Meshing Force Research Articles

Enhancing wind turbine energy efficiency: Tribo-dynamics modeling and shape modification

The performance of wind turbine gearbox planetary bearing systems directly influences the turbine's reliability, energy production efficiency, and economy. However, the lack of a comprehensive model to accurately predict the dynamic meshing load of helical gears and temperature effects hinders a deeper understanding of the transient performance of gearbox planetary sliding bearings. Additionally, research on shape modification for gearbox planetary sliding bearings remains inadequate. This study develops a comprehensive tribo-dynamics model that considers the dynamic meshing forces of helical gears and temperature effects. The model's effectiveness is validated by the concordance between experimental data from a full-size test bench and simulation results on oil film thickness and temperature. Transient simulation analysis indicates insufficient lubrication, high-temperature rise, and severe contact that reduce electricity production efficiency and reliability, all of which occur at bearing axial edges. Therefore, three modified bearing designs (super-elliptical, trapezoidal, and quadratic shapes) are introduced, and their improved performance is thoroughly compared. The super-elliptical design increases the minimum oil film thickness by 2.60 μm. The trapezoidal design reduces cumulative friction energy losses by 4.34 %. Each modified design successfully reduces the edge wear and oil temperature. The underlying enhancing mechanisms are revealed to be oil film uniform redistribution and lubrication states' alteration. This work can contribute to the reliability, electricity production efficiency, and economy of global wind turbines and support the achievement of net-zero emission goals.

Numerical investigation of vibratory response of planetary gear sets and modulation effects induced by carrier rotation

In geared system, the main source of excitation is generated by the mesh process itself. Depending on the dynamic conditions involved, the system may present a variety of problems, ranging from acoustic nuisance to system failure. Predicting and controlling the mesh process at an early design stage is a key point to avoid such issues. The problem is complex, mainly due to its multi-scale nature. Indeed, the vibroacoustic behavior of geared systems (on the scale of a meter) depend on the local micro-geometry of the teeth (of the scale of a micron), associated with the transmission error. Moreover, the problem is parametric in nature, due to the periodic fluctuation of the mesh stiffness. These parametric internal excitations generate dynamic mesh forces which are transmitted to the housing through wheel bodies, shafts and bearings. In the case of planetary gear sets, the numerical prediction presents a complementary challenge as, in many application, the carrier rotation modulates the housing vibration response, at its rotational frequency. This paper present an original simulation process to deal with modulation effects in planetary gear systems.

Automotive powertrain electrification: system methodology to guarantee acoustic comfort

For the past few years, electrification has disrupted the automotive industry. Surprisingly, Noise Vibration and Harshness (NVH) became a major issue as it is located in high frequencies (1 to 5 kHz). The noise has 2 origins: the electromagnetic forces in the electric motor and the gear mesh forces in the reducer. The first part focuses on the methodology developed in collaboration with car-makers in order to integrate the powertrain in a satisfying way in the vehicle. First, this process is focused on the structure-borne noise. Attention is paid on rubber mounts and on their fixation points. Second, the airborne transfer may become an issue. Despite the acoustic power requirement provided, the final vehicle performance is not guaranteed. Examples will illustrate these important topics. The second part pays attention to the prediction of reducer noise. Automotive stakeholders are approaching the gear mesh source by approximate linear tools. Recent works have shown that this methodology has limitations and leads to inaccurate results. This may be a major concern. A few examples will illustrate this risk and show that further simulation developments are necessary.

Investigation of contact ratio and dynamic characteristics of non-circular planetary gear train in hydraulic motor

As a basic component of the non-circular gear hydraulic motor (NGHM), the non-circular planetary gear train (NPGT) offers a number of advantages, including low velocity, high output torque and compact design. Two different types of NPGT pitch curves have been designed using the 4-6 type of NGHM as an example. Aiming at two kinds of pitch curves, the contact ratio solution methods for the planetary gear meshing respectively with the sun gear and the inner gear ring are proposed. A comparative analysis of an integrated pitch curve design and a segmented pitch curve design is conducted to evaluate the effects of varying addendum coefficient (AC) and tool tooth profile angle (TTPA) on the contact ratio. Furthermore, the influence of load, velocity, and contact ratio on the dynamic characteristics (DC) of the NPGT with a segmented pitch curve is investigated through dynamic simulation. The results show that AC and TTPA significantly affect the contact ratio, with an increase in contact ratio observed as TTPA decreases and AC increases. Additionally, the load has a notable impact on the dynamic meshing force and its fluctuation. A higher contact ratio is associated with greater transmission stability in the gear train. This study provides a theoretical foundation for the design and optimization of NGHMs, and expands the potential application of contact ratio effects on NPGTs in this field.

Analytical investigation on load sharing characteristics and speed difference of coaxial reverse closed differential herringbone gear transmission system with floating gear and errors

To investigate the influence of gear floating on the load sharing characteristics of the Coaxial Reverse Closed Differential Herringbone Gear Transmission System (CRCDHGTS) and the rotational speed difference between the upper and lower rotors, a dynamic Bending-Torsional-Axial-Pendular (BTAP) model of the CRCDHGTS was established using the centralized parameter method, which considers various excitation factors such as gear floating, errors, Time Varying Meshing Stiffness (TVMS), gyroscopic effect, and tooth friction. It considers the interaction between the closed-stage gear set and the differential-stage gear set, treating the herringbone gear as a symmetric helical gear connected through a receding slot. The dynamic model was solved using the Runge-Kutta method to obtain the dynamic meshing forces for each gear pair under single and combined floating modes. The Dynamic Load Sharing Coefficient (DLSC) of the system, which characterizes the Load Sharing Performance (LSP), was deduced. The load sharing characteristics of different floating modes were analyzed, as well as the influence of different floating displacement on the DLSC. The motion path of the gear floating was also determined. Additionally, the impact of manufacturing error and assembly error of each component on the DLSC under combined floating mode was analyzed. Finally, the influence of gear floating on the output rotation speeds of the upper and lower rotors of the system was investigated. The results indicate that both free-floating of the center gear and combined floating can effectively improve the LSP of the system. When the system adopts combined floating mode, the DLSC of inner and outer meshing changes between 0.91 and 1.09, demonstrating a significant improvement in the LSP. The DLSC of the system increases with the increase in error, with the eccentricity error having a greater impact on the DLSC compared to the assembly error. The optimal floating value for the sun gear is between 0.6 mm and 0.8 mm, while for the planetary gear, it is between 0.4 mm and 0.6 mm. The rotational speed difference between the upper and lower rotors can be controlled within 1r/min. These research findings provide a theoretical basis for further analysis of the dynamic stability and reliability of the system.

An analysis of abnormal vibration and noise caused by shaft coupling misalignment of high-speed train

This study conducts on-site testing and simulation analysis of the abnormal noise phenomenon generated during the operation of high-speed trains. The sound pressure characteristics in the cabin and the vibration of different vehicle components are recorded and subjected to comprehensive analysis. Test results indicate that significant abnormal noise occurs inside the cabin at the speed of 250 km/h, with frequencies of 87 Hz, 173 Hz, 259 Hz, and 346 Hz. Through sound source identification, vibration transmission analysis and theoretical derivation, it has been determined that the abnormal noise primarily originates from the transmission system, and it is further speculated that these abnormal vibrations and noises may be correlated with the shaft coupling misalignment within the transmission system. To verify the conjecture, a high-speed vehicle electromechanical coupling simulation model was established, incorporating the shaft coupling misalignment in the transmission system. The vibration characteristics of vehicle components were analyzed, confirming that shaft coupling misalignment leads to uneven meshing forces in gears, resulting in significant vibration and noise that affect the riding comfort of the vehicle. We propose replacing the shaft coupling to solve this problem, the test results showed that the abnormal vibration amplitudes of the transmission system at 87 Hz, 173 Hz, 259 Hz, and 346 Hz were significantly reduced after replacing the shaft coupling, and the amplitude of the corresponding frequencies on the cabin floor decreased by 91 %, 78 %, 98 %, and 66 %, respectively. The issue of abnormal noise has been effectively resolved.

Nonlinear Dynamics and Meshing State Transition Analysis of Spalling Defect Gears with Multi-Lubrication Conditions

The purpose of this paper is to analyze the dynamic characteristics and the meshing state transition characteristics of spalling defect gears under various lubrication conditions. The time-varying geometric parameters, motion parameters and load distribution of the gears in the state of positive meshing and reverse impact are analyzed. The time-varying meshing stiffness considering the time-varying friction coefficient under elastohydrodynamic lubrication (EHL), mixed lubrication and boundary lubrication are calculated, and the spalling defect is introduced in the stiffness calculation process. The equivalent lubrication model of the gear is established, the switching condition of the lubrication state is derived, and the distribution of the lubrication state in the torque-speed plane is discussed. The multimeshing state dynamic model of the spalling defect gear is established, and the evolution characteristics of the coexistence response and the transition of the meshing state under different lubrication conditions are simulated by using the attraction domain, phase trajectory, meshing force and bifurcation diagram. The results show that the phase trajectory of the gear with the spalling defect is deformed compared with that of the healthy gear. The change of lubrication state has little effect on the phase trajectory and attraction domain of the gear with spalling defect, but has a great influence on the meshing force. At the spalling boundary, the meshing force is changed abruptly, and the worse the lubrication state, the more obvious the mutation. Due to the influence of spalling on tooth stiffness, it will also affect the meshing force in the nonspalling area.

Modelling of electromechanical coupling dynamics for high-speed EHT system used in HEV and characteristics analysis

As the development of hybrid electric vehicle (HEV) to high-speed, heavy-load, the electromechanical coupling vibration becomes the bottleneck in high-speed electromechanical hybrid transmission (EHT) system. To explore the dynamics characteristics and optimization direction for high-speed EHT system, an electromechanical coupling dynamics model under multi-source excitations is established with lumped-distributed parameter method and verified with experiment data. The dynamics model shows higher accuracy in both time and frequency domain analysis. On this basis, firstly, the comparison between lumped-shaft and distributed-shaft model is studied under time and frequency domain. Comparing with the lumped-shaft model, the distributed-shaft model shows higher accuracy, and can better reflect the coupling vibration of multi-stage planetary gears (PGs). Secondly, the inherent vibration model is derived, and the effect of electromechanical coupling and high-speed working conditions on inherent vibration characteristics are studied. Thirdly, a new method called ‘machine-electricity-magnet coupling interface’ is proposed to reveal the coupling vibration phenomenon. In addition, the signal of stator current and electromagnetic torque includes the frequency of PGs, which is a basis on the fault diagnosis and state monitor of EHT system. Last but not the least, the vibration acceleration of EHT system is analysed under variable speed and load working conditions. Rotation speed and gear meshing force is found as the main influencing factor of series EHT system, and the specific optimization direction is also given.

Research on dynamic and wear prediction models of compound planetary transmission systems

Under high speeds and heavy loads, gear tooth surfaces will be worn, which will lead to accidents. The current wear prediction model is not comprehensive, but the wear prediction model that considers the temperature field and dynamic response can provide more accurate gear wear fault early warning than previous methods. Therefore, according to the Archard model, the discrete wear prediction model of the tooth surface is deduced in this paper, and the wear evolution trend of the tooth surface is predicted and analyzed in each operation stage. The tooth surface temperature field was simulated by the finite-element method, and the tooth surface wear prediction model was improved considering its influence on materials. In addition, the dynamic model of the compound planetary transmission system was established, and the wear prediction model was improved again by using its nonlinear meshing force. Finally, the tooth wear prediction model under the interaction of the dynamic response and temperature field was obtained. A wear measurement method based on duplicate adhesive film was proposed. The wear evolution trend along the tooth length direction and the tooth width direction were measured, and the accuracy of the wear prediction model was verified. The results show that the wear depth along the tooth width direction is larger in the middle part and smaller on both sides under the influence of temperature. After the interference of the dynamic response, the wear depth along the tooth rectangle fluctuates, which is very similar to the results of the theoretical prediction model. It provides a theoretical basis for the early warning of gear health status in practical engineering.

Theoretical characterization of the dynamics of a new planetary gearbox

Based on the newly designed planetary gear gearbox with reciprocating linear motion of its output shaft, research on its dynamic characteristics was conducted. The “kinematic mechanism method” was used to calculate the system’s transmission ratio, revealing its characteristic of having a relatively large transmission ratio. Combined with the calculation of transmission efficiency, the characteristic of high transmission efficiency was verified. The “velocity vector method” was used to calculate the relationship between the angular velocities of various components of the gearbox. By conducting a stress analysis on the planetary gear transmission system, the forces and torques acting on each component, as well as the meshing forces of the gears were calculated. The “central parameter method” was adopted to simulate the meshing contact between the gears in the planetary gear transmission system as undamped springs. Considering the two translational vibrations along the radial direction and the rotational twisting along the circumferential direction of each component, a translational-torsional coupled dynamic theoretical model of the system was constructed. Dynamic differential equations of the planetary gear transmission system were derived and solved to obtain the support forces and torques of each component at the bearing support positions, enhancing the research on the dynamic characteristics of the planetary gear transmission system.

Dynamic characteristics of compound rotor system of mechanically rectified permanent magnet generator

The compound rotor system of a mechanically rectified permanent magnet generator is the key structure to realize the rectification function. The dynamics of the compound rotor system under bidirectional input conditions are studied to analyze the vibration deformation degree of each component of the rotor system and to ensure the uniform distribution of the shunt load of each planetary gear. In this paper, based on the theory of concentrated mass parameters, a dynamic model of the compound rotor system under the condition of bidirectional input is established. The model is solved with the Runge-Kutta numerical integration method. The dynamics of each component under the condition of bidirectional input are obtained. The results show that the oscillations of torsional displacement of each component of the compound rotor system are all about 25 μm, and the standard deviations of the meshing forces of each planetary shunt are all about 200 N during the two-way input, indicating that the vibration degree of the compound rotor system is similar; The load sharing coefficient of meshing forces decreases obviously with the increase of input torque and tends to be gentle when the torque reaches 500 N·m. Therefore, increasing the input torque can improve the dynamic meshing force and load sharing performance, so that the compound rotor system can obtain better dynamic performance under the bidirectional input condition. The research results are of great significance for the vibration and noise reduction and reliable operation of the permanent magnet generator.

Performance reliability evaluation of high‐pressure internal gear pump

AbstractWith the development of the high‐end equipment technology, the performance requirements of the internal gear pump (IGP) under high pressure are also increasing. However, the increase of working pressure will lead to the instability of gear pump performance in terms of volumetric efficiency, noise, reliability and so on, it is necessary to reasonably evaluate the reliability level of high‐pressure IGP. The reliability analysis of the high‐pressure IGP is carried out from the aspects of flow, noise, and gear strength in this paper. First, the output flow rate and far‐field flow‐induced noise of the high‐pressure IGP were obtained through fluid numerical simulation, and experimental verification was conducted. Then, based on the time‐varying meshing stiffness, backlash function and static transmission error of the gear pair, a nonlinear dynamic model of the internal meshing gear pair was established. The time‐varying meshing force was obtained through the dynamic model of the gear pair, and then the tooth contact stress and tooth root bending stress were obtained. Finally, considering the uncertain factors affecting the performance of the high‐pressure IGP, Latin hypercube sampling (LHS) combined with dendrite network (DD) was used for random response modeling. The performance reliability of the high‐pressure IGP, including output flow rate, far‐field flow‐induced noise, and the strength of gear pair, were estimated based on the fourth moment‐based saddlepoint approximation (FMSA). The reliability analysis results can provide a theoretical basis for the structural optimization design of the high‐pressure IGP.

Analysis of the Dynamic Characteristics of Coaxial Counter-Rotating Planetary Transmission System

This paper presents a coaxial counter-rotating planetary transmission system. The transmission system under study is a two-stage planetary gear train (PGT) comprising a fixed-axes PGT and a differential PGT. A dynamic model of the transmission system is established, considering both the excitations caused by the time-varying mesh stiffness (TMS) and the transmission errors, respectively. The Runge–Kutta algorithm is used to calculate and analyze the dynamic characteristics of the system. This includes studying dynamic meshing forces, planet gear displacements, and load-sharing coefficients (LSCs) under both internal and external excitations, as well as different input torques. The results indicate that when considering external excitations, the variations in the meshing force curves become more pronounced. The radial displacements of the planet gears in the differential PGT are greater than that in the fixed-axes PGT. With increasing input torque, the average displacements of the planet gears in all directions tend to increase. The differential PGT, transmitting a higher power, demonstrates a better load-sharing performance compared to the fixed-axes PGT.

Dynamic behavior of rack vehicle-track(rack) coupled system on super-large-slope bridges

Rack railways are mainly used in mountainous areas, where inevitably, super-large-slope bridge structures appear. The dynamic behavior of the rack vehicle-track(rack) coupled system on super-large-slope bridge is rarely studied. To address this issue, a dynamic interaction model for rack vehicle-track(rack)-bridge system is established by considering the detailed dynamic meshing behavior of gear-rack and the dynamic contact behavior of the wheel-rail. On this basis, the gear-rack meshing force and the wheel-rail contact force of rack vehicles are studied under lines with varying slopes, and the dynamic behavior of the rack vehicle and the track-bridge system with a slope of 250‰ is further analyzed. Research results show that as the slope line increases, the gear and rack meshing force increases, but the wheel-rail vertical force decreases. Concurrently, the stability index of the vehicle changed considerably, and the stability of the vehicle decreases substantially. The maximum values of the vibration acceleration of the vehicle body and bridge are 0.4 m/s2 and 0.5 m/s2, respectively, meeting the requirements of the relevant standards for the vibration acceleration of the vehicle body and bridge. Further analysis reveals that the vibration of rack is mainly affected by the meshing force, and the vibration of the bridge is mainly affected by the wheel-rail force. These research results can offer a theoretical basis for the pre-design, post-operation, and maintenance of rack railways.

Dynamic Simulation Analysis of Aviation Gear Transmission Based on Rough Tooth Surface

In order to explore the influence of tooth surface microstructure on the dynamics of aviation gear transmission, this paper describes the profile of aviation gear considering rough surface based on fractal theory. With the help of the established gear fractal contact model, the dynamic parameters such as time-varying friction coefficient, time-varying meshing stiffness and transmission error of rough tooth surface are characterized. The nonlinear dynamic model of aviation gear is established to solve the dynamic response of smooth and rough tooth surface. The dynamic meshing force, dynamic friction force, vibration time domain and frequency domain diagram are obtained, and the corresponding experiments are carried out. The simulation and experimental results show that the fluctuation range of the dynamic simulation results of aviation gear transmission based on rough tooth surface will be larger, and it has a certain degree of disorder, which is closer to the experimental results.

Nonlinear dynamic meshing force analysis of PEEK-based polymer composite involute spline coupling system

The dynamic meshing force affects the stability and wear life of PEEK polymer composite involute spline couplings, but most of the dynamic meshing force is obtained by empirical formula, and there is no effective calculation method in practice. Aiming at the viscoelasticity and nonlinear behavior of PEEK material, this work established a nonlinear dynamic model of the drive system of PEEK-based polymer composite involute spline pair by using the concentrated mass method, taking into account time-varying meshing stiffness, tooth side gap, and comprehensive transmission error, and obtained a dimensionless dynamic matrix that eliminates rigid body displacement. Aiming at the thermal stability of PEEK material, the dynamic meshing stiffness and dynamic meshing force of the involute spline of PEEK-based polymer composite were calculated by considering the thermal effect of misalignment and meshing deformation. The influence of misalignment on the dynamic characteristics of the system under dynamic and static loads was studied. The results show that the dynamic meshing stiffness and dynamic meshing force of involute spline coupling of PEEK-based polymer composite materials under misalignment represent complex nonlinear characteristics; Vibration, load, and viscoelastic deformation have an impact on transmission accuracy and efficiency; And the optimal selection range for friction coefficient, Poisson's ratio, and Young's modulus were determined within the parameter range of involute spline coupling of PEEK-based polymer composite materials as the matrix. It provides a theoretical foundation for designing high-performance, high-precision, and highly reliable PEEK-based polymer composite components.

Investigation of Gear Meshing Vibration and Meshing Impact Resonance Intensity Assessment

Abstract Gear drive is one of the most widely used transmission forms. Its vibration analysis plays an important role in design and operation. Considering the gear meshing resonance phenomenon (MRP), the paper analyzes the influences of rotating speed and load on meshing resonance intensity (MRI). Based on the gear meshing impact mechanism, meshing force variation during the engagement process were obtained. It was considered as meshing impacts exerted on the gear system. By comparing the maximum meshing force under different circumstances, it was found that rotating speeds and loads were positively related to meshing forces. The vibration signals with different load torques and rotating speeds obtained from the gear pair were analyzed. The experiment results showed that the intensity of meshing impact increased with the increases of both rotating speed and load. It was also observed that due to the MRP, the gear meshing frequency was modulated to the resonance frequency band as meshing impacts. Consequently, the resonance frequency band contained most of the energy of the meshing impact. An indicator called resonance energy ratio (RER) was defined to represent the proportion of resonance energy due to meshing impact. The simulation and experiment result show that the proposed RER indicator can well assess the intensity of the vibration. By comparing the RER values of 20 sets of gear vibration data, the influences of rotating speed and load on MRI were discussed. The result shows that the proposed method is helpful to the vibration assessment and condition monitoring in different operational states.

Improved mesh stiffness model of spur gear considering spalling defect influenced by surface roughness under EHL condition

Gear tooth spalling is a typical tooth surface defects in gear transmission. The accurate calculation of the time-varying mesh stiffness of the gear pair with spalling defect under mixed elastohydrodynamic lubrication (EHL) plays an important role in tooth damage prediction and fault feature analysis. In this work, an improved time-varying mesh stiffness (TVMS) model of spalling faulty gear in mixed EHL line contact considering the coupled effect of rough surface topography is established. The proposed model considers the combined effect of spalling defect, surface roughness topography, and lubrication on the contact characteristics of the meshing interface to obtain a revised contact stiffness, which is further used to determine the comprehensive TVMS. The cylindrical contact coefficient for curved meshing interface with spalling fault is derived and incorporated into the statistical micro-contact Greenwood and Williamson model (GW model) to obtain the asperity contact stiffness. The revised contact stiffness at the rough faulty gear interface is obtained from the parallel action of the asperity contact stiffness and oil film stiffness under load-sharing concept. The dynamic responses of the gear system are analyzed using the established mesh stiffness model through the six degrees of freedom translational-torsional dynamic model, in which the dynamic meshing force is calculated iteratively using the transit surface topography and geometrical parameters along the line of contact instead of a quasi-static meshing force. Effects of multi-parameters as surface roughness, spalling fault size, and lubricant on the mesh characteristics and dynamic responses of the gear system are further investigated and discussed.

Investigation of mesh force features under different planet tooth faults in planetary gearboxes

The mesh force of planetary gearboxes is the major excitation source of vibration. Thus, comprehending how gear faults impact the mesh force is essential in identifying specific fault information from the vibration response for accurate fault diagnosis. In this paper, the internal mesh force and mesh stiffness models of the planetary gearbox are established to depict the influence mechanism of planet tooth faults on the internal mesh force. Further, the theoretical internal mesh force features are validated via the ring tooth root strain, where the strain simulation and measurement are carried out, and a strain separation method is developed to obtain the actual mesh force features. The experimental and theoretical results both demonstrate that different planet tooth faults exhibit specific phase and trend features in the internal mesh force, which provides a foundation for tooth fault classification in planetary gearboxes.

Vibration analysis of a double-row planetary gear set considering the sun gear axial position.

Double-row planetary gear set (PGS) is a common form of the PGS, which is relatively more complex than the regular PGSs. It consists of one sun gear, several long planets, several short planets, two ring gears, and one carrier. Due to the significantly wider tooth width of the long planet compared to the sun gear, the axial meshing position between the sun gear and the long planet can be adjusted. The vibrations of PGS should vary with different axial meshing positions. If the axial position of the sun gear is optimized, the vibrations of PGS can be reduced. This work establishes a dynamic model of a double-row PGS. The dynamic model considers the mesh forces of the gear pairs and the supporting forces of the bearing. The effect of the sun gear axial position on the sun gear and ring gear #2 vibrations are investigated. Finally, the recommended axial position for the sun gear is provided.