Tooth surface modification optimization method of pure rolling contact bevel gear

Abstract

The invention relates to the technical field of bevel gears, in particular to a tooth surface modification optimization method for a pure rolling contact bevel gear, which comprises the following steps: acquiring a transmission error function and an initial tooth surface # imgabs0 # of the pure rolling contact bevel gear, and resetting a theoretical contact trace of the pure rolling contact bevel gear as a modification target curve through the transmission error function; calculating a unit tangent vector alpha (1) and a tooth surface normal loss n (1) of the modification target curve according to the transmission error function; constructing a local coordinate system SF1 by taking any instantaneous contact point on the modification target curve as an original point and taking alpha (1), n (1) * alpha (1), n (1) as three base vectors; and performing coordinate transformation to obtain a pinion modification tooth surface equation of the pure rolling contact bevel gear: # imgabs1 #, in which M (t) is a coordinate transformation matrix from a coordinate system SF1 to a coordinate system S1, and S1 is a coordinate system corresponding to an initial tooth surface delta of the pure rolling contact bevel gear. The mounting error high sensitivity of the pure roller contact bevel gear caused by the constant transmission ratio condition can be reduced, and the meshing transmission performance of the pure roller contact bevel gear under the actual working condition is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of bevel gears, and in particular to a tooth surface modification optimization method for pure rolling contact bevel gears. Background Art

[0002] As the core device for power transmission between intersecting shaft systems, bevel gear transmission mechanisms play an important role in the field of mechanical transmission. Their typical applications include key scenarios such as automotive drive systems, rail vehicle bogies, and aircraft power transmission. The classical tooth profile design theory is based on the principle of meshing of conjugate surfaces, and in theory, a continuous line contact meshing state can be formed. However, in actual engineering applications, due to the requirements of processing deviation compensation, assembly error adaptability, and stress concentration control on the tooth end edge, a discrete point contact tooth surface form based on the processing motion trajectory is generally adopted. This type of improved tooth surface design focuses on the second-order parameter matching of the tooth surface curvature at the calibration reference point, but it cannot achieve precise control of the contact characteristics throughout the meshing motion process, resulting in the tooth surface contact area exhibiting rolling-sliding compound motion characteristics during the transmission process.

[0003] Based on the analytical framework of contact mechanics and fracture mechanics, sliding contact can easily induce multiple negative effects in transmission systems: on the one hand, it reduces power transmission efficiency, and on the other hand, it can induce typical failure conditions such as tooth scuffing and micropitting. In comparison, while rolling contact can result in contact stress concentration, the combined detrimental effects of the sliding component on bevel gear transmission systems are more significant. Notably, kinematic analysis of bevel gear pairs with intersecting shafts indicates that a characteristic point in the meshing region inevitably exists where the instantaneous relative velocity approaches zero. If the contact trajectory can be precisely located within this characteristic region, the occurrence of sliding contact can theoretically be completely suppressed. The emerging conjugate curve meshing theory offers significant advantages in this area: through mathematical modeling, it accurately calculates the spatial distribution of the contact trace, thereby establishing a mechanism for regulating contact behavior throughout the entire meshing cycle. However, existing pure rolling contact bevel gear meshing theories assume a constant transmission ratio, making them difficult to adapt to sudden changes in angular velocity at the cyclic joint caused by factors such as installation errors, which can lead to severe vibration and noise. Summary of the Invention

[0004] The purpose of the present invention is to provide a tooth surface modification optimization method for pure rolling contact bevel gears. By presetting the transmission error, the theoretical tooth surface is modified and optimized to reduce the high sensitivity of the pure rolling contact bevel gears to installation errors caused by the constant transmission ratio condition, and to improve the meshing transmission performance of the pure rolling contact bevel gears under actual working conditions.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A tooth surface modification optimization method for a pure rolling contact bevel gear, comprising:

[0007] Obtaining a transmission error function and an initial tooth surface θ of the pure rolling contact bevel gear; resetting a theoretical contact trace of the pure rolling contact bevel gear to a modification target curve using the transmission error function;

[0008] The unit tangent vector α of the modified target curve is calculated based on the transmission error function (1) and tooth surface method loss n (1) ;

[0009] Take any instantaneous contact point on the target curve as the origin and α (1) 、n (1) ×α (1) 、n (1) Construct a local coordinate system S for the three basis vectors F1 ;

[0010] After coordinate transformation, the tooth surface equation of the small wheel of the pure rolling contact bevel gear is obtained: S C1 (t) = M(t)θ, where M(t) is the F1 The coordinate transformation matrix to the coordinate system S1, the coordinate system S1 is the coordinate system corresponding to the initial tooth surface of the pure rolling contact bevel gear.

[0011] Furthermore, the transmission error function Δθ(t)=-κ(t-ε) 2 , κ is the parabola coefficient, t is the cone angle variable of the pinion of the pure rolling contact bevel gear, and ε is the corresponding angle parameter at the preset reference point.

[0012] Furthermore, the preset reference point is the midpoint of the theoretical contact trace.

[0013] Furthermore, the unit tangent vector α of the modified target curve is calculated based on the transmission error function Δθ(t): (1) and tooth surface method loss n (1) Specifically include:

[0014] The vector equation of the target curve of the modification is calculated based on the transmission error function Δθ(t):

[0015] r1 (1) (t)=(pf(t)sin(t-Δθ(t)) pf(t)cos(t-Δθ(t)) f(t) 1) T ;

[0016]

[0017] f(t)=be mt ;

[0018] n=sin(δ1), m=sin(δ1)cot(β k), b=cos(δ1), δ1 is the pitch angle of the small wheel, β k is the spiral angle of the theoretical contact trace, and T is the transpose of the matrix;

[0019] Unit tangent vector of the modified target curve

[0020] Tooth surface method of modifying target curve

[0021] is the component of the normal vector along each coordinate axis, specifically:

[0022]

[0023] Where, Δt=t-Δθ(t),

[0024]

[0025] C (α) The positive and negative values of correspond to the tooth surface normal vectors of the convex and concave surfaces of the modified small wheel respectively;

[0026] a n is the normal pressure angle.

[0027] Furthermore, the coordinate transformation matrix M(t) is:

[0028]

[0029] The operator “·” represents the dot product of two vectors, and the operator “(,,)” represents the mixed product of three vectors. s1 、j s1 and k s1 Represents the three basis vectors of the S1 coordinate system.

[0030] Furthermore, after obtaining the pinion modified tooth surface equation of the pure rolling contact bevel gear, the tooth surface equation is discretized within a preset range, and the coordinates of the discretized points are data processed and corrected. The processed discrete points are then imported into the 3D modeling software, and then the surface fitting or modeling function of the software is used to connect the discretized points into a smooth surface to obtain a 3D solid model of the pure rolling contact bevel gear.

[0031] The present invention has the following unexpected beneficial effects:

[0032] The method described in this paper effectively reduces the sensitivity of pure rolling contact bevel gears to installation errors by presetting the transmission error and resetting the theoretical contact trace to the target modification curve. Furthermore, tooth surface contact analysis results show that the transmission error curve derived using this modification optimization method is essentially consistent with the pre-set transmission error curve, demonstrating that this method can better adapt gears to installation errors and reduce the adverse effects caused by these errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the specific implementation of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the implementation or prior art description. Obviously, the drawings described below are only some embodiments of the present invention.

[0034] Figure 1 A schematic flow chart of the tooth surface modification optimization method of a pure rolling contact bevel gear according to an embodiment of the present invention is shown.

[0035] Figure 2 A schematic diagram showing the relative positions of the theoretical contact trace and the modified target curve is shown.

[0036] Figure 3 A schematic diagram of the transmission error curve under multi-tooth pair meshing is shown.

[0037] Figure 4 A schematic diagram of the modified tooth surface of the small wheel is shown.

[0038] Figure 5 A schematic diagram of the normal plane of the modified target curve is shown.

[0039] Figure 6 A schematic diagram of a three-dimensional solid model of a pure rolling contact logarithmic spiral bevel gear after modification is shown.

[0040] Figure 7a The schematic diagram of the mesh division of the pure rolling contact logarithmic spiral bevel gear after modification is shown.

[0041] Figure 7b A state diagram of the actual meshing transition point one is shown.

[0042] Figure 7c A schematic diagram showing the state where the contact point is located in the middle of the tooth surface.

[0043] Figure 7d A schematic diagram of the state of the actual meshing transition point 2 is shown.

[0044] Figure 8 A schematic diagram showing the comparison results between the actual transmission error curve and the theoretical transmission error curve is shown.

[0045] Figure 9A schematic diagram of the projection of the tooth surface contact trajectory on the shaft section is shown. DETAILED DESCRIPTION

[0046] The following describes the embodiments of the present invention with reference to the accompanying drawings and preferred embodiments. Those skilled in the art will readily appreciate the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the various details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are intended only to illustrate the present invention and are not intended to limit the scope of protection of the present invention.

[0047] It should be noted that the illustrations provided in the following embodiments are merely schematic illustrations of the basic concept of the present invention. The illustrations only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0048] In one embodiment, see Figure 1 As shown, a tooth surface modification optimization method for pure rolling contact bevel gears includes:

[0049] Obtaining a transmission error function and an initial tooth surface θ of the pure rolling contact bevel gear; resetting a theoretical contact trace of the pure rolling contact bevel gear to a modification target curve using the transmission error function;

[0050] The unit tangent vector α of the modified target curve is calculated based on the transmission error function (1) and tooth surface method loss n (1) ;

[0051] Take any instantaneous contact point on the target curve as the origin and α (1) 、n (1) ×α (1) 、n (1) Construct a local coordinate system S for the three basis vectors F1 ;

[0052] After coordinate transformation, the tooth surface equation of the small wheel of the pure rolling contact bevel gear is obtained: S C1 (t) = M(t)θ, where M(t) is the F1 The coordinate transformation matrix to the coordinate system S1, the coordinate system S1 is the coordinate system corresponding to the initial tooth surface of the pure rolling contact bevel gear.

[0053] The method described in this paper effectively reduces the sensitivity of pure rolling contact bevel gears to installation errors by presetting the transmission error and resetting the theoretical contact trace to the target modification curve. Furthermore, tooth surface contact analysis results show that the transmission error curve derived using this modification optimization method is essentially consistent with the pre-set transmission error curve, demonstrating that this method can better adapt gears to installation errors and reduce the adverse effects caused by these errors.

[0054] As a preferred embodiment of the present invention, the transmission error function Δθ(t)=-κ(t-ε) 2 , κ is the parabola coefficient, t is the cone angle variable of the pinion of the pure rolling contact bevel gear, and ε is the corresponding angle parameter at the preset reference point.

[0055] Existing pure rolling contact bevel gear meshing theory is based on a constant transmission ratio, making it difficult to adapt to sudden changes in angular velocity at the cyclic joint caused by factors such as installation errors, which in turn induces severe vibration and noise. Therefore, a pure rolling contact bevel gear tooth surface modification method based on preset transmission errors is proposed. This method modifies the theoretical tooth surface of the pinion to reduce its sensitivity to installation errors and minimize vibration and noise during bevel gear transmission.

[0056] One of the geometric characteristics of a pair of continuous pure rolling contact bevel gears is that the contact trace between the tooth surfaces is located on the pitch cone. Since the meshing theory of pure rolling contact bevel gears is based on the constant transmission ratio condition, theoretically no transmission error will occur in the meshing transmission. In order to preset the pure rolling contact bevel gear with transmission error, the theoretical contact trace Γ 1 Each instantaneous contact point rotates around its pitch cone axis to obtain the target curve Γ (1) The rotation angles of different contact points are different and satisfy the transmission error function Δθ(t). Therefore, the tooth line of the pinion tooth surface is determined by the theoretical contact trace Γ 1 Reset to the shaping target curve Γ (1) ,like Figure 2 shown.

[0057] Theoretical contact trace Γ 1 As one of the basic elements for constructing the theoretical tooth surface of the small wheel, after it is reset, the contact point trajectory between the tooth surfaces no longer follows Γ 1 Move along the target curve Γ (1) Move, so Γ 1 and Γ (1) The angular difference between them can be regarded as the transmission error. The preset parabolic transmission error can absorb the linear transmission error caused by the gear installation error, reduce the vibration and noise of the gear pair, make the transmission smooth, and reduce the error sensitivity. That is, the transmission error function Δθ(t) can be designed as: Δθ(t) = -κ(t-ε) 2 .

[0058] Furthermore, the preset reference point is the midpoint of the theoretical contact trace.

[0059] Since the theoretical contact trace Γ 1 and the target curve Γ (1) They only overlap at the preset reference point ε, so the transmission error is 0 when the contact point is at this point. Figure 3 Schematic diagram of the transmission error curve under multi-tooth meshing. In the single-tooth meshing state, the contact point is located on the modified target curve Γ (1) The transmission error amplitudes at the endpoints can be set equal, i.e. Δθ(t min )=Δθ(t max ). Therefore, the preset reference point ε is selected as the midpoint of the theoretical contact trace.

[0060] As a preferred embodiment of the present invention, the unit tangent vector α of the modified target curve is calculated based on the transmission error function Δθ(t): (1) and tooth surface method loss n (1) Specifically include:

[0061] The vector equation of the target curve of the modification is calculated based on the transmission error function Δθ(t):

[0062] r1 (1) (t)=(pf(t)sin(t-Δθ(t)) pf(t)cos(t-Δθ(t)) f(t) 1) T ;

[0063]

[0064] f(t)=be mt ;

[0065] n=sin(δ1), m=sin(δ1)cot(β k ), b=cos(δ1), δ1 is the pitch angle of the small wheel, β k is the spiral angle of the theoretical contact trace, and T is the transpose of the matrix;

[0066] Unit tangent vector of the modified target curve

[0067] Tooth surface method of modifying target curve

[0068] is the component of the normal vector along each coordinate axis, specifically:

[0069]

[0070] Where, Δt=t-Δθ(t),

[0071]

[0072] C (α) The positive and negative values of a correspond to the tooth surface normal vectors of the convex and concave surfaces of the modified small wheel respectively; n is the normal pressure angle.

[0073] The theoretical tooth surface of the small wheel is its cross-sectional curve Γ s1 Along the theoretical contact trace Γ 1 Consists of continuous changes, Γ 1 After reset, the target tooth surface of the small wheel can be regarded as a cross-sectional curve Γ located in the normal plane s(1) Along the target curve Γ (1) Continuous changes, such as Figure 4 According to this principle, the target curve Γ is modified (1) Any instantaneous contact point M on the (1) 、n (1) ×α (1) 、n (1) Three basis vectors construct a local coordinate system S F1 ; In coordinate system S F1 In the example, the basis vector n (1) ×α (1) and n (1) The plane where it is located is called the target curve Γ (1) The normal plane at this point is Figure 5 shown.

[0074] Furthermore, the coordinate transformation matrix M(t) is:

[0075]

[0076] The operator “·” represents the dot product of two vectors, and the operator “(,,)” represents the mixed product of three vectors. s1 、j s1 and k s1 Represents the three basis vectors of the S1 coordinate system.

[0077] As a preferred embodiment of the present invention, after obtaining the pinion modified tooth surface equation of the pure rolling contact bevel gear, the tooth surface equation is discretized within a preset range, and the coordinates of the discretized points are data processed and corrected, and then the processed discrete points are imported into the three-dimensional modeling software. Then, through the surface fitting or modeling function of the software, the discretized points are connected into a smooth surface to obtain a three-dimensional solid model of the pure rolling contact bevel gear.

[0078] Discretizing the tooth surface equations can transform complex tooth surface equations into a series of discrete points that accurately characterize the geometric features of the tooth surface. Data processing and correction of the discrete point coordinates can effectively remove errors and noise from the data, improving data accuracy. In actual operation, for example, measurement errors or computational inaccuracies may lead to deviations in the coordinates of discrete points. Through data processing and correction, the discrete points can more accurately reflect the actual shape of the tooth surface. By connecting the discrete points using the surface fitting or modeling functions of 3D modeling software, a smooth and accurate 3D solid model can be constructed that realistically represents the tooth surface shape of pure rolling contact bevel gears, providing a reliable model foundation for subsequent research and analysis.

[0079] After obtaining an accurate 3D solid model, specialized analysis software facilitates in-depth research on the performance of pure rolling contact bevel gears. This allows for tooth contact analysis, simulating gear contact under various operating conditions and observing the distribution of contact areas, the magnitude of contact stress, and changes. Based on these analysis results, targeted tooth surface optimization can be performed to further improve gear meshing performance. By varying tooth surface parameters, the model can be rebuilt and analyzed to identify the optimal tooth surface shape and parameter combination to meet the needs of various engineering applications, such as increasing gear load capacity and reducing vibration and noise.

[0080] Accurate 3D solid models provide key guidance for the machining and manufacturing of pure rolling contact bevel gears. Based on the model, machining personnel can obtain detailed tooth surface geometry information, including shape, size, curvature, and other information, thereby developing a more reasonable machining process plan. Model information can be used as a reference when selecting machining tools and determining cutting parameters to ensure good contact between the tool and the tooth surface and precise cutting during machining, thereby improving machining accuracy and efficiency. 3D solid models also facilitate the simulation and emulation of the machining process, enabling the early identification of potential machining problems, such as tool interference and uneven cutting allowances, allowing for timely adjustments and optimizations, reducing trial-and-error costs in actual machining and improving production efficiency and product quality.

[0081] The following analysis and explanation are combined with specific examples.

[0082] Taking a set of gear blank design parameters as an example, the gear blank design parameters are shown in Table 1.

[0083] Table 1 Gear blank design parameters

[0084] parameter symbol value Big-endian modulus <![CDATA[m t ]]> 7 Normal pressure angle <![CDATA[α n ]]> 20° Helix angle <![CDATA[β k ]]> 35° Head clearance coefficient C* 0.15 Tooth height coefficient <![CDATA[h c ]]> 0.3 Pitch angle <![CDATA[δ1,δ2]]> 18.435°,71.565° Tooth tip angle θ 1.087° tooth root angle <![CDATA[θ f ]]> 1.630° Cone angle <![CDATA[δ a1 ,d a2 ]]> 19.522°,72.652° Root cone angle <![CDATA[δ f1 ,d f2 ]]> 16.805°,69.935° Number of teeth <![CDATA[z1,z2]]> 10,30 gear ratio <![CDATA[i 21 ]]> 1:3 Axis angle ξ 90° Outer cone pitch diameter <![CDATA[d e1 ,d e2 ]]> 54mm,162mm Tooth width B 30mm

[0085] Reset the logarithmic spiral on the pitch cone to the target curve Γ (1) , in the S1 coordinate system Γ (1) The vector equation can be expressed as:

[0086] r1 (1)(t)=(ne mt sin(Δt) ne mt cos(Δt) be mt 1) T ; n=sin(δ1), m=sin(δ1)cot(β k ), δ1 is the pitch angle of the small wheel, β k is the helix angle of the (theoretical contact trace or modified target curve), and T is the transpose of the matrix.

[0087] According to the gear blank design parameters in Table 1, the preset reference point ε is taken as the midpoint of the theoretical contact trace, and we have:

[0088] In bevel gear transmission, the transmission error in the tooth length direction is generally in the order of arc seconds. Figure 3 As shown, it can be preset that when t=t min Or t=t max When the transmission error is 36 arc seconds, it is converted into radians:

[0089] Take t = t min , the parabola coefficient κ can be calculated as:

[0090] The preset transmission error Δθ(t) can be specifically expressed as:

[0091] After determining the transmission error Δθ(t), substitute it into the modified tooth surface equation, write the corresponding program in the programming software to generate the tooth surface points, and import the tooth surface point file into the 3D modeling software. According to the gear blank parameters in Table 1, generate the modified pure rolling contact logarithmic spiral bevel gear 3D solid model, as shown in the figure. Figure 6 shown.

[0092] Contact analysis of modified tooth surfaces: Tooth surface loading contact analysis is a method used to evaluate the contact state and contact performance of tooth surfaces during gear meshing. This method is of great significance for ensuring the smoothness of gear transmission, reducing noise and wear, and increasing the service life of gears.

[0093] This paper presents a numerical simulation method for bevel gear meshing contact, using the following technical approach for modeling and parameter setting: Based on Saint-Venant's principle of local effect, when the distance between the observation point and the tooth contact zone exceeds the characteristic dimension, the magnitude of the stress field perturbation affecting the contact zone is reduced to less than 1% of the baseline value. To balance computational accuracy and efficiency, this paper constructs a reduced model comprising three sets of tooth surfaces for contact nonlinear analysis.

[0094] In terms of element type selection, high-order solid elements (such as SOLID186) are prone to nodal force oscillation during contact iterations. This numerical instability can lead to misjudgment of contact states. After comparative testing, the SOLID185 hexahedral element with linear interpolation characteristics was ultimately selected for spatial discretization. A gradient distribution strategy was used for mesh density: a 0.2mm characteristic size element was set in the contact tooth surface area to capture stress gradients, while the element size was relaxed to 1-2mm in non-critical areas. Young's modulus E = 205 GPa and Poisson's ratio μ = 0.3 were taken as constant parameters.

[0095] Boundary conditions were set: an equivalent drag torque of 500 N·m was applied to the output, and a driving torque of 150 N·m was configured at the input with an angular velocity constraint of 0.3 rad / s. This load system transforms the three-dimensional contact problem into a quasi-static solution based on the principle of energy equivalence, ensuring the authenticity of the contact pressure distribution while effectively reducing the time-step sensitivity of the transient analysis. Specifically, the contact algorithm employs the augmented Lagrangian method for pressure transfer calculations, and adaptive step-size control technology improves convergence stability.

[0096] Pure rolling contact bevel gears are highly sensitive to installation errors due to the constant transmission ratio. This phenomenon causes local stress concentration at the edges of the tooth surface, which can lead to increased wear and shorten the life of the gear. In addition, edge contact can cause unstable gear meshing and abnormal noise, which may affect the stability of the entire transmission system in the long term. To reduce the sensitivity to installation errors, the theoretical tooth surface is modified using the above-mentioned method of presetting the transmission error. The mesh division of the modified pure rolling contact bevel gear is as follows: Figure 7a shown.

[0097] Figure 7b The actual meshing transition point 1 shows that the previous tooth is transitioning from the start of meshing out to the start of meshing in of another tooth; when the contact point reaches the middle of the tooth surface from the meshing point of the tooth, only one pair of teeth is meshing, such as Figure 7c As shown; Figure 7d The actual meshing transition point 2 shows that the tooth switches from starting to mesh out to starting to mesh in with the next tooth.

[0098] According to the finite element analysis results, the actual transmission error curve is derived and compared with the preset theoretical transmission error curve. The comparative analysis results are as follows: Figure 8 shown.

[0099] Figure 8 In the figure, the blue dotted line is the actual transmission error curve derived from the finite element analysis; the transmission error function obtained by calculation is A preset theoretical transmission error curve (the solid red line) can be plotted. Comparison shows that there is only a slight deviation between the actual transmission error curve and the preset theoretical transmission error curve. In multi-pair meshing transmissions, the intersection of the transmission error curves corresponds to the actual meshing transition point during the gear meshing process; the amplitude of the actual transmission error curve at this point is -16.3287, while the amplitude of the theoretical transmission error curve at this point is -14.5785. Compared to other contact points, the deviation between the two at the meshing transition point is slightly larger; overall, the two trends are essentially consistent, and the actual transmission error curve is parabolic, which helps reduce error sensitivity, vibration, and noise, demonstrating the effectiveness of tooth surface modification.

[0100] Corresponding to the above, Figure 9 The figure shows the projection of the tooth surface contact trajectory on the shaft section. The left and right endpoints of the contact trajectory are the actual engagement points T of the gear transmission. a and the actual meshing point T b . Actual engagement point T a and the actual meshing point T b The coordinates are (4.144, 2.299) and (23.296, 2.5106) respectively. Clearly, the actual engagement point is away from the tooth tip, toward the tooth root; the actual engagement point is also away from the tooth tip, toward the tooth tip. The overall contact area is skewed toward the center of the tooth surface, which helps avoid edge contact and stress concentration.

[0101] This invention optimizes the theoretical tooth surface of bevel gears by modifying it based on a preset transmission error. Contact analysis of the modified tooth surfaces shows that the derived transmission error curve is essentially consistent with the preset transmission error curve, validating the effectiveness of the tooth surface modification. The overall contact area is positioned away from the tooth edges, effectively avoiding edge contact and stress concentration, thus reducing vibration and noise.

[0102] The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Any equivalent substitution or modification made by those skilled in the art based on the present invention is within the protection scope of the present invention.

Claims

1. A tooth surface modification optimization method for pure rolling contact bevel gears, characterized in that: include: Obtain the transmission error function and the initial tooth surface θ of the pure rolling contact bevel gear; Resetting the theoretical contact trace of the pure rolling contact bevel gear to a modified target curve through the transmission error function; The unit tangent vector α of the modified target curve is calculated based on the transmission error function (1) and tooth surface method loss n (1) ; Take any instantaneous contact point on the target curve as the origin and α (1) 、n (1) ×α (1) 、n (1) Construct a local coordinate system S for the three basis vectors F1 ; After coordinate transformation, the tooth surface equation of the small wheel of the pure rolling contact bevel gear is obtained: S C1 (t) = M(t)θ, where M(t) is the F1 The coordinate transformation matrix to the coordinate system S1, the coordinate system S1 is the coordinate system corresponding to the initial tooth surface of the pure rolling contact bevel gear.

2. The tooth surface modification optimization method for pure rolling contact bevel gears according to claim 1, characterized in that: The transmission error function Δθ(t)=-κ(t-ε) 2 , κ is the parabola coefficient, t is the cone angle variable of the pinion of the pure rolling contact bevel gear, and ε is the corresponding angle parameter at the preset reference point.

3. The tooth surface modification optimization method of pure rolling contact bevel gear according to claim 2, characterized in that: The preset reference point is the midpoint of the theoretical contact trace.

4. The tooth surface modification optimization method of pure rolling contact bevel gear according to claim 1, characterized in that: The unit tangent vector α of the modified target curve is calculated based on the transmission error function Δθ(t): (1) and tooth surface method loss n (1) Specifically include: The vector equation of the target curve of the modification is calculated based on the transmission error function Δθ(t): r1 (1) (t)=(pf(t)sin(t-Δθ(t))pf(t)cos(t-Δθ(t))f(t)1) T ; f(t)=be mt ; n=sin(δ1), m=sin(δ1)cot(β k ), b=cos(δ1), δ1 is the pitch angle of the small wheel, β k is the spiral angle of the theoretical contact trace, and T is the transpose of the matrix; Unit tangent vector of the modified target curve Tooth surface method of modifying target curve is the component of the normal vector along each coordinate axis, specifically: Where, Δt=t-Δθ(t), C (α) The positive and negative values of correspond to the tooth surface normal vectors of the convex and concave surfaces of the modified small wheel respectively; a n is the normal pressure angle.

5. The tooth surface modification optimization method of pure rolling contact bevel gear according to claim 4, characterized in that: The coordinate transformation matrix M(t) is: The operator "·" represents the dot product of two vectors, and the operator "(,,)" represents the mixed product of three vectors. s1 、j s1 and k s1 Represents the three basis vectors of the S1 coordinate system.

6. The tooth surface modification optimization method of pure rolling contact bevel gear according to claim 1, characterized in that: After obtaining the pinion modified tooth surface equation of the pure rolling contact bevel gear, the tooth surface equation is discretized within a preset range, and the coordinates of the discretized points are data processed and corrected. The processed discrete points are then imported into the 3D modeling software. Then, through the surface fitting or modeling function of the software, the discretized points are connected into a smooth surface to obtain the 3D solid model of the pure rolling contact bevel gear.

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