Mount Stiffness Research Articles

Optimization of Cabin Mounting System for Tractor using a Genetic Algorithm

Abstract Purpose To analyze the behavior of a tractor cabin mounting system, a six-degrees-of-freedom (6-DOF) simulation model was developed, and a genetic algorithm was integrated into the model to optimize the design variables of the cabin mounting system. The performance and characteristics of the optimized cabin-mounting system were analyzed. Methods Eigenvalue analysis was performed using the developed model. Rigid-body mode decoupling theory was applied to optimize the design variables, and the energy decoupling method (EDM) was used to evaluate the degree of rigid-body mode decoupling. The design variables were optimized using NSGA-II genetic algorithm. Optimizations for two cases (Case #1: optimizing the stiffness and position of the mounts; Case#2: optimizing only the stiffness of the mounts) were conducted. Results energy decoupling rate (EDR) for Case #1 increased from 66.73% to 87.65%. As the position constraints relaxed, the mounts tended to move upwards and were widely distributed widely. EDR for Case #2 increased from 66.73% to 84.41%. In both cases, the mount stiffness decreased. Conclusions The EDR of the cabin mounting system was significantly improved due to optimization, and the rigid body mode frequencies were optimized within the target range.

About the Wing and Whirl Flutter of a Slender Wing–Propeller System

Next-generation aircraft designs often incorporate multiple large propellers attached along the wingspan (distributed electric propulsion), leading to highly flexible dynamic systems that can exhibit aeroelastic instabilities. This paper introduces a validated methodology to investigate the aeroelastic instabilities of wing–propeller systems and to understand the dynamic mechanism leading to wing and whirl flutter and transition from one to the other. Factors such as nacelle positions along the wing span and chord and its propulsion system mounting stiffness are considered. Additionally, preliminary design guidelines are proposed for flutter-free wing–propeller systems applicable to novel aircraft designs. The study demonstrates how the critical speed of the wing–propeller systems is influenced by the mounting stiffness and propeller position. Weak mounting stiffnesses result in whirl flutter, while hard mounting stiffnesses lead to wing flutter. For the latter, the position of the propeller along the wing span may change the wing mode shapes and thus the flutter mechanism. Propeller positions closer to the wing tip enhance stability, but pusher configurations are more critical due to the mass distribution behind the elastic axis.

Optimization of Vehicle Powertrain Mounting System Based on Generalized Inverse Cascade Method under Uncertainty

This paper presents a summary of the optimization design process for a multi-objective, two-level engineering problem, utilizing the generalized inverse cascade method under uncertainty. The primary objective is to enhance the vibration isolation performance of a mounting system, considering the influence of uncertain factors on its stiffness. The focus is on determining the value range of the design variables at the bottom layer, ensuring that the design goal is met with a specified confidence level. To illustrate the application of this methodology, the optimization design of a powertrain mount is used as a case study. A data-driven approach is adopted, establishing a quantitative mapping relationship between mount stiffness, force transmission rate, modal decoupling rate, and other design indicators. This is achieved through the development of a CRBM-DBN approximate model, which combines Conditional Restricted Boltzmann Machines (CRBMs) and a Deep Belief Network (DBN). Additionally, an intelligent optimization algorithm and interval search technology are employed to determine the optimal design interval for the mount stiffness. Simulation and experimental verification are conducted using selected parameter combinations. The results demonstrate notable improvements in the vibration isolation performance, modal decoupling rate, and vehicle NVH performance when compared to the original state. These findings provide valuable insights for the interval optimization design of similar multi-objective, as well as two-level engineering problems, serving as useful references for future research and applications.

Constitutive relation expansion of large load metal rubber engine mount stress bivariate function relationship using the strain and strain rate

Metal rubber materials were first used for vibration cushioning and noise protection applications in aviation equipment. With the recent developments in science and technology, metal rubber materials have been gradually implemented in Vehicle Vibration Suppressing. Metal rubber has significant advantages over ordinary rubber materials, in terms of its vibration damping in extreme environments. Along these lines, the objective of this work was to develop a mechanical model of metal rubber mount for mining vehicles, which can be used to predict the equivalent stress change of large load metal rubber mount in actual operation. Starting from the mechanical model of the mount and then expanding the macroscopic one-dimensional relationship of force and displacement to the binary relationship between the force and displacement and velocity, the microscopic one-dimensional relationship of stress and strain was expanded to the binary relationship between the stress and strain and strain rate. This work focused on the three-dimensional intrinsic structure model of stress, strain, and strain rate for metal rubber mounts. Moreover, the mechanical properties of the metal rubber mounts were explored in conjunction with the Mooney–Rivlin model, while the constitutive relationship of its stress, strain, and strain rate was deduced. The three-dimensional hysteresis curves were plotted by using software simulation analysis of the metal rubber mounts, and the metal rubber mounts hysteresis surface was also fitted. A combination of simulated and experimental data was used to test the accuracy of the proposed mechanical model of the metal rubber mount. From the acquired results, it was demonstrated that the errors of the relevant parameters (c10,c01, and c11) of the mechanical model of the metal rubber mount were about 10%. On top of that, the errors of the simulated stiffness values and the damping ratios of the metal rubber mount and the experimental stiffness values and damping ratios were within 10%. Excluding the interference of the metal rubber mount fabrication error, the proposed mechanical model met the mechanical analysis of the metal rubber mount with a large load and the mechanical model was accurate. The influence of the strain and strain rate on the stiffness and damping of the metal rubber mounts was also clarified, and the expansion method of the constitutive relationship of the metal rubber mount stress and strain was systematically explored. From the analysis of the metal rubber mounts’ mechanical properties, a reference basis for its vibration analysis and for the mechanical analysis of other nonlinear materials was provided.

Rubber Creep Model and Its Influence on Mounting Stiffness

The mount of the engine will creep under the action of long-term load. Creep will change its original structure, resulting in changes in static and dynamic characteristics and fatigue life. In order to solve the problem of mounting rubber creep, the creep characteristics were studied in this paper. In order to study the influence of creep characteristics on engine mounting stiffness, a theoretical model of mount creep was established based on the creep mechanism of rubber. The effects of different loads on the creep characteristics of engine mount were studied. The static viscoelastic parameters and creep analysis of rubber mounting were analyzed numerically. The creep variation law of suspension under different loads is obtained. By analyzing the static and dynamic characteristics of no creep, 2.98 mm creep and 3.83 mm creep of engine mount, the creep characteristics and the variation law of mount stiffness of rubber mount were revealed. The results show that the static stiffness of suspension increases with the increase of creep. When the frequency is constant and the creep increases, the dynamic stiffness of the suspension increases obviously. In this paper, the creep characteristics of rubber mount are analyzed, and the results of the analysis provide a design method for rubber mount design.

Optimal Motorcycle Engine Mount Design Parameter Identification Using Robust Optimization Algorithms

Mechanical vibrations have a significant impact on ride comfort; the driver is constantly distracted as a result. Volumetric engine inertial unbalances and road profile irregularities create mechanical vibrations. The purpose of this study is to employ optimization algorithms to identify structural elements that contribute to vibration propagation and to provide optimal solutions for reducing structural vibrations induced by engine unbalance and/or road abnormalities in a motorcycle. The powertrain assembly, swing-arm assembly, and vibration-isolating mounts make up the vibration-isolating system. Engine mounts are used to restrict transferred forces to the motorbike frame owing to engine shaking or road irregularities. Two 12-degree-of-freedom (DOF) powertrain motorcycle engine systems (PMS) were modeled and examined for design optimization in this study. The first model was used to compute engine mount parameters by reducing the transmitted load through the mounts while only considering shaking loads, whereas the second model considered both shaking and road bump loads. In both configurations, the frame is infinitely stiff. The mount stiffness, location, and orientation are considered to be the design parameters. The purpose of this study is to employ computational methods to minimize the loads induced by shaking forces. To continue the optimization process, Grey Wolf Optimizer (GWO), a meta-heuristic swarm intelligence optimization algorithm inspired by grey wolves in nature, was utilized. To demonstrate GWO’s superior performance in PMS, other optimization methods such as a Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) were used for comparison. To minimize the engine’s transmitted force, GWO was employed to determine the optimal mounting design parameters. The cost and constraint functions were formulated and optimized, and promising results were obtained and documented. The vibration modes due to shaking and road loads were decoupled for a smooth ride.

Design optimization of engine mounting system for a modular electric vehicle platform with different powertrain characteristics

In recent days, there is much focus on the modularity of the platform to reduce the cost and improve the system-level design efficiency. In this paper, a study has been done for various non-linear input torque (different powertrain) and optimization with a modular powertrain mounting system where only stiffness is varied to achieve the optimization goal. Here, the optimization goals are maximization of kinetic energy distribution to improve the decoupling rate and minimization of powertrain CoG movement under torque. HEEDS and MATLAB optimization tools are used for analysis. First, three different powertrains are considered individually for optimization. Then, all three powertrains for a particular location on the modular platform are optimized with different mount stiffness. Different mount stiffnesses are chosen in such a way that the stiffness can be achieved only by hardness adjustment or minimum design modification without any change in complete mount design. Proposed results show that a properly chosen mounting system can address the platform modularity quite quickly.

A novel dynamics model of a trailer bogie brake system and its application in stability analysis

The dynamic performance of the trailer bogie brake system is essential for the safe operation of a high-speed train during the braking process. In this work, we developed a novel ten-degree-of-freedom (ten-DOF) dynamics model of a trailer bogie brake system based on dynamic and tribological theories. The non-linear factors including disc-pad non-linear friction and wheel-rail non-linear interactions were considered. The field test results demonstrated that more intense vibrations occur at low vehicle speeds, which is also supported by numerical simulations based on the novel dynamics model. The abnormal vibration is caused by the limit cycle oscillation of the brake unit, and it leads to the instability of the whole system. To further understand the instability of the trailer bogie brake system, the equilibrium points and the linear stability of the system under different braking conditions and suspension parameters were investigated based on the Lyapunov theory. Then, the non-linear vibration response and stability of the trailer bogie brake system affected by the suspension parameters were further calculated by numerical integration methods. The results demonstrated that the mounting stiffness of the brake unit approached 3.4×107N/m and the primary suspension stiffness approached 6.0×105N/m or remained within the range of 10×105-14×105N/m, causing more violent vibrations and increased system instability. A primary suspension damping exceeding 2.4×104N·s/m was conducive to improving system stability.

Failure analysis of crack on cold-rolled steel panels of truck cabin

This article examines the failures of cabin sheet metal panels in depth. The truck cabin segments' failures are examined in relation to one another. The failure distributions are evaluated to determine their correlation coefficients and then classified. The frequency of failures in cabin-in-white (CiW) structural panels and cabin mount elastomeric bushings was determined in this investigation. Later investigation of the elastomer mount's stiffness fluctuation during field operation established that the fractures in the cabin panels were caused by the elastomer bush rotating out of position and resulting changes in transmissibility. Experiments conducted in a variety of working conditions established the existence of high stress zones predicted by finite element modeling. Finally, preventative measures are offered to avert such failures.

Parametric whirl flutter study using different modelling approaches

This paper demonstrates the importance of assessing the whirl flutter stability of propeller configurations with a detailed aeroelastic model instead of local pylon models. Especially with the growing use of electric motors for propulsion in air taxis and commuter aircraft whirl flutter becomes an important mode of instability. These configurations often include propeller which are powered by lightweight electric motors and located at remote locations, e.g. the wing tip. This gives rise to an aeroelastic instability called whirl flutter, involving the gyroscopic whirl modes of the engine. The driving parameters for this instability are the dynamics of the mounting structure. Using a generic whirl flutter model of a propeller at the tip of a lifting surface, parameter studies on the flutter stability are carried out. The aeroelastic model consists of a dynamic MSC.Nastran beam model coupled with the unsteady ZAERO ZONA6 aerodynamic model and strip theory for the propeller aerodynamics. The parameter studies focus on the influence of different substructures (ranging from local engine mount stiffness to global aircraft dynamics) on the aeroelastic stability of the propeller. The results show a strong influence of the level of detail of the aeroelastic model on the flutter behaviour. The coupling with the lifting surface is of major importance, as it can stabilise the whirl flutter mode. Including wing unsteady aerodynamics into the analysis can also change the whirl flutter behaviour. This stresses the importance of including whirl flutter in the aeroelastic stability analysis on aircraft level.

Effect of Driveshaft Angle on Turning Noise in Electric Vehicles and Solution Development Approach

<div class="section abstract"><div class="htmlview paragraph">Electric vehicles (EV’s) are very much noise, vibration and harshness (NVH) sensitive due to the absence of engine noise. The outline of this paper is based on vehicle level turning noise evaluation. The impact of the driveshaft angle in the frequency range of 1000-2000Hz. The level of noise while turning at driver and co-driver side is evaluated first. Then the possible countermeasure to address such noise issues are also discussed. The impact on the angular adjusted roller (AAR) joint and driveshaft angle is studied along with the impact on other parameters like powertrain mount stiffness, ground clearance and vehicle architecture.</div></div>

Research on ride comfort of vibratory rollers: Part-1 Study on the effect of different cab isolation mounts

In order to evaluate the ride quality of vibratory roller’s cab used the different isolation mounts including the traditional rubbers, hydraulics, and hydro-pneumatics, a nonlinear dynamics model of the vibratory roller under interaction of the deformable terrain and drum has been established based on Matlab/Simulink software. The root-mean-square (RMS) of the accelerations of the vertical driver’s seat and the cab’s pitch angle have been used as objective studies. The influence of damping and stiffness coefficients of different isolation mounts on the cab’s ride quality has been respectively simulated and analyzed under a hard ground at an excitation 28 Hz of the vibration drum. The research results indicate that the characteristics of non-linear damper and high-static stiffness of the hydro-pneumatic mounts can greatly reduce the vertical driver’s seat vibration and cab shaking when compared to vibratory roller’s cab using the traditional rubber mounts and hydraulic mounts under stiffness and damping coefficients of the vehicle and cab isolations. Particularly with the dynamics parameters of Kc= [0.8 to 1.2]×Kc0, Cc= [0.8 to 1.0]×Cc0, Kt,d= [0.6 to 1.0]×Kt0,d0, and Ct,d= [1.0 to 1.2]×Ct0,d0.

Prediction and Optimization of Full-Vehicle Road Noise Based on Random Response Analysis

Based on the theory of random response analysis, a road noise prediction method is proposed. A finite element model of acoustic-structure coupling for the full-vehicle was established, and the road surface texture measured in the actual vehicle test was converted into a power spectrum, which is the excitation of FE model. Under the conditions of coast down from 80km/h to 20km/h on Belgian pavement, the prediction of road noise in the 20- 200Hz frequency band was achieved. The driver’s ear sound pressure obtained from the simulation is in good agreement with the test results, which verifies the effectiveness of the simulation model and prediction method. The sensitivity of the driver’s ear-side sound pressure level to the stiffness of the suspension mounts was further analysed. The stiffness of the bushings that had a large impact was determined. The Response Surface Methodology was used to optimize road noise. The results show that the average sound pressure level near the driver’s ear is reduced by 1.81 dBA. The simulation analysis and optimization methods introduced in this paper can provide a reference for the virtual development process of vehicle road noise.

Design sensitivity and optimization of powertrain mount system design parameters for rigid body modes and kinetic energy distributions

This study evaluates the influences of the powertrain mount design parameters on the frequencies of powertrain rigid body modes and their kinetic energy distributions (KEDs), which play an important role in the low-frequency vibration of vehicles. A total of 12 design parameters (x, y, z position of mount locations and translational stiffness of the front and rear powertrain mounts) were evaluated in terms of their contributions to the aforementioned metrics. A multi-body dynamics simulation model was used in a 512-run modal analysis by varying the design variables across their common range, and the results were used in design sensitivity analysis. Response surface models for the frequencies of each powertrain rigid body mode and their KEDs were derived and subsequently used in optimization studies. It was shown that front and rear powertrain mount stiffness in y-direction has a strong influence on the frequency of powertrain lateral mode (21.5% and 24.5%, respectively). Front mount location in the x-direction demonstrates a strong influence on the pitch mode (25.7%), while the rear mount stiffness in the z-direction is the most influential on frequency of powertrain vertical mode with 29.1%. The location of the rear powertrain mount in the z-direction has a significant effect on the KED of fore-aft mode with 37.8% sensitivity. NSGA-II genetic algorithm with 100 generations was used for optimization to meet a set of design targets compiled from the literature. For the placement of the frequencies of powertrain rigid body modes with desired KED, design sensitivities, which are derived from a system-level approach, give important design direction to address the complex interactions between powertrain mount locations and stiffness and key metrics of the powertrain mount systems. Knowledge of design sensitivity of design parameters is important in the vehicle design cycle for OEMs to prioritize their design decisions. Finally, the optimization methodology is key to tune the design parameters to meet the conflicting design targets more efficiently.

The computational method of substructure’s frequency response function in transfer path analysis

The multi-degree-of-freedom coupled vibration system with “engine-mount-body” as the transfer path was divided into active substructure (engine), passive substructure (body) and linking components (mounts) between active and passive substructure. According to the dynamic equation of multi-degree-of-freedom coupling vibration system, the computational method of the substructure’s Frequency Response Function (FRF) was proposed. For the coupled vibration system of the real vehicle’s transfer path, the computational method of the substructure’s FRF was used to obtain the FRF of substructure and dynamic mount stiffness based on the FRF of system obtained by the hammering test. Combining the dynamic mount stiffness with the vibration acceleration of the active and passive sides of the mount, the operating load was identified based on the mount-stiffness method of the transfer path analysis. Combining the operating load with the FRF of substructure to analyze the contribution of the transfer path, the contribution of each path to the target location (the Z-direction of the front floor of the cab) was presented. The correctness of the computational method of the substructure’s FRF was presented by calculating the vibration isolation ratio of the mount, which provided theoretical support for the research of dynamic characteristics of the substructure and linking components.

Bench for the study of static and dynamic indicators of vibration isolators

A test bench is developed to evaluate the properties of vibration mounts intended for vibration isolation of units, assemblies and workplaces of vehicle operators and technological equipment. The estimation of static and dynamic indicators of vibration isolators under loading close to operating conditions is presented. Keywords vibration isolator, vibration protection, vibration mount stiffness, damping, bench. ilialebedinski@gmail.com

Design and analysis of five-link-rod rigid constraint support scheme for engine–accessory system vibration control

Vibration generated by engine and its accessories deteriorates product performance. At present, lacking global model, mounting design of engine and accessories are separate, not conductive to solving the vibration of engine, belt, and accessories as a whole. In this article, three problems of the typical structure are analyzed, that is, the belt tension is unstable, static preloading makes engine mount design deviate, and the belt is prone to lateral vibration. Then, a rigid constraint rod is proposed to fix the center distance. The vibrational motion equation is established. By matrix analysis, the accessory mount along the rod is canceled. Then, engine and accessories can be analyzed as independent systems. Among them, the vibration isolation of the engine tends to be good, and for accessories and belts, the influences of the accessory mount stiffness on the force and torque transmission rate and belt vibration response were comprehensively evaluated, and that the infinite stiffness is presented. The innovative design of five-rod structure mainly composed of two connecting rods is obtained which does not transfer vibration perpendicular to rod and the vibration of engine, belt, and accessories are all well controlled. This experiment proves the five-link structure as a useful solution.

Transfer path analysis and its application in low-frequency vibration reduction of steering wheel of a passenger vehicle

The demands on improving the noise, vibration and harshness of passenger vehicles are growing rapidly. Low-frequency vibration of steering wheel is one of the most important factors leading to the discomfort of drivers. This study proposes a systematic analysis methodology to reduce the low-frequency vibration of steering wheel using classical transfer path analysis (CTPA). The theoretical basics of TPA using dynamic stiffness approach and inverse matrix approach are briefly introduced, and then the experimental apparatus and analysis procedures in performing the TPA are introduced. The static forces in the rubber mounts of the powertrain system are calculated, the dynamic stiffness of the rubber mounts are estimated, and the operational forces are determined. The contributions of different transfer paths to the vibration of steering wheel are analyzed and compared, and the predominant causes are identified. The results show that the vibration of steering wheel along the X direction is protruded at the engine ignition frequency, and the vibration of the exhaust system along the X direction contributes most to the vibration because of large frequency response function. The mounting structure of the exhaust system is modified based on modal analysis results using finite element method to reduce the vibration of steering wheel.

Low-frequency structure-borne noise refinement based on rigid-flexible coupling model of powertrain mounting system

The refinement of low-frequency structure-borne noise generated by automotive powertrain mounting system usually adopts Transfer Path Analysis (TPA) and vehicle body plate optimisation, which require a lot of simulation or experiment work based on the vehicle body. This paper aims to propose a simple method to provide an optimal mount stiffness target for the refinement of structure-borne noise. The method is based on rigid-flexible coupling model of powertrain mounting system, and the model requires complete and accurate parameters such as mass, inertia, position and stiffness. The excitation forces of engine which are used as input of the rigid-flexible coupling model are identified by an indirect semi-experiment method. Based on this model, the direction of mount stiffness with maximum sensitivity to the dynamic characteristics of the powertrain mounting system is identified. Then, the low-frequency structure-borne noise is refined by changing the mount stiffness in this direction.

Low-frequency structure-borne noise refinement based on rigid-flexible coupling model of powertrain mounting system

The refinement of low-frequency structure-borne noise generated by automotive powertrain mounting system usually adopts Transfer Path Analysis (TPA) and vehicle body plate optimisation, which require a lot of simulation or experiment work based on the vehicle body. This paper aims to propose a simple method to provide an optimal mount stiffness target for the refinement of structure-borne noise. The method is based on rigid-flexible coupling model of powertrain mounting system, and the model requires complete and accurate parameters such as mass, inertia, position and stiffness. The excitation forces of engine which are used as input of the rigid-flexible coupling model are identified by an indirect semi-experiment method. Based on this model, the direction of mount stiffness with maximum sensitivity to the dynamic characteristics of the powertrain mounting system is identified. Then, the low-frequency structure-borne noise is refined by changing the mount stiffness in this direction.