Radial Force Variation Research Articles

Evaluation of ride quality in a passenger car with non-uniform tyre radial stiffness

This study is dedicated to examining the influence of varying radial stiffness along the circumference of tyres on a road vehicle ride quality and with a specific focus on aspects relevant to maintenance. Computer simulations employing a three-dimensional road-vehicle model, developed within commercial multi-body software, were conducted to explore the multifaceted factors influencing vehicle behaviour. These factors encompass road unevenness, driving speed, and the range of radial force variation resulting from harmonic changes in tire radial stiffness. Furthermore, simulation tests were carried out using a model of a diagnostic wheel balancing machine, which holds significance in vehicle maintenance practices. Measurements obtained from a passenger car equipped with standard tires with minimal non-uniformity, served as reference values for assessing the car's vibration levels. Additionally, selected scenarios were examined, involving vehicle with multiple wheels exhibiting non-uniform radial stiffness. The findings underscore that non-uniform radial stiffness can magnify the detrimental effects of road irregularities, potentially leading to amplified vibration levels and a heightened need for maintenance considerations.

Modelling Intrinsic Sources of Nonuniformity and Their Interplay

ABSTRACT Uniformity characteristics of a tire are a direct reflection of the quality of the manufacturing process that produced it. This is realized in the homogeneity of its different stiffnesses and dimensions around the tire. Evidently, this is the most closely monitored aspect for consistency, from the original equipment manufacturers and manufacturers alike, and the requirement for tighter acceptance criteria is ever-increasing. However, the authors endeavor to find the lowest theoretical level for the same, given the intrinsic sources. The current study attempts to establish a framework to investigate the effect of the most pronounced factors individually, their interplay, and how their combined effect can be minimized. The present work on a 185/65R15 passenger car radial tire attempts to determine the effect of variable pitch sequencing as well as splicing and tread runout for a patterned tire on radial force variation (RFV). The study is carried out using finite element simulation for it presents the opportunity to study the individual effects systemically and economically. The study reveals a nearly 20% of the specification limit can be due to tread pattern sequence while the effect of the overlapping components may vary by 10% of the same limit. The study also suggests spotting arrangements to target and avoid. Finally, the authors present a method, captured in a MATLAB program that benefits the tire designer, plant engineer, and quality control manager.

Stochastic analysis for in-plane dynamic responses of low-speed uniformity of tires due to geometric defects

Tire uniformity is defined as the dynamic mechanical characteristics of pneumatic tires due to the defects originating in tire components during manufacturing processes. These defects lead to deviations in the structural and material parameters of tires and, in turn, induce variations in the dynamic response. In this scenario, this paper proposes a probabilistic model of the low-speed uniformity analysis for predicting the impacts of the uncertainties in the geometric defects and the vertical load on the dynamic responses. The deterministic coupled rigid–flexible ring model, combined with the generalized polynomial chaos expansion theory, is developed to simulate the radial force variation due to radial run-out. In this approach, the non-uniform tire radius and the vertical load are selected as a set of random variables and are approximated by the generalized polynomial chaos expansions. The distributions of these input variables are identified from 200 measured tires by the Pearson model. A non-intrusive probabilistic collocation method is adopted to evaluate the coefficients of the generalized polynomial chaos expansions, and the selection of collocation points is also illustrated. Finally, the distributions of the radial force variation and its first harmonic due to the geometric defects and vertical loads are predicted in comparison with measurements. Moreover, the distributions of the dynamic response caused by each parameter and different variance levels are discussed and verified by the measurement data from 1130 tires.

Research on Influence of Switching Angle on the Vibration of Switched Reluctance Motor

Switched Reluctance Motors (SRMs) have emerged as a viable competitor to other established electrical machines. Although SRMs have many advantages, such as a rare earth free nature, simple structure, high fault tolerance capability and low cost, vibration problems due to radial force variations is still a major issue faced by SRMs. Hence, aimed at the problem of vibration suppression for SRMs, this paper proposes a method that focuses on the influence of the change of the turn-on angle and turn-off angle on the vibration of the SRM under the switching angle control (SAC) strategy. Firstly, the influence of the turn-on and turn-off angles on the harmonic components of the current is analyzed in detail. Then, the vibration caused by the frequency of the harmonic components of the current and the natural frequency of the motor is mainly studied. The results show that the harmonic order affecting vibration is related to the rotational speed, and by analyzing the value of this harmonic order, the variation law of vibration with the switching angle can be obtained. When the turn-off angle is constant, the amplitudes of the current harmonic component and vibration first decrease and then increase with the increase of the turn-on angle. Additionally, when the turn-on angle is constant, the current harmonic and vibration show the tendency of periodic oscillation with the variation of the turn-off angle, and the oscillation period is related to the harmonic order. The combination of switching angles that minimizes the certain current harmonic component also minimizes vibration. The effectiveness of the variation law was verified on a 12/8 poles and 1.5 KW SRM drive system test bench, which provide a new perspective on vibration suppression of SRMs.

Energy Loss and Radial Force Variation Caused by Impeller Trimming in a Double-Suction Centrifugal Pump.

Impeller trimming is an economical method for broadening the range of application of a given pump, but it can destroy operational stability and efficiency. In this study, entropy production theory was utilized to analyze the variation of energy loss caused by impeller trimming based on computational fluid dynamics. Experiments and numerical simulations were conducted to investigate the energy loss and fluid-induced radial forces. The pump’s performance seriously deteriorated after impeller trimming, especially under overload conditions. Energy loss in the volute decreased after trimming under part-load conditions but increased under overload conditions, and this phenomenon made the pump head unable to be accurately predicted by empirical equations. With the help of entropy production theory, high-energy dissipation regions were mainly located in the volute discharge diffuser under overload conditions because of the flow separation and the mixing of the main flow and the stalled fluid. The increased incidence angle at the volute’s tongue after impeller trimming resulted in more serious flow separation and higher energy loss. Furthermore, the radial forces and their fluctuation amplitudes decreased under all the investigated conditions. The horizontal components of the radial forces in all cases were much higher than the vertical components.

Prediction of the Variation on Steering Wheel Shimmy due to Tangential and Radial Force Variation of the Tyres

<div class="section abstract"><div class="htmlview paragraph">The objective of this work is to develop a process that predicts the amount of steering wheel shimmy in a vehicle due to the tangential and radial force variation in the Tyre/Wheel assembly and also other components affecting shimmy. Steering wheel shimmy is defined as the torsional oscillation of the steering wheel due to excitation at the wheels. The tangential and radial force variation was modelled based on test data and applied on the wheels as excitation. Variation of these forces with the vehicle velocity was considered. The various factors that affect shimmy were then established. These factors were then divided into two categories - Geometric and Non-Geometric. A DOE was done, while considering the manufacturing variations, to study the sensitivity of those factors on shimmy. The DOE results were used to fit a regression model that predicts the shimmy velocity while considering the factors as inputs. The regression model was then considered for a Montecarlo simulation to estimate the distribution of shimmy velocity. A Normal or Weibull distribution was considered for the MonteCarlo Simulation for each of the factors in the DOE study. This distribution was then compared against a target. The target was used to design the suspension such that it is robust enough to withstand the manufacturing variations of the factors effecting shimmy.</div></div>

Energy-Saving Performance and Production Accuracy of the Direct-Pressure Tire Curing Technology with an Expandable Steel Internal Mold

Due to the low thermal conductivity and low rigidity of the rubber bladder, the traditional tire curing process faces problems such as low efficiency, high energy consumption, and low production accuracy. To eliminate defects, this work presents a novel direct-pressure curing technology (DPCT) with a steel internal mold heated by electromagnetic induction. Special equipment featuring this novel technology was developed and used for trial-production of tire with a specific size. The energy consumption of sample tires was measured for comparison between the new technology and the traditional one. Nonuniformity and unbalance of tires are tested, meanwhile, physical properties of tread and sidewall parts of cured tires are tested. Furthermore, a finite element analysis (FEA) is carried out to investigate the heating rate of the new curing technology and to optimize the curing process. According to the results, with the new curing technology, the energy consumption per cure cycle is cut down by about 86%, while the curing efficiency and the tensile strength of sidewall part of the cured tire are improved by 22.5% and increased by 13.9%, respectively. In addition, the radial force variation (RFV), couple unbalance mass and curing temperature difference are also reduced by 16.8%, 37%, and 8 °C, respectively. These results suggest that DPCT has excellent energy-saving performance and production accuracy.

カーシェイク低減のためのタイヤホイールRFVの力学モデルに関する研究

カーシェイク低減のためのタイヤホイールRFVの力学モデルに関する研究

The Influence of Radial Area Variation on Wind Turbines to the Axial Induction Factor

Improvements in the aerodynamic design will lead to more efficiency of wind turbines and higher power production. In the present study, a 3D parametric gas turbine blade geometry building code, 3DBGB, has been modified in order to include wind turbine design capabilities. This approach enables greater flexibility of the design along with the ability to design more complex geometries with relative ease. The NREL NASA Phase VI wind turbine was considered as a test case for validation and as a baseline by which modified designs could be compared. The design parameters were translated into 3DBGB input to create a 3D model of the wind turbine which can also be imported into any CAD program. Design modifications included replacing the airfoil section and modifying the thickness to chord ratio as a function of span. These models were imported into a high-fidelity CFD package, Fine/TURBO by NUMECA. Fine/TURBO is a specialized CFD platform for turbo-machinery analysis. A code-geomturbo was used to convert the 3D model of the wind turbine into the native format used to define geometries in the Fine/TURBO meshing tool, AutoGrid. The CFD results were post processed using a 3D force analysis code. The radial force variations were found to play a measurable role in the performance of wind turbine blades. The radial component of the blade surface area as it varies in span is the dominant contributor of the radial forces. Through the radial momentum equation, this radial force variation is responsible for creating the streamline curvature that leads to the expansion of the streamtube (slipstream) that is responsible for slowing the wind velocity ahead of the wind turbine leading edge, which is quantified as the axial induction factor. These same radial forces also play a role in changing the slipstream for propellers. Through the design modifications, simulated with CFD and post-processed appropriately, this connection with the radial component of area to the radial forces to the axial induction factor, and finally the wind turbine power is demonstrated. The results from the CFD analysis and 3D force analysis are presented. For the case presented, the power increases by 5.6% due to changes in airfoil thickness only.

Numerical calculation and analysis of radial force on the single-action vane pump

Unbalanced radial force is a serious adversity that restricts the working pressure and reduces service life of the single-action vane pump. For revealing and predicting the distribution of radial force on the rotor, a numerical simulation about its transient flow field was performed by using dynamic mesh method with RNG κ ε-turbulent model. The details of transient flow characteristic and pressure fluctuation were obtained, and the radial force and periodic variation can be calculated based on the details. The results show: the radial force has a close relationship with the pressure pulsation; the radial force can be reduced drastically by optimizing the angle of port plate and installing the V-shaped cavity; if the odd number vanes are chosen, it will help reduce the radial force of rotor and optimize the pressure fluctuation effectively.

A Truck Cab Abnormal Vibration Test and Analysis

This paper introduces a combination of testing and finite element simulation for the abnormal vibration of a truck cab in specific speed. Vibration characteristics of the truck is tested. The factors that caused the abnormal vibration of the truck is found. The finite element model is established and the modal analysis is performed, the correctness of the test results is verified, and a reliable finite element model for the follow-up solution is provided. The abnormal vibration was caused by the frequencies of radial force variation which almost equal to the truck natural frequency under the vehicle velocities of 50km/h. The approach described in this paper can be applied to similar vibration problem diagnosis.

1301 カーシェイク向上のためのタイヤホイール組立体の起振力予測技術(OS2-1 自動車ダイナミクスのモデリング,OS2 交通・物流システムのダイナミクス,オーガナイズド・セッション(OS))

Car shake is one of many kinds of vehicle vibration that causes customer dissatisfaction. Uniformity of tire and wheel assembly affects the vehicle vibration including car shake. In this study, the authors developed the estimation method to calculate the radial force vibration of tire and wheel assembly. The parameters used in this method are the radial force variation of tire, the radial runout of wheel, and so on. This estimation method is based on the complex functions and the Monte Carlo calculations. The complex functions are used to study the assembly condition of a tire and a wheel. The Monte Carlo calculations are applied to calculate the parameters from their statistical data such as averages and standard deviations. The estimated results are in good agreement with the experimental results. The authors concluded that this method is an effective tool to reduce car shake.

Analytical Model of Bump-Type Foil Bearings Using a Link-Spring Structure and a Finite-Element Shell Model

A complete analytical model of bump-type foil bearings taking into consideration the effects of four factors, i.e., the elasticity of bump foil, the interaction forces between bumps, the friction forces at the contact surfaces, and the local deflection of top foil, is presented in this investigation. Each bump is simplified to two rigid links and a horizontally spaced spring, the stiffness of which is determined from Castigliano’s theorem. The interaction forces and the friction forces are coupled with the flexibility of bumps through the horizontal elementary spring. The local deflection of the top foil is described using a finite-element shell model and added to the film thickness to predict the air pressure with Reynolds’ equation. The bump deflections of a strip with ten bumps calculated using the presented model under different load distributions are consistent with the published results. Moreover, the predicted bearing load and film thickness obtained from a foil bearing with a bump circumferential extend of 360 deg also agree very well with the experimental data, especially for predictions with a proper selection of radial clearance (preload of foil structure) and friction coefficients. In addition, the radial clearance and friction force variations in the foil bearing are noted to significantly change the performance of the foil bearing. The predictions demonstrate that the radial clearance of the foil bearing has an optimum value for the maximum load capacity.

Effect of Vulcanization and Shaping Process on Radial Force Variation of TBR Tire

The study was based on researching various parameter of vulcanization shaping process for effect of radial force variation (RFV).The experimental results showed that reducing the first and second shaping pressure, and increasing hole diameter of N2 on curing bladder, and extending times of discharged N2 in shaping process, and reducing pressure of expanded bladder at the moment of closing mold, could reduce RFV of TBR tire and improve uniformity of tire and provide base data of product process.

CUTTING DISTURBANCES INFLUENCED BY VARIATIONS IN CONTACT SURFACE GEOMETRY

The significant cutting disturbances appearing in hard turning processes cause shifting of the process dynamics. Therefore, in this paper the turning process is evaluated by radial force variation analysis, as a function of depth of cut, tool nose radius and effective lead edge angle, through static and dynamic indicators. The tool/workpiece contact zone is, in the case of hard turning, mostly limited within the tool nose radius region. Therefore in this paper, geometry of the tool/workpiece contact line is analyzed. The depth of cut is calculated as a geometric difference of prior and instantaneous tool pass profiles. The calculated values of the depth of cut are time dependant, and can vary by 60%. Various process monitoring techniques have been used to identify and confirm these variations, as well as quantify the level of process stability. The results obtained confirm the assumption that effective lead edge angle and radial force are influenced by depth of cut, feed rate and tool nose radius. Additionally, it is shown that low values of depth of cut and geometry of prior pass-machined surface valleys shift the hard turning process to a dynamically more sensitive level as compared the case of soft machining.

Analytical modelling and experimental verification of tyre non-uniformity

This paper presents the development of a non-uniform tyre model for system identification to fit experimental High-Speed Uniformity (HSU) measurements, which ultimately results in the determination of the tangential and radial hub forces. The analytical model includes the mass imbalance, stiffness non-uniformity, and radial run-out in addition to hysteretic energy dissipation and a longitudinal slip model. The system identification, based on a genetic algorithm, uses the experimental tangential and radial first harmonic wheel hub force variations as the target outputs. The results demonstrate that non-uniformities produce wheel hub forces at multiple combination frequencies of the first harmonic frequency.

Finite Element Analysis of Nonuniformity of Tires with Imperfections

Abstract The effects of variations in stiffness and geometry on the nonuniformity of tires are investigated by using the finite element analysis. In order to evaluate tire uniformity, a three-dimensional finite element model of the tire with imperfections is developed. This paper considers how imperfections, such as variations in stiffness or geometry and run-out, contribute to detrimental effects on tire nonuniformity. It is found that the radial force variation of a tire with imperfections depends strongly on the geometrical variations of the tire.

Analysis and optimization of dynamically loaded porous metal sliding bearings under conditions of elastohydrodynamic lubrication

PurposeThis paper aims to develop a simulating model of a journal porous metal bearing under elastohydrodynamic conditions and combined (radial, friction and thermal) load distribution and to carry out structural optimization.Design/methodology/approachThe structure analysis is carried out for each kind of load separately and for the combined load distribution of the bearing, where a dynamically loaded porous metal bearing is simulated. This simulating model is developed by finite elements method using the structure analysis module of the CATIA V5 software. Further, a parameter optimization of a porous metal bearing is presented considering the elastic deformations of the bearing shell.FindingsIt is revealed that the bearing, even at points with maximum displacements, could not reach the mounting clearance value during its operational life. Relatively small bearing dimensions produce very high values of eigenfrequency response (over 150 kHz) and common dynamic loads met in all sorts of sliding bearing are not dangerous for bearing damage compared with static loads. In the stage of structural optimization based on the correlation between stress and geometric bearing parameters like wall thickness and outer diameter, the influence of finite element dimension on calculated results can be also analyzed and a proper choice of the latter is achieved.Research limitations/implicationsThe present porous bearing optimization model with the aid of CATIA V5 module for optimum design uses only single objective optimization. For a complete optimum design a multi‐objective optimization has to be carried out.Practical implicationsThe analysis under dynamic load conditions proved that relatively small dimensions of bearing commonly used in micro technique and precision mechanics result in extended safe and reliable operation.Originality/valueThis paper provides a methodology for bearing stress and deformation analysis in the elastic range and on the basis of this analysis it is possible to develop an optimization model for porous bearings offering help to designers for the selection of optimal bearing dimensions considering the bearing load caused by dynamic radial force, friction and temperature variation.

829 弾性ホイールの動的挙動の解析

Flexible wheels have been developed to improve the ride comfort. This wheel is equipped with unique fiber reinforced rubber rings between the disc and the rim, in order to reduce noise and vibration without any compromises with handling and stability. This paper discusses effectiveness of the flexible wheel when weight unbalance added through the uniformity tests, and proposes a new uniformity test method which can simulate more realistic conditions of driving than the conventional method. Simulation analysis was carried out for the new test method, showing that flexible wheels could reduce more radial force variation compared with the conventional wheels.

Finite Element Analysis of the Radial Force Variation of A Ring Stent

The purpose of this paper is to investigate the condition of the stent deployed into the artery. The finite element contact simulation between the stent and the artery is developed in this research. The stent is made of nitinol, which has shape memory effect and superelasticity. The cross-sectional area of the stent is considered to be an interruption factor for the blood flow. Therefore, the evaluation parameter with respect to the cross-sectional area is defined. As a result, it is confirmed the simulation is useful for the stent design.