears by adjusting the parameters of helical gears, or balance helical gears by adjusting the parameters of bevel gears (such as helix angle). This mechanism makes the axial forces generated by the two gears cancel each other out, thereby allowing designers to choose a larger helix angle to improve the overlap ratio and load-bearing capacity of the gears without increasing the additional bearing load.

[0015] 3. Achieving lightweight and compact design of the gearbox: This invention effectively eliminates the axial couple generated during transmission by establishing a unified balance equation, so that the support structures at both ends of the transmission shaft do not need to bear large axial thrust, directly reducing the rigidity requirements of the bearing housing and gearbox structure in resisting axial thrust. Therefore, the size of the required bearing series and installation space can be reduced. At the same time, the gearbox no longer needs to have additional thickened walls or added reinforcing ribs to withstand deformation caused by axial loads. Thus, while ensuring structural reliability, it is conducive to achieving lightweighting of the gearbox structure and even the entire transmission device, reducing material consumption and manufacturing costs, and meeting the needs of modern machinery for high power density and compact design. Attached Figure Description

[0016] Figure 1This is a schematic diagram of the bevel gear and cylindrical helical gear transmission of the present invention; Figure 2 This is a schematic diagram of the axial force in the transmission between bevel gears and cylindrical helical gears in this invention; Figure 3 This is a schematic diagram of the forces acting on the cylindrical helical gear in this invention; Figure 4 This is a schematic diagram of the forces acting on the bevel gear in this invention.

[0017] In the diagram: 1. Input shaft; 2. Bevel gear drive wheel; 3. Bevel gear driven wheel; 4. Secondary transmission shaft; 5. First sleeve; 6. Helical gear drive wheel; 7. Helical gear driven wheel; 8. Second sleeve; 9. Tertiary transmission shaft; F r3 F is the radial force on the driven gear of the bevel gear. a3 F is the axial force on the driven wheel of the bevel gear. r6 Radial force on the driving gear of a helical gear; F a6 F3´: Projection of the normal force on the driving gear of the helical gear; F6´: Projection of the normal force on the driving gear of the bevel gear; F n For normal force; F r For radial force; F a For axial force; F t Circumferential force; F´ is the projection of the normal force; T is the torque; d is the pitch circle diameter; δ is the pitch cone angle; d m It is the pitch circle diameter at the midpoint of the tooth width. Detailed Implementation

[0018] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0019] Please refer to the instruction manual appendix. Figure 1-4 The present invention provides the following technical solutions: Example 1: A self-balancing design method for axial forces of bevel gears and helical gears, which matches and designs cylindrical helical gears based on given straight bevel gear parameters.

[0020] This embodiment uses Figure 1 and Figure 2The following is an example of a typical three-stage coaxial transmission system of bevel gears and helical gears. In this system, the bevel gear drive wheel 2 on the input shaft 1 drives the bevel gear driven wheel 3. The bevel gear driven wheel 3 and the helical gear drive wheel 6 are rigidly connected to the secondary transmission shaft 4 via a key or other means, and rotate together. The helical gear drive wheel 6 then drives the helical gear driven wheel 7, transmitting power to the tertiary transmission shaft 9. The first sleeve 5 and the second sleeve 8 are used for axial positioning. The core focus of this invention is: how to design the parameters of the bevel gear driven wheel 3 and the helical gear drive wheel 6, which are fixed to the secondary transmission shaft 4, to achieve self-balancing of the axial forces generated by them.

[0021] In this embodiment, it is assumed that the driven bevel gear 3 has been determined to be a straight bevel gear due to spatial layout or strength requirements, and its parameters cannot be changed. Therefore, it is necessary to match it with a suitable cylindrical helical gear driving gear 6.

[0022] Step S101: Given the initial geometric parameters and operating conditions.

[0023] 3 parameters of the driven gear of the bevel gear: pitch circle diameter at the midpoint of the tooth width d m3 =71 mm; normal pressure angle α3=20°; helix angle β3=0° (straight teeth); number of teeth on the driving bevel gear z2=24, number of teeth on the driven bevel gear z3=35.

[0024] The cone angle δ3 needs to be calculated as follows: δ3 = arctan(z3 / z2) = arctan(35 / 24) ≈ 55.56°.

[0025] Preset parameters for the cylindrical helical gear drive wheel 6: The pitch circle diameter d6 = 76 mm is initially determined based on the transmission ratio and center distance.

[0026] Operating conditions: The rated torque T required to be transmitted by the secondary drive shaft 4 is 2000 Nm.

[0027] Step S102: Calculate the axial force coefficient k of the bevel gear. a .

[0028] Since the driven gear 3 of the bevel gear has spur teeth, its axial force coefficient is calculated as follows: k a3 =tanα3sinδ3=tan20°sin55.56°≈0.300.

[0029] Step S103: Establish and solve the equilibrium equation to determine the helix angle of the helical gear.

[0030] The k obtained in step S102 a3 Substituting into the axial couple equilibrium equation: tanβ (斜) / d (斜) =k a / d (m，锥) Substituting the numerical values, we get: tanβ6 = 0.300 × 76 / 71 β6=arctan(0.300×76 / 71)≈17.803°.

[0031] Step S104: Determine the direction of the helix to achieve couple cancellation.

[0032] according to Figure 2 Force analysis shows the axial force F generated by the driven gear 3 of the bevel gear in the indicated rotational direction. a3 The direction is to the left (pointing to the larger end). To achieve cancellation, the driving gear 6 of the cylindrical helical gear must generate an axial force F in the right direction. a6 According to the axial force direction determination criterion for helical gears ("left-hand rule"), when the driving gear 6 of the cylindrical helical gear is the driving gear and needs to generate an axial force to the right, it should be designed as a right-hand helical gear. Thus, the parameter design of the cylindrical helical gear that perfectly matches the given spur bevel gear is completed.

[0033] Step S105: Verification.

[0034] Substitute the design parameters into the axial force formula for calculation: Axial force of bevel gear driven wheel 3: F a3 =2000T / d m3 ×k a3 = (2000×2000) / 71×0.300≈16901 N (direction to the left).

[0035] Axial force on the driving gear of the cylindrical helical gear: F a6 =2000T / d6×tanβ6=(2000×2000) / 76×tan17.803°≈16901 N (direction to the right).

[0036] The axial forces of both are equal in magnitude and opposite in direction, acting on the same shaft system, thus achieving self-balancing of the axial couple. Therefore, the bearing supporting the secondary transmission shaft 4 mainly bears the radial force, and a deep groove ball bearing can be selected, simplifying the shaft system structure.

[0037] Example 2: A self-balancing design method for axial forces of bevel gears and helical gears, which matches and designs spiral bevel gears based on given cylindrical helical gear parameters.

[0038] In this embodiment, the cylindrical helical gear driving gear 6 is a standard part or is constrained by other factors, and its helix angle β6=15∘ (right-hand) and pitch circle diameter d6=76 mm are fixed. Now, it is necessary to design a bevel gear driven gear 3 to match it and achieve axial force self-balancing.

[0039] Step S201: Given initial parameters.

[0040] Fixed parameters of the cylindrical helical gear drive wheel 6: β6=15°, d6=76 mm.

[0041] Preset basic parameters for the driven gear 3 of the bevel gear: pitch circle diameter at the midpoint of the tooth width d m3 =71 mm; expected cone angle δ3=55.56°.

[0042] Operating conditions: Torque T = 2000 Nm.

[0043] Step S202: Determine the required axial force coefficient k based on the equilibrium equation. a .

[0044] By inversely deducing from the equilibrium equation: k a目标 =d m3 / d6×tanβ6=71 / 76×tan15°≈0.250 This k a目标 =0.250, which is the target value of the axial force coefficient that bevel gear 3 must achieve in order to achieve balance.

[0045] Step S203: Coordinate the adjustment of bevel gear parameters to meet the target k a value.

[0046] k a目标 Substituting =0.250 and δ3=55.56° into the formula: k a =tanβ3cosδ3±(tanα3sinδ3) / cosβ3 To make the axial force F a3 With F a6 The directions are opposite (cancel each other out), and the sign needs to be determined based on the direction of rotation. In this embodiment, the helical gear 6 is right-handed and generates a rightward axial force, therefore the bevel gear 3 is required to generate a leftward axial force (pointing towards the larger end), and the formula should use a "+" sign. Thus, we have: 0.250=tanβ3cos55.56°+(tanα3sin55.56°) / cosβ3 If we take the standard pressure angle α3 = 20° and substitute it into the above formula: 0.250=tanβ3cos55.56°+(tan20°sin55.56°) / cosβ3 Numerical calculation yields β3≈-5.19°. The negative sign indicates a left-hand helix (matching the helix direction of the helical gear to cancel out forces). In this design, the absolute value of the helix angle is relatively small, which may lead to insufficient overlap or poor transmission smoothness.

[0047] To obtain a larger absolute value of the helix angle to improve transmission smoothness (contact ratio), the pressure angle can be used as a variable. For example, adjusting the normal pressure angle to α3 = 22.5° and substituting it into the formula again: 0.250=tanβ3cos55.56°+(tan22.5°sin55.56°) / cosβ3 Numerical calculation yields β3≈-9.6°. Increasing the pressure angle from 20° to 22.5°, while maintaining the same axial force balance objective, changes the helix angle from -5.19° to -9.6°. The increase in its absolute value is beneficial for improving the overlap ratio and load-bearing capacity of the bevel gear.

[0048] Step S204: Verification.

[0049] Substituting the finally determined α3 ​​and β3 into the formula, we obtain k. a All values ​​are equal to the target value of 0.250, thus ensuring complete balance of axial forces. This embodiment demonstrates the flexibility of the method of the present invention in the selection of gear parameters, that is, it allows for the flexible selection of the optimal parameter combination that is more beneficial to gear strength, contact ratio, or machining process by coordinating the adjustment of the pressure angle and helix angle, while ensuring complete balance of axial forces.

[0050] Structures, components, and connection methods not described in detail in this invention are all prior art known to those skilled in the art unless otherwise specified. It is obvious to those skilled in the art that this invention is not limited to the details of the above exemplary embodiments, and that the invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the invention. Therefore, the above embodiments should be regarded as exemplary and non-limiting in all respects. The scope of this invention is defined by the appended claims rather than the foregoing description, and therefore all changes falling within the meaning and scope of the equivalents of the claims are intended to be included within this invention.

Claims

1. A self-balancing design method for axial forces of bevel gears and helical gears, characterized in that, Includes the following steps: S1: Given or determine the initial geometric parameters of the coaxially arranged bevel gear and helical gear, wherein the initial geometric parameters include at least the pitch circle diameter d of the bevel gear at the midpoint of the tooth width. (m，锥) δ, the cone angle (锥) Helix angle β (锥) With normal pressure angle α (锥) The pitch circle diameter d of the cylindrical helical gear (斜) With helix angle β (斜) , and the same torque T transmitted by both; S2: Establish the axial force F generated by the bevel gear. (a，锥) The axial force F generated by the cylindrical helical gear (a，斜) The equilibrium equation for axial couples that achieve balance and mutual cancellation; S3: Based on the aforementioned axial couple balance equation, the geometric parameters of the bevel gear and the helix angle β of the cylindrical helical gear are... (锥) By performing coordinated parameter matching design, the axial forces generated by the two gear pairs under the torque T are equal in magnitude and opposite in direction, thereby achieving self-balancing of the axial couple of the transmission shaft system.

2. The self-balancing design method for axial forces of bevel gears and helical gears according to claim 1, characterized in that, The axial couple equilibrium equation mentioned in step S2 is as follows: tanβ (斜) / d (斜) =k a / d (m，锥) Where, k a is the axial force coefficient of the bevel gear.

3. The self-balancing design method for axial forces of bevel gears and helical gears according to claim 2, characterized in that, The axial force coefficient k of the bevel gear a Calculated using the following formula: k a =(tanα (锥) sinδ (锥) ) / cosβ (锥) ±tanβ (锥) cosδ (锥) The "±" sign in the formula is determined based on the helical direction and rotation direction of the bevel gear. When the axial force points to the larger end, a positive sign is used, and vice versa.

4. The self-balancing design method for axial forces of bevel gears and helical gears according to claim 3, characterized in that, When the bevel gear is a straight bevel gear, its helix angle β (锥) =0, the axial force coefficient k a The calculation formula is simplified to: k a =tanα (锥) sinδ (锥) .

5. The self-balancing design method for axial forces of bevel gears and helical gears according to claim 2, characterized in that, The collaborative parameter matching design in step S3 is a bidirectional matching design, including any of the following implementation paths: Path 1: Preset the geometric parameters of the bevel gear and calculate its axial force coefficient k. a The required helix angle of the cylindrical helical gear is determined based on the equilibrium equation. Path 2: Preset the helix angle β of the cylindrical helical gear. (斜) The required target axial force coefficient k is calculated by reverse calculation based on the equilibrium equation. a The value relationship is determined by adjusting the helix angle β of the bevel gear. (锥) and / or normal pressure angle α (锥) The value of k makes the calculated value... a The value relationship is satisfied.

6. The self-balancing design method for axial forces of bevel gears and helical gears according to claim 5, characterized in that, When executing path two, the helix angle β of the bevel gear is adjusted collaboratively. (锥) and normal pressure angle α (锥) To satisfy target k a The value is a multi-solution optimization process used to simultaneously optimize the overlap ratio, tooth root bending strength, or machinability of the gear pair while satisfying the self-balancing of axial couples.

7. A gear transmission system, characterized in that, The transmission shaft includes a bevel gear and a cylindrical helical gear rigidly coaxially connected by the same drive shaft. The geometric parameters of the bevel gear and the cylindrical helical gear are matched using the design method described in any one of claims 1 to 6, such that under rated operating conditions, the axial force generated by the bevel gear is equal in magnitude and opposite in direction to the axial force generated by the cylindrical helical gear, thereby ensuring that the bearings at both ends of the drive shaft do not bear net axial load.

8. The gear transmission system according to claim 7, characterized in that, The driven gear of the bevel gear and the driving gear of the cylindrical helical gear are fixed on the same transmission shaft.

Images