Dynamic Mesh Force Research Articles

A spatial dynamics model for heavy-haul electric locomotives considering the dynamic coupling effect of gear transmissions

A locomotive is usually powered by the electromagnetic torque which is transmitted from the traction motor to the wheelset by gear transmission. In order to investigate the dynamic coupling effects from the gear transmission subsystems on the entire locomotive dynamics system, a comprehensive spatial locomotive dynamics model that considers the dynamic coupling effect of the gear transmissions is developed based on the multibody dynamics theory. In this model, the moved Marker technique is employed to calculate the dynamic mesh force of the gear pairs through which more accurate time-varying gear mesh stiffness excitations could be imported, which is the core of this dynamic model. Then, the established locomotive dynamics model is validated by comparing with the experimental test results. Finally, the dynamic effects of the gear transmissions are revealed by comparing with the results from the traditional locomotive dynamics model without considering the dynamic excitations from the gear transmissions. The results indicate that the gear transmissions have negligible effects on the vibrations of the carbody and the bogie frame, and on the lateral vibrations of the motor and the wheelset. However, the gear transmissions have significant effects on the vertical and, in particular, the longitudinal vibrations of the motor and the wheelset. Thus, it is suggested that the dynamic effects of the gear transmissions are considered in the locomotive dynamics modeling, especially when the vibrations of the motors and the wheelsets are taken into account.

Dynamic meshing force and blunt effects on atomistic scale ductile-brittle behavior of the crack in bcc iron

This work investigates the dynamic meshing force and blunt effects on atomistic scale ductile-brittle behavior of the crack in bcc iron through molecular dynamics. Two engineering factors including upload ratio and contact ratio are introduced to reveal the effects of force amplitude and distribution. Under different upload and contact ratios, normal stress fields are diverse and crack can propagate in ductile-to-brittle, weak ductile, and strong ductile ways. The increase of blunt layer leads to modest increase in critical applied load for crack ductile propagation, but it leads to obvious enhancement of crack toughness during single-tooth meshing.

Dynamic Response Analysis for NW Planetary Gear Transmission Used in Electric Wheel Hub

Taking the NW planetary gear transmission of an electric wheel hub as the research object, the mesh model was developed to calculate the mesh parameters using Masta. Then the lump parameter method was used to establish the dynamic model of the NW planetary transmission system considering the time-varying mesh stiffness, transmission error and bearing stiffness. The impacts of the torque load on the dynamic characteristics including the dynamic mesh force, center trajectory, offsets and load sharing coefficients were investigated. Results show that the dynamic mesh force waveform and spectral characteristics of each planetary gear at high and low speeds under the rated and maximum torque load are almost identical. Compared to the peak response at speed 485 rpm and 1770 rpm, both the magnitude and location of the third response at relative high speed about 4300 rpm are increased due to the load increasing. The mean and fluctuation range of the offsets in the radial direction are both larger than the tangential direction. As the load increases, the mean value of the radial offset increases and the magnitude decreases significantly. The mean value of the tangential offset decreases significantly, but the magnitude increases first and then decreases. The load sharing characteristics of the low-speed stage of the NW planetary gear is better than the first stage. With the increase of the load, the load sharing performance of a two-stage planetary transmission gets better and the difference in load sharing between the high-speed and low-speed stages also decreases.

On Dynamic Mesh Force Evaluation of Spiral Bevel Gears

The mesh model and mesh stiffness representation are the two main factors affecting the calculation method and the results of the dynamic mesh force. Comparative studies considering the two factors are performed to explore appropriate approaches to estimate the dynamic meshing load on each contacting tooth flank of spiral bevel gears. First, a tooth pair mesh model is proposed to better describe the mesh characteristics of individual tooth pairs in contact. The mesh parameters including the mesh vector, transmission error, and mesh stiffness are compared with those of the extensively applied single‐point mesh model of a gear pair. Dynamic results from the proposed model indicate that it can reveal a more realistic and pronounced dynamic behavior of each engaged tooth pair. Second, dynamic mesh force calculations from three different approaches are compared to further investigate the effect of mesh stiffness representations. One method uses the mesh stiffness estimated by the commonly used average slope approach, the second method applies the mesh stiffness evaluated by the local slope approach, and the third approach utilizes a quasistatically defined interpolation function indexed by mesh deflection and mesh position.

Vibration response from the planetary gear with flexible ring gear

This paper investigates the vibration response from the planetary gearbox with a flexible ring gear, supported by various constraints, resulting in quite different vibration spectra. The ring gear with its supports was modelled in ANSYS as a transient finite element moving load beam problem to formulate the vibration response. The moving load was represented by the dynamic gear mesh forces, which were obtained from a planetary gear lumped-parameter model. Two support conditions were analysed in this research. In the uniform support condition, it was found that the modulation effect from the carrier arm rotation can be accurately predicted and the vibration spectra matched well with previous publications. In the pin support condition, the spectra from different ring gear rim locations can result in different vibration spectra and it provides a primer guideline for further understanding the effect of the sensor location on the planetary gear vibration monitoring.

Vibration response from the planetary gear with flexible ring gear

This paper investigates the vibration response from the planetary gearbox with a flexible ring gear, supported by various constraints, resulting in quite different vibration spectra. The ring gear with its supports was modelled in ANSYS as a transient finite element moving load beam problem to formulate the vibration response. The moving load was represented by the dynamic gear mesh forces, which were obtained from a planetary gear lumped-parameter model. Two support conditions were analysed in this research. In the uniform support condition, it was found that the modulation effect from the carrier arm rotation can be accurately predicted and the vibration spectra matched well with previous publications. In the pin support condition, the spectra from different ring gear rim locations can result in different vibration spectra and it provides a primer guideline for further understanding the effect of the sensor location on the planetary gear vibration monitoring.

Frequency and Vibration Characteristics of High‐Speed Gear‐Rotor‐Bearing System with Tooth Root Crack considering Compound Dynamic Backlash

Considering the microstructure of tooth surface and the dynamic characteristics of the vibration responses, a compound dynamic backlash model is employed for the gear transmission system. Based on the fractal theory and dynamic center distance, respectively, the dynamic backlash is presented, and the potential energy method is applied to compute the time‐varying meshing stiffness, including the healthy gear system and the crack fault gear system. Then, a 16‐DOF coupled lateral‐torsional gear‐rotor‐bearing transmission system with the crack fault is established. The fault characteristics in the time‐domain waveform and frequency response and statistics data are described. The effect of crack on the time‐varying meshing stiffness is analyzed. The vibration response of three backlash models is compared. The dynamic response of the system is explored with the increase in crack depth in detail. The results show that the fault features of countershaft are more obvious. Obvious fluctuations are presented in the time‐domain waveform, and sidebands can be found in the frequency domain responses when the tooth root crack appears. The effect of compound dynamic backlash on the system is more obvious than fixed backlash and backlash with changing center distance. The vibration displacement along meshing direction and dynamic meshing force increases with the increase in crack depth. Backlash and variation of center distance show different tendencies with increasing crack depth under different rotational speeds. Amplitude of the sidebands increases with crack depth increasing. The amplitude of multiplication frequency of rotational frequency has an obvious variation with growing crack depth. The sidebands of the multiplication frequency of meshing frequency show more details on the system with complex backlash and crack fault.

Research on Dynamic Load-Sharing Characteristics of Two-Stage Asymmetric Star Gear System

It is well known that the asymmetric gears of the transmission system enhances the load carrying capacity of system, but there is no relevant conclusion about the dynamic load-sharing characteristics of the asymmetric gear transmission system. In order to analyze the dynamic performance of an asymmetric gear system, taking two-stage asymmetric helical gear star drive system as the research object, the load-sharing model of the two-stage asymmetrical helical star gear system is established by the centralized mass method and Newton's second law. The load sharing characteristic of the star gear is studied about the floating member and the tooth profile pressure angle. The influence of eccentricity error, load and input speed on the load sharing performance of the system is analyzed. Based on ADAMS virtual prototype model, through the simulation analysis of the dynamic meshing force of gears, the load sharing coefficient of each star gear is calculated, compare the results with the MATLAB solution to verify the correctness of the theory.

Research on vibration characteristics of multistage gears transmission system driven by internal and external excitation

In order to accurately describe the complex transmission systems and clarify the effects of internal and external excitation on the vibration characteristics for large complex transmission systems, a dynamics model considering gear meshing error and time-varying meshing stiffness is established at two-stage planetary gears systems. The coupling model is established by matrix set method for two-stage planetary gears and multistage spur gears transmission systems. The random load excitation verified by experiments is the external excitation in the system, and the excitation caused by the time-varying meshing stiffness and meshing error is the internal excitation. The research on the response of the vibration systems shows that the internal excitation caused by gear meshing stiffness and gear meshing error has important influence on the dynamic load behavior of spur gears transmission in complex systems. For the planetary system with heavy external load, the dynamic behavior mainly depends on the external load, and the influence of internal excitation on the dynamic meshing force is less than that of the external excitation for the planetary system. The external excitation mainly affects the low-frequency region of the dynamic meshing force for the system, and the internal excitation affects the high-frequency region of the dynamic force for the system. The frequency influence interval of the internal excitation is much larger than that of the external excitation.

Dynamic Mesh Forces in Accounting of the Time Variable Mesh Stiffness of a Gear Train

The paper considers the problems connected with the periodic variation of the tooth stiffness during the engagement in a spur gear train that arise due to the different number of teeth involved in torque transmission. Thus, the process of engagement is accompanied by a redistribution of the dynamic forces between the teeth at the boundaries of the engagement phases from the one-pair contact to the double-pair contact. As a result, it can cause forced and parametric vibrations. The dynamic mesh forces caused by kinematic error and time variable mesh stiffness are associated with the periodic mesh of the teeth. It is further shown that the load on the meshing pairs of teeth can be several times higher than the nominal forces. As a result, the operation of a machine is accompanied by high level of noise and vibration.

Simulation of oil whirl for geared rotor journal bearing system

This study developed a dynamic model of gear-pair system, involving nonlinear oil film force of hydrodynamic bearings and the gear mesh force with backlash. Based on this model, numerical simulations are made about instability led by the oil whirl in geared rotor journal bearing system. By comparing responses between single rotor journal bearing system and geared rotor system, evolution of oil whirl from individual rotor to adjacent geared rotors is examined. The results show that dynamic mesh force can transfer the excitations from the adjacent rotors, making different influences on the stability for individual rotors. The stabilities of the geared rotors are not independent with each other, but coupled by the mesh force. This coupling can be accompanied with tooth separation.

Dynamic characteristics of the planetary gear train excited by time-varying meshing stiffness in the wind turbine

Wind power has attracted increasing attention as a renewable and clean energy. Gear fault frequently occurs under extreme environment and complex loads. The time-varying meshing stiffness is one of the main excitations. This study proposes a 5 degree-of-freedom torsional vibration model for the planetary gear system. The influence of some parameters (e.g., contact ratio and phase difference) is discussed under different conditions of a single teeth pair and double pairs of teeth. The impact load caused by the teeth face fault, ramped load induced by the complex wind conditions, and the harmonic excitation are investigated. The analysis of the time-varying meshing stiffness and the dynamic meshing force shows that the dynamic design under different loads can be made to avoid resonance, can provide the basis for the gear fault location of a wind turbine, and distinguish the fault characteristics from the vibration signals.

An Efficient Hybrid Analytical-Computational Method for Nonlinear Vibration of Spur Gear Pairs

This work develops a hybrid analytical-computational (HAC) method for nonlinear dynamic response in spur gear pairs. The formulation adopts a contact model developed in (Eritenel, T., and Parker, R. G., 2013, “Nonlinear Vibration of Gears With Tooth Surface Modifications,” ASME J. Vib. Acoust., 135(5), p. 051005) where the dynamic force at the mating gear teeth is determined from precalculated static results based on the instantaneous mesh deflection and position in the mesh cycle. The HAC method merges this calculation of the contact force based on an underlying finite element static analysis into a numerical integration of an analytical vibration model. The gear translational and rotational vibrations are calculated from a lumped-parameter analytical model where the crucial dynamic mesh force is calculated using a force-deflection function (FDF) that is generated from a series of static finite element analyses performed before the dynamic calculations. Incomplete tooth contact and partial contact loss are captured by the static finite element analyses and included in the FDF, as are tooth modifications. In contrast to typical lumped-parameter models elastic deformations of the gear teeth, including the tooth root strains and contact stresses, are calculated. Accelerating gears and transient situations can be analyzed. Comparisons with finite element calculations and available experiments validate the HAC model in predicting the dynamic response of spur gear pairs, including for resonant gear speeds when high amplitude vibrations are excited and contact loss occurs. The HAC model is five orders of magnitude faster than the underlying finite element code with almost no loss of accuracy.

Influence of oil film stiffness on natural characteristics of single-rotor three-input helicopter main gearbox

The elastohydrodynamic lubrication (EHL) contact model is established, the oil film stiffness is calculated based on Dowson-Higginson empirical minimum thickness equation. The vibration model of single-rotor three-input helicopter main reducer is proposed by lumped mass method, and nonlinear factors like oil film stiffness, dynamic meshing force are taken into account. The influence of oil film stiffness on system natural frequency is analyzed as well. The results show that oil film stiffness of the internal and external meshing pairs in the planetary gear system have greater impact on the natural frequency, which tends to destabilize the system. Therefore, the planetary gear train is the most crucial branch regarding the system splash lubrication. When all the oil film stiffness in the system are greater than 4×109 N/m, the natural frequencies tend to be stable. This study can provide the theoretical reference for the lubrication characteristics in the single-rotor multi-input helicopter.

Hybrid dynamic modeling of shearer's drum driving system and the influence of housing topological optimization on the dynamic characteristics of gears

The drum shearer is one of the main equipments of the long-wall mining system that has been widely used in coal mining for decades. Influenced by large fluctuation and intensive impact of drum load, the drum driving system is a weak part of the drum shearer due to the large dynamic deformation on ranging arm housing and the changes of gear meshing state. Since previous studies did not consider the coupling effects of housing and gearing transmission system, this study is concerned with hybrid finite element/lumped parameter dynamic modeling of the housing-transmission coupled system. In order to model the drum driving system, it is subdivided into two substructures: housing and transmission system. The housing is modeled by finite element method while the transmission system is modeled by lumped parameter method. The dynamic sub-structuring method (DSM) is used to develop a hybrid dynamic model, taking elastic coupling between the housing and transmission system into consideration. Then the influence of housing topological optimization on the dynamic characteristics of drum driving system is also analyzed through the hybrid dynamic model. The housing topological optimization is conducted through the Optistruct solver in Hypermesh, aiming at increasing the natural frequency of housing. It can be concluded that the ranging arm housing topological optimization could reduce the dynamic deformation of the housing and thus also reduce the equivalent mesh misalignment. However, the influence of housing topological optimization on the dynamic meshing force is not very significant.

Dynamic characteristics of a planetary gear system based on contact status of the tooth surface

Studies on the planetary gear have attracted considerable attention because of its advantages, such as compactness, large torque-to-weight ratio, vibrations, and high efficiency, which have resulted in its wide applications in industry, wind turbine, national defense, and aerospace fields. We have established a novel dynamic model of the planetary gear transmission by using Newton’s theory, in which some key factors such as time-variant meshing stiffness, phase relationships, and tooth contact characteristics are considered. The influences of gear axial tipping, operating conditions, and the meshing phase on the contact characteristics and the dynamic characteristics were researched systematically. It was found that the contact area of the tooth surface was moved due to the axial gear tipping, which obviously affected the meshing stiffness. With the increase in the inclination angle of the sun gear, the meshing stiffness decreases, which produces an evident influence on the high natural frequency in the planetary transmission system. In terms of the dynamic characteristics of the system, the component of rotating frequency appeared in the dynamic meshing force of the sun gear and the planetary gear. Moreover, the floating track of the center wheel varied significantly and exhibited an oval distribution as the inclination angle of the sun gear changed. When the inclination angle of the sun gear increased, the rotating frequency component increased significantly, but the other meshing frequency components remained unchanged; meanwhile, the deformation of the floating track also increased. If the inclination angle of the sun gear changes, the vibration state of the system and the collision impact could become more serious, and the lifetime of the planetary transmission system will reduce. Furthermore, when the load was increased, we found that the gear-tooth contact zone transformed from line contact to surface contact, the meshing stiffness increased, the effect of high natural frequency on the planetary transmission system became more evident, but its low-order natural frequency remained stable. With regard to the dynamic characteristics of the system, the components of the major frequency at the external gearing remained unchanged, but the rotation frequency of the sun gear and the meshing frequency amplitude increased linearly with the increase in load. In conclusion, the variation in the meshing stiffness of the planetary gear system had minor impact on the low-order natural frequency, but had a significant impact on the high natural frequency of the planetary transmission system due to the phase variation of the gear.

Surrogate‐Based Multisource Sensitivity Analysis of TBM Driving System

TBM cutterhead driving system is generally an extraordinarily large and complex machine containing lots of parameters; understanding and assessment of its dynamic characteristics are a great challenge as each of these parameters has uncertainty. In this work, a hierarchical modeling method for the dynamic model of the complex gear transmission system is proposed based on the generalized finite element modeling idea. On this basis, the whole machine dynamic model of cutterhead driving system is established; both the characteristics of vibration responses and the meshing force are revealed. Vibration responses under the action of simulated load are estimated and verified by comparing with the data measured on the tunneling field, where the error is about 18%~50%. With the vibration response of the key nodes and the dynamic meshing force for the system dynamic characteristic evaluation index, considering the change of input parameters such as external loads, material parameters, meshing parameters, and coupling parameters, the global parameter sensitivity of system dynamic characteristics is analyzed based on the technology of surrogate model. Finally, variation of dynamic characteristics considering the interaction of polytypic parameters is obtained.

Locomotive dynamic performance under traction/braking conditions considering effect of gear transmissions

ABSTRACTTraction or braking operations are usually applied to trains or locomotives for acceleration, speed adjustment, and stopping. During these operations, gear transmission equipment plays a very significant role in the delivery of traction or electrical braking power. Failures of the gear transmissions are likely to cause power loses and even threaten the operation safety of the train. Its dynamic performance is closely related to the normal operation and service safety of the entire train, especially under some emergency braking conditions. In this paper, a locomotive–track coupled vertical–longitudinal dynamics model is employed with considering the dynamic action from the gear transmissions. This dynamics model enables the detailed analysis and more practical simulation on the characteristics of power transmission path, namely motor–gear transmission–wheelset–longitudinal motion of locomotive, especially for traction or braking conditions. Multi-excitation sources, such as time-varying mesh stiffness and nonlinear wheel–rail contact excitations, are considered in this study. This dynamics model is then validated by comparing the simulated results with the experimental test results under braking conditions. The calculated results indicate that involvement of gear transmission could reveal the load reduction of the wheelset due to transmitted forces. Vibrations of the wheelset and the motor are dominated by variation of the gear dynamic mesh forces in the low speed range and by rail geometric irregularity in the higher speed range. Rail vertical geometric irregularity could also cause wheelset longitudinal vibrations, and do modulations to the gear dynamic mesh forces. Besides, the hauling weight has little effect on the locomotive vibrations and the dynamic mesh forces of the gear transmissions for both traction and braking conditions under the same running speed.

Research on vibration characteristics of gear-coupled multi-shaft rotor-bearing systems under the excitation of unbalance

To find out the effect of eccentricity of a gear wheel on inherent characteristics of a gear-rotor system, this paper establishes a pair of general transverse-rotational-axial-swinging multi degrees of freedom coupling helical gear meshing dynamic model based on the finite element method (FEM). Considering the influence of the azimuth, the meshing angle, the helix angle and the rotation direction of driving shaft on mesh stiffness matrix, it analyzes the effect of mesh stiffness and mesh damping on the inherent characteristics and the transient response of the system. It obtains the displacement response curve and the dynamic meshing force curve of all nodes responding to the incentives of static transmission error and unbalance while considering mesh damping. It concludes that the effects of gear coupling and eccentricity of gear wheel should be taken into account in a multi-parallel-shaft gear meshing rotor system.

Influence analysis of system parameters on characteristics of the nutation drive with double circular arc spiral bevel gears

Gear transmission systems are one of the most frequently used systems for power transmission. The characteristics of a gear transmission system have important guiding significance in the design, manufacture and application of transmissions. This paper focuses on the influence of system parameters on the characteristics of a specific type of gear transmission, the nutation drive with double circular arc spiral bevel gears. Based on the transmission ratio analysis of single-stage and two-stage nutation drive systems, the system parameters, including nutation angle, gear spiral angle, pitch angle and cone distance, were defined. An analysis of the influence of system parameters on transmission efficiency was performed. Furthermore, the influence of system parameters on axial misalignment and cone displacement error was investigated. Finally, by changing the input frequency, input load, nutation angle, and spiral angle, variation regularity of the dynamic meshing force was obtained. A transmission performance analysis based on the influence of system parameters was achieved and provides the theoretical basis for better design of the nutation drive with double circular arc spiral bevel gear.