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.

Non-linear elastic ring tyre model using the absolute nodal coordinate formulation

2009 ◽  
Vol 223 (3) ◽  
pp. 211-219 ◽  
Author(s):  
H Sugiyama ◽  
Y Suda
Keyword(s):  
Moving Boundary ◽  
Absolute Nodal Coordinate Formulation ◽  
Elastic Ring ◽  
Tyre Model ◽  
Inertia Effects ◽  
Absolute Nodal Coordinate ◽  
Linear Elastic ◽  
Proposed Model ◽  
Road Surfaces ◽  
Non Linear

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

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.

scholarly journals Modeling and Simulation of a Moving Yarn Segment: Based on the Absolute Nodal Coordinate Formulation

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Shujia Li ◽  
Yongxing Wang ◽  
Xunxun Ma ◽  
Shengze Wang
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Longitudinal Direction ◽  
Three Dimensions ◽  
Actual Process ◽  
Absolute Nodal Coordinate ◽  
Proposed Model ◽  
Air Resistance ◽  
The Absolute ◽  
Experimental Comparisons

A new finite element dynamic model of a moving yarn segment has been proposed in this paper based on the absolute nodal coordinate formulation (ANCF). Apart from taking into account the elastic properties of the yarn in three dimensions, the model also considers the viscosity in the longitudinal direction and takes into account the effect of gravity and air resistance. In this paper, the simulation described the movement of the yarn segment that is pulled by the fixer on the guideway. Then, a corresponding experiment was proposed to evaluate the theoretical model. The theoretical and experimental comparisons of the motion tracing exhibited good agreement, demonstrating that the new model could predict the actual moving trace of the yarn segment. Moreover, another simulation of the spatial motion of the yarn segment was presented, to elucidate the role of the model in predicting the movement of the yarn segment. After considering the parameters of the actual process and its constraints, the authors established that the proposed model could be used to predict the trajectory of a yarn segment in the actual production process, which is vital when fabricating textile products.

Study on Elastic Forces of the Absolute Nodal Coordinate Formulation for Deformable Beams

1999 ◽  
Author(s):  
Yoshitaka Takahashi ◽  
Nobuyuki Shimizu
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Nonlinear Function ◽  
Absolute Nodal Coordinates ◽  
Large Rotation ◽  
Inertia Effects ◽  
Absolute Nodal Coordinate ◽  
Elastic Forces ◽  
The Absolute

Abstract There are three basic finite element formulations which are used in the dynamics of flexible beams. These are the floating frame of reference approach, the finite segment method and the large rotation vector approach. Recently, the absolute nodal coordinate formulation was proposed by A.A.Shabana et al. In this procedure, there is no need to transform the element matrices since the equations of motion are defined in terms of absolute nodal coordinates. The mass matrix becomes constant, whereas the stiffness matrix becomes nonlinear function of time, even in case of linear elastic problems. One possible method to avoid such cumbersome of the absolute nodal coordinate formulation in calculating clastic forces is to assume the infinitesimal deformation theory against beams undergoing large rotation. In this paper, a new formulation to calculate the elastic forces and add the rotary inertia effects in the expression of the inertia forces. This formulation is based on the assumption that the deformations within each element remain very small. The expression of the resulting clastic force is simple, and the need for performing coordinate transformation is avoided. As the method assumes that the deformation of the beam from a selected beam axis is very small, a large number of finite elements is required for large deformation problems. However, the formulation has been found to be efficient for large rotation and medium deformation problems. Numerical examples are demonstrated for this formulation by using planar flexible pendulum problems.

Longitudinal Tire Dynamics Model for Transient Braking Analysis: ANCF-LuGre Tire Model

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Hiroki Yamashita ◽  
Yusuke Matsutani ◽  
Hiroyuki Sugiyama
Keyword(s):  
Structural Deformation ◽  
Model Parameters ◽  
Force Distribution ◽  
Force Model ◽  
Tire Model ◽  
Elastic Ring ◽  
Contact Patch ◽  
Tire Force ◽  
Tire Dynamics ◽  
Tire Friction

In this investigation, the flexible tire model based on the absolute nodal coordinate formulation (ANCF) is integrated with LuGre tire friction model for evaluation of the longitudinal tire dynamics under severe braking scenarios. The ANCF-LuGre tire model developed allows for considering the nonlinear coupling between the dynamic structural deformation of the tire and its transient tire force distribution in the contact patch using general multibody dynamics computer algorithms. To this end, the contact patch obtained by the ANCF elastic ring tire model is discretized into small strips and the state of friction at each strip is defined by the differential equation associated with the discretized LuGre friction parameters. The normal contact pressure distribution predicted by the ANCF elastic ring elements that are in contact with the road surface are mapped onto the LuGre strips in the contact patch to evaluate the tangential tire force distribution and then the tire forces evaluated at LuGre strips are fed back to the generalized tangential contact forces of the ANCF elastic ring tire model. By doing so, the structural deformation of the ANCF elastic ring tire model is dynamically coupled with the LuGre tire friction in the final form of the governing equations. Furthermore, the systematic and automated parameter identification procedure for the LuGre tire force model is developed. It is shown that use of the proposed procedure with the modified friction curve proposed for wet road conditions leads to accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Several numerical examples are presented in order to demonstrate the use of the in-plane ANCF-LuGre tire model for the longitudinal transient dynamics of tires under severe braking scenarios.

A novel absolute nodal coordinate formulation thin plate tire model with fractional derivative viscosity and surface integral-based contact algorithm

2018 ◽  
Vol 233 (3) ◽  
pp. 583-597
Author(s):  
Peng Lan ◽  
Yaqi Cui ◽  
Zuqing Yu
Keyword(s):  
Fractional Derivative ◽  
Contact Pressure ◽  
Thin Plate ◽  
Absolute Nodal Coordinate Formulation ◽  
Tire Model ◽  
Plate Element ◽  
Absolute Nodal Coordinate ◽  
Contact Patch ◽  
Contact Algorithm ◽  
The Absolute

A new absolute nodal coordinate formulation thin plate tire model, which includes the damping property of the rubber and an efficient tire–road contact algorithm is given. The fractional derivative viscosity constitutive model is proposed in this paper based on the complete form of the absolute nodal coordinate formulation thin plate element, which is created to describe the stress-free initially curved configuration of the tire. A new contact algorithm based on the integration of the contact pressure within the contact patch is developed. By solving the simultaneous equations of the tire geometry and road profile, the dimensionless coordinates for the boundary points of contact patch could be obtained directly. A self-adaptable Gauss integration strategy is introduced to perform the integration of the contact pressure within the varying region, so the integration could reach high precision by few integration points. The calculation of contact force is determined based on penalty method and smoothed Coulomb friction model. The application of fractional derivative viscosity on the absolute nodal coordinate formulation thin plate element is demonstrated by numerical results. A pressurized Golf tire model is given to show the feasibility of the proposed tire–ground contact algorithm.

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.

Development of a Simulink-CarSim Interaction Package for ABS Simulation of Discrete Tire Models

2016 ◽  
Vol 44 (1) ◽  
pp. 2-21 ◽  
Author(s):  
Karan R. Khanse ◽  
Yaswanth Siramdasu ◽  
Saied Taheri
Keyword(s):  
High Frequency ◽  
Design Tool ◽  
Tool Development ◽  
Tire Model ◽  
Vehicle Model ◽  
Rule Based ◽  
Straight Line ◽  
Software Interfaces ◽  
Antilock Braking ◽  
Tire Models

ABSTRACT Automotive and tire companies have to spend extensive amounts of time and money to tune their products through prototype testing at dedicated test facilities. This is mainly because of the limitations in the simulation capabilities that exist today. With greater competence in simulation comes more control over designs in the initial stages, which in turn lowers the demand for the expensive stage of tuning. This article aims at taking today's simulation capabilities a step forward by integrating models that are best developed in different software interfaces. An in-plane rigid ring tire model has been developed to understand the transient response of tires to various high-frequency events such as antilock braking and short-wavelength road disturbances. A rule-based antilock braking systems (ABS) model performed the high-frequency braking operation. The tire and ABS models were created in the Matlab-Simulink environment. A vehicle model was developed in CarSim. The models developed in Simulink were integrated with the vehicle model in CarSim, in the form of a design tool that can be used by tire as well as car designers for further tuning of the vehicle functional performances, as they relate to handling and braking maneuvers. The straight-line ABS performance was predicted using these models for a sample vehicle, and the results were substantiated through physical outdoor tests on the same vehicle to validate the developed integration package. The tool development, simulation results, and the objective test will be discussed.

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.

Versatile Absolute Nodal Coordinate Formulation Model for Dynamic Folding Wing Deployment and Flutter Analyses

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Keisuke Otsuka ◽  
Yinan Wang ◽  
Kanjuro Makihara
Keyword(s):  
Rigid Body ◽  
Frequency Domain ◽  
Time Domain ◽  
Absolute Nodal Coordinate Formulation ◽  
Absolute Nodal Coordinate ◽  
Coupled Motion ◽  
Proposed Model ◽  
Flutter Analysis ◽  
Folding Wing ◽  
The Time Domain

Aircraft performance can be improved using morphing wing technologies, in which the wing can be deployed and folded under flight conditions, providing a wide flight envelope, good fuel efficiency, and reducing the space required to store the aircraft. Because the deployment of the wing is a nonlinear-coupled motion comprising large rigid body motion and large elastic deformation, a nonlinear folding-wing model is required to perform the necessary time-domain deployment simulation, while a linear model is required to perform the frequency-domain flutter analysis. The objective of this paper is to propose a versatile model that can be applied to both the time-domain and frequency-domain analyses of a folding wing, based on flexible multibody dynamics (MBD) using absolute nodal coordinate formulation (ANCF) and unsteady aerodynamics. This new versatile model expands the application range of the flexible MBD using ANCF in time-domain simulation, allowing it to express the coupled motion of extremely large elastic deformations and large rigid body motions that arise in next-generation aircraft. The time-domain deployment simulation conducted using the proposed model is useful for parametric deployment-system design because the model has improved calculation time. In the frequency-domain flutter analysis of a folding wing, the flutter speed obtained from the proposed model agrees with that obtained from an experiment, with an error of 4.0%, showing promise for application in next-generation aircraft design.

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