The gearbox can be used to change the torque of the vehicle’s drive wheels, transmitting power from the engine to the vehicle’s drive wheels during operation. It is usually composed of multiple gears, and different gear ratios are achieved through the meshing of different gears. When the gearbox is composed of a set of gears and a clutch, the two have higher efficiency and lower meshing noise. To achieve automatic selection of the optimal gear ratio for the gearbox, this study combines the hydraulic system and electronic control unit to achieve gear shifting operation, as shown in Figure 1.

Figure 1 shows the key components of the gearbox during shifting operations. The hydraulic system is the main component of manufacturing hydraulic pressure. When the gearbox needs to shift gears, the electronic control unit will send a signal to the clutch for shifting. During this process, the transfer of control signals is achieved through the rotation of the gear set. To study the rotational relationship between gears, this study calculates the tooth ratio in GO, as shown in Eq. 1. Re a , b = α • d a d t 2 + β • d b d t 2 + c (1)

In Eq. 1, the ratio of the number of teeth between two gears is represented by Re a , b . α , β represents the time step required for two gears to rotate once. a , b represents their radii, and the contact duration during this period is denoted as c . This parameter is used to make decisions on the speed ratio of gear transmission, thereby describing the mechanical advantages of gear transmission. The device’s working state involves a reduction in speed and an increase in torque to adjust the system’s output speed, following Eq. 2. C v 1 = C v 0 + ∫ − x x 0.5 • x 2 + 6 − 1 • x 3 d x x i (2)

In Eq. 2, the initial speed of gear rotation is denoted as C v 0 . C v 1 is its real-time calculation speed. The time interval between two speed measurements is represented by x i . ∫ − x x 0.5 * x 2 + 6 − 1 * x 3 d x represents the gear wear during this period. During the operation of gears, the vibrations generated between them are inevitable, leading to meshing noise that affects the experimental results. To study the reliability of this characteristic, this study combines the GR concept in GO to study the internal performance and working conditions of gears. The relationship between them is Eq. 3. I p g = C v 1 + ∂ • χ 2 / ∂ δ 1 + x i / 2 W o g = ∫ ∫ 0 x A 1 + 2 • A 2 + 4 • A 3 + A 4 d A + C v 0 (3)

In Eq. 3, the inherent properties of the gear are represented by W o g . A 1 , A 2 , A 3 , A 4 represents the smoothness, friction, tooth circumference, and hardness of the gear. I p g can describe the working environment of gear components. χ , δ 1 represent the ambient temperature and the humidity inside the container, respectively. This method can be used to analyze poor gear phenomena and reduce transmission noise. To reduce the dynamic load of gears, this study first considers both GR and GO, and then establishes a coupled model GRO of the two in the gearbox, as shown in Figure 2.

In Figure 2, the various components in the system are mutually constrained. To control meshing noise, the coupling system optimizes the geometric shape of the gears and reduces noise by minimizing the impact of gear meshing. Numerical simulation methods were used to analyze the mechanism of noise generation in the dynamic data of the transmission system. The aim was to identify the key gears responsible for noise generation. This method verifies the effective performance of the established system through simulation experiments, in which the interaction between the system and the environment is simulated through the simulation environment. The performance of the observation system in different situations is studied and compared with traditional methods. Its working state is analyzed as shown in Eq. 4. W L g = I p g • ⁡ sin ε + W o g • ⁡ cos ε + Δ γ + e (4)

In Eq. 4, the shape changes of the two gears are represented by ε , Δ γ . e is the dynamic meshing stress between gears in a rotating state. In a coupled system, ε and Δ γ interact with each other, and a higher GRO energy level will increase the vibration of the gear, thereby affecting its response characteristics. This characteristic will have an impact on the selection of GO. Thus, this study optimizes both values before designing the gearbox to comprehensively consider the relationship between GR and GO, as shown in Eq. 5. Im ε = ϕ 0 • A w ε + ϕ 1 • Z w ε − W L g • ⁡ cos ϕ Im Δ γ = φ 1 • ∑ i = 1 n S t Δ γ • ⁡ sin φ + Δ γ − φ 2 • D a Δ γ (5)

In Eq. 5, the rotation angle of the gear during operation is denoted as A w ε . Z w ε represents the displacement of the gear caused by rotational vibration. ϕ 0 , ϕ 1 represents the running resistance between the gears during these two processes, and the stress angle between the two is denoted as ϕ . The torsional resistance of the gear itself is denoted as S t Δ γ , and the damping it experiences during deformation is represented by D a Δ γ . φ 1 and φ 2 represent the meshing strength and meshing stress of the gear, respectively. Through the calculation of these data, the smoothness of the gears has achieved good results. To reduce GR and improve the selection of GO, this study proposes Eq. 6 to calculate the operating speed of the stressed gear during LS. L s g = max Z w ε • η / ∑ ε = 1 I A w ε (6)

In Eq. 6, the transmission power of the gear is denoted as η , which refers to the power transmitted by the gear transmission. The size of LS can determine the force on the tooth surface. In gear transmission, the average load borne on the gear tooth surface can affect the lifespan of the gear. To improve the service life of gear transmission, this study combines LS with GRO and designs the transmission ratio of the gearbox reasonably, as shown in Figure 3.

Figure 3 shows the transmission ratio design method of the gearbox. This study first optimizes the gear ratio of the gearbox to improve transmission performance, and adjusts the size of the gears to adapt to environmental conditions. In this process, GRO’s goal is to select the optimal gear ratio to provide optimal acceleration performance. When designing the transmission ratio of the gearbox, this study uses LS technology to consider the load situation of the gears, thereby providing a better working environment for the gears, as shown in Eq. 7. L o 1 = 3 • L s g • S t a g − R o t g • L o 2 / 2 (7)

In Eq. 7, the gear load at the current moment is denoted as L o 1 . The initial load of the gear is represented by L o 2 . The number of stators and rotors during the transmission process is S t a g , R o t g , respectively. Through this method, this study can to some extent reduce GR and improve the selection of GO. By comprehensively considering the geometric shape and material of the gears, the design optimization of the gearbox can be achieved to reduce gear load, thereby achieving a coupling system related to LS.

To control the meshing noise of the gears in the gearbox during operation, this study designs a control strategy based on GR and LS based on the results of dynamic analysis. This study optimizes the structure of the gearbox by changing its working parameters, while controlling the time series of gear meshing process to weaken the propagation of meshing noise. This method reduces propagation loss by reducing the propagation path of noise, thereby reducing the impact range of noise. Its working principle is Figure 4.

In Figure 4, this study optimizes the path from the engine to the driving device on the power transmission route of the gearbox. On this propagation route, power is transmitted from the engine to the transmission shaft. It achieves power output through the meshing of gears with different particle sizes, thereby meeting the speed changing process of the gearbox. During this process, GRO can determine the gear operating characteristics of the gearbox, thereby reducing gear whistling during operation. Its calculation method is Eq. 8. H o 0 = H o 1 − ι 0 • ∫ Δ M t 1 d w + ι 1 • ∑ w = 0 ι M t w • H o w (8)

In Eq. 8, M t represents the total gear torque within a certain distance. The gear torque of the engine is denoted as M t 1 , and the degree of gear meshing is represented by H o 1 . H o w represents the total gear howling. The application of this method can improve the damping performance of the bearing system, thereby reducing the generation of meshing noise. For the dampers in the GRO system, this study uses a direct torque control system to disperse vibration energy and achieve the goal of reducing noise levels. The principle follows Eq. 9. D t m = ∫ i = 1 n D t n • ⁡ sin 2 • κ • π • A m n / λ n + D t c (9)

In Eq. 9, the torque stiffness between gears is denoted as D t n . The vibration amplitude of a single tooth gear is represented by κ . The baseline distance of the applied gear is A m n . λ n is the vibration frequency of the driven gear. The relative speed of the two gears is denoted as D t n . This method can control the drive of AC motors, but traditional motors use vector methods, which contain complex feedback loops. To reduce energy loss, this study combined SET and constructed a GRO based TMN control system, i.e. SET-GRO, as shown in Figure 5.

Figure 5 shows a gear noise reduction system combining GRO and SET. To avoid complex mathematical models, this study first chose to directly measure the magnetic flux of the motor to achieve control. For the time-varying excitation signals in the system, this study implements the adjustment process of the feedback loop on the core of the direct torque control system. By processing the measured values of magnetic flux, precise control of the motor can be achieved, as shown in Eq. 10. M a x = 0.5 • μ t • I p • M a t / D t m + 1 1 / 2 (10)

In Eq. 10, μ t represents the magnetic flux of the SET-GRO system affected by time. M a t is the cross-sectional area during gear transportation. The torsional damping coefficient of the applied gear is denoted as I p . Compared with traditional magnetic flux measurement methods, this control system has faster dynamic response capability. In the motor drive system modified from a gearbox, it can provide higher efficiency. For the problem of long transmission distance, this study proposes a simplified control system design, as shown in Eq. 11. T i a = 30 π / ν a • Δ ο + R s a • T i b − 30 π / ν b • ο a − ο b (11)

In Eq. 11, the rotational adhesion ability between the applied gears is denoted as ο a , ο b . Their rotational speeds within the regional time are represented by ν a , ν b . R s a is the compensation torque for both. The simplified transmission distance before and after is T i b , T i a . For the dynamic system calculated by this method, the operational length of the system varies with the dynamic characteristics. When gear meshing noise occurs, the system simulates engineering with nonlinear time-varying characteristics, as shown in Eq. 12. N t c = θ − 1 • ∫ 0 t Δ T i a − sgn ϖ d t + ϑ 0.5 • p y 0 − p y 1 (12)

In Eq. 12, the approaching speed of the simulated engineering is denoted as sgn ϖ . θ represents its network loss during operation. The state of gears before and after nonlinear time-varying is represented by p y 0 , p y 1 , respectively. ϑ is their actual rotational speed. After nonlinear time-varying, the material properties of the system change, which in turn affects external loading conditions. Therefore, this study chose to control the parameters of SET to accurately display grid noise, as shown in Figure 6.

The method chosen in this study for controlling this parameter is the combined gear speed control method. In Figure 6, this study adjusts the gear transmission ratio in the transmission system to change the external excitation applied to the system. This method can adjust the dynamic characteristics of the system to meet the requirements at different time intervals. For the SET-GRO system, the gear speed control joint method can adapt to the design requirements of the system. During this process, the parameter changes of the system are represented by Eq. 13. σ a , b • 0.35 • ⁡ ln ⁡ C p a − 1 = 100 • N t c • ⁡ cos C p b − A r 2 2 (13)

In Eq. 13, C p a , C p b represent the cross-sectional area of the force applied gear, and its arrangement during rotation is denoted as A r . This formula calculates the resonance and frequency variation of the gear system, thereby obtaining the stability level during gear transmission. After designing the control system, this study simultaneously considers the process of SET and Alternating Current (AC) motor drive, and designs the power transmission process of the gearbox according to the drive mode, as shown in Eq. 14 below. P t x = Δ V a s + 2 π • σ a , b / ∫ a b ⁡ sin P t 1 / P t 2 d t (14)

In Eq. 14, the position of the transmission power at a certain time is denoted as P t x . P t 1 and P t 2 represent the power magnitude of adjacent times, respectively. The working time in the current state is represented by Δ V a s . The SET-GRO system will adjust the stiffness parameters of the gearbox based on the actual working conditions of the two gears, thereby achieving precise feedback control methods. When the system is adjusted to different operating conditions, this study selects environmental parameters using the method described in Eq. 15. E v a = 100 • ς g / 60 • τ g ∑ g = 1 G ξ g • P t x sin 2 π + υ g (15)

In Eq. 15, the meshing noise of the gearbox is denoted as ς g . The knot line of the gear tooth is represented by τ g . ξ g , υ g represent the temperature and humidity outside the gearbox. By controlling environmental factors, the problem of reduced gearbox accuracy caused by them has been solved. Under these conditions, the transmission ratio and external excitation of the gears are controlled, thereby improving the dynamic characteristics of the gear transmission system and providing an accurate gearbox meshing noise control system.

This study divided the data in the Gmnoi dataset into two groups in a 1:1 ratio to verify the learning performance and noise reduction performance of the system, respectively. As shown in Table 1, prior to the experiment, the equipment and parameters for the experiment were determined in this study.

After determining the experimental parameters according to Table 1, for the model verification of the calculation process, this study conducted gear noise control experiments under different lubrication states. The SET-GRO system was compared with Long and Short Term Memory (LSTM) system, Quantum Genetic (QG) system, and GRO system to verify its superiority. The experimental results are shown in Figure 7.

Figure 7A shows that in a low lubrication gear system, the meshing noise of the gears increases gradually as the gear particle size increases for all four systems. When the gear radius reaches 10.8 cm, the meshing noise level of the gear reaches its maximum, which is 742, 831, 923, and 976 in the four systems, respectively. This indicates that for gears under the same conditions, the gear meshing noise of the SET-GRO system is the smallest. In Figure 7B, the suppression effects of SET-GRO, GRO, LSTM, and QG systems on gear meshing noise are 98.4%, 95.8%, 93.5%, and 92.7%, respectively. This indicates that the SET-GRO system has the best noise reduction effect on low lubrication gear systems. But a single experiment cannot demonstrate the scalability of the system. To verify the noise reduction effect of the system in different environments, this study changed the external environment of the gearbox and conducted separate experiments to verify the noise control effect of the system. The results are shown in Figure 8.

Figure 8 compares the scalability of four systems. In Figure 8A, among the 50 experiments conducted, the SET-GRO system performs the best in noise control, with a value of 0.715. The experimental results of the other three systems are 0.618, 0.524, and 0.475, respectively. In Figure 8B, the control performance of the four systems for meshing noise is 47, 35, 28, and 11, respectively. This experiment can demonstrate the control performance of the SET-GRO system for small gear trains, but it cannot demonstrate the application effect of large gears. To verify it, this study conducted experiments on a large gear system, as shown in Figure 9.

Figure 9 shows the control effect of the SET-GRO system in a large gear system. The SET-GRO system has the best noise reduction effect in large gear trains, with a noise reduction effect of 97.4%. This result can demonstrate the meshing noise control effect of the SET-GRO system in the same gear combination, but there are still shortcomings in experiments on gears of different materials, so further experiments are also needed.

To compare the meshing noise control effect of the SET-GRO system in different material gear groups, this study changed the gear material while controlling the same gear particle size and lubrication degree. By calculating the gear meshing noise control under different conditions, experiments on the stability and robustness of the SET-GRO system were conducted. The stability experiment results of the system are shown in Figure 10.

Figure 10 shows an experiment on the stability of the SET-GRO system. In Figure 10A, the noise control effect of all four systems increases with the increase of gear hardness. The highest performance of SET-GRO, GRO, LSTM, and QG systems are 623, 514, 406, and 423, respectively. In Figure 10B, the performance of the SET-GRO system is still superior in low precision gear systems. This indicates that the SET-GRO system can stably control the meshing noise of gears. This result is similar to that of Freisinger et al., 2024. To conduct experiments on its robustness, the composition materials of the gears were replaced in this study, as shown in Figure 11.

In Figure 11A, the control effect of the four systems on meshing noise is directly proportional to the degree of gear meshing. The accuracy of the SET-GRO system is 97.2%, which performs the best among the four systems. Figure 11B shows that the F1 values of the four systems vary with the increase of gear meshing degree. However, the SET-GRO system consistently has the lowest F1 value among the four systems. Adamzadeh et al., 2023 got the same result. The experimental results indicate that the coupling system is highly robust in controlling gear meshing noise. It effectively addresses the defects present in the theoretical background and is suitable for optimizing gear meshing.