scholarly journals Tire Model with Temperature Effects for Formula SAE Vehicle

2019 ◽  
Vol 9 (24) ◽  
pp. 5328 ◽  
Author(s):  
Diwakar Harsh ◽  
Barys Shyrokau
Keyword(s):  
Steady State ◽  
Measurement Data ◽  
Transient Behavior ◽  
Lateral Acceleration ◽  
Tire Model ◽  
Magic Formula ◽  
Vehicle Simulation ◽  
Formula Sae ◽  
Full Vehicle ◽  
Design Competition

Formula Society of Automotive Engineers (SAE) (FSAE) is a student design competition organized by SAE International (previously known as the Society of Automotive Engineers, SAE). Commonly, the student team performs a lap simulation as a point mass, bicycle or planar model of vehicle dynamics allow for the design of a top-level concept of the FSAE vehicle. However, to design different FSAE components, a full vehicle simulation is required including a comprehensive tire model. In the proposed study, the different tires of a FSAE vehicle were tested at a track to parametrize the tire based on the empirical approach commonly known as the magic formula. A thermal tire model was proposed to describe the tread, carcass, and inflation gas temperatures. The magic formula was modified to incorporate the temperature effect on the force capability of a FSAE tire to achieve higher accuracy in the simulation environment. Considering the model validation, the several maneuvers, typical for FSAE competitions, were performed. A skidpad and full lap maneuvers were chosen to simulate steady-state and transient behavior of the FSAE vehicle. The full vehicle simulation results demonstrated a high correlation to the measurement data for steady-state maneuvers and limited accuracy in highly dynamic driving. In addition, the results show that neglecting temperature in the tire model results in higher root mean square error (RMSE) of lateral acceleration and yaw rate.

scholarly journals Vehicle Cornering Performance Evaluation and Enhancement Based on CAE and Experimental Analyses

2019 ◽  
Vol 9 (24) ◽  
pp. 5428
Author(s):  
Hsing-Hui Huang ◽  
Ming-Jiang Tsai
Keyword(s):  
Steady State ◽  
Suspension System ◽  
Lateral Acceleration ◽  
Phase Lag ◽  
Handling Performance ◽  
Yaw Rate ◽  
Full Vehicle ◽  
Camber Angle ◽  
Simulation Results ◽  
Initial Camber

A full-vehicle analysis model was constructed incorporating a SLA (Short Long Arm) strut front suspension system and a multi-link rear suspension system. CAE (Computer Aided Engineering) simulations were then performed to investigate the lateral acceleration, yaw rate, roll rate, and steering wheel angle of the vehicle during constant radius cornering tests. The validity of the simulation results was confirmed by comparing the computed value of the understeer coefficient (Kus) with the experimental value. The validated model was then used to investigate the steady-state cornering performance of the vehicle (i.e., the roll gradient and yaw rate gain) at various speeds. The transient response of the vehicle was then examined by means of simulated impulse steering tests. The simulation results were confirmed by comparing the calculated values of the phase lag, natural frequency, yaw rate gain rate, and damping ratio at various speeds with the experimental results. A final series of experiments was then performed to evaluate the relative effects of the cornering stiffness, initial toe-in angle, and initial camber angle on the steady-state and transient-state full-vehicle cornering handling performance. The results show that the handling performance can be improved by increasing the cornering stiffness and initial toe-in angle or reducing the initial camber angle.

A Full Vehicle Model for the Development of a Variable Camber Suspension

2007 ◽  
Author(s):  
Isao Kuwayama ◽  
Fernando Baldoni ◽  
Federico Cheli
Keyword(s):  
Simulation Models ◽  
Dynamics Simulation ◽  
Tire Model ◽  
Electronic Components ◽  
Vehicle Model ◽  
Active Systems ◽  
Additional Degree ◽  
Vehicle Simulation ◽  
Full Vehicle ◽  
Multi Body

The accuracy of the recent vehicle dynamics simulation technology, represented by Multi-Body Simulations along with reliable tire models, has been remarkably progressing and provides reasonable simulation results not only for conventional passive vehicles but also for advanced active vehicles equipped with electronic components; however, when it comes to advanced vehicle applications with complex active systems, the complexity causes a longer simulation time. On the other hand, even though simple numerical vehicle simulation models such as single-track, two-track and a dozen degrees of freedom (dofs) models can provide less information than those of multi-body models, they are still appreciated by specific applications particularly the ones related to the development of active systems. The advantages of these numerical simulation models lie in the simulation platform, namely the Matlab/Simulink environment, which is suitable for modeling electronic components. In this paper, an 18 dofs vehicle model has been proposed for the development of a type of active suspension named Variable Camber which has an additional degree of freedom in camber angle direction and a description of the models and some preliminary results are reported: the control strategy for the variable camber suspension will be published ([3]). The model can reproduce a passive vehicle with a passive suspension as well; all the necessary dimensions, parameters, and physical properties are derived from a specific multi-body full vehicle model which has been fully validated with respect to a real one on the track. As for a tire model, Magic Formula 5.2 has been implemented on both the numerical and the multi-body vehicle models respectively so that the same tire model can be applied.

Validation of vehicle-based tyre testing methods

2018 ◽  
Vol 233 (1) ◽  
pp. 18-27
Author(s):  
Anton Albinsson ◽  
Fredrik Bruzelius ◽  
Bengt Jacobson ◽  
Shenhai Ran
Keyword(s):  
Steady State ◽  
Development Process ◽  
Simulation Models ◽  
Operating Conditions ◽  
Road Surface ◽  
Model Verification ◽  
Slip Angle ◽  
Tyre Model ◽  
Vehicle Simulation ◽  
Full Vehicle

The development process for passenger cars is both time- and resource-consuming. Full vehicle testing is an extensive part of the development process that consumes large amount of resources, especially within the field of vehicle dynamics and active safety. By replacing physical testing with complete vehicle simulations, both the development time and cost can potentially be reduced. This requires accurate simulation models that represent the real vehicle. One major challenge with full vehicle simulation models is the representation of tyres in terms of force and moment generation. The force and moment generation of the tyres is affected by both operating conditions and road surface. Vehicle-based tyre testing offers a fast and efficient way to rescale force and moment tyre models to different road surfaces, in this study the Pacejka 2002 model. The resulting tyre model is sensitive to both the operating conditions during testing and the road surface used. This study investigates the influence of the slip angle sweep rate and road surface on the lateral tyre force characteristics of the fitted tyre model. Tyre models fitted to different manoeuvres are compared and the influence on the full vehicle behaviour is investigated in IPG Carmaker. The results show that by using the wrong road surface, the resulting tyre model can end up outside the tolerances specified by the ISO standard for vehicle simulation model verification in steady-state cornering. The use of Pacejka 2002 models parameterized in a steady-state manoeuvre to simulate the vehicle behaviour in sine-with-dwell manoeuvres is also discussed.

An Iterative Approach for Steady State Handling Analysis of Vehicles

2008 ◽  
Author(s):  
Indrasen Karogal ◽  
Beshah Ayalew ◽  
E. Harry Law
Keyword(s):  
Steady State ◽  
Test Data ◽  
Lateral Force ◽  
Lateral Acceleration ◽  
Iterative Approach ◽  
Tire Model ◽  
Passenger Car ◽  
Lateral Forces ◽  
Simulation Results ◽  
Weight Transfer

In this paper, we present an iterative approach for analyzing the steady state handling behavior of a two-axled vehicle. This approach computes lateral forces iteratively from two separate submodels. The first submodel is an appropriate tire model that computes per wheel lateral forces as functions of slip angles, from formulations preferably expressed in a non-dimensional format. The second is a lateral weight transfer submodel that computes per-axle lateral force contributions for a given lateral acceleration. The combination then allows for the estimation of the required steer angles for the prevailing lateral acceleration. Subsequent corrections are then applied to take into account steer effects such as roll steer, lateral force compliance steer and aligning moment compliance steer. The usefulness of the approach is demonstrated by comparing simulation results with test data for a small passenger car.

A Dynamic Tire Model for ABS Maneuver Simulations

2010 ◽  
Vol 38 (2) ◽  
pp. 137-154 ◽  
Author(s):  
Francesco Braghin ◽  
Edoardo Sabbioni
Keyword(s):  
Steady State ◽  
Order Differential Equation ◽  
Transient Behavior ◽  
Slip Angle ◽  
Tire Model ◽  
Relaxation Length ◽  
Steady State Condition ◽  
First Order ◽  
Significant Parameter ◽  
Tire Models

Abstract Due to the dimensions of the tire-road contact area, transients in a tire last approximately 0.1 s. Thus, in the case of abrupt maneuvers such as ABS braking, the use of a steady-state tire model to predict the vehicle’s behavior would lead to significant errors. Available dynamic tire models, such as Pacejka’s MF-Tire model, are based on steady-state formulations and the transient behavior of the tire is included by introducing a first order differential equation of relevant quantities such as the slip angle and the slippage. In these differential equations the most significant parameter used to describe the transient behavior is the so-called relaxation length, i.e., the distance traveled by the tire to settle to a new steady-state condition once perturbated. Usually this parameter is assumed to be constant.

scholarly journals A Brush-Type Tire Model with Nonsmooth Representation

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Ryo Kikuuwe
Keyword(s):  
Steady State ◽  
Numerical Integration ◽  
Friction Force ◽  
Static Friction ◽  
Mathematical Representation ◽  
Generic Model ◽  
Tire Model ◽  
Integration Algorithm ◽  
Magic Formula ◽  
Proposed Model

This paper proposes a brush-type tire model with a new mathematical representation. The presented model can be seen as a generic model that describes the distributed viscoelastic force and Coulomb-like friction force, which are balancing each other at each point, in the contact patch. The model is described as a partial differential algebraic inclusion (PDAI), which involves the set-valuedness to represent the static friction. A numerical integration algorithm for this PDAI is derived through the implicit Euler discretization along both space and time. Some numerical comparisons with Magic Formula and a LuGre-based tire model are presented. The results show that, with appropriate choice of parameters, the proposed model is capable of producing steady-state characteristics similar to those of Magic Formula. It is also shown that the proposed model realizes a proper static friction state, which is not realized with a LuGre-based tire model.

An Analytical Transient Tire Model

2001 ◽  
Vol 29 (2) ◽  
pp. 108-132 ◽  
Author(s):  
A. Ghazi Zadeh ◽  
A. Fahim
Keyword(s):  
Transient Behavior ◽  
Stability Control ◽  
Vehicle Stability ◽  
Tire Model ◽  
Steering Angle ◽  
First Order ◽  
Vehicle Stability Control ◽  
Proposed Model ◽  
Depth Study ◽  
And Performance

Abstract The dynamics of a vehicle's tires is a major contributor to the vehicle stability, control, and performance. A better understanding of the handling performance and lateral stability of the vehicle can be achieved by an in-depth study of the transient behavior of the tire. In this article, the transient response of the tire to a steering angle input is examined and an analytical second order tire model is proposed. This model provides a means for a better understanding of the transient behavior of the tire. The proposed model is also applied to a vehicle model and its performance is compared with a first order tire model.

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.

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