Vertical Vibration Acceleration Research Articles

Fatigue Life Prediction and Verification of Railway Fastener Clip Based on Critical Plane Method

Accurately predicting the fatigue life of fastener clips is crucial for improving material processing technology, enhancing the anti-fatigue design level, and guiding the maintenance and repair of track structures. Conventional methods that solely evaluate the fatigue life of fastener clips based on the uniaxial stress index under displacement loads may lead to significant errors. In this paper, the stress field of a type-III clip under displacement loading conditions was numerically simulated based on fatigue test standards, and the fatigue life of the clip was analyzed using the Fatemi–Socie (FS) multiaxial fatigue criterion based on the critical plane method. A comparison with standard fatigue test results revealed that, under non-resonance conditions, the predicted position of the fatigue critical plane of the fastener clip coincided with the fracture surface observed at the middle of the measured small arc, with a life prediction error of 7.3%. To further investigate the predictive capability of the FS multiaxial fatigue criterion for the fatigue life of the fastener clip under resonance conditions, the stress levels of the clip under non-resonance and resonance conditions were compared through on-site testing, and the effects of inertial loads caused by vertical and lateral vibration acceleration on the stress field of the clip were analyzed in numerical simulation according to the results of clip acceleration tests; the fastener clip’s resonance fracture position and fatigue life were also predicted based on the aforementioned multiaxial fatigue criterion. To verify the accuracy of the predicted results, a testing method was proposed that equates the high-frequency resonant inertial load of the fastener clip to a low-frequency additional preload under the premise of consistent stress fields. A comparison with the numerical simulation results shows that considering only vertical inertial loads would result in a discrepancy between the measured fracture location and the actual one. Considering both vertical and lateral inertial loads, the fracture location (at the heel of the small arc) under resonance conditions could be accurately determined, with a life prediction error of 13.8%. Compared to the non-resonant displacement loading condition, the inertial loads caused by acceleration under resonance conditions led to a reduction in fatigue life of approximately 77.8%.

Dynamic analysis of aircraft towing slip-out system considering vertical wheel constraints

Abstract To analyze the vertical dynamic characteristics of the aircraft towing system under different constraints on the nose landing gear wheels of the aircraft during the towing slip-out mode, a dynamic model of the towing system considering the constraints between the clamping mechanism and the aircraft nose landing gear wheels was established based on the general towing system dynamic model. On this basis, an analysis was conducted to determine whether considering the aircraft wheel constraints affects the vertical vibration acceleration of the towing vehicle and the nose landing gear in low-speed (10 km/h) and high-speed (40 km/h) operating conditions. With the consideration of constraints at both ends of the aircraft wheels, the vertical acceleration of the towing vehicle's center of mass increased by 153% and 172% at low speed and high speed, respectively, compared to not considering the aircraft wheel constraints. Additionally, with the consideration of constraints at both ends of the aircraft wheels, the vertical acceleration of the nose landing gear's center of mass decreased to 20% and 57% at low speed and high speed, respectively, compared to not considering the aircraft wheel constraints. An analysis of the vertical vibration acceleration of the towing vehicle under different wheel constraint conditions found that the RMS value of the vertical vibration acceleration of the towing vehicle's center of mass was minimized when the clamping angles of the clamping mechanism to the nose landing gear wheels were 63° and 64°, respectively. Under this clamping angle, the influence of the clamping forces at both ends of the clamping mechanism on the vertical vibration acceleration of the towing vehicle was minimal. The research results provide valuable reference for the direct constraints between the clamping mechanism and the nose landing gear wheels in the aircraft towing slip-out system.

Monitoring and analysis of railway-induced vibration and structure-borne noise in a transit oriented development project

With the rapid development of modern cities, the construction of over-track buildings and buildings along the subway line are increasing gradually. In order to evaluate the influence of rail transit on these buildings, the railway-induced vibration and structure-borne noise of subway stations and buildings in a Transit Oriented Development (TOD) project are monitored and analyzed in this paper. The vibration monitoring data in the subway station shows that the vibration acceleration response of the measuring point in the station caused by the train entering and leaving the station is the largest in the vertical direction, followed by the along-track direction, and the vertical-track direction is the smallest. The corresponding predominant frequency of vibration is usually in the range of 100 Hz-200 Hz. The vibration monitoring data of the building foundation along the subway line shows that the railway-induced vibration of the building foundation along the track near the subway station decreases with the reduction of the distance from the subway station. The monitoring vibration results of the over-track building on the metro depot are different from the buildings near the main line. The predominant frequency of the vibration at the measuring point is in the range of 30 Hz-40 Hz. The small vertical vibration acceleration response of the measuring point corresponds to a high vibration level. In addition, the amplitude of railway-induced vibration in some building rooms near the metro depot is basically consistent with the amplitude of background vibration, but the monitoring value of the structure-borne noise is obviously higher than the background noise. The research results of this paper show the influence of railway-induced vibration on the over-track buildings and the buildings along the subway line, which has important reference value for the comprehensive development of rail transit.

Dynamic interactions of tram-turnout coupling system in embedded turnout area

Embedded turnout is one of the key facilities in the embedded track network of modern tram systems. In this study, the damping performance and track stiffness of an embedded turnout are tested on site. A multi-rigid body dynamics model of the tram and a finite-element dynamics model of the embedded turnout are established, and the two models are coupled based on the wheel-rail contact theory for the turnout area. Next, the dynamic responses of the tram passing through the embedded turnout are analyzed. The results show that the embedded turnout has favorable damping performance. The high stiffness of variable section rails at the switch and frog would lead to an increase in the wheel-rail dynamic force. When the tram passes through the embedded turnout, the wheel-rail vertical force reaches maximum values of 106.3 and 35.2 kN at the frog and switch, respectively; the maximum wheel derailment coefficient and wheel weight reduction rate are 0.49 and 0.57, respectively, which are within the safety limit specified in the Standards; the maximum lateral and vertical vibration accelerations of the tram body are 0.38 and 0.71 m/s2, respectively, satisfying the comfort requirements; the wheel–rail wear work at the switch is greater than that at the frog.

Performance of Floating Slab Track with Rubber Vibration Isolator

This study systematically introduces a floating slab track (FST) with rubber vibration isolator (RVI) and investigates its behavior in urban rail transit. The FEM is used for modal analysis to clarify the modal parameters of the FST system. A vehicle–slab track coupling sub-model and a tunnel–soil coupling sub-model were established and the propagation law was analyzed by calculating the vertical vibration accelerations beneath the shield wall as well as the vertical vibratory acceleration levels of the surrounding soil. A wheel-set drop test was carried out to verify the actual vibration isolation effect compared with the numerical models. The results reveal that the vibratory acceleration levels at the distance of 20[Formula: see text]m from the tunnel center-line basically meet the requirements for vibration in most areas of a city. The variation trend of the vibratory acceleration level measured in laboratory tests agrees well with the calculated values from the numerical simulation. The attenuation amplitude of the levels reaches 19.33[Formula: see text]dB with the German high disturbance irregularity and 20.05[Formula: see text]dB with the short-wave irregularity in the simulation, and the levels are reduced by 45–58[Formula: see text]dB in laboratory tests which demonstrate the FST with RVI performs well in vibration isolation.

Simulation Analysis and Online Monitoring of Suspension Frame of Maglev Train

A maglev train is a new type of high-speed railway transportation. A high-temperature superconducting (HTS) maglev system is one of the typical representatives in the field of maglev trains. In order to research the levitation characteristics of an HTS maglev train, the force characteristics and operation performance of the train were researched. However, at present, there is still no research that simulates the real load situation of a running maglev train while analyzing the suspension frame. Regarding this issue, in this paper, the suspension frame is simulated and analyzed to simulate the real load situation of a maglev train. The results show that the suspension frame of an HTS maglev train can bear corresponding loads under different working conditions, and its strength and stiffness meet the requirements of use, safety, and reliability. Random irregularity in the permanent magnet track of an HTS maglev train route is inevitable, which will make the suspension frame produce a vibration response under different running speeds of the train. Vibration of the suspension frame of the train is inevitable. For the electromagnetic levitation (EMS) train, researchers considered monitoring the train status. However, at present, there is no suspension frame condition monitoring device for an HTS maglev train. In addition, the levitation height of the suspension frame affects the suspension performance and traction performance of the vehicle, and the vibration of the suspension frame during running affects the dynamic performance and safety of the suspension frame and the vehicle. Regarding the issue above, through a suspension frame monitoring system, the lateral and vertical vibration acceleration and levitation height of the suspension frame are monitored at different train speeds. The maximum value of vibration acceleration and the fluctuation range of levitation height are within the safe range. It is verified that the simulation analysis of the suspension frame of an HTS maglev train is correct, the suspension frame is safe, and the train can run safely.

Dynamic analysis on the structure of metro station under high-speed railway load

High-speed railways often run over underground metro stations. Dynamic load induced by high-speed train can influence the internal force of underground structure and hence can pose danger to the underground structure. Hence, it is necessary to estimate the safety of underground structure due to high-speed train load. In this paper, the effects of dynamic load induced by high-speed train on metro station are investigated by carrying out three-dimensional numerical analysis. Guinan high-speed railway, which is designed to run over Jinqiao metro station in Nanning, Guangxi province of China are adopted as the background of this case study. The hardening soil model with small-strain stiffness was adopted to model the behaviour of soil. Two typical speed of railway train (i.e., 160 km/h and 350 km/h) are considered in this study. Based on the numerical analysis, vertical vibration acceleration and bending moment of the structure of the metro station are presented and analysed.

Performance Analysis of Short-Span Simply Supported Bridges for Heavy-Haul Railways with A Novel Prefabricated Strengthening Structure

A novel prefabricated strengthening structure (NPSS) is proposed to improve the vertical stiffness and load-bearing capacity of existing short-span bridges for heavier axle-load trains passing through. The strengthening principle of the NPSS is revealed through theoretical derivation. A refined calculation model is prepared to investigate the effects of two important parameters on the structural behavior of the bridge, including the support stiffness and the installation location of the NPSS. The calculation model is also verified with four-point bending test of a bridge removed from a heavy-haul railway. With the calculation model and the response surface methodology (RSM), the functional relationships among the crucial mechanical indexes of the bridge and the two parameters of the NPSS are methodically established. Thus, the optimal values of the parameters are determined via a multi-objective optimization model and the analysis hierarchy process-fuzzy comprehensive evaluation method. Furthermore, the feasibility of the optimal parameters is appropriately verified based on simulations of the vehicle–track–bridge dynamics. The existence of the NPSS with optimal parameters could enhance the vertical stiffness of the bridge by 21.0% and bearing capacity by 19.5%. In addition, it could reduce the midspan dynamic deflection amplitude by 23.4% and vertical vibration acceleration amplitude of the bridge by 25.2%. The results of the study are expected to contribute to the capacity development and rehabilitation of existing heavy-haul railways with low cost and convenient construction without railway outage.

Effects of different wheel wear positions on dynamic performance of metro vehicles

PurposeMetro wheels running on different lines can undergo wear at different positions. This paper aims to investigate the effects of wheel wear at two typical positions, i.e. wheel flange and tread, on the dynamic performance of metro vehicles and analyzes the differences, with an aim of providing theoretical support on wheel reprofiling for different metro lines.Design/methodology/approachWheel profile data were measured on two actual metro lines, denoted A and B. It was observed that wheel wear on Lines A and B was concentrated on flanges and treads, respectively. A metro vehicle dynamics model was built using multibody dynamics software SIMPACK. Then it was applied to analyze the differences in effects of wheel wear at different positions on vehicle dynamic performance (VDP) for various speeds (50, 60 and 70 km/h) and line conditions (straight line, R1000m, R600m and R300m curves). Critical speed and vibration acceleration were used as indicators of VDP during linear motion (on straight track), while VDP during curvilinear motion (on curved track) was evaluated in terms of wheel/rail lateral force, wheel/rail vertical force, derailment coefficient and wheel unloading rate.FindingsFirst, compared to wheel profile with tread wear, wheel profile with flange wear showed better performance during linear motion. When the distance traveled reached 8 × 104 and 14 × 104 km, the vehicle’s critical speed was 12.2 and 21.6% higher, respectively. The corresponding vertical and lateral vibration accelerations were 59.7 and 74.8% lower. Second, compared to wheel profile with flange wear, that with tread wear showed better performance during curvilinear motion, with smaller wheel/rail lateral force, derailment coefficient and wheel unloading rate. When the vehicle speed was 50, 60 and 70 km/h, the maximum difference in the three indicators between the two wheel profiles was 40.2, 44.7 and 23.1%, respectively. For R1000m, R600m and R300m curves, the corresponding maximum difference was 45.7, 69.0 and 44.4%, respectively.Practical implicationsThe results of the study can provide a guidance and theoretical support on wheel reprofiling for different metro lines. On lines with large proportions of curved sections, metro vehicles are more prone to wheel flange wear and have poorer dynamic performance during curvilinear motion. Therefore, more attention should be paid to flange lubrication and maintenance for such lines. On lines with higher proportions of straight sections, metro vehicles are more prone to tread wear and have poorer performance on straight sections. So, tread maintenance and service requires more attention for such lines.Originality/valueExisting research has focused primarily on the effects of wheel wear on VDP, but fails to consider the differences in the effects of wheel wear at different positions on VDP. In actual metro operation, the position of wheel wear can vary significantly between lines. Based on measured positions of wheel wear, this paper examines the differences in the effects of wheel wear at two typical positions, i.e. tread and flange, on VDP in detail.

Generalized mathematical formulation for active vibration control of rotating machines with voltage‐driven electrodynamic actuators between machine feet and steel frame foundation

AbstractIn the paper, a generalized mathematical formulation for active vibration control of rotating machines with voltage‐driven electrodynamic actuators between machine feet and steel frame foundation is derived. This generalized mathematical formulation is based on a state space description in the Laplace domain, where the state space vector is lead back, for considering the actuator forces. The aim of the paper is that this generalized mathematical formulation can be used now for arbitrarily models of rotating machines—1D‐, 2D‐, and 3D‐models—with voltage‐driven electrodynamic actuators between machine feet and steel frame foundation, and where the vertical vibration acceleration at each machine foot is lead back to a separate controller. Of course, this mathematical formulation can also be adopt easily to other boundary conditions. As an example, the generalized mathematical formulation is used here for a 1D‐model of a rotating machine, to calculate the poles and the frequency response functions.

Identification method for subgrade settlement of ballastless track based on vehicle vibration signals and machine learning

High-frequency train loads and complex environmental factors over a long period will inevitably cause subgrade settlement, an issue that adversely affects line smoothness. The existing monitoring methods are inefficient, manpower consuming and small in scope. This paper takes the subgrade settlement disease of the double-block ballastless track as the research object and proposes a subgrade settlement identification method based on vehicle vibration signals. In addition, it establishes a vehicle-track-subgrade vertical coupling model that combines feature extraction with algorithms such as support vector machines (SVMs) and convolutional neural networks (CNNs) to accurately identify subgrade settlement diseases on ballastless tracks. The results show: I) the subgrade settlement is far more impactful than fastener failure and debonding of the supporting layer on the vehicle vibration, with the main frequency band concentrated in 0 to 10 Hz, and the vertical vibration acceleration of the vehicle body and bogie can be used as a sensitive feature to identify ballastless track subgrade settlement, II) both the particle swarm optimization (PSO)-SVM and CNN-SVM algorithms can effectively determine the existence of subgrade settlement and the values of the settlement wavelength and amplitude. Both algorithms run a 100 % identification of subgrade settlement, with the lowest identification rates of settlement wavelength being 97.56 % and 100 %, respectively and the lowest identification rates of amplitude being 84.78 % and 97.56 %, respectively. In general, the overall accuracy of the CNN-SVM always outperforms PSO-SVM, and III) changes to the vehicle passing speed will create a more obvious interference effect on the identification of the settlement amplitude. For the PSO-SVM algorithm, the identification rate for the amplitude has a difference of up to 8.70 %, while this is 2.44 % for the CNN-SVM algorithm, indicating the CNN-SVM algorithm is more robust than the PSO-SVM algorithm.

A prediction method for indoor vibration over metro depot throat area based on coupled interactions of wheel-rail

Environmental vibration pollution is the primary environmental problem faced by the superstructure of metro depots. The throat area is especially prone to high wheel-rail impact vibration due to multiple joints and turnouts, which may cause high annoyance to the residents in the superstructures both on the upper cover and surrounding areas. In this paper, based on the coupled dynamic analysis of wheel-turnout, a prediction method to evaluate the indoor vibration of over-track building is established. Firstly, subway turnout with variable sections on switch, connection part and frog and vehicle models are established, and wheel-rail force is obtained through multibody dynamics calculation. Secondly, the track-foundation-structure finite element numerical model was built, loading the wheel-rail force excitation, then the indoor vibration could be obtained. The accuracy of this method is verified taking a 32 story residential superstructure in North China as an example. The vertical vibration accelerations were measured on every other floor when a A-type train travelled on a 7-turnout. The error between the measured data and the calculated results was within 5%, indicating that this prediction method has certain accuracy. The research results have certain guiding significance for the prediction and control of vibration in metro depot.

Vehicle-track coupled dynamics model for superconducting electrodynamic suspension train

In the previous studies of superconducting EDS train, the magneto-electric coupling between superconducting magnets (SCMs) and null-flux coils (NFCs), was equivalent to a vibration system with constant stiffness. This premise has decoupled the magnetic/track interaction and is not able to study the dynamics issues in an accurate and comprehensive level. Therefore, the vehicle-track coupled dynamics model of superconducting EDS train, with magneto-electric-force coupling fully considered, was established to explore the vehicle-track interaction relationship in this paper. A mathematical model based on Newton’s laws and 3-D dynamic co-simulation model were built respectively by Simulink and MATLAB-SIMPACK to compare the operating performances with the time/frequency domain. Meanwhile, the dynamic electromagnetic forces were calculated by dynamic circuit theory rather than merely assuming the constant stiffness. The dynamic responses of suspension vehicle show that, the vibration of carbody and frame are mainly concentrated about 1 Hz and 5 Hz respectively. The use of equivalent model in the previous studies has overestimated the negotiation capacity of superconducting EDS train. Furthermore, the vertical vibration accelerations of frame in the coupled model are relatively larger, whereas the lateral vibration is comparatively smaller. Therefore, the electromagnetic calculation of superconducting EDS train with constant stiffness overestimates/underestimates the dynamic performances.

Parameters of the oscillatory process of the sleeper base in the area of the rail joint when using elastic spacers

The article presents the results of field tests of under-rail pads in order to assess the effect of stiffness and the number of standard and experimental pads-shock absorbers on the amplitude-frequency characteristic of vibrations that occur in the ballast layer in the rail joint zone when the rolling stock is moving. To achieve this goal, we measured the vertical vibration accelerations arising during the passage of trains in the area of the rail joint with a different number of standard under-rail shock absorbers TsP-204-M-ARS (standard) and Getzner Sylodyn NF shock absorber pads with increased elasticity (experimental). On the basis of the obtained values, the amplitude-frequency characteristic of the oscillatory process was determined by means of the Fourier transform. The main (carrier) frequencies, at which the maximum amplitudes of vibration accelerations are recorded, are determined, first of all, not by the material of the damper pad, but by the magnitude of the force effect. The use of experimental shock absorber pads allows to reduce and redistribute the vibration energy transmitted to the ballast layer.

A Study on the Train-Induced Vibration Responses of Heavy Haul Railway Subgrade in Seasonally Frozen Regions Using Field Experiments

The dynamic response resulting from heavy haul train leads to the deterioration of the railway subgrade, especially those built in seasonally frozen regions. In this work, a typical heavy haul railway section in a seasonally frozen region is monitored on-site. The time domain and the frequency domain analysis of the subgrade vertical vibration acceleration, dynamic speed, and displacement during the non-frozen period and the frozen period are investigated. The results show that the vibration response of the subgrade is affected by various factors, including the train type, locomotive, traveling speed, train formation, heavy load, and the prevalent season. Further, it is observed that the maximum and average vertical acceleration of the subgrade, the vibration speed, and the dynamic displacement increase during the frozen period. However, the main frequency of the natural vibration remains significantly higher than that before freezing. Moreover, the frozen soil has a significant amplification effect both on the acceleration and the attenuation rate. Similarly, the subgrade’s vibration mode has a low frequency and high amplitude during the freezing period, and the dynamic response characteristics become increasingly apparent as the axle load increases.

EXPERIMENTAL RESEARCH ON THE VIBRATION CHARACTERISTICS OF BRIDGE'S HORIZONTAL ROTATION SYSTEM

As a new construction method, the bridge horizontal rotation construction method can reduce the impact of traffic under the bridge. During the horizontal rotation of the bridge, the overall structure will inevitably lead to a vibration response due to the construction error of the contact surface of the spherical hinge. Due to the large weight of the structure and the longer cantilever of the superstructure, the vibration at the spherical hinge will be amplified at the girder end, which will adversely affect the stability of the structure. Taking a 10,000-ton rotating bridge as a reference, a scaled model was made to test the vibration of the girder during the rotating process of the horizontal rotating system.And by analyzing the frequency domain curve of girder vibration and the results of simulation calculation, it is found that the vertical vibration displacement response is related to the first three modes of longitudinal bending of the girder structure, but has nothing to do with the higher modes or other modes. Applying the harmonic response analysis module in ANSYS software method, it is proposed that the structural vibration effect will reach the smallest by controlling the rotating speed in order to control the excitation frequency within the first-order mode frequency of girder. Also in this research, the expression of the relationship between the vertical vibration velocity and acceleration of the girder end of the horizontal rotation system and the vibration frequency of the girder is established. Based on that, it is proposed that the stability of the horizontal rotation can be predicted by monitoring the vertical velocity and acceleration of the cantilever girder end during the horizontal rotation.

Attenuation and propagation characteristics of railway load-induced vibration in a loess area

The long-term vibration caused by the operation of high-speed trains not only reduces the strength and stability of a roadbed but also affects infrastructure such as buildings along the line, resulting in a series of engineering–environmental problems. In this study, field tests were conducted to examine the ground vibrations caused by the operation of the Datong-Xi’an high-speed railway; three different line forms––viaducts, embankments, and embankment culverts––were considered. First, the propagation law and attenuation characteristics of environmental vibration caused by high-speed railways in typical loess areas were analyzed using time-domain and frequency-domain features. Second, based on the Bornitz model and combined with the measured data, the geometric attenuation coefficient and damping attenuation coefficient of the formula are discussed, and the optimized Bornitz model is used to predict the ground vibration caused by high-speed trains in a loess area. The results showed the following: (1) The ground vibration caused by high-speed train operation is a periodic excitation, and there is an obvious superimposition effect at the bogie of the train. The vertical vibration acceleration of the ground surface decays continuously as the distance from the vibration source increases. The dominant frequency also decreased with an increase in distance. (2) The geometric attenuation coefficient of the bridge and embankment sections decrease with an increase in the distance from the vibration source, and the overall attenuation is a power function. Different distances should be regarded as different types of vibration sources, and the damping attenuation coefficient differs at different measurement points. (3) The improved Bornitz model was used to predict ground vibrations caused by the operation of high-speed trains. A comparison with the measured data showed good agreement, explaining the amplification effect in the attenuation of ground vibration.

A dynamic detection method for polygonal wear of railway wheel based on parametric power spectral estimation

Severe wheel polygon will cause the strong repeated wheel-rail excitation, accelerating the failure of vehicle key components. Nevertheless, the traditional spectral estimation methods are not ideal for dealing with these wheel fault signals, making the characteristic frequencies caused by wheel polygon hardly detected. This paper proposes a dynamic detection method for wheel polygon based on parametric power spectral estimation for the first time. Firstly, according to the dynamic characteristics of the wheel polygon, the harmonic frequency recovery model is established. Secondly, the order of the harmonic frequency recovery model is determined based on singular value decomposition and normalised error analysis. Then, the total least square method is used to calculate the parameters of the harmonic recovery model. Finally, the power spectrum of the fault signal is evaluated according to the Cadzow estimation theory. The simulation signal and the measured axle-box vertical vibration acceleration signal of a metro vehicle are taken as case studies to verify the feasibility and effectiveness of the proposed method thoroughly. The results show the proposed method can avoid the inherent defects of traditional detection and analysis methods, weaken the influence of background noise, and is highly advantageous in detecting the initial stage of wheel polygonal wear.

Study on the influence of wheel polygon on the vibration characteristics of bogie system

As one of the important core components of train running parts, the wheel rail related force will directly affect the vehicle running performance and passenger comfort. Take a high-speed train as the research object, the vehicle track coupling dynamic model is established. The influence of wheel polygon on the vibration characteristics of bogie system is analyzed through simulation. The results show that when the wheel polygon wear occurs, the effective value of lateral acceleration of polygonal wheel set axle box is about 18.9 % higher than that of normal wheel set axle box; at the same speed, with the increase of the wave depth of the wheel polygon, the effective values of the transverse and vertical acceleration of the axle box gradually increase; the effective value of axle box vertical vibration acceleration caused by wheel polygon with different amplitude increases first, then decreases and then increases with the change of vehicle speed. The effective value of axle box transverse and vertical acceleration caused by wheel polygon increases with the increase of wave depth or polygon order; the analysis shows that the polygonal wear of the wheel has a great impact on the vibration characteristics of the axle box and can cause the high-frequency vibration of the axle box.

Vibration characteristics analysis and suspension parameter optimization of tractor/implement system with front axle suspension under ploughing operation condition

To improve the riding comfort and driving safety of the tractor system, it’s necessary to build a vibration model of wheeled tractor/implement system to analyze its corresponding vibration characteristics. A discrete element model of plough-soil coupling system was developed in this work to obtain the tillage resistance and its effectiveness is verified through experiment. Then, the vibration model of wheeled tractor/implement system with front axle suspension under ploughing condition was constructed and the corresponding vibration characteristics of the tractor system under road transportation, farmland transportation and plough operation conditions were simulated. It’s demonstrated that the simulated vibration responses agree well with the measured data and the validity of the proposed model is proved. The simulation results show that the natural frequency of the tractor system almost remains constant under the three working conditions above and the natural frequencies of vertical vibration for front axle, cabin, driver seat and implement are 2.09 Hz, 2.84 Hz, 2.84 Hz and 2.09 Hz, respectively. The existence of front axle suspension will deteriorate the ride comfort of driver but improve the handing stability obviously. The farmland road roughness and tillage resistance can reduce the vibration responses of the wheeled tractor/implement system with front axle suspension significantly. With the increase of tillage speed or depth, the vibration responses of the tractor system rise tremendously. When the tillage speed or depth is constant, the largest vertical vibration acceleration exists on the front axle. In addition, the multi-objective optimization of stiffness and damping parameters for the front axle suspension is implemented through particle swarm algorithm and the optimal stiffness and damping are recommended to be 60 kNm−1 and 8.919 kNsm−1, respectively.