1. Research Background and Significance
| Aspect | Description |
|---|---|
| Importance of Comfort | In recent years, with the rapid development of the automotive industry, people have higher requirements for car comfort. The NVH performance of the drive axle directly affects the ride comfort of the whole vehicle. |
| Drive Axle Composition | The drive axle transmission system mainly consists of the main reducer, differential, and half shafts. The core part is the main reducer, which transmits power. |
| Vibration and Noise Sources | The vibration and noise of the drive axle mainly come from two aspects: gear meshing impact and external forces. When the vibration frequency coincides with the natural frequency of the drive axle, resonance occurs, resulting in greater vibration and noise. |
| Hypoid Gear Advantages | Hypoid gears are widely used in the drive axle due to their large contact ratio, stable transmission, and high load-carrying capacity. However, to improve the NVH performance of the drive axle, it is necessary to study the meshing performance of the hypoid gear. |
2. Research Status at Home and Abroad
2.1 Tooth Contact Analysis Research Status
| Researcher | Research Content | Results |
|---|---|---|
| M.L.Baxter | Proposed the term Tooth Contact Analysis (TCA) and initially applied it to the simulation analysis of the meshing rotation of spiral bevel gears and hypoid gears. | – |
| Wang Y Z et al. | Studied the solution method of the tooth surface equation and the contact solution formula of the face gear based on the meshing theory of the face gear. | – |
| Shen Y B et al. | Established an edge contact solution model and found that edge contact is prone to occur during the meshing-in state. | – |
| Cao X M et al. | Proposed a new algorithm for tooth contact analysis, reducing the number of solution equations and computational complexity. | The new algorithm is correct. |
| Wang X L et al. | Studied the sensitivity of the contact pattern to four types of installation errors and established a sensitivity optimization model. | Reduced the sensitivity of installation errors to the tooth surface pattern. |
| Tang J Y et al. | Analyzed the tooth surface contact of the gear pair under machining and installation errors and compared it with the results without considering errors. | Machining and installation errors have a significant impact on the tooth surface contact quality. |
| Fan Q | Proposed a tooth contact analysis method based on the mismatch relationship, which can more intuitively display the relationship between tooth surface mismatch and contact pattern. | – |
| D | Directly used the midpoint of the large gear tooth surface as the initial value and set the initial value constraints of the large and small gears according to the meshing principle of the gear pair to solve the initial value point of the small gear. | – |
| Krenzer | Proposed the Tooth Loaded Contact Analysis (LTCA), which simulates the meshing rotation of gears under load and obtains results such as the loaded tooth surface contact pattern, loaded transmission error, and contact stress. | – |
| Litvin et al. | Considered the deviation between the actual tooth surface and the theoretical tooth surface due to machining errors and established a loaded tooth surface contact analysis model consistent with the real tooth surface. | – |
| Pu T P | Based on ABAQUS and CATIA software, studied the influence of hexahedral mesh on the accuracy of tooth surface contact analysis and gave the preprocessing method of ABAQUS load contact analysis. | – |
| Wu W H et al. | Established a finite element model of double circular arc spiral bevel gears based on Ansys Workbench and analyzed the variation law of gear meshing performance under different loads. | – |
| Lai C F et al. | Calculated the meshing misalignment of the hypoid gear pair under actual working conditions using MASTA software and performed a loaded contact analysis considering the meshing misalignment. | – |
2.2 Tooth Surface Modification Research Status
| Researcher | Research Content |
|---|---|
| Zhang R F | Set the tool parameters as optimization variables, established a target optimization algorithm, and improved the meshing performance of the hypoid gear by changing the tool cutting edge shape. |
| Fan Q | Introduced the concept of Ease off topology and proposed a design and manufacturing method of face-hobbing spiral bevel gears on a computer numerical control hypoid gear processing machine. |
| Simon et al. | Studied the micro-modification of the hypoid gear and proposed to improve the tooth surface load distribution and reduce the transmission error amplitude by designing the optimal tool parameters. |
| Fan Q et al. | Used the Ease off topology concept to describe the mismatch between the tooth surfaces during the meshing process of the bevel gear and proposed a tooth surface modification method by presetting the shape and position of the best loaded contact area, reducing the loaded transmission error amplitude, and contact stress. |
| Jiang J K, Wang Z R et al. | Designed the Ease off topological surface of the small gear by the preset method, established a multi-objective optimization modification model, obtained the best modification surface, derived the tooth surface correction amount, and established a tooth surface correction model based on the sensitivity of the machining parameters. |
| Wang X et al. | Took the direction of the contact path and the amplitude of the geometric transmission error as optimization variables, aimed to minimize the amplitude of the loaded transmission error, designed the machining parameters using an optimization algorithm, and verified the correctness and feasibility through a loaded contact analysis. |
| Du J F, Deng X Z et al. | Derived the conjugate tooth surface of the small gear that is completely conjugate with the large gear based on the conjugate theory, modified the conjugate tooth surface of the small gear along the meshing line and the contact path direction according to the meshing performance requirements of the hypoid gear, and obtained the target tooth surface that satisfies the meshing performance. |
| Yang J J et al. | Proposed a method to construct the Ease off topology of the large gear by curvature correction and obtained the target tooth surface. The experimental results showed that the meshing performance of the target tooth surface meets the preset requirements and the machining parameters do not need to be adjusted twice. |
| Li G et al. | Proposed a topology modification method to improve the meshing performance of the hypoid gear by converting the fourth-order transmission error into the equivalent error of the small gear tooth surface and then performing the Ease off topology modification of the small gear tooth surface. |
| Mu Y M et al. | Proposed a novel topology modification method for high-contact-ratio spiral bevel gears by using the concave surface transmission error instead of the parabolic transmission error to reduce the loaded transmission error of the high-contact-ratio spiral bevel gear. |
| Gonzalez P et al. | Analyzed the sensitivity of different machining parameters to the tooth surface error and provided guidance for tooth surface error correction. |
| Ding H | Established the corresponding relationship between the gear meshing performance and the machine tool machining parameters based on the loaded contact analysis of the hypoid gear and evaluated different correction schemes by setting different proportions of different machining parameters. |
| Ming X Z et al. | Proposed to use the sequential quadratic programming method (SQP) to solve the tooth surface error correction model and proved its feasibility through experiments. |
| Tian C et al. | Analyzed the correlation between the sensitivity of the machining parameters and the tooth surface error and corrected the tooth surface error by reducing the number and amount of machining parameter adjustments. Compared with other error correction methods, it has less computational complexity and higher accuracy. |
| Mo Y M et al. | Analyzed a large amount of vehicle loading road test data and concluded that simply controlling the tooth surface contact area cannot meet the NVH performance requirements of the gear, and the gear transmission error amplitude should be controlled within a reasonable range. |
| Nie S W et al. | Constructed the tooth surface mismatch graph and approximated it with a second-order surface polynomial. By changing the polynomial coefficients, the target tooth surface was obtained, and a machining parameter correction mathematical model was established. The least square method was used to solve the model because it is an overdetermined linear equation, making the actual tooth surface approach the target tooth surface. |
| Yang J J et al. | Proposed a method for synchronous modification design of the convex and concave tooth surfaces of the spiral bevel gear. By using the midpoint of the tooth groove as a reference point, the design of the two tooth surfaces was carried out to meet the meshing performance requirements. The finite element simulation verified the effectiveness of the method. |
2.3 Drive Axle Vibration and Noise Research Status
| Researcher | Research Content |
|---|---|
| Ma H T et al. | Studied the noise excitation sources and propagation paths of the drive axle, combined with after-sales cases, found the root causes of the drive axle noise, and proposed improvement solutions. The bench test verified the effectiveness of the solutions and reduced the noise. |
| Jiao D F | Constructed a correlation calculation model of the factors affecting the drive axle vibration and noise, obtained the correlation of each factor, obtained the lowest noise value and the corresponding combination of factors through orthogonal experiments, analyzed the sensitivity of the noise-influencing factors, constructed a multi-objective optimization function, and obtained a method that can optimize multiple factors simultaneously. The experimental verification was carried out. |
| Hu L, Fu C et al. | Compared the methods of controlling the drive axle noise after considering the structure and working environment of the drive axle. They proposed two methods: damping vibration and noise reduction technology and Helmholtz resonator noise reduction technology. |
| Zhou R | Analyzed the road test results and found that the main noise of the vehicle was the 8th and 16th order meshing noise and resonance of the main reducer gear. Therefore, the meshing performance of the main reducer gear was improved, and the rear axle noise was significantly reduced. At the same time, based on the resonance problem of the rear axle, a dynamic vibration absorber was installed at the main reducer housing through modal analysis, and the vehicle noise was effectively reduced. |
| Guo N C et al. | Established a drive axle assembly model for overall dynamic simulation. The surface vibration data of the drive axle obtained from the simulation results were consistent with the data measured by the bench test, and the internal data of the drive axle obtained from the simulation results had guiding significance for improving the vibration and noise of the drive axle. |
| Mao S W et al. | Detected the noise of a certain vehicle and concluded that the main cause of the noise of the drive rear axle was the meshing vibration of the main reducer gear by comparing the frequencies of the first-order noise and the total noise. |
| Zhang Q, Wang J et al. | Detected the vibration and noise of the whole vehicle and found that the order of the generated noise was consistent with that of the main reducer. Therefore, the tooth surface of the main reducer gear was modified, and the influence of the tooth surface modification on the vehicle noise was verified. |
| Zhang J et al. | Established a drive axle model, analyzed its vibration and noise, simplified the components with little influence on the vibration and noise in the analysis results, established a finite element analysis model, analyzed the vibration and noise using the finite element method, optimized the structure of the main parts generating vibration and noise without affecting other components, and achieved the effect of reducing noise. |
| Li Z et al. | Analyzed the vibration of the drive axle and the frequency response of the axle housing and found that the rear cover of the drive axle was the place with the largest noise radiation. Based on the Virtual.Lab software, reinforcements or cross ribs were applied to the rear cover of the axle housing, which was the place with the largest noise radiation of the drive axle, for simulation verification. The results showed that the noise was indeed reduced. |
| Tang J H et al. | Analyzed the modal of the drive axle housing and found that the main cause of the vibration and noise of the drive axle housing was the meshing of the hypoid gear of the main reducer. To effectively control the vibration and noise, the transient response and harmonic response of the drive axle were analyzed to find the parts of the axle housing that were most affected by the excitation, and the structure of these parts was optimized. |
| Mark A | Analyzed the meshing performance and vibration performance of the hypoid gear using finite element software and analyzed the vibration and noise transfer path of the drive axle. He proposed many methods to control the vibration and noise of the drive axle. |
| Choi B J et al. | Analyzed the possible causes of the noise of the hypoid gear, explored the parameters that should be considered in the optimal design of the hypoid gear and the steps to optimize these parameters, and obtained the stress-strain nephogram and transmission error of the gear through a torsion test bench. |
| Karagiannis et al. | Established a dynamic model of the hypoid gear of the main reducer based on the engine output torque as the excitation and studied the influence law of the size of the tooth surface contact area on the vibration and noise of the gear pair when the gear pair rotates at high speed. |
3. Main Research Contents of This Article
| Research Content | Details |
|---|---|
| HFT Method-based Hypoid Gear Model | Establish the HFT method-based hypoid gear grinding mathematical model, solve the numerical tooth surface through the spatial rotation projection relationship, and build the gear three-dimensional model. |
| Gear Meshing Mathematical Model | Establish the gear meshing mathematical model, conduct theoretical contact analysis on the tooth surface, establish the finite element loaded contact analysis method of the hypoid gear through ABAQUS software, establish the drive axle model based on MASTA software, and study the NVH simulation analysis method of the drive axle. |
| Tooth Surface Ease off Topology Model | Based on the complete conjugate principle, establish the tooth surface Ease off topology model, decompose it with a second-order surface, calculate the |
3. Main Research Contents of This Article
| Research Content | Details |
|---|---|
| HFT Method-based Hypoid Gear Model | Establish the HFT method-based hypoid gear grinding mathematical model, solve the numerical tooth surface through the spatial rotation projection relationship, and build the gear three-dimensional model. |
| Gear Meshing Mathematical Model | Establish the gear meshing mathematical model, conduct theoretical contact analysis on the tooth surface, establish the finite element loaded contact analysis method of the hypoid gear through ABAQUS software, establish the drive axle model based on MASTA software, and study the NVH simulation analysis method of the drive axle. |
| Tooth Surface Ease off Topology Model | Based on the complete conjugate principle, establish the tooth surface Ease off topology model, decompose it with a second-order surface, calculate the tooth surface mismatch coefficient, pre-control and correct the mismatch coefficient to modify the topology of the small gear tooth surface, analyze the sensitivity of the machining parameters, construct the sensitivity matrix, and use the numerical optimization algorithm to inversely calculate the small gear machining parameters. |
| Influence of Tooth Surface Modification on NVH | Consider the actual working conditions, calculate the meshing misalignment of the hypoid gear under load, analyze the loaded contact performance of the tooth surface before and after modification and the NVH simulation of the drive axle, explore the influence law of the tooth surface modification loading performance on the NVH of the drive axle, complete the drive axle bench test and road test, and compare the experimental results with the simulation results to verify the effectiveness of the tooth surface modification and NVH simulation methods. |
4. Hypoid Gear Numerical Tooth Surface Calculation and Three-dimensional Modeling
| Section | Method/Process | Key Equations/Results |
|---|---|---|
| Small Gear Tooth Surface Equation | Derived from the tool surface equation and unit normal vector through coordinate transformation and considering the meshing equation. | , , $n_{i}=\frac{N_{i}}{\left |
| Large Gear Tooth Surface Equation | Established based on the relative motion and position relationship between the cutter head and the large gear. | Similar to the small gear, the large gear tooth surface equation and unit normal vector are obtained. |
| Tooth Root Transition Surface Equation | Derived from the cutter tip arc equation and unit normal vector for both the large and small gears. | For the large gear, the cutter tip arc equation (with for inner and outer cutters respectively) and the corresponding unit normal vector $n_{s}’=\frac{N_{s}’}{\left |
| Numerical Tooth Surface Calculation | Discretize the tooth surface by grid division, calculate the coordinates of grid points on the rotation projection plane, and then solve the three-dimensional coordinates of the tooth points. | The grid division is shown in Fig. 2 – 5, and the coordinates of the boundary points , , , are calculated using equations such as and . The slopes of the boundary lines are calculated, and new boundary equations are derived. The coordinates of the grid points are calculated, and finally, the three-dimensional coordinates of the tooth points are obtained by solving the equations related to the tooth surface equation and the rotation projection plane grid points. |
| Three-dimensional Model Building | Use the calculated tooth point coordinates to build the three-dimensional models of the small and large gears and assemble them. | The geometric and machining parameters of the hypoid gear are shown in Tables 2 – 1 and 2 – 2. The tooth point coordinates are calculated and imported into UG software to build the models. The modeling process is shown in Figs. 2 – 6 and 2 – 7, and the assembled gear pair is shown in Fig. 2 – 8. |
5. Hypoid Gear Finite Element Loading Analysis and NVH Simulation
5.1 Tooth Surface Contact Analysis
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Mathematical Model Establishment | Based on the relative position and motion relationship of the hypoid gear pair during meshing. | The mathematical model is shown in Fig. 3 – 1, and the small gear tooth surface equation , unit normal vector , large gear tooth surface equation , and unit normal vector are transformed into the fixed coordinate system using coordinate transformation matrices. The meshing equations , , , and are obtained, where the matrices , , , , , , , and are defined as in the text. |
| Contact Point Calculation | Solve the contact points by giving the value of and using the meshing equations. | Five independent scalar equations are obtained from the meshing equations, and by giving the value of , the other five unknowns can be solved to obtain the contact points. |
| Transmission Error Calculation | Calculate the transmission error using the formula based on the actual and initial rotation angles of the gears. | The transmission error is defined as , where and are the actual rotation angles of the small and large gears, and and are the initial meshing rotation angles at the reference point. The transmission error curve is obtained by substituting the parameters of the contact points into this formula. |
| Results | The tooth surface contact area and transmission error are obtained as shown in Fig. 3 – 2. | – |
5.2 Loading Meshing Performance Analysis Based on ABAQUS Software
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Finite Element Preprocessing | 1. Build the finite element model by importing and assembling the single-tooth model and auxiliary surface files and arraying the single tooth. 2. Set the material properties by defining the material density, elastic modulus, and Poisson’s ratio and creating and assigning sections. 3. Build the mesh system by dividing the grid, making the contact surface grid denser and other parts relatively sparser. | The preprocessing parameters are shown in Table 3 – 1. |
| Finite Element Solution Setting | 1. Set the solver as the dynamic implicit type with three analysis steps, including restricting the degrees of freedom of the large gear, then the small gear, and finally allowing both gears to rotate. 2. Build the connection relationship by setting the face-to-face contact between the small and large gear tooth surfaces. 3. Set the boundary conditions by specifying the rotational speeds and applied torque of the small and large gears. | The solution process parameters are shown in Table 3 – 2. |
| Finite Element Postprocessing | Extract the contact stress cloud diagram and use a Python script to obtain the maximum contact stress at each unit on the tooth surface during the meshing process. | The instantaneous contact ellipse is shown in Fig. 3 – 6, and the extraction process is shown in Fig. 3 – 7. The loaded contact area of the tooth surface is obtained as shown in Fig. 3 – 8, and the maximum contact stress on the large gear concave and convex surfaces is obtained. The tooth root bending stress cloud diagram and curve are shown in Figs. 3 – 9 and 3 – 10, and the loaded transmission error is shown in Fig. 3 – 11. |
5.3 Drive Axle MASTA Three-dimensional Model Establishment
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Model Building | Build the drive axle model by importing the models of each component built in UG into Hypermesh for meshing and preprocessing, and then importing them into MASTA to build the two-dimensional and three-dimensional models. | The drive axle structure is shown in Fig. 3 – 12, and the MASTA three-dimensional model is shown in Fig. 3 – 13. The hypoid gear parameters in the model are consistent with those in the finite element loading contact analysis model. |
5.4 Vibration and Noise Analysis
| Aspect | Method/Process |
|---|---|
| NVH Analysis Method | Use the NVH analysis module in MASTA software, import the stiffness and mass matrices of the housing, and select the single meshing squeal analysis option with the transmission error of the hypoid gear pair as the excitation. |
| Measurement Point Arrangement | Arrange the measurement points on the drive axle model at the same position as in the actual test, usually above the outer bearing housing of the small gear. |
| Results | Obtain the vibration noise waterfall diagram and curves in different directions, and analyze the vibration noise source. |
6. Tooth Surface Mismatch Modification and Machining Parameter Adjustment
6.1 Construction of Ease off Topology Map
6.1.1 Construction of Small Gear Reference Tooth Surface
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Conjugate Meshing Mathematical Model | Based on the conjugate meshing relationship of the hypoid gear. | The model is shown in Fig. 4 – 1, and the large gear tooth surface equation and unit normal vector are transformed into the fixed coordinate system using the coordinate transformation matrices and . The meshing equation is used to calculate the relative velocity , and then the equation is obtained. By substituting this equation back, the large gear tooth surface equation and unit normal vector in the fixed coordinate system are obtained. Finally, the small gear tooth surface equation and unit normal vector that are completely conjugate with the large gear are obtained, where the matrices , , , and are defined as in the text. |
6.1.2 Tooth Surface Deviation Calculation
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Discretization and Rotation | Discretize the small gear actual tooth surface and reference tooth surface equations, and rotate the actual tooth surface to make the midpoints coincide. | The rotation angle is calculated using the equation , and the coordinates of the rotated actual tooth surface points are calculated using . |
| Deviation Calculation | Calculate the tooth surface deviation between the actual tooth surface and the reference tooth surface. | The tooth surface deviation is calculated using the equations , and the Ease off topology graph is constructed, which reflects the mismatch relationship between the small gear actual tooth surface and the large gear actual tooth surface. |
6.2 Ease off Topology Decomposition and Correction
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Topology Approximation | Approximate the Ease off topology with a second-order surface polynomial. | The polynomial is , where and represent the tooth length and height directions respectively, and are coefficients. |
| Coefficient Calculation | Solve the coefficients of the second-order surface polynomial using the least square method. | By substituting the known tooth surface deviations into the equation (where is the tooth surface deviation at each grid point), the coefficients are obtained. |
| Mismatch Relationship Adjustment | Adjust the tooth surface mismatch relationship by changing the coefficients of the second-order surface. | Different coefficients correspond to different mismatch patterns as shown in Fig. 4 – 5, and by pre-controlling and correcting the coefficients, the tooth surface meshing performance can be adjusted. |
6.3 Construction of Small Gear Modification Target Tooth Surface
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Target Tooth Surface Calculation | Calculate the modification target tooth surface based on the reference tooth surface and the tooth surface deviation. | The modification target tooth surface satisfies the equations , where is the reference tooth surface and is the unit normal vector at any point on the reference tooth surface. The position relationship between the small gear reference tooth surface, modification target tooth surface, and actual tooth surface is shown in Fig. 4 – 6. |
6.4 Correction of Small Gear Machining Parameters
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Parameter Correction Principle | Correct the small gear machining parameters to make the actual tooth surface approach the modification target tooth surface. | The tooth surface deviation vector is , where is the machining parameter. By differentiating both sides and dot-multiplying with the actual tooth surface unit normal vector, the equation is obtained. Considering that and , the equation is simplified to . The tooth surface deviation sensitivity coefficient , and the equation for each grid point is , where is the tooth surface deviation at the -th grid point, is the sensitivity coefficient of the -th machining parameter to the -th grid point, and is the correction amount of the -th machining parameter. |
| Solution Method | Solve the machining parameter correction amounts using the sequential quadratic programming method with constraints. | The objective function is set as $min F\left(\Delta \xi_{j}^{\tau}\right)=max \left |
6.5 Modification Example
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Modification Scheme Determination | Determine the topology modification scheme according to the requirements of improving the tooth surface contact performance. | The original tooth surface contact performance is shown in Fig. 3 – 2. To reduce the high-speed squeal of the drive axle, the modification scheme is to reduce the diagonal trend in the tooth surface contact area, increase the contact area, and reduce the transmission error amplitude. |
| Ease off Topology Map Construction and Coefficient Calculation | Construct the original and modified Ease off topology maps and calculate the coefficients. | The original Ease off topology map is shown in Fig. 4 – 8, and the coefficients are , , , , . After modification, the coefficients are , , , , , and the modified Ease off topology map is shown in Fig. 4 – 9. |
| Tooth Surface Deviation Calculation | Calculate the tooth surface deviation between the original and modified tooth surfaces. | The tooth surface deviation is shown in Fig. 4 – 10. |
| Machining Parameter Selection and Sensitivity Matrix Calculation | Select the machining parameters to be corrected and calculate the sensitivity matrix. | The selected machining parameters include cutter tip radius, |
6.5 Modification Example
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Machining Parameter Selection and Sensitivity Matrix Calculation | Select the machining parameters to be corrected and calculate the sensitivity matrix. | The selected machining parameters include cutter tip radius, cutter tilt angle, cutter rotation angle, radial cutter position, angular cutter position, installation angle, vertical wheel position, axial wheel position, bed position, and roll ratio. The sensitivity matrix is calculated using the VC++ software shown in Fig. 4 – 11, and the calculated sensitivity matrix is shown in the text. |
| Machining Parameter Correction | Calculate the correction amounts of the selected machining parameters. | The correction amounts of the machining parameters are calculated using the sensitivity matrix and the tooth surface deviation, and the results are shown in Table 4 – 1. The modified small gear tooth surface is obtained, and the tooth surface deviation between the modified tooth surface and the target tooth surface is shown in Fig. 4 – 11. The maximum tooth surface deviation is , indicating that the modified tooth surface is approximately equivalent to the target tooth surface. |
| TCA Analysis | Analyze the tooth surface contact performance before and after modification using TCA. | The TCA simulation results of the tooth surface contact area and transmission error before and after modification are shown in Fig. 4 – 12. After modification, the diagonal trend in the tooth surface contact trace is reduced, the long axis of the instantaneous contact ellipse is increased, the contact area is increased, and the transmission error amplitude is reduced from to , meeting the expected modification requirements. |
7. Influence of Loading Meshing Performance on Drive Axle NVH Curve
7.1 Calculation of Gear Meshing Misalignment
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Torque Measurement and Analysis | Measure the input maximum torque of the drive axle main reducer in different gears and analyze the meshing misalignment under actual working conditions. | The torque of the drive axle main reducer in different gears is obtained by testing the engine peak torque and converting it through the gear ratio. In the deceleration stage of the vehicle test, the torque of the drive axle main reducer is in the range of -40 N m to -100 N m. The meshing misalignment includes the axial misalignment of the large and small gears ( and ), the shaft angle misalignment (), and the offset misalignment (), as shown in Fig. 5 – 1. These misalignments cause the tooth surface contact area to shift during meshing. |
| Meshing Misalignment Calculation | Calculate the meshing misalignment of the gear reverse surface using MASTA software. | The meshing misalignment amounts of the main reducer gear reverse surface under different torques are shown in Table 5 – 2. The meshing misalignment is mainly caused by the deformation of the shaft and gear under load and is related to the gear geometric parameters. Therefore, the meshing misalignment amounts before and after the tooth surface modification of the reverse surface do not change. |
7.2 Comparison of Tooth Surface Loading Performance Before and After Modification
7.2.1 Comparison of Tooth Surface Loading Contact Areas
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Simulation Model Setup | Set the meshing misalignment constraints in the hypoid gear three-dimensional model assembly and import the models into ABAQUS for simulation analysis under different loads. | The original and modified tooth surface loading contact areas under different loads are shown in Figs. 5 – 2 and 5 – 3. |
| Contact Area and Stress Analysis | Analyze the tooth surface contact area and maximum contact stress under different loads. | As the load increases, the tooth surface contact area increases. Under the same load, the diagonal in the modified tooth surface contact area is smaller than that in the original tooth surface contact area, and the modified tooth surface contact area is larger than the original tooth surface contact area. The maximum contact stress also increases with the load, and under the same load, the maximum contact stress of the modified tooth surface is smaller than that of the original tooth surface, as shown in Fig. 5 – 4. |
7.2.2 Comparison of Loading Transmission Errors
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Transmission Error Simulation | Simulate the tooth surface loading transmission error before and after modification using ABAQUS. | The loading transmission error curves of the tooth surface before and after modification are shown in Fig. 5 – 5. |
| Error Amplitude Analysis | Analyze the variation of the transmission error amplitude with the load. | As the load increases, the transmission error amplitude decreases. Under the same load, the loading transmission error amplitude of the modified tooth surface is significantly smaller than that of the original tooth surface, as shown in Fig. 5 – 6. |
7.2.3 Comparison of Tooth Root Midpoint Bending Stresses
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Stress Extraction and Analysis | Extract the tooth root bending stress of the middle unit of the tooth surface from meshing in to meshing out and analyze the stress under different loads. | The tooth root midpoint bending stress curves of the original and modified tooth surfaces under different loads are shown in Figs. 5 – 7 and 5 – 8. |
| Stress Comparison | Compare the tooth root midpoint bending stresses before and after modification under the same load. | As the load increases, the tooth root midpoint bending stress also increases. Under the same load, the tooth root midpoint bending stress of the modified tooth surface is smaller than that of the original tooth surface, as shown in Fig. 5 – 9. |
7.3 Comparison of NVH Performance Before and After Modification
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| NVH Simulation | Simulate the NVH of the drive axle after tooth surface modification using MASTA software and compare it with that before modification. | The NVH vibration and noise curves before and after modification under different loads are shown in Figs. 5 – 10 and 5 – 11. |
| Performance Analysis | Analyze the improvement of the NVH performance after tooth surface modification. | Under the four loads of -40 N m, -60 N m, -80 N m, and -100 N m, the NVH vibration and noise curves after modification are lower than those before modification, indicating that the tooth surface modification effectively improves the NVH performance of the drive axle. The variation trends of the loading transmission error amplitude and the vibration noise with the load are consistent, and the changes in the tooth surface contact stress and the loading transmission error amplitude before and after modification are also consistent with the changes in the vibration noise curve, as shown in Figs. 5 – 4, 5 – 6, 5 – 10, and 5 – 11. |
7.4 Drive Axle NVH Bench and Road Test Experiments
7.4.1 Gear Grinding Experiment
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Grinding and Measurement | Use the gear grinding process and digital closed-loop manufacturing to control the meshing performance of the convex and concave tooth surfaces and eliminate the tooth surface error. | The small gear grinding and tooth surface measurement process is shown in Fig. 5 – 12, and the tooth surface measurement results of the small and large gears are shown in Figs. 5 – 13 and 5 – 14. The measurement results show that the error of the processed tooth surface is small and is equivalent to the theoretical design tooth surface. |
| Contact Area Verification | Verify the consistency between the actual tooth surface contact area obtained by rolling inspection and the TCA simulation contact area. | The contact areas of the original and modified large gear concave surfaces obtained by rolling inspection and TCA simulation are shown in Fig. 5 – 15. The results show that the shape, position, and size of the rolling inspection contact area are basically consistent with the simulation contact area. |
7.4.2 Drive Axle EOL Bench Experiment
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Bench Test Setup | Install the modified and original hypoid gears on the drive axle EOL bench and test the NVH performance under actual working conditions. | The EOL bench test setup is shown in Fig. 5 – 16, and the test conditions are shown in Table 5 – 3. |
| Test Results Analysis | Analyze the dynamic torque curve obtained from the test to evaluate the NVH performance of the drive axle. | The dynamic torque curves of the drive axle before and after modification are shown in Figs. 5 – 17 and 5 – 18. The results show that the original tooth surface does not meet the NVH performance requirements, while the modified tooth surface improves the NVH performance of the drive axle. |
7.4.3 Road Test LMS Experiment
| Aspect | Method/Process | Key Equations/Results |
|---|---|---|
| Test Setup | Conduct a vehicle road test with sensors arranged on the drive rear axle to measure the vibration and noise. | The sensor arrangement is shown in Fig. 5 – 19, and the test is carried out in the 5th gear deceleration condition with a gear ratio of 0.76 and a corresponding gear order of . |
| Test Results Analysis | Analyze the vibration and noise curves obtained from the test to evaluate the NVH performance of the drive axle. | The noise curves of the original and modified tooth surfaces are shown in Fig. 5 – 20. The results show that the minimum difference between the gear order noise curve and the total noise curve of the original tooth surface is 4.21 dB, and that of the modified tooth surface is 9.49 dB. The gear order noise curve of the modified tooth surface is lower than that of the original tooth surface, indicating that the tooth surface modification improves the NVH performance of the drive axle. |
8. Conclusions and Prospects
8.1 Conclusions
| Conclusion | Details |
|---|---|
| Research Achievements | 1. Established the numerical tooth surface calculation method of the hypoid gear, including deriving the tooth surface equation, calculating the three-dimensional coordinates of the tooth points, and building the gear model. 2. Established the finite element loading contact analysis and NVH simulation methods of the gear, obtaining the loading meshing performance and NVH curves of the tooth surface before and after modification. 3. Proposed the tooth surface topology pre-control modification method, calculating the conjugate tooth surface of the small gear, constructing the topology map, obtaining the target meshing performance, and calculating the modified machining parameters. 4. Explored the influence law of the tooth surface loading meshing performance on the NVH curve, and verified the effectiveness and feasibility of the modification method and simulation method through experiments. |
8.2 Prospects
| Prospect | Details |
|---|---|
| Optimization Algorithm Comparison | Compare the performance of different optimization algorithms in the process of inversely calculating the machining parameters to improve the accuracy and efficiency of the tooth surface modification. |
| Multiple Rounds of Modification | Conduct multiple rounds of tooth surface modification to further optimize the meshing performance and NVH performance of the hypoid gear. |