Tooth surface active design-based comprehensive performance optimization method for hypoid gear with high reduction ratio

Abstract

The invention provides a tooth surface active design-based comprehensive performance optimization method for a hypoid gear with a high reduction ratio. Comprising the following steps: obtaining original tooth surface equations of a large gear and a small gear according to geometric parameters of the high-reduction-ratio hypoid gear; obtaining a small wheel conjugate curved surface according to a meshing principle; obtaining a contact trace on the conjugate tooth surface of the small wheel according to the relation of the position vectors of the paired tooth surfaces at the meshing points; a contact mark is preset, a contact trace line is designed to be large inclined, three-section parabola modification is carried out in the meshing line direction of each contact point so as to control a contact area, and a target tooth surface is obtained; obtaining the normal deviation of the theoretical tooth surface and the target tooth surface of the small wheel; the theoretical tooth surface machining parameters of the small wheel are adjusted to enable the newly obtained tooth surface to approach the target tooth surface; and performing tooth surface contact analysis and tooth surface loading contact analysis on the two tooth surfaces, and comparing the comprehensive performance. According to the method, the tooth surface contact trace is designed to be large inclination through the tooth surface active design technology, and the comprehensive performance of the gear pair is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of high reduction ratio hypoid gear modification, and in particular to a method for optimizing the comprehensive performance of high reduction ratio hypoid gears based on active tooth surface design. Background Art

[0002] Following the harmonic reducer and RV reducer, the hypoid gear transmission reducer has become another new transmission form for robots. Usually, the hypoid gear reducers used in cars or helicopters are mainly small reduction ratios and low transmission accuracy, which are difficult to meet the high rigidity, high precision and lightweight requirements of industrial robots. High reduction ratio hypoid gears have the advantages of small space occupation, large reduction ratio, lightweight transmission and strong load-bearing capacity, which can meet the needs.

[0003] However, the pinion of a high reduction ratio hypoid gear has fewer teeth, and the entire tooth surface has a relative sliding speed. The friction times of each tooth surface are greater, causing more serious problems such as tooth surface wear, tooth surface bonding and noise. Therefore, the traditional transmission error modification design can no longer meet the requirements of high reduction ratio hypoid gear transmission devices. It is of great significance to study the tooth surface modification design method with strong anti-bonding ability, large load capacity and low noise. Summary of the invention

[0004] In order to improve the comprehensive load-bearing capacity of high-reduction ratio hypoid gears, this paper first uses the active tooth surface design technology to explore the influence of the length of the contact trace on the comprehensive performance of the tooth surface when the contact trace is designed with a large inclination. On this basis, the contact trace length and the length of the major semi-axis of the contact ellipse are preset to obtain the target tooth surface and compare it with the original tooth surface. Combining the tooth surface contact analysis (TCA) and the tooth surface load contact analysis (LTCA), the transmission error, load transmission error, tooth surface discrete point load distribution, tooth root bending stress and tooth surface flash temperature are obtained to explore the influence of the contact trace length on these performance parameters.

[0005] In order to achieve the above object, the present invention provides a method for optimizing the comprehensive performance of a high reduction ratio hypoid gear based on active tooth surface design, which is characterized by comprising the following steps:

[0006] S1, establish the original tooth surface of the large wheel and the small wheel;

[0007] S2, obtain the conjugate surface of the small wheel based on the meshing principle;

[0008] S3, according to the relationship between the position vectors of the paired tooth surfaces at the meshing point, the contact trace on the conjugate tooth surface of the pinion is obtained;

[0009] S4, preset the contact mark and modify the gear surface with a second-order parabola to obtain the target gear surface;

[0010] S5, obtaining the normal deviation between the theoretical tooth surface of the small wheel and the target tooth surface, and adjusting the machining parameters of the theoretical tooth surface of the small wheel so that the newly obtained tooth surface approaches the target tooth surface;

[0011] S6, tooth surface contact analysis and tooth surface loading contact analysis are performed on the two tooth surfaces to compare their comprehensive performance. Further, the original tooth surface equations of the large wheel and the small wheel established in S1 are constrained by the following mathematical model:

[0012] r1=M 1b M bE2 M E2E0 M E0E1 M E1t M tf r f

[0013] n1=L 1b L bE2 L E2E0 L E0E1 L E1t L tf n f

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] r1 is the radial vector of the small wheel, n1 is the normal vector of the small wheel, M 1b YesS b The spatial transformation matrix from the coordinate system to the S1 coordinate system, M bE2 YesS E2 Coordinate system to S b The spatial transformation matrix of the coordinate system, M E2E0 YesS E0 Coordinate system to S E2 The spatial transformation matrix of the coordinate system, M E0E1 YesS E1 Coordinate system to S E0The spatial transformation matrix of the coordinate system, M E1t YesS t Coordinate system to S E1 The spatial transformation matrix of the coordinate system, M tf YesS f Coordinate system to S t The spatial transformation matrix of the coordinate system; L 1b M 1b Remove the last column and the last row of the rotation matrix, L bE2 M bE2 Remove the last column and the last row of the rotation matrix, L E2E0 M E2E0 Remove the last column and the last row of the rotation matrix, L E0E1 M E0E1 Remove the last column and the last row of the rotation matrix, L E1t M E1t Remove the last column and the last row of the rotation matrix, L tf M tf Remove the last column and row of the rotation matrix. f is the radial vector of the cutting surface of the small wheel cutter, n f is the normal vector of the cutting surface of the small wheel cutter, r p is the tool tip radius, s p is the displacement in the direction of the tool tip, α1 is the pressure angle of the outer tool of the small wheel cutter, θ p The knife disc corner.

[0024] S E0 (O E0 X E0 Y E0 Z E0 ) is the machine tool coordinate system, which is fixed to the machine tool and has its origin O E0 For machine tool center, X E0 ,

[0025] Y E0 , Z E0 are its XYZ axes respectively; S p (O p X p Y p Z p ) is the cradle coordinate system, fixed to the cradle, X p , Y p , Z p are its XYZ axes, its coordinate origin O p With machine tool center O E0 Overlap, swing around Z p Axis rotation, q is the angular tool position, is X p With X E0 The angle of E1(O E1 X E1 Y E1 Z E1 ) is the auxiliary coordinate system, which is related to the machine tool coordinate system S E0 parallel, with its origin O E1 is the center of the cutter head, S r1 S is the radial tool position; t (O t X t Y t Z t ) is the tool rotation coordinate system, O t With O E1 coincidence, j is the knife turning angle; S f (O f X f Y f Z f ) is the cutterhead coordinate system, fixed to the cutterhead, with the origin O f With O t Overlap, Z f With Z t The angle i is the blade inclination angle. S1(O1X1Y1Z1) is the small wheel coordinate system, which is fixedly connected to the small wheel blank. X1, Y1, and Z1 are its XYZ axes respectively, and its coordinate origin O1 is the designed intersection point of the small wheel; S b (O b X b Y b Z b ) is the auxiliary coordinate system, X b , Y b , Z b are its XYZ axes, whose origin coincides with O1, For the small wheel to process the corner, it is X b Angle with X1; S E2 (O E2 X E2 Y E2 Z E2 ) is the auxiliary coordinate system, which is related to the machine tool coordinate system S E0 parallel, its origin coincides with O1, X b1 It is called bed, X g1 It is called the axial wheel position, E1 is called the vertical wheel position, and γ1 is called the small wheel installation angle.

[0026] By replacing all the above small wheel parameters with the corresponding large wheel parameters, we can get the radial vector r2 and unit normal vector n2 of the large wheel.

[0027] Furthermore, the small wheel conjugate surface obtained in S2 is constrained by the following mathematical model:

[0028] r n1 =M n1n2 Mn22 r2

[0029] n n1 =L n1n2 L n22 n2

[0030]

[0031]

[0032] n n1 ·v n1 =0

[0033] r c =M 1n1 r n1

[0034]

[0035]

[0036] Where r2 and n2 are the wheel radius vector and normal vector. E is the offset distance. n1 The radial vector of the large wheel reference point in the coordinate system is r n1 and normal vector n n1 , respectively, are obtained by spatial transformation of the wheel radius vector and normal vector. n1n2 YesS n2 Coordinate system to S n1 The spatial transformation matrix of the coordinate system, M n22 It is the S2 coordinate system to S n2 The spatial transformation matrix of the coordinate system, M 1n1 YesS n1 The spatial transformation matrix from the coordinate system to the S1 coordinate system; L n1n2 M n1n2 Remove the last column and the last row of the rotation matrix, L n22 M n22 Remove the last column and the last row of the rotation matrix, L 1n1 M 1n1 Remove the last column and the last row of the rotation matrix. ψ1 and ψ2 are the initial rotation angles of the small wheel and the large wheel at the reference point. From the meshing equation, we can solve the initial rotation angle ψ2 of the large wheel of the gear pair at the reference point, and substitute it to get r n1 , n n1 . Convert it to the small wheel coordinate system S1 and get the radial vector r of the conjugate small wheel c With normal vector n c .

[0037] Furthermore, the position vector relationship of the paired tooth surfaces at the meshing point in S3 is:

[0038]

[0039] Among them, v 12 It is the relative speed between the large wheel and the small wheel when meshing, obtained by subtracting the small wheel speed from the corresponding large wheel speed. s p and θ p is the displacement and tool tip radius of the small wheel cutter, s g and θ g is the displacement and tool tip radius corresponding to the large wheel cutter.

[0040] Then, the meshing angle ψ1 of the small wheel is given with a certain step size and iterative solution is performed to obtain the contact trace of the gear pair.

[0041] Further, obtaining the target tooth surface in S4 includes the following steps:

[0042] The contact trace direction angle is preset to be greater than 140° so that the contact trace is greatly inclined; the length of the major semi-axis of the contact ellipse is preset to be 45%-55% of the tooth width; the contact trace is designed to be a straight line. c Parabolic modification is performed along the meshing line direction of the contact point, and the vertex of the modification curve is on the contact trace. In the designed contact area, the modification is performed along the meshing line direction according to parabola I, and outside the meshing area, the modification is performed along the meshing line direction according to parabola II, and finally the target tooth surface of the small wheel Σ is obtained. t .

[0043] The modified parabola is constrained by the following mathematical model:

[0044] The equation of the modified parabola I in the contact area is:

[0045] The equation of the modified parabola II outside the contact area is:

[0046] Where a is the length of the preset long semi-axis of the contact ellipse, δ is the deformation, σ is the deformation adjustment amount different from δ, the x direction is the direction of the long axis of the contact ellipse, and y is the direction of the normal line of the tooth surface.

[0047] Further, obtaining the small wheel processing parameters of the target tooth surface in S5 includes the following steps:

[0048] The radial vector and normal vector of any point M on the tooth surface can be expressed as:

[0049] r t =r c +δ y n c

[0050]

[0051] Taking the contact point P as the midpoint, the tooth surface is discretized by numerical method, r t and n t is the radial vector and normal vector of any point M on the tooth surface. Adjust the small wheel processing parameters to make the small wheel tooth surface close to the modified tooth surface, and the goal is to minimize the sum of the squares of the normal deviations between the small wheel tooth surface and the modified tooth surface at each grid point, so as to obtain the small wheel processing parameters.

[0052] Furthermore, S6 compares the comprehensive performance of the theoretical tooth surface and the target tooth surface, including the following steps:

[0053] The tooth surface contact analysis is carried out to obtain the transmission error diagram and the tooth surface contact area. The loading contact analysis is carried out to load the large wheel with torque to obtain the tooth surface contact stress diagram and the tooth root stress diagram; then the load transmission error and the tooth surface flash temperature are calculated. The parameters of the two tooth surfaces are compared to draw conclusions. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A schematic flow chart of a method for optimizing the comprehensive performance of a high reduction ratio hypoid gear based on active tooth surface design provided by an embodiment of the present invention;

[0055] Figure 2 This is the cutting surface diagram of the small wheel cutter;

[0056] Figure 3 This is the small wheel machining coordinate system diagram;

[0057] Figure 4 is the original tooth surface contact area diagram;

[0058] Figure 5 is the contact area diagram of the target tooth surface;

[0059] Figure 6 It is the original tooth surface transmission error curve;

[0060] Figure 7 is the target tooth surface transmission error curve;

[0061] Figure 8 It is the ease-off topology diagram of the original tooth surface;

[0062] Fig. 9 is the ease-off topology map of the target tooth surface;

[0063] Figure 10 is a comparison of the contact stress between the two tooth surfaces. Fig.10a is the stress diagram under 100N·m loading, Fig.10b is the stress diagram under 200N·m loading, Fig.10c This is the stress diagram under 400N·m loading;

[0064] Fig.11 It is the maximum tooth root bending stress diagram under multiple loads;

[0065] Fig.12 is the graph of tooth root bending stress variation;

[0066] Fig.13 This is the peak value diagram of flash temperature on tooth surface under multiple loads;

[0067] Fig.14 It is the overall flash temperature distribution diagram of the original tooth surface;

[0068] Fig.15 It is the overall flash temperature distribution diagram of the target tooth surface; DETAILED DESCRIPTION

[0069] In order to enable those skilled in the art to better understand the scheme of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0071] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described below are only some embodiments of the present invention, not all embodiments.

[0072] See also Figure 1 As shown, it is a flow chart of a method for optimizing the comprehensive performance of a high reduction ratio hypoid gear based on active tooth surface design provided by an embodiment of the present invention, and the method comprises the following steps:

[0073] S1, establish the original tooth surface of the large wheel and the small wheel;

[0074] Specifically, Figure 2 is the cutting surface of the small wheel cutter. First, the radial vector r of the small wheel cutting surface is expressed f and normal vector n f ;

[0075]

[0076]

[0077] Among them, r p is the tool tip radius, s p is the displacement in the direction of the tool tip, α1 is the pressure angle of the outer tool of the small wheel cutter, θp is the cutter head rotation angle. Further, the original tooth surface equations of the large wheel and the small wheel established in S1 are constrained by the following mathematical model:

[0078] r1=M 1b M bE2 M E2E0 M E0E1 M E1t M tf r f

[0079] n1=L 1b L bE2 L E2E0 L E0E1 L E1t L tf n f

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] r1 is the radial vector of the small wheel, n1 is the normal vector of the small wheel, M 1b YesS b The spatial transformation matrix from the coordinate system to the S1 coordinate system, M bE2 YesS E2 Coordinate system to S b The spatial transformation matrix of the coordinate system, M E2E0 YesS E0 Coordinate system to S E2 The spatial transformation matrix of the coordinate system, M E0E1 YesS E1 Coordinate system to S E0 The spatial transformation matrix of the coordinate system, M E1t YesS t Coordinate system to S E1 The spatial transformation matrix of the coordinate system, M tf YesS f Coordinate system to S t The spatial transformation matrix of the coordinate system; L 1b M 1bRemove the last column and the last row of the rotation matrix, L bE2 M bE2 Remove the last column and the last row of the rotation matrix, L E2E0 M E2E0 Remove the last column and the last row of the rotation matrix, L E0E1 M E0E1 Remove the last column and the last row of the rotation matrix, L E1t M E1t Remove the last column and the last row of the rotation matrix, L tf M tf Remove the last column and row of the rotation matrix. f is the radial vector of the cutting surface of the small wheel cutter, n f is the normal vector of the cutting surface of the small wheel cutter, r p is the tool tip radius, s p is the displacement in the direction of the tool tip, α1 is the pressure angle of the outer tool of the small wheel cutter, θ p The knife disc corner.

[0088] S E0 (O E0 X E0 Y E0 Z E0 ) is the machine tool coordinate system, which is fixed to the machine tool and has its origin O E0 For machine tool center, X E0 ,

[0089] Y E0 , Z E0 are its XYZ axes respectively; S p (O p X p Y p Z p ) is the cradle coordinate system, fixed to the cradle, X p , Y p , Z p are its XYZ axes, its coordinate origin O p With machine tool center O E0 Overlap, swing around Z p Axis rotation, q is the angular tool position, is X p With X E0 The angle of E1 (O E1 X E1 Y E1 Z E1 ) is the auxiliary coordinate system, which is related to the machine tool coordinate system S E0 Parallel, its origin O E1 is the center of the cutter head, S r1 S is the radial tool position; t (Ot X t Y t Z t ) is the tool rotation coordinate system, O t With O E1 coincidence, j is the knife turning angle; S f (O f X f Y f Z f ) is the cutterhead coordinate system, fixed to the cutterhead, with the origin O f With O t Overlap, Z f With Z t The angle i is the blade inclination angle. S1(O1X1Y1Z1) is the small wheel coordinate system, which is fixedly connected to the small wheel blank. X1, Y1, and Z1 are its XYZ axes respectively, and its coordinate origin O1 is the designed intersection point of the small wheel; S b (O b X b Y b Z b ) is the auxiliary coordinate system, X b , Y b , Z b are its XYZ axes, whose origin coincides with O1, For the small wheel to process the corner, it is X b Angle with X1; S E2 (O E2 X E2 Y E2 Z E2 ) is the auxiliary coordinate system, which is related to the machine tool coordinate system S E0 parallel, its origin coincides with O1, X b1 It is called bed, X g1 It is called the axial wheel position, E1 is called the vertical wheel position, and γ1 is called the small wheel installation angle.

[0090] By replacing all the above small wheel parameters with the corresponding large wheel parameters, we can get the radial vector r2 and unit normal vector n2 of the large wheel.

[0091] According to the meshing relationship of hypoid gears, the following is established: Figure 3 The tooth surface conjugate geometry model shown in the figure, S2 (O2X2Y2Z2) and S1 (O1X1Y1Z1) are the large wheel coordinate system and the small wheel coordinate system, rotating around the axis Z2 and Z1 respectively, and the axis intersection angle between X2 and X1 is 90°. n1 With S n2 is the stationary auxiliary coordinate system. E is the offset distance;

[0092] Using space coordinate transformation, we can obtain S n1 The radial vector r of the large wheel reference point in the coordinate system n1 and normal vector nn1 , and is constrained by the following mathematical model:

[0093] r n1 (ψ2)=M n1n2 M n22 (ψ2)r2

[0094] n n1 (ψ2) = L n1n2 L n22 (ψ2)n2

[0095]

[0096]

[0097] Where r2 and n2 are the wheel radius vector and normal vector. E is the offset distance. n1 The radial vector of the large wheel reference point in the coordinate system is r n1 and normal vector n n1 , respectively, are obtained by spatial transformation of the wheel radius vector and normal vector. n1n2 YesS n2 Coordinate system to S n1 The spatial transformation matrix of the coordinate system, M n22 It is the S2 coordinate system to S n2 The spatial transformation matrix of the coordinate system; L n1n2 M n1n2 Remove the last column and the last row of the rotation matrix, L n22 M n22 Remove the last column and the last row of the rotation matrix. ψ1 and ψ2 are the initial rotation angles of the small wheel and the large wheel at the reference point. From the meshing equation, we can solve the initial rotation angle ψ2 of the large wheel of the gear pair at the reference point, and substitute it to get r n1 , n n1 . Convert it to the small wheel coordinate system S1 and get the radial vector r of the conjugate small wheel c With normal vector n c .

[0098] At the reference point, the instantaneous transmission ratio of the gear pair is equal to the gear ratio. Let the angular velocity of the small wheel be 1. Find the angular velocity of the large wheel in the coordinate system S. n1 The angular velocity ω n1 , and then the relative speed v of the two tooth surfaces in this coordinate system is obtained 12 When the large wheel and the small wheel are meshed at the reference point, they are constrained by the following mathematical model:

[0099] n n1 ·v n1 =0

[0100] The initial rotation angle ψ2 of the large wheel of the gear pair at the reference point can be solved and substituted into r n1, n n1 .

[0101] Convert it to the pinion coordinate system S1, and the conjugate pinion tooth surface equation is constrained by the following mathematical model:

[0102] r c =M 1n1 r n1

[0103]

[0104]

[0105] Among them, the radial vector of the conjugate small wheel is r c , the normal vector is n c . M 1n1 YesS n1 The spatial transformation matrix from the coordinate system to the S1 coordinate system, L 1n1 M 1n1 Remove the last column and row of the rotation matrix.

[0106] S3, according to the relationship between the position vectors of the paired tooth surfaces at the meshing point, the contact trace on the conjugate tooth surface of the pinion is obtained;

[0107] Furthermore, the position vector relationship of the paired tooth surfaces at the meshing point in S3 is:

[0108]

[0109] Among them, v 12 It is the relative speed between the large wheel and the small wheel when meshing, obtained by subtracting the small wheel speed from the corresponding large wheel speed. s p and θ p is the displacement and tool tip radius of the small wheel cutter, s g and θ g is the displacement and tool tip radius corresponding to the large wheel cutter.

[0110] Then, the meshing angle ψ1 of the small wheel is given in steps of 1° and solved iteratively to obtain the contact trace of the gear pair.

[0111] S4, preset the contact mark and modify the gear surface with a second-order parabola to obtain the target gear surface;

[0112] The contact trace direction angle is preset to be greater than 140° so that the contact trace is greatly inclined; the length of the major semi-axis of the contact ellipse is preset to be 45%-55% of the tooth width; the contact trace is designed to be a straight line. cParabolic modification is performed along the meshing line direction of the contact point, and the vertex of the modification curve is on the contact trace. In the designed contact area, the modification is performed along the meshing line direction according to parabola I, and outside the meshing area, the modification is performed along the meshing line direction according to parabola II, and finally the target tooth surface of the small wheel Σ is obtained. t .

[0113] As described in S4, the modified parabola is constrained by the following mathematical model:

[0114] The equation of the modified parabola I in the contact area is:

[0115] The equation of the modified parabola II outside the contact area is:

[0116] Where a is the length of the preset long semi-axis of the contact ellipse, δ is the deformation, σ is the deformation adjustment amount different from δ, the x direction is the direction of the long axis of the contact ellipse, and y is the direction of the normal line of the tooth surface.

[0117] In this example, the preset contact ellipse major semi-axis length a is 2.425 mm, and the contact trace length gradually increases from 5.726 mm to 9.662 mm. The deformation δ is 0.00635 mm, σ∈(0.005, 0.0077), and the unit is mm.

[0118] S5, obtaining the normal deviation between the theoretical tooth surface of the small wheel and the target tooth surface, and adjusting the machining parameters of the theoretical tooth surface of the small wheel so that the newly obtained tooth surface approaches the target tooth surface;

[0119] The radial vector and normal vector of any point M on the tooth surface can be expressed as:

[0120] r t =r c +δ y n c

[0121]

[0122] With the contact point P as the midpoint, the tooth surface is discretized using a numerical method. t and n t is the radial vector and normal vector of any point M on the tooth surface. Adjust the small wheel processing parameters to make the small wheel tooth surface close to the modified tooth surface, and the goal is to minimize the sum of the squares of the normal deviations between the small wheel tooth surface and the modified tooth surface at each grid point, so as to obtain the small wheel processing parameters.

[0123] Taking a pair of hypoid gears as an example, the machining parameters of the small wheel machine tool before and after modification are shown in Table 1:

[0124]

[0125] S6, tooth surface contact analysis and tooth surface loading contact analysis are performed on the two tooth surfaces to compare their comprehensive performance.

[0126] The tooth surface contact analysis is carried out to obtain the transmission error diagram and the tooth surface contact area. The loading contact analysis is carried out to load the large wheel with torque to obtain the tooth surface contact stress diagram and the tooth root stress diagram; then the load transmission error and the tooth surface flash temperature are calculated. The parameters of the two tooth surfaces are compared to draw conclusions.

[0127] Figure 4 and Figure 5 They are the contact areas of the original tooth surface and the target tooth surface. The center point of the target tooth surface is closer to the midpoint of the tooth surface. The contact trace is close to a straight line and has a large inclination, presenting a diagonal contact. The contact area almost covers the entire tooth width, and the contact area is larger than the contact area of ​​the original tooth surface.

[0128] Figure 6 and Figure 7 is the transmission error curve. The transmission error peaks of the two tooth surfaces are not much different.

[0129] Figure 8 and Fig. 9 This is the ease-off topology diagram of the original tooth surface and the target tooth surface. Compared with the original tooth surface, the target tooth surface has less material at the large end and more material at the small end after modification. The overall tooth surface deviation does not change much, and the transmission errors of the two are not much different.

[0130] The large wheel loading torques of 100 N·m, 200 N·m and 400 N·m were selected for comparative analysis, and the results are shown in Figure 10. By comparing the tooth surface loading contact area and contact stress value, it is found that the maximum contact stress area of ​​the original tooth surface is concentrated at the tooth top, and as the load increases, it is more concentrated toward the tooth top, and the edge contact risk is greater; the maximum contact stress area of ​​the target tooth surface is concentrated in the middle of the tooth surface, and the overall contact stress is less than the original tooth surface; as the load increases, the contact area extension trend is weak, the anti-dislocation sensitivity of the tooth surface meshing is strong, the risk of edge contact is small, the vibration and noise of the gear in actual working conditions are reduced, and the contact area of ​​the target tooth surface is internally diagonal, the contact area is larger, and the strength of the gear is improved.

[0131] Maximum tooth root bending stress under multiple loads Fig.11 When the input torque of the large wheel is less than 100 N·m, the maximum tooth root bending stress of the two is close. As the load increases, the maximum tooth root bending of the target tooth surface is smaller than that of the original tooth surface.

[0132] Fig.12 The graph of the tooth root bending stress variation shows that only between the 10th meshing position and the 22nd meshing position at the meshing end, the tooth root bending stress of the target tooth surface is less than that of the original tooth surface, and vice versa for the other meshing positions. The maximum value of the tooth root bending stress of the original tooth surface is 1104.4N / mm 2, appears at the 18th meshing position at the meshing end; the maximum bending stress of the target tooth surface root appears at the 21st meshing position at the meshing end, with a value of 971.3N / mm 2 , which is 12% lower than the original tooth surface.

[0133] Fig.13 Figure 2 is the peak value diagram of flash temperature on the tooth surface under multiple loads. When the input torque of the large wheel is less than 100 N·m, the peak values ​​of flash temperature on the two tooth surfaces are similar. As the load increases, the peak value of flash temperature on the target tooth surface is smaller than that on the original tooth surface.

[0134] Tooth surface flash temperature Fig.14 and Fig.15 , the maximum flash temperature of the original tooth surface is 148.9℃, and the maximum flash temperature of the target tooth surface is 139.5℃, which is 6.3% lower than that of the original tooth surface, and the overall flash temperature of the contact area is lower. After the modification, the modification amount at both ends of the meshing and meshing is large, the gap is increased, the load is reduced, the thickness of the oil film is increased, and the lubrication state of the tooth surface is better, so the flash temperature of the target tooth surface is reduced. The closer to the tooth root, the greater the relative sliding speed, and the higher the flash temperature of the tooth surface. The tooth width utilization rate of the target tooth surface is much greater than that of the original tooth surface, and the overall flash temperature distribution is more uniform.

[0135] The embodiments of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in the relevant technical field without departing from the purpose of the present invention.

Claims

1. A comprehensive performance optimization method for high reduction ratio hypoid gears based on active tooth surface design, characterized in that: The steps include: Establish the original tooth surface of the large wheel and the small wheel; Based on the meshing principle, the conjugate surface of the small wheel is obtained; According to the relationship between the position vectors of the paired tooth surfaces at the meshing point, the contact trace on the conjugate tooth surface of the pinion is obtained; Preset the contact mark and modify the gear surface with a second-order parabola to obtain the target tooth surface; Obtain the normal deviation between the theoretical tooth surface of the small wheel and the target tooth surface, and adjust the machining parameters of the theoretical tooth surface of the small wheel to make the newly obtained tooth surface close to the target tooth surface; Tooth surface contact analysis and tooth surface loading contact analysis are performed on the two tooth surfaces to compare their comprehensive performance.

2. The comprehensive performance optimization method for high reduction ratio hypoid gears with active tooth surface design according to claim 1 is characterized in that: The original tooth surface equations of the large wheel and the small wheel are constrained by the following mathematical model: r1=M 1b M bE2 M E2E0 M E0E1 M E1t M tf r f n1=L 1b L bE2 L E2E0 L E0E1 L E1t L tf n f in: r1 is the radial vector of the small wheel, n1 is the normal vector of the small wheel, M 1b YesS b The spatial transformation matrix from the coordinate system to the S1 coordinate system, M bE2 YesS E2 Coordinate system to S b The spatial transformation matrix of the coordinate system, M E2E0 YesS E0 Coordinate system to S E2 The spatial transformation matrix of the coordinate system, M E0E1 YesS E1 Coordinate system to S E0 The spatial transformation matrix of the coordinate system, M E1t YesS t Coordinate system to S E1 The spatial transformation matrix of the coordinate system, M tf YesS f Coordinate system to S t The spatial transformation matrix of the coordinate system; L 1b M 1b Remove the last column and the last row of the rotation matrix, L bE2 M bE2 Remove the last column and the last row of the rotation matrix, L E2E0 M E2E0 Remove the last column and the last row of the rotation matrix, L E0E1 M E0E1 Remove the last column and the last row of the rotation matrix, L E1t M E1t Remove the last column and the last row of the rotation matrix, L tf M tf Remove the last column and the last row of the rotation matrix; r f is the radial vector of the cutting surface of the small wheel cutter, n f is the normal vector of the cutting surface of the small wheel cutter, r p is the tool tip radius, s p is the displacement in the direction of the tool tip, α1 is the pressure angle of the outer tool of the small wheel cutter, θ p is the knife disc turning angle; S E0 (O E0 X E0 Y E0 Z E0 ) is the machine tool coordinate system, which is fixed to the machine tool and has its origin O E0 For machine tool center, X E0 , Y E0 , Z E0 are its XYZ axes respectively; S p (O p X p Y p Z p ) is the cradle coordinate system, fixed to the cradle, X p , Y p , Z p are its XYZ axes, its coordinate origin O p With machine tool center O E0 Overlap, swing around Z p Axis rotation, q is the angular tool position, is X p With X E0 The angle of E1 (O E1 X E1 Y E1 Z E1 ) is the auxiliary coordinate system, which is related to the machine tool coordinate system S E0 parallel, with its origin O E1 is the center of the cutter head, S r1 S is the radial tool position; t (O t X t Y t Z t ) is the tool rotation coordinate system, O t With O E1 coincidence, j is the knife turning angle; S f (O f X f Y f Z f ) is the cutterhead coordinate system, fixed to the cutterhead, with the origin O f With O t Overlap, Z f With Z t The angle i is the inclination angle of the cutter; S1 (O1X1Y1Z1) is the small wheel coordinate system, which is fixedly connected to the small wheel blank, X1, Y1, Z1 are its XYZ axes respectively, and its coordinate origin O1 is the designed intersection point of the small wheel; S b (O b X b Y b Z b ) is the auxiliary coordinate system, X b , Y b , Z b are its XYZ axes, whose origin coincides with O1, For the small wheel to process the corner, it is X b Angle with X1; S E2 (O E2 X E2 Y E2 Z E2 ) is the auxiliary coordinate system, which is related to the machine tool coordinate system S E0 parallel, its origin coincides with O1, X b1 It is called bed, X g1 is called the axial wheel position, E1 is called the vertical wheel position, and γ1 is called the small wheel installation angle; Replacing all the above small wheel parameters with the corresponding large wheel parameters will give the radial vector r2 and unit normal vector n2 of the large wheel.

3. The comprehensive performance optimization method for high reduction ratio hypoid gears with active tooth surface design according to claim 1 is characterized in that: The conjugate surface of the small wheel obtained based on the meshing principle is constrained by the following mathematical model: r n1 =M n1n2 M n22 r2 n n1 (ψ2)=L n1n2 L n22 n2 n n1 ·v n1 =0 r c ＝M 1n1 r n1 Among them, r2 and n2 are the wheel radius vector and normal vector; E is the offset distance; S n1 The radial vector of the large wheel reference point in the coordinate system is r n1 and normal vector n n1 , respectively, are obtained by spatial transformation of the wheel radius vector and normal vector; M n1n2 YesS n2 Coordinate system to S n1 The spatial transformation matrix of the coordinate system, M n22 It is the S2 coordinate system to S n2 The spatial transformation matrix of the coordinate system, M 1n1 YesS n1 The spatial transformation matrix from the coordinate system to the S1 coordinate system; L n1n2 M n1n2 Remove the last column and the last row of the rotation matrix, L n22 M n22 Remove the last column and the last row of the rotation matrix, L 1n1 M 1n1 Remove the last column and the last row of the rotation matrix; ψ1 and ψ2 are the initial rotation angles of the small wheel and the large wheel at the reference point; solve the meshing equation to get the initial rotation angle ψ2 of the large wheel of the gear pair at the reference point, and substitute it into the equation to get r n1 , n n1 ; Convert it to the small wheel coordinate system S1 to obtain the radial vector r of the conjugate small wheel c With normal vector n c .

4. The comprehensive performance optimization method for high reduction ratio hypoid gears with active tooth surface design according to claim 3 is characterized in that: The contact trace on the conjugate tooth surface of the small wheel is constrained by the following mathematical model: In the formula, v 12 is the relative speed between the large wheel and the small wheel when meshing, obtained by subtracting the small wheel speed from the corresponding large wheel speed; s p and θ p is the displacement and tool tip radius of the small wheel cutter, s g and θ g is the displacement and tool tip radius corresponding to the large wheel cutter disc; The meshing angle ψ1 of the small wheel is given in steps of 1° and an iterative solution is performed to obtain the contact trace of the gear pair.

5. The comprehensive performance optimization method for high reduction ratio hypoid gears with active tooth surface design according to claim 1 is characterized in that: Preset the contact mark and modify the gear surface with a second-order parabola to obtain the target gear surface, including the following steps: Preset the contact trace direction angle, and set its value to be greater than 140° to make the contact trace tilt greatly; preset the contact ellipse major semi-axis length, and its value is 45%-55% of the tooth width; design the contact trace as a straight line; set the tooth surface Σ c The parabola modification is performed along the meshing line direction of the contact point, and the vertex of the modification curve is on the contact trace line; within the designed contact area, the modification is performed along the meshing line direction according to parabola I, and outside the meshing area, the modification is performed along the meshing line direction according to parabola II, and finally the target tooth surface of the small wheel is obtained, and the target tooth surface is recorded as Σ t ; The equation of the modified parabola I in the contact area is: The equation of the modified parabola II outside the contact area is: Where a is the length of the preset semi-major axis of the contact ellipse, δ is the deformation, σ is the deformation adjustment amount different from δ, x is the direction of the major axis of the contact ellipse, and y is the direction of the normal line of the tooth surface.

6. The comprehensive performance optimization method for high reduction ratio hypoid gears with active tooth surface design according to claim 5 is characterized in that: Obtaining the normal deviation between the theoretical tooth surface and the target tooth surface, and adjusting the machining parameters of the theoretical tooth surface of the small wheel so that the newly obtained tooth surface approaches the target tooth surface is constrained by the following mathematical model: r t =r c +d y n c Taking the contact point P as the midpoint, the tooth surface is discretized by numerical method, r t and n t are the radial vector and normal vector of any point M on the tooth surface; adjust the small wheel processing parameters to make the small wheel tooth surface close to the modified tooth surface, and the goal is to minimize the sum of the squares of the normal deviations between the small wheel tooth surface and the modified tooth surface at each grid point, so as to obtain the small wheel processing parameters.

7. The comprehensive performance optimization method for high reduction ratio hypoid gears with active tooth surface design according to claim 1 is characterized in that: The tooth surface contact analysis and tooth surface loading contact analysis are performed on the two tooth surfaces to compare their comprehensive performance, including the following steps: Conduct tooth surface contact analysis to obtain the transmission error diagram and tooth surface contact area; conduct loaded contact analysis, apply torque to the large wheel, and obtain the tooth surface contact stress diagram and tooth root stress diagram; then calculate the load-bearing transmission error and tooth surface flash temperature; and compare the parameters of the two tooth surfaces.

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