Tire Vibration Modes and Tire Stiffness

2002 ◽  
Vol 30 (3) ◽  
pp. 136-155 ◽  
Author(s):  
B. G. Kao
Keyword(s):  
Vibration Modes ◽  
Tire Model ◽  
Static Stiffness ◽  
Wheel Load ◽  
Radial Stiffness ◽  
Modeling Concept ◽  
Tire Stiffness ◽  
Tire Dynamics ◽  
Tire Models ◽  
The Relationship

Abstract Tire radial stiffness is traditionally calculated from the wheel load deflection measurement. Statically, this stiffness serves to provide the support for the vehicle. However, this stiffness does not provide sufficient understanding of how the tire behaves dynamically: the tire first radial modes, no matter how they were measured, cannot be correlated with this statically measured stiffness. A comprehensive explanation for this phenomenon is needed for better understanding of tire dynamics and hence building the dynamic tire models. In this paper, the relationship between the tire static stiffness and the tire radial vibration modes is investigated using the bushing analogy tire (BAT) modeling concept. It is found that the tire first radial mode, though it can be of different values through different measuring methods, can be explained consistently with this model. A procedure to obtain consistent tire stiffness for the tire model is also proposed as a result of this investigation.

A Three-Dimensional Dynamic Tire Model for Vehicle Dynamic Simulations

2000 ◽  
Vol 28 (2) ◽  
pp. 72-95 ◽  
Author(s):  
B. G. Kao
Keyword(s):  
Three Dimensional ◽  
Rigid Bodies ◽  
Dynamic Responses ◽  
Tire Model ◽  
Vehicle Dynamic ◽  
Vehicle Simulation ◽  
Modeling Concept ◽  
Tire Modeling ◽  
Tire Models ◽  
Force Calculation

Abstract Traditional multibody dynamic (MBD) tire models concentrate on the tire patch force development and the tire in-plane characteristics. The tire lateral dynamics and nonlinear effects caused by the tire compliances during rough terrain driving and severe maneuvers are mostly neglected in vehicle analytical simulations. The tire finite element models, though capable of dealing with these phenomena, are basically not designed for quick vehicle dynamic evaluations. A simple three-dimensional (3-D) MBD tire model for full vehicle performance and maneuvering simulations over various road surfaces is therefore desirable for the ever expanding analysis capabilities and the improved accuracy of the computer-aided vehicle design analysis. In this paper a tire modeling concept to extend the in-plane dynamic tire model to full 3-D tire dynamics is proposed. Essentially, this tire model divides the traditional tire/wheel system model into three elements: two rigid bodies representing the wheel mass/inertia and the tire tread mass/inertia, and a spring/damper representing the sidewall visco-elasticity. Thus, 6 degrees-of-freedom (DOFs) are added for each tire over traditional tire models. Using any existing tire patch force calculation model, this proposed model can be used to simulate full 3-D dynamic responses of a vehicle. To implement this model, techniques to extract the nonlinear spring rates of the sidewalls and to enhance the tire patch force calculations over uneven terrains are explained in this paper. Results of the vehicle simulation using this tire model were compared with measured field data. They showed that this tire modeling concept yields a practical representation for tire 3-D nonlinear dynamic characteristics.

scholarly journals Efficient In-Plane Tire Mode Identification by Radial-Tangential Eigenvector Compounding

2015 ◽  
Vol 43 (1) ◽  
pp. 71-84
Author(s):  
Vasilis Tsinias ◽  
George Mavros
Keyword(s):  
Experimental Studies ◽  
Modal Testing ◽  
Mode Shapes ◽  
Model Parameters ◽  
Tire Model ◽  
Mode Identification ◽  
Tire Dynamics ◽  
Efficient Processing ◽  
Noise Vibration ◽  
Tire Models

ABSTRACT Tire modal testing is frequently used for validation of numerical tire models and identification of structural tire model parameters. Most studies focus primarily on in-plane dynamic tire behavior and adopt the approach of the fixed boundary condition at the wheel center. Here, an identification method of in-plane tire dynamics was developed for the case of a free tire-rim combination. This particular case is important when the aim is to construct a full tire model, capable of predicting ride and noise, vibration, and harshness involving the whole vehicle, all from modal testing. Key attributes of the proposed approach include ease of implementation and efficient processing of measurements. For each type of excitation, i.e., radial and tangential, both radial and tangential responses were recorded. Compounding of the corresponding radial/tangential eigenvectors, which, in the context of the present work, refers to expressing the motion of the tire belt as a combination of the radial and tangential responses, results in smooth mode shapes that were found to agree with those published in other analytical and experimental studies.

Road Load Analysis

2003 ◽  
Vol 31 (1) ◽  
pp. 19-38 ◽  
Author(s):  
M. Sobhanie
Keyword(s):  
Single Layer ◽  
Suspension System ◽  
Tire Model ◽  
Equilibrium Equations ◽  
Shell Elements ◽  
Tire Stiffness ◽  
Tire Forces ◽  
Suspension Model ◽  
Explicit Dynamic ◽  
Tire Models

Abstract Severe loading in a tire/suspension system arises when a rolling tire impacts an obstacle, such as a curb or pothole. Forces and moments at suspension hard points are needed during an impact for component specification, component durability, and endurance analysis. Today, automotive manufacturers and suppliers are promoting virtual prototyping by use of a computer-aided engineering (CAE) tool. CAE consists of a tire model, a suspension model, and a solver for equilibrium equations. The tire models can be classified either by a parametric tire model (PTM) or by a finite element tire model. In the former tire model, tire stiffness is represented by a set of springs; tire forces and moments are estimated by Pajeka equations. This class of tire models is limited to modeling a vehicle's performance, such as ride and handling. In recent years, explicit dynamic modeling of a rolling tire impacting a road imperfection has been used to calculate forces transmitted to a suspension system. The tire model consisted of a single layer of shell elements; solid elements were considered for the tread cap. The beads were not considered in this tire model. In this analysis, ABAQUS Explicit was used to model the rolling and transient impact of a tire. ABAQUS Explicit's modeling results were compared to ABAQUS Standard's results. The comparison included the tire forces, footprint pressure distribution at a free rolling condition, and resonant frequencies. In addition, modeling results of a tire/suspension system traversing an obstacle were presented. The suspension components, except spring and shock, were modeled by rigid elements connected together.

Modeling Nonlinear Flexible Tire Belt in the Study of In-Plane Tire Dynamics

2007 ◽  
Author(s):  
Hiroyuki Sugiyama ◽  
Yoshihiro Suda
Keyword(s):  
High Frequency ◽  
Moving Boundary ◽  
Absolute Nodal Coordinate Formulation ◽  
Tire Model ◽  
Elastic Ring ◽  
Inertia Effects ◽  
Absolute Nodal Coordinate ◽  
Proposed Model ◽  
Tire Dynamics ◽  
Tire Models

In this investigation, a modeling procedure for a tire with flexible belt is developed. The elastic deformation of the belt is modeled using the finite element absolute nodal coordinate formulation which allows for describing large rotational motion and the nonlinear inertia effects; the curved structure of the flexible belt; and moving boundary resulting from tread/road interaction. Using a concept of elastic ring tire models, the sidewall flexibility of tires is modeled using circumferential/radial springs and dampers between the belt and rim, while the tangential tread/road contact force is modeled using friction elements defined at contact nodes within the curved belt elements. Numerical examples are presented in order to demonstrate the use of the flexible tire model developed in this investigation. Good agreements in the tire vibration characteristics obtained using the experiments and the proposed model are demonstrated. It is also shown that the proposed tire model can be used for assessing dynamic characteristics of tires in high frequency ranges resulting from the interaction to uneven roads.

A Modified Dugoff Tire Model for Combined-slip Forces

2010 ◽  
Vol 38 (3) ◽  
pp. 228-244 ◽  
Author(s):  
Nenggen Ding ◽  
Saied Taheri
Keyword(s):  
Vehicle Dynamics ◽  
Tire Model ◽  
Magic Formula ◽  
Model Based ◽  
Proposed Model ◽  
Road Friction ◽  
On Line ◽  
Double Lane Change ◽  
Tire Forces ◽  
Tire Models

Abstract Easy-to-use tire models for vehicle dynamics have been persistently studied for such applications as control design and model-based on-line estimation. This paper proposes a modified combined-slip tire model based on Dugoff tire. The proposed model takes emphasis on less time consumption for calculation and uses a minimum set of parameters to express tire forces. Modification of Dugoff tire model is made on two aspects: one is taking different tire/road friction coefficients for different magnitudes of slip and the other is employing the concept of friction ellipse. The proposed model is evaluated by comparison with the LuGre tire model. Although there are some discrepancies between the two models, the proposed combined-slip model is generally acceptable due to its simplicity and easiness to use. Extracting parameters from the coefficients of a Magic Formula tire model based on measured tire data, the proposed model is further evaluated by conducting a double lane change maneuver, and simulation results show that the trajectory using the proposed tire model is closer to that using the Magic Formula tire model than Dugoff tire model.

A Double Interaction Brush Model for Snow Conditions

2019 ◽  
Vol 47 (2) ◽  
pp. 118-140
Author(s):  
Artem Kusachov ◽  
Fredrik Bruzelius ◽  
Mattias Hjort ◽  
Bengt J. H. Jacobson
Keyword(s):  
Low Complexity ◽  
Large Set ◽  
Tire Model ◽  
Vehicle Handling ◽  
Real Time Applications ◽  
Snow Conditions ◽  
Double Interaction ◽  
Tire Models ◽  
Force Characteristics ◽  
Model Approach

ABSTRACT Commonly used tire models for vehicle-handling simulations are derived from the assumption of a flat and solid surface. Snow surfaces are nonsolid and may move under the tire. This results in inaccurate tire models and simulation results that are too far from the true phenomena. This article describes a physically motivated tire model that takes the effect of snow shearing into account. The brush tire model approach is used to describe an additional interaction between the packed snow in tire tread pattern voids with the snow road surface. Fewer parameters and low complexity make it suitable for real-time applications. The presented model is compared with test track tire measurements from a large set of different tires. Results suggest higher accuracy compared with conventional tire models. Moreover, the model is also proven to be capable of correctly predicting the self-aligning torque given the force characteristics.

scholarly journals Influence of the flexibility of beams and slabs in static response and dynamic properties

2016 ◽  
Vol 9 (6) ◽  
pp. 842-855 ◽  
Author(s):  
J. R. BUENO ◽  
◽  
D. D. LORIGGIO ◽  
Keyword(s):  
Finite Element Method ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Vibration Modes ◽  
Linear Regime ◽  
Static Response ◽  
The Finite Element Method ◽  
Standard Code ◽  
The Relationship ◽  
Brazilian Standard

Abstract This article examines numerically the flexibility influence of support beams in static response and dynamic properties of a symmetric plate formed by massive slabs of reinforced concrete in elastic linear regime, using the Finite Element Method. In the static response the variation of bending mo-ments and displacements are evaluated, which depend on the relationship between the flexibility of the slab and the beam. The evaluation of dynamic properties is held in undamped free vibration, through which the vibration modes and the values of the natural frequencies is obtained, which are compared with the limits of the Brazilian standard code for design of concrete structures. Results show that the response may show great variation due to the change in the relationship between bending stiffness of the slabs and the beams.

scholarly journals Characterization and Modelling of Various Sized Mountain Bike Tires and the Effects of Tire Tread Knobs and Inflation Pressure

2020 ◽  
Vol 10 (9) ◽  
pp. 3156 ◽  
Author(s):  
Andrew Dressel ◽  
James Sadauckas
Keyword(s):  
Simple Model ◽  
Lateral Stiffness ◽  
Tire Model ◽  
Laboratory Measurements ◽  
Inflation Pressure ◽  
Mountain Bike ◽  
Basic Model ◽  
Radial Stiffness ◽  
In Series ◽  
Distinguishing Features

Mountain bikes continue to be the largest segment of U.S. bicycle sales, totaling some USD 577.5 million in 2017 alone. One of the distinguishing features of the mountain bike is relatively wide tires with thick, knobby treads. Although some work has been done on characterizing street and commuter bicycle tires, little or no data have been published on off-road bicycle tires. This work presents laboratory measurements of inflated tire profiles, tire contact patch footprints, and force and moment data, as well as static lateral and radial stiffness for various modern mountain bike tire sizes including plus size and fat bike tires. Pacejka’s Motorcycle Magic Formula tire model was applied and used to compare results. A basic model of tire lateral stiffness incorporating individual tread knobs as springs in parallel with the overall tread and the inflated carcass as springs in series was derived. Finally, the influence of inflation pressure was also examined. Results demonstrated appreciable differences in tire performance between 29 × 2.3”, 27.5 × 2.8”, 29 × 3”, and 26 × 4” knobby tires. The proposed simple model to combine tread knob and carcass stiffness offered a good approximation, whereas inflation pressure had a strong effect on mountain bike tire behavior.

scholarly journals Effect of adding mass to rotor on in-plane squeal in automotive disc brake

2018 ◽  
Vol 211 ◽  
pp. 13006
Author(s):  
Takashi Nakae ◽  
Takahiro Ryu ◽  
Hiroki Goto ◽  
Daisuke Sato
Keyword(s):  
Dry Friction ◽  
Coulomb Friction ◽  
Disc Brake ◽  
Vibration Modes ◽  
Concentrated Mass ◽  
Mass Model ◽  
Out Of Plane ◽  
The Relationship

This study experimentally examined disc brake-generated inplane squeal by looking at vibration modes. The in-plane squeal was determined to be closely related to both the out-of-plane squeal that has directionality caused by Coulomb friction and the in-plane squeal caused by dry friction. The characteristics of in-plane squeal were also analytically investigated using a concentrated mass model formed by connected massless beams, and the relationship between mass added to the rotor and squeal suppression was clarified.

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