Derivation and validation of nonlinear governing equations for an analysis of vehicle handling.
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| Title: | Derivation and validation of nonlinear governing equations for an analysis of vehicle handling. |
|---|---|
| Authors: | Yang, S.1 sungmo.yang@renaultsamsungM.com, Kim, J.1 |
| Source: | International Journal of Automotive Technology. Aug2011, Vol. 12 Issue 4, p561-570. 10p. |
| Subjects: | Lagrange equations, Automobile handling, Equations of motion, Rotational motion (Rigid dynamics), Analytical mechanics |
| Abstract: | Nonlinear governing equations used to analyze the handling of a ground vehicle are derived from the Lagrange equations of motion. The derived equations are coded using VBA (Visual Basic for Applications) embedded in Microsoft's Excel Software and simulated in the time domain using the 4th-order Runge-Kutta method. A total of six degrees of freedom are used in the equations; three of these are the directional translation, lateral translation, and yaw of a platform (unsprung) on the base of an inertial ground coordinate, and the other three are the roll, pitch, and yaw of a body (sprung) by a platform-fixed coordinate. Four driving torques and four wheel angles of all tires are used as input control parameters. A simplified Calspan tire model is adopted for the generalized forces of the equations. This is a combined model that can be used to obtain tractional (or braking) and side forces using the inputs of the directional and side-slip ratios and the vertical force. The VBA code realized in this study is validated by comparisons with trimmed equilibrium results and the test data cited in published papers. The major characteristics of this study are: (1) the coordinate systems of the equations are mixed with the inertial frame and the platform-fixed frame, and, as a result, almost all types of driving conditions with long mileages can be simulated; (2) vertical movement is eliminated due the focus on the handling analysis; (3) the body-yaw degree of freedom is separated from the platform-yaw degree of freedom; and (4) the programming is performed by VBA, which is rarely used in the vehicle dynamics field. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Automotive Technology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Derivation and validation of nonlinear governing equations for an analysis of vehicle handling. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yang%2C+S%2E%22">Yang, S.</searchLink><relatesTo>1</relatesTo><i> sungmo.yang@renaultsamsungM.com</i><br /><searchLink fieldCode="AR" term="%22Kim%2C+J%2E%22">Kim, J.</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Automotive+Technology%22">International Journal of Automotive Technology</searchLink>. Aug2011, Vol. 12 Issue 4, p561-570. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Lagrange+equations%22">Lagrange equations</searchLink><br /><searchLink fieldCode="DE" term="%22Automobile+handling%22">Automobile handling</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+of+motion%22">Equations of motion</searchLink><br /><searchLink fieldCode="DE" term="%22Rotational+motion+%28Rigid+dynamics%29%22">Rotational motion (Rigid dynamics)</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+mechanics%22">Analytical mechanics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Nonlinear governing equations used to analyze the handling of a ground vehicle are derived from the Lagrange equations of motion. The derived equations are coded using VBA (Visual Basic for Applications) embedded in Microsoft's Excel Software and simulated in the time domain using the 4th-order Runge-Kutta method. A total of six degrees of freedom are used in the equations; three of these are the directional translation, lateral translation, and yaw of a platform (unsprung) on the base of an inertial ground coordinate, and the other three are the roll, pitch, and yaw of a body (sprung) by a platform-fixed coordinate. Four driving torques and four wheel angles of all tires are used as input control parameters. A simplified Calspan tire model is adopted for the generalized forces of the equations. This is a combined model that can be used to obtain tractional (or braking) and side forces using the inputs of the directional and side-slip ratios and the vertical force. The VBA code realized in this study is validated by comparisons with trimmed equilibrium results and the test data cited in published papers. The major characteristics of this study are: (1) the coordinate systems of the equations are mixed with the inertial frame and the platform-fixed frame, and, as a result, almost all types of driving conditions with long mileages can be simulated; (2) vertical movement is eliminated due the focus on the handling analysis; (3) the body-yaw degree of freedom is separated from the platform-yaw degree of freedom; and (4) the programming is performed by VBA, which is rarely used in the vehicle dynamics field. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Automotive Technology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s12239-011-0066-0 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 561 Subjects: – SubjectFull: Lagrange equations Type: general – SubjectFull: Automobile handling Type: general – SubjectFull: Equations of motion Type: general – SubjectFull: Rotational motion (Rigid dynamics) Type: general – SubjectFull: Analytical mechanics Type: general Titles: – TitleFull: Derivation and validation of nonlinear governing equations for an analysis of vehicle handling. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yang, S. – PersonEntity: Name: NameFull: Kim, J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2011 Type: published Y: 2011 Identifiers: – Type: issn-print Value: 12299138 Numbering: – Type: volume Value: 12 – Type: issue Value: 4 Titles: – TitleFull: International Journal of Automotive Technology Type: main |
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