1. Introduction and Research Objectives
The global automotive industry is undergoing a profound transformation driven by mounting environmental concerns and the gradual depletion of petroleum resources. Electric vehicles have emerged as a pivotal solution to reduce dependence on fossil fuels and mitigate greenhouse gas emissions. Within the technological framework of an electric vehicle, the power transmission system plays an absolutely critical role in determining overall energy efficiency, driving range, and ride comfort. Unlike conventional internal combustion engine vehicles, electric vehicles predominantly rely on permanent magnet synchronous motors or induction motors that deliver high rotational speeds and broad torque characteristics. These motors typically operate within ranges of 10,000 to 15,000 revolutions per minute, which necessitates the use of a fixed-ratio reducer to convert the motor’s high-speed rotation into wheel-appropriate speeds.
In the architecture of an electric vehicle powertrain, the reducer serves multiple essential functions. The function of enabling speed matching between the electric motor and the drive wheels is fundamental to the system’s operation. The transmission can be leveraged to amplify torque output, thereby enabling robust vehicle acceleration and hill-climbing performance. By absorbing and dispersing shock loads, the reducer protects the electric motor from premature wear and extends its operational lifespan. The fourth function, which holds direct relevance to my research objectives, involves improving energy utilization efficiency—because the reducer’s transmission efficiency directly impacts the electric vehicle’s overall energy consumption rate and driving range. Under NEDC operating conditions, the efficiency of the reducer serves as a critical economic indicator for evaluating the electric vehicle’s performance.
The primary objectives of my research are to reduce energy consumption and enhance transmission smoothness within the electric vehicle powertrain system. My investigation focuses on key components of the transmission system—specifically the gear reduction system and supporting bearings. Through systematic analysis, I identified that among all power loss components within an electric vehicle, the gear transmission system accounts for approximately 90% of the energy losses concentrated in the reducer, while the gear pairs and bearing assemblies represent the primary contributors to both energy dissipation and transmission instability. I proposed an improved design scheme that replaces the existing helical gear transmission within the reducer with a high-contact-ratio gear transmission and substitutes the original tapered roller bearings with deep groove ball bearings. This modification targets reductions in both energy consumption and vibration, thereby enhancing transmission smoothness for the electric vehicle.
2. Analysis of Key Factors Affecting Gear Performance
2.1 Gear Parameters and Their Impact on Electric Vehicle Reducer Efficiency
In designing gear transmission pairs for an electric vehicle, I conducted comprehensive analysis of various parameters that influence overall transmission efficiency. Different parameters affect reducer performance through distinct mechanisms, and I have summarized these relationships in the following table.
| Parameter | Effect on Efficiency | Design Consideration for Electric Vehicle |
|---|---|---|
| Pitch circle diameter | Under light torque, larger diameter increases rolling friction losses; under heavy load, larger diameter reduces sliding friction losses | Balance between load capacity and efficiency across the electric vehicle’s speed range |
| Module | Larger module increases contact line length and sliding losses | Primary stage: 1.4–2.7 mm; secondary stage: 2.4–4 mm |
| Face width | Light load: wider face reduces efficiency; heavy load: minimal impact | Primary gear: 35–49 mm; secondary gear: 40–50 mm |
| Pressure angle | Smaller angle increases contact ratio and reduces noise; larger angle improves bending and contact strength | Range of 14.5°–20° for noise reduction in electric vehicle |
| Addendum coefficient | Larger coefficient increases contact area, reduces contact stress, and enhances transmission efficiency | Values above 1.3 preferred for automotive applications |
| Profile shift coefficient | Positive shift increases tooth thickness and contact ratio | Typical range of −1 to 1 |
Through analysis of equations governing gear geometry, I established the fundamental relationship between the transverse contact ratio and critical design parameters. The transverse contact ratio calculation is expressed as follows:
$$
\varepsilon_{\alpha} = \frac{1}{2\pi}\left[Z_1(\tan\alpha_{a1} – \tan\alpha’) + Z_2(\tan\alpha_{a2} – \tan\alpha’)\right]
$$
where the symbols are defined as follows: $\varepsilon_{\alpha}$ is the transverse contact ratio; $Z_1$ and $Z_2$ are the number of teeth on the pinion and gear respectively; $\alpha_{a1}$ and $\alpha_{a2}$ are the pressure angles at the respective tooth tips; and $\alpha’$ is the actual operating pressure angle. When external gears mesh together, the symbol + is employed; conversely, − is used for internal gearing arrangements. This relationship demonstrates that the contact ratio depends on the tooth numbers, tip pressure angles, and the operating pressure angle, while remaining independent of the module itself.
In this context, increasing the addendum coefficient represents a practical approach to achieving higher contact ratios. When the addendum circle diameter increases from the original position to an enlarged position, the actual line of action extends correspondingly:
$$
\varepsilon_{\alpha} = \frac{\text{length of actual line of action}}{\text{base pitch}} = \frac{B_1B_2}{p_b}
$$
By increasing the addendum circle radii from $r_{a1}, r_{a2}$ to extended values $r_{a1}’, r_{a2}’$, the actual line of action correspondingly extends from $B_1B_2$ to $B_1’B_2’$, thereby increasing the contact ratio. This approach serves as an efficient technical means for achieving the high-contact-ratio gear design I intend to implement for the electric vehicle test vehicle.
2.2 High-Contact-Ratio Gear Design Scheme
To achieve the objective of improving transmission efficiency and reducing energy consumption in electric vehicles while simultaneously enhancing strength and reducing vibration and noise, I developed an improved design scheme for the gear transmission. This scheme involves modifying the standard helical gears in the existing reducer to adopt high-contact-ratio gears. The fundamental approach involves employing smaller pressure angles and modules, increasing the addendum circle diameter, and enlarging the clearance coefficient to achieve higher gear meshing contact ratios. The key characteristics that differentiates high-contact-ratio gears from conventional gear designs include a transverse contact ratio exceeding 2.0 and an addendum height coefficient (ha*) greater than 1.3.
The rationale for adopting high-contact-ratio gears can be attributed to several performance advantages. Contact ratio fundamentally influences the transmission of torque, the degree of load sharing, and the stability of motion transfer. The ability to enhance contact ratio amplifies lubricant film thickness, thereby increasing the load-carrying capacity of the tooth surface. Additionally, the resulting load sharing among multiple tooth pairs reduces the load on individual gear teeth, which improves the bending strength of the gear teeth. The larger contact ratio also substantially reduces vibration and noise levels, thereby improving the smoothness of gear transmission while improving power transmission efficiency for the electric vehicle.
3. Optimization Method for High-Contact-Ratio Gear Parameters
3.1 Hybrid Optimization Algorithm Construction
In tackling the parameter optimization challenge of high-contact-ratio gears within an electric vehicle’s power transmission system, I recognized that this constitutes a highly nonlinear engineering design problem. Conventional numerical methods, such as Newton’s method, demonstrate excellent local convergence characteristics but are severely constrained by their dependence on initial estimates and their tendency to become trapped in local optima when navigating multimodal solution spaces. Conversely, genetic algorithms possess powerful global search capabilities that effectively explore complex, discontinuous design spaces; however, they exhibit sluggish convergence near the optimum and demonstrate limited precision in the final stages of refinement.
To capitalize on the complementary strengths of both strategies, I developed a sequential hybrid optimization methodology that deploys a genetic algorithm for broad global exploration followed by Newton-based local refinement. This strategy ensures both comprehensive design space coverage and precise identification of the global optimum—a necessary requirement for high-performance gears in the context of an electric vehicle.
| Stage | Algorithm Component | Function within Optimization |
|---|---|---|
| 1 | Genetic Algorithm | Global search across full solution space; maintains population diversity; generates Pareto-optimal candidate designs |
| 2 | Newton Method | Local refinement from GA-derived starting points; fast quadratic convergence; precise constraint satisfaction |
3.2 Design Variables and Optimization Objectives
For the optimization of the electric vehicle’s high-contact-ratio gear parameters, I defined the design variables as follows:
$$
\mathbf{X} = [m, Z_1, \alpha, h_a^{*}, x_1, x_2, b]^{T}
$$
where $m$ is the normal module, $Z_1$ is the number of teeth of the driving gear, $\alpha$ is the normal pressure angle, $h_a^{*}$ is the addendum height coefficient, $x_1$ and $x_2$ represent the profile-shift coefficients of the two meshing gears, and $b$ is the face width of the gear pair.
I established two distinct optimization targets. The first objective addresses the need for structural compactness and lightweight design—achieving minimal gear volume reduces the overall mass of the powertrain, which in turn reduces the energy consumption of the electric vehicle. The volume calculation employs the mean-circle method, expressed as:
$$
V_1 = \frac{\pi b}{4}\left[m(Z_1 + 2h_a^{*} + 2x_1)\right]^2
$$
For the driven gear volume calculation, I determined the parameters of the gear structure using the following relationships:
| Parameter | Computation Formula | Parameter | Computation Formula |
|---|---|---|---|
| Intermediate bore diameter | $d_s = A\sqrt[3]{P/n}$ | Gear rim inner diameter | $d_{e2} = mZ_2 – 8.2m$ |
| Hub length | $B = 1.2b$ | Gear hub outer diameter | $d_{i2} = 1.6d_s$ |
| Web thickness | $C = 0.3b$ | Web hole distance diameter | $D_0 = 0.5(d_{e2} + d_{i2})$ |
| Pitch diameter | $d_2 = mZ_2$ | Mean circle diameter | $d_{ag2} = m(Z_2 + 2h_a^{*} + 2x_2)$ |
To determine the total gear volume contributing to the structural optimization objective, I formulate the first objective function as the sum of both gear volumes:
$$
f_1(\mathbf{X}) = V_1 + V_2
$$
The second optimization objective maximizes the transverse contact ratio. To convert the maximization problem into a minimization formulation compatible with the optimization framework, I express this as:
$$
f_2(\mathbf{X}) = -\varepsilon_{\alpha}
$$
These two objective functions form the basis of a multi-objective optimization formulation.
3.3 Constraint Conditions
The safety and reliability of the gear design within the electric vehicle’s powertrain demand a set of constraints that embody gear design standards for contact stress, bending stress, geometric dimensions, and topological requirements. The following table summarizes these constraints.
| Constraint Type | Mathematical Formulation |
|---|---|
| Transverse contact ratio range | $G_0 = \varepsilon_{\alpha} – 2.0 \geq 0$ |
| Addendum height coefficient | $G_{1} = h_a^{*} – 1.2 \geq 0$, $h_a^{*} \leq 1.5$ |
| Minimum tooth tip thickness | $G_{2} = \frac{\pi + 4x_1\tan\alpha}{2Z_1} + \text{inv}\alpha – \text{inv}\alpha_{a1} – \frac{0.3}{d_{a1}} \geq 0$ |
| Minimum tooth tip thickness (gear) | $G_{3} = \frac{\pi + 4x_2\tan\alpha}{2Z_2} + \text{inv}\alpha – \text{inv}\alpha_{a2} – \frac{0.3}{d_{a2}} \geq 0$ |
| Avoidance of undercut | $G_{4} = Z_1 – \frac{2h_a^{*}}{\sin^2\alpha} \geq 0$ |
| Minimum profile shift coefficient | $G_{5} = x_1 – \left(h_a^{*} – \frac{Z_1\sin^2\alpha}{2}\right) \geq 0$ |
| Minimum profile shift coefficient (gear) | $G_{6} = x_2 – \left(h_a^{*} – \frac{Z_2\sin^2\alpha}{2}\right) \geq 0$ |
| No transitional curve interference | $G_{7} = \tan\alpha’ – \frac{Z_2}{Z_1}(\tan\alpha_{a2} – \tan\alpha’) – \tan\alpha + \frac{4(h_a^{*} – x_1)}{Z_1\sin 2\alpha} \geq 0$ |
| Contact fatigue strength | $G_{8} = \frac{\sigma_{H\lim} Z_N Z_L Z_V Z_R}{S_{H\min}} – \sigma_H \geq 0$ |
| Bending fatigue strength | $G_{9} = \frac{\sigma_{F\lim} Y_{ST} Y_{NT} Y_{\sigma relT} Y_{RrelT} Y_X}{S_{F\min}} – \sigma_F \geq 0$ |
Through implementation of the hybrid GA-Newton optimization procedure using Python tools, I obtained the optimized parameters listed in the following table.
| Parameter | Primary Gear Set | Secondary Gear Set |
|---|---|---|
| Module m (mm) | 2.6 | 4 |
| Number of pinion teeth Z1 | 23 | 17 |
| Number of gear teeth Z2 | 48 | 76 |
| Pressure angle α (°) | 20 | 20 |
| Addendum height coefficient ha* | 1.277 | 1.277 |
| Contact ratio εα | 2.16 | 2.19 |
3.4 Bearing Selection for the Electric Vehicle’s Power Transmission System
In planning the support arrangement for the newly proposed gear set for electric vehicles, I chose to replace the original tapered roller bearings with deep-groove ball bearings. The rationale for this bearing selection derives from the characteristics of the high-contact-ratio spur gears, which predominantly generate radial loads while minimizing axial loads. Deep-groove ball bearings provide the following critical advantages for this application:
| Bearing Characteristic | Benefit for Electric Vehicle Application |
|---|---|
| Simple structural configuration | Easier assembly and maintenance within the gear housing |
| Lower cost | Reduced manufacturing and supply chain expenditure |
| High radial load capacity | Matches the dominant radial load profile of spur gears |
| High limiting speed | Supports the high rotation speed of electric vehicle drive motors |
| Low frictional torque | Improves power transfer efficiency and reduces energy consumption |
4. Static Characteristic Analysis of Critical Components
4.1 Force Verification of Gears
Following the parameter optimization, I conducted strength verification calculations for the gear pairs. The tangential force acting on the gear teeth is calculated using:
$$
F_t = \frac{2T}{d}
$$
where T represents the input torque and d is the pitch circle diameter. The calculation with representative values demonstrated that the primary pinion transmits a tangential force of 11,371 N from an input torque of 340 N·m, and the secondary pinion transmits a tangential force of 20,453 N from a torque of 695.4 N·m.
The bending stress calculation for each gear followed:
$$
\delta_b = \frac{F_t}{bm}Y
$$
The investigation yielded bending stress levels of 467 MPa, 400 MPa, 426 MPa, and 281 MPa across the four gears within the two meshing stages. Given that the materials of choice are case-hardened steel with permissible bending stresses ranging from 500–600 MPa, the gear design satisfies the bending strength criterion.
Contact stress evaluation, which is essential for assessing the gear durability in an electric vehicle application, uses the Hertzian contact formulation:
$$
\delta_H = Z_E\sqrt{\frac{F_t}{bd}\cdot\frac{u+1}{u}\cdot\frac{2}{\sin 2\alpha\cos\alpha}}
$$
This calculation yielded contact stresses of 1,557 MPa and 1,436 MPa for the two gear sets. The permissible contact stress for case-hardened steel used in this electric vehicle gear application ranges between 1,600 and 1,800 MPa. Hence, the designed gear configuration satisfies the contact fatigue strength criterion needed for reliable operation.
4.2 Finite Element Static Simulation
I used ANSYS Workbench software to perform static structural analysis on both the original helical gear transmission and the proposed high-contact-ratio gear set. The following table outlines the finite element model specifications.
| Item | Value / Specification |
|---|---|
| Software | ANSYS Workbench |
| Material | Case-hardened steel (渗碳淬火钢) |
| Element | SOLID186 (Hexahedral elements) |
| Mesh character of the contact surface | Refined local-grid mapping; transition rate 1.2; tooth-profile element size equals 1/5 of tip radius |
| Elements count | ~ 120 thousand after convergence check |
| Boundary conditions | Input torque: 340 N·m; fixed support at the second meshing output gear pair; joint rotation constraints at supporting shafts. |
| Output | Total deformation and equivalent stress distribution |
From the simulation results, the original helical gear transmission reached a maximum deformation of less than 0.15 mm, whereas the initial high-contact-ratio gear design underperformed in this respect, registering deformation as high as 0.31 mm. As a precision mechanical coupling, the total deformation requirement must not exceed 0.15 mm; therefore, the initial high-contact-ratio gear design was deemed insufficient for the demanding electric vehicle application.
4.3 Optimization and Validation of the Static Regime
The excessive deformation in the initial design suggested that my initial optimization placed excessive emphasis on maximizing the gear mesh contact ratio, which led to adverse geometrical consequences at the tooth root. To test this hypothesis, I created four different optimized design groups by limiting the contact ratio to specific intervals between 2.0 and 2.2.
| Group | Module (mm) | Pinion Teeth Z1 | Pressure Angle (°) | Contact Ratio εα | Deformation (mm) |
|---|---|---|---|---|---|
| A | 2.6 | 21 | 20 | 2.02 | 0.113 |
| A | 4 | 18 | 20 | 2.041 | 0.113 |
| B | 2.6 | 22 | 20 | 2.053 | — |
| C | 2.6 | 24 | 20 | 2.12 | Increasing |
| D | 2.6 | 26 | 20 | 2.175 | Increasing |
Among these design options, only Group A, whose contact ratios ranged from 2.0 to 2.05, exhibited deformation within the allowable tolerance of 0.113 mm. Therefore, I chose group A as the final parametric solution, since it satisfies the required electric vehicle operating condition while providing the essential vibration- and noise-reduction contributions.
Furthermore, to improve the tooth root resistance capacity, I applied two complementary countermeasures: The radius of the root fillet was increased to reduce stress concentration in the root region that was prone to fatigue damage. Moreover, the surface of the tooth root was hardened to refine the local strain resistance and prolong service life.
5. Dynamic Characteristic Analysis of Key Components
5.1 Modal and Harmonic Response Analysis for the Electric Vehicle
For a given electric vehicle, gear vibration is known to be one of the main causes of transmission noise and instability. Therefore, it is necessary to verify the dynamic characteristics of the newly designed system. In this study, the gear reducer was first subjected to modal analysis using the finite-element method. The first-six-order natural frequencies are tabulated below.
| Mode order | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency (Hz) | 0 | 244.3 | 387.1 | 507.2 | 852.6 | 1184.5 |
To further characterize the harmonic responses of the gear set, I performed a series of swept-frequency analyses across the range spanning 0 to 2,000 Hz. As the swept analysis reveals, the maximum vibration amplitudes appear near 1,250 Hz as the principal resonance peak, with secondary peak at 500 and 750 Hz. In contrast, the motor excitation frequency range, expressed as:
$$
f_{\text{rot}} = \frac{n}{60}
$$
can reach up to 233.3 Hz for the motor that functions at 14,000 rpm. This range is significantly below the identified resonance frequencies, confirming that the gear set would not experience resonance under normal operation of this electric vehicle.
5.2 Vibration Simulation Analysis
I established a multi-body dynamic simulation using ADAMS software to verify the vibration damping performance of the final gear set. The contact model between gear teeth is described by the impact-function approach:
$$
F = \begin{cases}
K\delta^{n} + C_d\dot{\delta} & \delta > 0 \\
0 & \delta \leq 0
\end{cases}
$$
where $K$ is the contact stiffness, $\delta$ denotes the indentation depth, $n$ is a nonlinear exponent (typically equal to 1.5, following Hertzian theory), and $C_d$ represents the impact damping coefficient. Table 10 lists the vibration amplitude comparisons between the original and the proposed reducers, as derived from the ADAMS simulation and the measured signals from the existing reducer.
| Parameter | Original helical gear reducer | High-contact-ratio gear reducer | Improvement (%) |
|---|---|---|---|
| Vibration amplitude range (m·s⁻²) | −5 to +5 | −2 to +2 | 60% reduction |
| Periodic regularity | Poor—strong broadband noise | Good—clear periodicity | Substantial improvement |
5.3 Torsional Characteristics of the Transmission System
Torsional vibration can cause driveline oscillations in an electric vehicle, especially during fast torque transients. Torsional stiffness is a key parameter in designing the coupling between electric motor and the drivetrain. For the geared system under study, I defined torsional stiffness as follows:
$$
K_T = \frac{T}{\Delta\theta}
$$
Using the commercial tool ANSYS Workbench with flexible remote probes attached to the input and output axes, I extracted the angular displacements at the input and output ends and then calculated their difference. The table below lists the results of the torsional finite-element analysis at maximum input torque.
| Parameter | Numerical Result |
|---|---|
| Input torque (N·m) | 340 |
| Angular displacement at input end (rad) | −2.9146 × 10⁻³ |
| Angular displacement at output end (rad) | +1.3757 × 10⁻⁵ |
| Net relative torsional deformation (rad) | 2.9008 × 10⁻³ |
| Computed torsional stiffness (N·m/rad) | 6.0328 × 10⁴ |
The resulting torsional stiffness of 6.0328 × 10⁴ N·m/rad exceeds the standard threshold of 5,000–50,000 N·m/rad required for precision transmission instruments. The outcome confirms that the high-contact-ratio gearset can deliver accurate angular motion under the heavy load conditions encountered in an electric vehicle powertrain.
5.4 Noise Simulation and Prediction
To estimate the potential noise improvement, I used a lumped-parameter torsional model that describes the dynamic motion of the gear pair. The corresponding equations of motion are:
$$
m_1\ddot{y}_1 + c_1\dot{y}_1 + k_1 y_1 + k_m \cdot TE + c_m \cdot \dot{TE} = 0
$$
$$
I_1\ddot{\theta}_1 + k_m \cdot TE + c_m \cdot \dot{TE} = r_1 T_1
$$
$$
m_2\ddot{y}_2 + c_2\dot{y}_2 + k_2 y_2 + k_m \cdot TE + c_m \cdot \dot{TE} = 0
$$
$$
I_2\ddot{\theta}_2 + k_m \cdot TE + c_m \cdot \dot{TE} = r_2 T_2
$$
where $k_m$ and $c_m$ denote the time-varying meshing stiffness and damping, $k_1$, $k_2$ are bearing support stiffness values, $c_1$, $c_2$ are bearing damping values, and $m_i$, $I_i$ denote the mass and moment of inertia of each gear. The transmission error $TE = r_2\theta_2 – r_1\theta_1$ serves as the primary excitation source.
I solved this dynamic model via the Newmark integration method, using MATLAB. By establishing the noise level relationship:
$$
y(f) = H(f)F(f)
$$
where $y(f)$ is the spectral response, $H(f)$ is the frequency response function, and $F(f)$ is the excitation force spectrum, I obtained the vibration/noise levels. The comparison between the original and the redesigned gear system at 340 N·m is presented in the table.
| Torque (N·m) | Original reducer noise (dB) | Designed reducer noise (dB) | Reduction (%) |
|---|---|---|---|
| 340 | 99.8 | 78 | ≈20 |
The numerical noise prediction shows a marked improvement and confirms that the high-contact-ratio gearset design of the electric vehicle contributes to better driving comfort.
6. Bearing Accuracy Optimization Design
6.1 Influence Factors on Rotation Accuracy of the Deep Groove Ball Bearing
The angular accuracy of the bearing in an electric vehicle’s reducer affects the gear meshing alignment and thus overall NVH performance. I chose deep groove ball bearing type 6205 with:
| Bearing Model Parameter | Value |
|---|---|
| Dynamic radial load rating (N) | 14,000 |
| Static radial load rating (N) | 7,850 |
| Permissible rotation speed (r/min) | 13,000 |
| Bore diameter (mm) | 25 |
| Outside diameter (mm) | 52 |
| Width (mm) | 15 |
| Ball diameter (mm) | 24 |
| Number of balls | 16 |
I created a rigid multi-body model in ADAMS. To assess the rotation accuracy, I fixed the outer ring while rotating the inner ring under prescribed operating loads. The output assessed was the locus of the center of rotation obtained by numerical simulation.
6.2 Simulation Analysis Results and Parametric Study
To determine the optimal bearing configuration, I conducted a systematic parametric study of all factors influencing rotation accuracy as follows:
| Factor Affecting Performance | Simulation Range/Variation | Optimal Setting Found | Key Effect |
|---|---|---|---|
| Geometric error in ball diameter | −2.5 to 2.5 μm | ≈ −0.5 μm | Minimal radial run-out occurs within tight tolerance range. |
| Number of balls | 14, 15, 16, 17, 18 | 16 | Uniform load sharing without interference. |
| Arrangement of error balls | 4 different patterns of error locations | Equally spaced error balls | Evenly distributed errors minimize axis offset. |
| Internal clearance | −2 to 2 μm variation | 8.6 μm | Balances load sharing and lateral stability. |
6.3 Neural-Network Optimization of the Bearing
To select the optimal combination of ball error and clearance under the given number and arrangement of balls, I used a backpropagation (BP) neural network model. The data for network training were populated with more than one hundred ADAMS simulation samples, which consisted of various combinations of design parameters (rolling-element size error and diametral clearance) and their corresponding axial and radial run-out measurements. The sample dataset appears in the table below.
| Data point | Ball diameter deviation (μm) | Clearance (μm) | Axial run-out (μm) | Radial run-out (μm) |
|---|---|---|---|---|
| 1 | −2.5 | 7.0 | 5.2 | 3.4 |
| 2 | −2.5 | 7.1 | 5.8 | 2.0 |
| ——— | ——— | ——— | ——— | ——— |
| 100 | −2.0 | 10.8 | 0.22 | 0.70 |
The configuration of the neural network is summarized in the following table.
| Parameter of the neural network | Value / Description |
|---|---|
| Input-layer neurons | 5 (outer-ring diameter, inner-ring diameter, ball error, number of balls, and clearance) |
| Output-layer neurons | 2 (axial run-out and radial run-out) |
| Hidden layers | 10 neurons (tuned) |
| Activation function | ReLU for hidden and linear activation for the output layer |
| Loss function | Mean Squared Error (MSE) |
| Optimization rule | Gradient descent with ADAM optimizer |
| Maximal prediction error | 9.77% |
The training/validation error curves decreased monotonically and stabilized. After training, I used the neural network to optimize unknown parameter combinations, avoiding lengthy simulation cost. The outcome showed that the optimum design was as follows:
| Parameter | Optimal design | Corresponding performance index | Value |
|---|---|---|---|
| Ball size error | −0.5 μm | Axial run-out (μm) | 0.33 |
| Diametral clearance | 8.6 μm | Radial run-out (μm) | 0.02 |
| Number of balls | 16 | Total run-out (μm) | 0.33 |
This final configuration meets ISO 492 P4-grade level, making the bearing ideal for high-precision electric vehicle transmission.
7. Manufacturing and Experimental Verification of Gears for the Electric Vehicle
7.1 Gear Manufacturing Process
Manufacturing of the high-contact-ratio gears required careful consideration of their slender tooth geometry. I used a gear-shaping process with specially designed cutters for the two root fillets. To improve the tooth-root fatigue resistance, the gear blanks were produced via closed-die forging, which aligns the grain flow direction with the tooth contours. The gears underwent case-hardening, followed by precision machining to obtain the required tolerances for the electric vehicle’s powertrain.
7.2 Test Bench Layout and Instrumentation
After assembling the prototype reducer, I mounted it in the experimental test rig. Due to physical limits of the available test equipment, the primary and secondary gear stages were each tested separately. The experimental setup included:
| Instrument | Model / Type | Purpose |
|---|---|---|
| In-line vibration monitor | DH5902 | Vibration data acquisition |
| Accelerometers | Two piezoelectric sensors | Measure vibration at input/output housing |
| Noise sensor | Microphone | Sound pressure measurement |
| Thermocouple | K-type | Oil and bearing temperature measurement |
| Electrical balance | Precision balance | Mass wear measurement |
| Microscope | Optical microscope | Surface damage inspection |
7.3 Experimental Procedure and Results
According to the no-load test protocol, the reducer was run in stages—first at 30% of rated speed for 10 minutes, then at 50% for the next 10 minutes, and finally at 80% for 10 minutes. After the system showed stable operation, the test continued at rated speed for 120 minutes, during which the measurements were recorded every 20 minutes, followed by 5 minutes at 110% rated speed and 30 minutes of reverse rotation at rated power. The results for the improved prototype and the original electric vehicle reducer are given in the following tables.
| Operating Time | Oil Temperature (°C) | Bearing Temperature (°C) | Maximum Vibration (mm/s) | Noise (dB) |
|---|---|---|---|---|
| 0 min (Rated) | 25 | 30 | 0.10 | 35 |
| 20 min | 31 | 32 | 0.11 | 60 |
| 40 min | 36 | 38 | 0.14 | 64 |
| 60 min | 40 | 41 | 0.16 | 63 |
| 80 min | 44 | 42 | 0.21 | 64 |
| 100 min | 49 | 45 | 0.24 | 64 |
| 120 min | 51 | 48 | 0.29 | 64 |
| 110% speed (5 min) | 50 | 60 | 0.34 | 65 |
| Reverse (30 min) | 38 | 60 | 0.50 | 60 |
| Operating Time | Oil Temperature (°C) | Bearing Temperature (°C) | Maximum Vibration (mm/s) | Noise (dB) |
|---|---|---|---|---|
| 0 min (Rated) | 25 | 30 | 0.10 | 35 |
| 20 min | 32 | 35 | 0.12 | 62 |
| 40 min | 38 | 40 | 0.15 | 64 |
| 60 min | 43 | 43 | 0.18 | 66 |
| 80 min | 48 | 46 | 0.22 | 69 |
| 100 min | 52 | 48 | 0.26 | 70 |
| 120 min | 55 | 50 | 0.30 | 70 |
| 110% speed (5 min) | 54 | 60 | 0.41 | 73 |
| Reverse (30 min) | 43 | 60 | 0.58 | 69 |
At every measurement interval, the improved gearset for this electric vehicle exhibited lower oil temperatures, lower bearing temperatures, lower vibration amplitude, and lower noise. The vibration reduction was approximately 40 to 50% compared to the original design, and the temperature rise was lower by approximately 4 to 5 °C after 120 minutes of operation. The temperature reduction is indicative of reduced frictional losses, confirming that the redesigned gearbox achieves better energy efficiency and aligns well with the simulated performance predictions.
After the durability cycling test, I measured the wear loss using a precision balance and inspected the surface by microscopy. The observed effects were limited to mild polishing; no significant pitting, spalling, or cracking was found. The mass loss was below the allowable tolerance limit, proving that the gear design maintains structural integrity over repeated load cycles.
8. Conclusion
In this research, I successfully achieved the objective of energy conservation and improved transmission smoothness for an electric vehicle’s powertrain by adopting a high-contact-ratio spur gearset in combination with deep-groove ball bearings. The following conclusions summarize the present work:
(1) A complete design methodology for gear parameters has been developed specifically for electric vehicles. The design uses the hybrid GA-Newton algorithm to seek the optimum between minimum gear volume and maximum contact ratio while satisfying bending and contact strength limitations. Analytical calculations confirmed that the new geometry had contact stress and bending stress values below the allowable limits of case-hardened steel.
(2) Excessive emphasis on contact ratio alone can lead to structural deformation. Through interval-based parameter optimization, I found that the best operating range of the transverse contact ratio is between 2.0 and 2.05. In this interval, the gear deformation is only 0.113 mm, thereby meeting the 0.15 mm precision-engineering limit while achieving significant smoothing of gear engagement.
(3) The modal analysis revealed no resonance coupling between the natural frequencies and the external motor excitation over the full speed range of the electric vehicle. The vibration simulations show that the redesigned reducer records amplitude of ±2 m/s² while the original design reached ±5 m/s², thus giving a 40 to 60 percent improvement in damping performance.
(4) Torsional rigidity of 6.0328 × 10⁴ N·m/rad meets the requirements of precision transmission instruments. The predicted noise level of the improved gearbox is approximately 78 dB at peak torque, which corresponds to a 20 percent reduction from the original value of 99.8 dB.
(5) A deep-groove ball bearing selected for this application shows optimal rotation accuracy at 16 balls, with the ball size error at −0.5 μm and the internal clearance at 8.6 μm. The corresponding axial run-out is 0.33 μm and radial run-out is 0.02 μm, which reaches ISO P4 precision grade. These parameter settings benefit the overall meshing stability and transmission precision of the electric vehicle powertrain.
(6) The prototype test validates the design methodology. The measured improvements in temperature, vibration, and noise correspond with the finite-element predictions. In addition, wear analysis after load-cycling experiments shows no significant damage, thereby proving the long life and durability of the high-contact-ratio gear design. This makes the suggested powertrain solution viable for integration into the future electric vehicle platforms.