• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.3
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• pp.50-61
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• 1994

A method for performing dynamic design sensitivity analysis of vehicle suspension systems which have three dimensional closed-loop kinematic structure is presented. A recursive form of equations of motion for a MacPherson suspension system is derived as basis for sensitivity analysis. By directly differentiating the equations of motion with respect to design variables, sensitivity equations are obtained. The direct generalize for the application of multibody dynamic sensitivity analysis. Based on the proposed sensitivity analysis, optimal design of a MacPherson suspension system is carried out taking unsprung mass, spring and damping coefficients as design variables.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.67-80
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• 2004

In the present paper, a numerical algorithm for the kinematic analysis of a MacPherson strut motor-vehicle suspension system is developed. The kinematic analysis is carried out in terms of the rectangular Cartesian coordinates of some defined points in the links and at the joints. The presented formulation in terms of this system of coordinates is simple and involves only elementary mathematics. The resulting constraint equations are mostly either linear or quadratic in the rectangular Cartesian coordinates. The proposed formulation eliminates the need to write redundant constraints and allows to solve a reduced system of equations which leads to better accuracy and a reduction in computing time. The algorithm is applied to solve the initial positions as well as the finite displacement, velocity and acceleration problems for the MacPherson strut motor-vehicle suspension system.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.7
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• pp.137-143
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• 1997

In this study, handling simulation of a passenger car is carried out to see the effects of suspension compliance, roll stabilizef bar and chassis flexibility. The front suspension of the car is a MacPherson strut type and the rear suspension is a multi-link type. The following five DADS models are constructed and compared to verify the effects of suspension compliance and chassis flexibility during lane change. (1) Vdhicle model without hard point compliance and stabilizer, (2) Vehicle model with hard point compoiance, (3) Vehicle model with hard point compliance and stabilizer, (4) Vehicle model with hard point compoiance, stabilizer, and one vibration mode of the chaxxis. (5) Vehicle model with hard point compliance, stabilizer, and three vibration modes of the chassis. The result shows that hard point compliance and stabilizer are significant in roll angle, and the flexibility of the chassis affects the yaw angle and yaw rate.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.38-48
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• 1997

A method for performing kinematic design sensitivity analysis of vehicle suspension systems is presented. For modeling of vehicle suspensions, the multibody dynamic formulation is adopted, where suspensions are assumed as combination of rigid bodies and ideal frictionless joints. In a relative joint coordinate setting, kinematic constraint equations are obtained by imposing cut-joints that transform closed-loop shape suspension systems into open-loop systems. By directly differentiating the constraint equations with respect to kinematic design variables, such as length of bodies, notion axis, etc., sensitivity equations are derived. By solving the sensitivity equations, sensitivity of static design factors that can be used for design improvement, can be obtained. The validity and usefulness of the method are demonstrated through an example where kinematic sensitivity analysis of a MacPherson strut suspension of performed.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1961-1968
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• 2003

In this paper, an efficient numerical algorithm for the kinematic analysis of the standard MacPherson suspension system is presented. The kinematic analysis of the suspension mechanism is carried out in terms of the rectangular Cartesian coordinates of some defined points in the links and at the kinematic joints. Geometric constraints that fix the distances between the points belonging to the same rigid link are introduced. The nonlinear constraint equations are solved by iterative numerical methods. The corresponding linear equations of the velocity and acceleration are solved to yield the velocities and accelerations of the unknown points. The velocities and accelerations of other points of interest as well as the angular velocity and acceleration of any link in the mechanism can be calculated.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.2
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• pp.43-53
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• 1998

This paper addresses an optimization for reducing a steering error of a rack-and-pinion steering linkage with a MacPherson strut independent front suspension system. The length, orientations and inner joint positions of a tie-rod are selected as design variables and Ackerman geonetry, understeer effect, minimum turn radius, wheel alignment and packaging are considered as design constraints. Nonlinear kinematic analysis of the steering system is performed for calculating the values of cost and constraints, and Augmented Lagrange Multiplier(ALM) method is used for solving the constrained optinization problem. The optimization results show that the steering error are considerably reduced while satisfying all the constraints.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.1
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• pp.205-213
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• 1997

In this study, dynamic analysis of a passenger car is carried out to analyze ride quality over a random road profile. The front suspension of the car is a MacPherson strut type and the rear suspension is a multi- link type. The following five different models are constructed and compared to see the effects of engine vibration and chassis flexibility in the ride quality. (1) one rigid chassis model, (2) a rigid chassis and rigid engine model, (3) a rigid engine and flexible chassis model with one vibration mode, (4) one flexible chassis model with six engine vibration modes and one chassis vibration mode, (5) one flexible chassis model with seven vibration modes and four static correction modes. The result shows that engine vibration modes and the first bending mode of the chassis are important in the ride quality.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.3
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• pp.486-494
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• 2001

This paper presents a real-time multibody vehicle dynamic analysis method using recursive Kanes formulation and suspension composite joints. To shorten the computation time of simulation, relative coordinate system is used and the equations of motion are derived using recursive Kanes formulation. Typical suspension systems of vehicles such as MacPherson strut suspension system is modeled by suspension composite joints. The joints are derived and utilized to reduce the computation time of simulation without any degradation of kinematical accuracy of the suspension systems. Using the develop program, a multibody vehicle dynamic model is formed and simulations are performed. Accuracy of the simulation results is compared to the real vehicle field test results. It is found that the simulation results using the proposed method are very accurate and real-time simulation is achieved on a computer with single PowerPC 604 processor.