• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.10
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• pp.1034-1042
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• 2009

In this paper, the magic formula model was applied for a friction damper in a drum-type washing machine. To describe characteristics of the hysteretic damping force, Physical tests were first carried out to get experimental results using an MTS machine. Then, parameters for the magic formula model were determined from the experimental curves. The ADAMS and MATLAB programs were used for the multibody modeling of the damper and process for parameter identification. The model of drum-type washing machine was applied for a dynamic model of friction damper, in which the accuracy of the proposed damper model was verified.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.11
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• pp.92-99
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• 2021

Agricultural tractors drive and operate both off-road and on-road. Tire-road interaction significantly affects the tractive performance of a tractor, which is difficult to predict numerically. Many empirical models have been developed to predict the tractive performance of tractors using the cone index, which can be measured through simple tests. However, a magic formula model that can determine the tractive performance without a cone index can be used instead of traditional empirical models as the cone index cannot be measured on asphalt roads. The aim of this study was to predict the tractive performance of a tractor using the magic formula tire model. The traction force of the tires on an asphalt road was measured using an agricultural tractor. The dynamic wheel load was calculated to derive the coefficients of the traction-slip curve using the measured static wheel load and drawbar pull of the tractor. Curve fitting was performed to fit the experimental data using the magic formula. The parameters of the magic formula tire model were well identified, and the model successfully determined the coefficient of traction of the tractor.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.110-119
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• 1997

Four wheel steering(4WS) systems which can control the lateral and yaw motions of vehicles by steering front and rear wheels simultaneously, have been regarded as effective for improving the stability and handing performance of vehicles. However, since the 4WS systems depend only on the lateral force of tire, they have some limitation due to the nonlinear characteristics of tire related with the saturation phenomenon of lateral force to the slip angle of tire in a near-limit-performance maneuvering range. In this study, in other to evaluate the effect of nonlinear characteristics of tire on the dynamic performance of vehicles, a new concept for driving the cornering stiffness of nonlinear tire by using the "Magic Formula" tire model is proposed. In addition, the nonlinear 4WS vehicle model is constructed based on the proposed cornering stiffness of nonlinear tire. It is noted from simulation that the nonlinear characteristics of tire affect greatly on the 4WS vehicle performance.rformance.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.6
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• pp.722-728
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• 1998

In this paper real-time estimation methods for identifying the tire-road friction coefficient are presented. Taking advantage of the Magic Formula Tire Model, the similarity technique and the specific model for the vehicle dynamics, a reduced order observer/filtered-regressor-based method is proposed. The Proposed method is evaluated on simulations of a full-vehicle model with an eight state nonlinear vehicle/transmission model and nonlinear suspension model. It has been shown through simulations that it is possible to estimate the tire-road friction from measurements of engine rpm, transmission output speed and wheel speeds using the proposed identification method. The proposed method can be used as a useful option as a part of vehicle collision warning/avoidance systems and will be useful in the implementation of a warning algorithm since the tire-road friction can be estimated only using RPM sensors.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.6
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• pp.89-102
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• 1997

In this study, the steady state cornering behavior of a vehicle is investigated by using a numerical model that has parameters associated with roll motion. The nonlinear characteristics of tire cornering forces and aligning torques are presented in analytical forms using the magic formula. The sets of nonlinear algebraic equations that govern the cornering motion are solved by the Newton-Raphson iteration method. The vehicle design parameters are measured by SPMD(Suspension Parameter Measuring Device), and its results are verified by carrying out a skid pad test. The design parameters that are most affecting the steady state cornering behavior are classified into four factors, and the contributions of the factors to understeer gradient are then calculated.

• Journal of Auto-vehicle Safety Association
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• v.13 no.4
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• pp.33-38
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• 2021

This paper presents a comparative study between the parameter-optimized Pacejka model and artificial neural network model for the tire force estimation. The two different approaches are investigated and compared in this study. First, offline optimization is conducted based on Pacejka Magic Formula model to determine the proper parameter set for the minimization of tire force error between the model and test data set. Second, deep neural network model is used to fit the model to the tire test data set. The actual tire forces are measured using MTS Flat-Track test platform and the measurements are used as the reference tire data set. The focus of this study is on the applicability of machine learning technique to tire force estimation. It is shown via the regression results that the deep neural network model is more effective in describing the tire force than the parameter-optimized Pacejka model.

• Transactions of the Korean Society of Automotive Engineers
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• v.24 no.6
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• pp.730-736
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• 2016

Recent research suggests the various applications of Model Predictive Control on vehicle systems. In numerous cases, nonlinear tire models such as the Magic Formula, which are highly complex and are more detailed than necessary, are used. This paper presents a nonlinear tire model that excludes the region of negative slope but expresses the nonlinear properties of tire well enough for tracking the lane of a racing course. The proposed inverse tire model can also be used to calculate the slip angle from the tire force. Thus, the model can be utilized to design the Model Predictive Controller.

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.4
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• pp.169-176
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• 2000

Longitudinal and lateral forces acting on tires are known to be closely related to the tract-ability braking characteristics handling stability and maneuverability of ground vehicles. In thie paper in order to develop tire force monitoring systems a monitoring model is proposed utilizing not only the vehicle dynamics but also the roll motion. Based on the monitoring model three monitoring systems are developed to estimate the tire force acting on each tire. Two monitoring systems are designed utilizing the conventional estimation techniques such as SMO(Sliding Mode Observer) and EKF(Extended Kalman Filter). An additional monitoring system is designed based on a new SKFMEC(Scaled Kalman Filter with Model Error Compensator) technique which is developed to improve the performance of EKF method. Tire force estimation performance of the three monitoring systems is compared in the Matlab simulations where true tire force data is generated from a 14 DOF vehicle model with the combined-slip Magic Formula tire model. The built in our Lab. simulation results show that the SKFMEC method gives the best performance when the driving and road conditions are perturbed.

• Journal of Mechanical Science and Technology
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• v.14 no.7
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• pp.730-736
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• 2000

In this paper, several tire models (Magic formula, Carpet plot, VA tire, DADS tire and STI tire) are implemented and compared. Since the STI (System Technology Inc.) tire model in the AutoDyn7 program is in a good agreement to NADSdyna STI tire model and experiment, it is selected as a reference tire model for the comparison. To compare tire models, input parameters of each tire model are extracted from the STI tire model to preserve the same tire properties. Several simulations are carried out to compare performances of tire models, i. e., bump simulation, lane change simulation, and pulse steering simulation. The performances in vehicle maneuverability are also compared with the four parameter evaluation method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.7 s.178
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• pp.1871-1877
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• 2000

Longitudinal and lateral forces acting at tire are known to be closely related to the tractive ability, braking characteristics, handling stability and maneuverability of ground vehicles. However, it is not feasible in the operating vehicles to measure the tire forces directly because of high cost of sensors, limitations in sensor technology, interference with the tire rotation and harsh environment. In this paper, in order to develop tire force monitoring system, a new vehicle dynamics monitoring model is proposed including the roll motion. Based on the monitoring model, tire force monitoring system is designed to estimate the lateral tire force acting at each tire. A newly proposed SKFMEC (Scaled Kalman Filter with Model Emr Compensator) method is developed utilizing the conventional EKF (Extended Kalman Filter) method. Tire force estimation performance of the SKFMEC method is evaluated in the Matlab simulations where true tire force data is generated from a 14 DOF vehicle model with a combined-slip Magic Formula tire model.