Abstract
In oil-lubricated helical gears transmission systems, the “surge” phenomenon occurs when the tooth surfaces stall after collision during power transmission, leading to functional failure of the equipment. The occurrence of “surge” increases gear wear, reduces gear lifespan, and may cause fatigue damage, cracks, or even fractures due to the alternating stress, significantly impacting the smooth operation and reliability of the equipment. Despite its importance, the “surge” mechanism, stall and vibration characteristics, and suppression strategies remain unclear due to the lack of mature and unified analysis methods. This study aims to establish a “surge” model for helical gears, couple it with a dynamic model to derive specific parameters for the occurrence and development of “surge,” and propose control strategies to mitigate it.
1. Introduction
1.1 Background and Significance
The manufacturing industry serves as the fundamental and strategic pillar of national economic development, contributing key technologies and equipment to various industries’ growth, national defense construction, and global economic competition. Among modern mechanical devices, gear transmission systems play a crucial role, integrated into the power transmission systems of advanced defense equipment such as new-generation surface combatants, submarines, and aerospace engines. The technical level of gear transmission systems significantly influences the overall performance of these equipment.
With the evolving market demands, gear transmission systems are rapidly moving towards smaller sizes, higher load capacities, longer lifespans, and higher reliability. This trend imposes stricter standards on the stability of gear transmissions, particularly under high-speed and heavy-load conditions, where vibration and noise directly affect operational stability and reliability. Therefore, an in-depth study of the lubrication and dynamic behavior during gear meshing is essential to enhance the efficiency and reliability of gears, thereby strengthening the overall competitiveness of China’s manufacturing industry and enabling it to effectively address the opportunities and challenges brought about by domestic and international economic changes.
“Surge” is not exclusive to gas machinery equipment; it also frequently occurs in fluid-lubricated machinery. In gear transmission systems, factors such as manufacturing and installation errors, surface topography, oil supply, and collisions can lead to the “surge” phenomenon. When “surge” occurs in gear systems, it can cause unstable flow of the lubricating oil, resulting in low-frequency oscillations of flow rate and pressure parameters over time. This phenomenon significantly increases gear wear, reduces service life, generates noise, and affects the smooth operation of the gear transmission system, lowering operational efficiency and imposing additional loads on surrounding structures and equipment. In severe cases, it may even lead to system instability, equipment failure, or accidents.
1.2 Research Status
1.2.1 Research on “Surge”
“Surge” is generally an unstable aerodynamic phenomenon that occurs in aero-engines and other gas machinery, commonly seen in compressors and fans. Due to manufacturing and installation errors, gears inevitably have backlash, which can cause impact between meshing gear teeth, thereby inducing system vibration. Under high-speed and heavy-load conditions, gears experience engagement and disengagement impacts, leading to complex and variable loading and speeds of the lubricating oil, resulting in the “surge” phenomenon in gear transmission systems.
Research on “surge” dates back to 1955 when Emmons introduced the concepts of rotating stall and surge, focusing on the flow near the stall cell, its size, and its impact on blade vibration. Moore et al. established the MG model to describe stall and surge, proposing a parameter B to determine the occurrence of surge. Yan et al. studied the relationship between inlet distortion index and surge margin, providing important data support for the safe operation of engines under corresponding conditions. Vacula et al. experimentally measured 20 different operating points within the entire operating characteristic range of a centrifugal compressor. Zheng et al. constructed a multi-dimensional simulation method for aero-engines and conducted surge experiments on a turboshaft engine using high-pressure air injection technology. Zhang et al. proposed a neural network model based on multi-branch feature fusion using the powerful feature extraction capabilities of deep neural networks for real-time surge prediction. Minchev et al. modified the MG model and studied the airflow in the compressor exhaust duct through this modified model, proposing an equation for airflow acceleration. Serrano et al. analyzed two turbochargers under steady and transient operating conditions in the low torque operating range. Zhang et al. proposed a new real-time surge prediction model based on the surge mechanism, which can effectively simulate the complete surge process of a turboshaft engine under different operating conditions. Biglarian et al. simulated a jet engine model with a scale ratio of 1/30 using fluid dynamics, which has 3 million hexahedral grids and can approximate the characteristics of a real engine. Moreno et al. explored the impact of two different surge excitation methods on the maximum loads observed during the surge process and provided explanations for the main physical processes causing these loads. Asanaka et al. tested the flow distribution under pulsating conditions for the compressor of a certain type of supercharger to determine the surge occurrence range through experimental testing. Rajendran et al. studied an integrated airframe-engine-VPF model, focusing on the airflow distortion at the core engine inlet caused by the VPF in reverse thrust mode. Muchowski et al. comprehensively calculated the flow conditions of specific variable guide vanes in an engine with an 8-stage axial compressor under low, medium, and high load speeds. Galindo et al. discussed the impact of different inlet geometries on the performance of centrifugal compressors, particularly under low mass flow conditions, revealing the sensitivity of key compressor performance parameters to changes in the upstream geometry of the inlet.
Jian Guangxiao et al. studied the contact impact phenomenon caused by speed differences at gear meshing points, comparing and analyzing the influence of dynamic loads, steady loads, contact impact positions, and impact speeds on the transient elastohydrodynamic lubrication results of involute spur gears. Although the concept of gear “surge” was introduced in this study, no in-depth research was conducted. Cao Jujiang et al. applied the relevant integral method to analyze the dynamic pressure signals during the transition from stable operating conditions to surge in a centrifugal compressor, aiming to quantitatively identify different stages of surge development. Simultaneously, they utilized the Fourier transform to enhance signal resolution during the transition and surge periods. Sun Tao et al. combined the integral method with a refined fast Fourier transform technique to conduct a frequency domain analysis of the pressure signals throughout the development of a complete surge phenomenon, proposing an innovative surge prediction method. Zhang Yizhuo et al. proposed an innovative feature extraction technique to effectively identify and analyze the nonlinear characteristics of compressors during surge.
In summary, most scholars currently study the internal fluid dynamics of compressors and changes during surge through theoretical analysis and experimental observations. Existing research has revealed the complex relationship between surge and parameters such as flow rate, pressure, and rotational speed. However, there is relatively little research on the “surge” phenomenon in gear transmission systems. Most existing studies have only revealed that the presence of lubricating oil and contact pressure in gear transmission systems can also lead to a “surge” phenomenon similar to that in compressors. However, research on “surge” models and the impact of “surge” on the smoothness of gear transmission systems remains insufficient. The mathematical model analysis of gear transmission system “surge” can draw on research methods for surge in compressors to study the influence of oil supply, pressure, rotational speed, and load on “surge” in gear transmission systems, explore specific laws, and aim to reduce the occurrence of “surge” in gear transmission systems and improve transmission smoothness.
1.2.2 Research on Elastohydrodynamic Lubrication of Gear Transmission Systems
In actual gear meshing, lubrication conditions can be classified into three types: elastohydrodynamic lubrication (full-film lubrication), mixed lubrication, and boundary lubrication. Many factors influence the lubrication state, including the sliding speed generated by the rolling and sliding of gears, the heat generated during gear meshing, tooth surface topography, contact pressure, initial viscosity of the lubricating oil, viscosity-pressure and viscosity-temperature coefficients of the lubricating oil, etc. These factors collectively influence and even determine the lubrication characteristics of gear transmission systems.
As early as 1886, Reynolds derived the Reynolds equation using the basic theory of fluid mechanics, a breakthrough that laid the foundation for subsequent research. The theory of elastohydrodynamic lubrication combines Hertz’s theory of elastic contact with Reynolds’ fluid theory. The application of elastohydrodynamic lubrication theory in the field of mechanical engineering has gradually matured. Dowson and Higginson proposed a general formula for the minimum oil film thickness through research on point contact gear elastohydrodynamic lubrication. Zuo Mingyu studied the lubrication performance of asymmetric polymer gears under transient and reversing conditions, revealing the performance laws of asymmetric gears under different operating conditions and providing a theoretical basis for energy conservation, emission reduction, and improving transmission system lifespan. Zhang Yuhao studied the elastohydrodynamic lubrication characteristics of herringbone gears, analyzing the influence of factors such as herringbone gear line contact theory, structure, transmission characteristics, temperature, and tooth surface roughness on elastohydrodynamic lubrication, pointing out that reasonable parameter selection can enhance lubrication effectiveness. Xu Chunhui analyzed the lubrication problems in gear transmission using numerical methods, discussing the influence of factors such as entrainment speed and load on oil film pressure and thickness. Simultaneously, he analyzed the lubrication conditions considering thermal effects and time-varying effects, concluding that compared to thermal effects, load impact and surface roughness have a more significant impact on oil film performance. Huang et al. constructed a new model considering time-varying meshing stiffness, incorporating factors such as EHL effects, gear coupling flexibility, and modified tooth stiffness, while also deriving the iterative relationship between coupling and deformation coordination equations to more specifically describe the dynamic meshing characteristics of gears. Xing et al. proposed a wear prediction model for mixed elastohydrodynamic lubrication of spur gears considering dynamic loads. Yao Lu coupled the dynamic model and thermal elastohydrodynamic lubrication model of herringbone gears through an oil film stiffness model, considering the influence of surface roughness, and ultimately establishing a flash temperature distribution model on the tooth surface. This research provides a certain theoretical support for the design of herringbone gears, helping to improve their performance and lifespan under extreme conditions.
Zhang Yu took helical gears as the research object, constructing a line contact elastohydrodynamic lubrication model and a nonlinear dynamic model. By studying the variation laws of oil film pressure and thickness, he analyzed the influence of system parameters on lubrication performance and further studied the influence of parameter changes on dynamic characteristics, aiming to improve gear transmission performance and reduce wear. Felix proposed a method for establishing a transient mixed elastohydrodynamic lubrication model of gears considering thermal effects and used this model to analyze the friction characteristics of low-loss gears. Zhao proposed a new model combining the analytical slicing method and the two-dimensional elastohydrodynamic lubrication model, aiming to accurately describe the three-dimensional meshing characteristics of spur gears and provide a more accurate model for in-depth research on the contact state and meshing characteristics of gear pairs under elastohydrodynamic lubrication conditions. Gu Zonglin discussed the influence of tooth surface roughness generated by different processing methods on lubrication performance and the effect of changes in operating parameters on lubrication contact performance, providing a theoretical basis for gear lubrication design and fatigue life prediction. Jian Guangxiao considered the interaction between vibration and friction for high-speed and heavy-load aeronautical gear systems, constructing a dynamic model including tooth surface friction and analyzing lubrication performance under dynamic load effects. Zhang Jinxi established a dynamic model considering factors such as friction excitation and a coupling model of dynamic load and thermal elastohydrodynamic lubrication, analyzing the influence of friction on gear dynamic characteristics. The fully coupled model revealed the bidirectional coupling mechanism between dynamics and lubrication and compared the distribution laws of friction coefficients and temperature fields under different operating conditions. Zhang et al. explored the influence of surface coating materials on the elastohydrodynamic lubrication characteristics of the tooth contact interface, constructing a local fluid-solid coupling model and using ADINA software for numerical solution. Simultaneously, they conducted secondary development considering lubricant viscosity, density, non-Newtonian fluids, and cavitation phenomena. Wang et al. proposed an improved model for calculating the meshing stiffness of helical gear pairs, considering factors such as the influence of surface roughness on transverse and axial stiffness under EHL conditions. They also studied the time-varying friction coefficient and analyzed the influence of friction force on stiffness. Xu Zhijun used three-dimensional software simulation analysis for the meshing interface of aviation gear pairs, deeply discussing the influence of non-Newtonian effects on lubrication. Ding Huafeng et al. studied the thermal elastohydrodynamic lubrication characteristics of helical gears under oil-starved conditions, establishing a thermal elastohydrodynamic lubrication model for oil-starved helical gears and discussing the influence of oil supply, rotational speed, and tooth surface roughness on lubrication performance. Wang Yanzhong et al. analyzed the tooth surface lubrication and friction characteristics of herringbone gears through thermal elastohydrodynamic lubrication, finding that the minimum oil film thickness and the highest oil film temperature first increase and then decrease, while the maximum oil film pressure first decreases and then increases. Additionally, torque has a positive relationship with gear modification amount and oil film pressure and temperature curves. Guo Manli et al. established a finite long elastohydrodynamic lubrication model for helical gears, considering the influence of the free end face of the gear. Liu et al. proposed a modified thermal elastohydrodynamic lubrication model for helical gear pairs that corrects the entrainment speed term in the Reynolds equation, incorporating an interface slip model under the limit shear stress. Hu et al. constructed a TEHL model considering surface roughness and developed a numerical calculation method for computing frictional heat generation. Sun Xiaoxia et al. further discussed the dynamic characteristics of the oil film and its lubrication behavior during gear vibration through theoretical analysis of the dynamic characteristics of time-varying meshing stiffness excitation. Ge Hao explored the influence of non-Newtonian fluid line contact elastohydrodynamic lubrication on friction coefficient and meshing efficiency for herringbone gear transmission systems. Zhang Huan used finite element simulation to calculate and analyze the influence of parameters such as load, oil-air ratio, and ambient temperature on the elastohydrodynamic lubrication characteristics of the gear contact interface, explaining the variation laws of subsurface stress, stress depth, friction depth, and oil film thickness. Wang et al. accurately calculated the contact trajectory, contact line length, and tooth surface load distribution of helical gear pairs based on the EHL theoretical framework, proposing a new method for calculating the sliding friction coefficient on the tooth surface of helical gear pairs based on these results. Wang Mingkai introduced the dynamic meshing force solved in the lubrication analysis into the dynamic model using a decoupling method for solution, feedback the results to the dynamic model, and repeat the process until the dynamic meshing force meets the convergence criteria. Based on this model, he further discussed the relationship between dynamics and friction characteristics, providing theoretical support for related research. Zhang Xijin et al. conducted simulation calculations on the relationship between relevant modification parameters and tooth surface friction loss, finding that both tooth profile modification and topology modification are beneficial for transmission, while the tooth trace modification length is positively correlated with loss, which is detrimental to transmission. Wei Cong et al. established an elastohydrodynamic lubrication calculation model by equating straight bevel gears to cone roller models. Pan Lijun took herringbone gears as the research object, considering tooth modification, and established a thermal elastohydrodynamic lubrication model for point contact on herringbone gears. Wang et al. constructed a dynamic model of planetary gears comprehensively considering friction effects under mixed elastohydrodynamic lubrication, time-varying meshing stiffness, and tooth surface clearance, and comprehensively analyzed the system’s dynamic bifurcation and chaos characteristics. William established a model of running-in and initial micropitting of ground gear surfaces under mixed lubrication conditions based on gear contact, evaluating the influence of contact pressure, slide-roll ratio, and entrainment speed using a full factorial experimental design. Jian et al. studied the thermoelastohydrodynamic lubrication characteristics of modified gear systems under the influence of modification coefficients, vibration, and dynamic loads, focusing on the influence of modification coefficients on flash temperature and lubrication characteristics. Lu Fengxia et al. established a corresponding thermal elastohydrodynamic lubrication model for helical gears under non-Newtonian fluid and large slide-roll ratio conditions, considering the time-variability of tooth surface load and the meshing line length during meshing. Huang et al. proposed an elastic fluid impact model considering squeeze effect and thermal effect, focusing on the influence of sinusoidal pulse load, sinusoidal pulse entrainment speed, and multi-frequency vibration on lubrication characteristics. Hu Mingjian analyzed the influence of parameter changes on lubrication performance by establishing a microscopic model incorporating parameters such as oil film thickness, pressure, and temperature, and further studied the influence of different factors on system dynamic characteristics in combination with oil film damping. Zhang Qinwei established a finite long line contact elastohydrodynamic lubrication model for helical gears and solved and analyzed the influence of factors such as thermal effects, surface roughness, and surface modification, providing a theoretical basis for optimizing lubrication conditions, improving gear reliability, and predicting lifespan for helical gears.
1.2.3 Research on Gear Transmission System Dynamics
Gear systems are crucial components in mechanical equipment, and their dynamic performance directly affects the performance, reliability, and lifespan of the entire mechanical system. Therefore, mastering the dynamic characteristics of the system is essential for developing efficient vibration and noise reduction strategies, enhancing transmission system smoothness and work efficiency, which has extensive applications in fields such as mechanical design, aerospace, and the automotive industry.
The vibration noise and transmission smoothness of gear transmission systems are key indicators for evaluating dynamic performance, directly impacting the operational efficiency and lifespan of mechanical equipment. Severe vibration can cause premature fatigue wear of mechanical structures, reducing transmission system efficiency and increasing energy consumption. Simultaneously, unstable transmission may cause load fluctuations, affecting work performance. Therefore, an in-depth study of the vibration and transmission smoothness of gear transmission systems is not only beneficial for improving equipment operational reliability but also for extending the lifespan of mechanical systems, having a profound impact on the development of modern manufacturing and mechanical design fields.
Dynamic modeling and analysis of gear transmission systems play a vital role in understanding and mitigating the adverse effects of vibrations and noise. This section delves deeper into the various aspects of gear dynamics, including the modeling approaches, analysis methods, and the impact of various parameters on the system’s performance.
One of the primary focuses in gear dynamics research is the development of accurate and comprehensive models that can capture the system’s behavior under different operating conditions. These models often incorporate factors such as time-varying mesh stiffness, backlash, and friction. The time-varying mesh stiffness, for instance, accounts for the variations in stiffness during the meshing cycle due to changes in the contact area and the deformation of gear teeth. Backlash, on the other hand, represents the clearance between mating gear teeth and can lead to impacts and vibrations, especially during rapid changes in load or speed.
In addition to these physical factors, the dynamic behavior of gear systems is also significantly influenced by external excitations, such as those arising from the powertrain or the operating environment. These excitations can interact with the system’s natural frequencies, leading to resonance and amplified vibrations. Therefore, it is crucial to include such excitations in the dynamic models to accurately predict the system’s response.
Another important aspect of gear dynamics research is the analysis of nonlinear phenomena, such as chaos and bifurcation. These phenomena can arise due to the system’s sensitivity to initial conditions and parameter variations. Understanding these nonlinear behaviors is essential for designing robust control strategies that can maintain stable operation under a wide range of conditions.
Experimental validation is also a critical component of gear dynamics research. Through experiments, researchers can validate the predictions made by the models and gain insights into the system’s actual behavior. Experiments also provide data that can be used to refine and improve the models, making them more accurate and reliable.
In recent years, advances in computational techniques, such as finite element analysis (FEA) and multi-body dynamics (MBD) simulation, have significantly enhanced the capabilities of gear dynamics research. These techniques allow for more detailed and accurate modeling of the system, including the complex interactions between gears, bearings, shafts, and other components.
Moreover, the integration of control theory with gear dynamics research has opened up new avenues for the development of active and semi-active control strategies. These strategies can adjust the system’s parameters in real-time to mitigate vibrations and improve transmission smoothness.
In conclusion, the dynamics of gear transmission systems is a complex and multifaceted field of study that requires a combination of theoretical modeling, experimental validation, and computational techniques. By gaining a deeper understanding of the system’s dynamic behavior, researchers can develop more efficient and reliable gear transmission systems, contributing to the advancement of mechanical design and engineering.