Dynamics of the Impact with Benson
Friction Model
Dan B. Marghitu and Dorian Cojocaru
Abstract An analytical model for the impact of a rigid link in planar pure rotation
with a solid surface is developed. The free end of the link undergoes elastic and elastoplastic deformations during the compression phase of the impact. The restitution is
considered elastic with a permanent deformation. During the impact, a friction force
based on Benson model is employed. The differential impact equations are solved for
different initial impact incident angle and distinct values of the coefficient of kinetic
friction.
1 Introduction
An impact occurs in a very short interval of time in which the system has instantaneously change of velocities. Bhatt and Koechling analyzed the trace of the sliding
velocity at the contact point for a three-dimensional impact [1]. Flow patterns that
show the evolution of impact were defined. Also, three-dimensional parameters that
govern the defining equations for the sliding behavior of the contact point were identified. The qualitative behavior during impact was determined based on the region
which contains the parameters for a given impact configuration.
Yen and Wu proposed and verified experimentally a method to identify both the
impact location and the transverse impact force history from strain responses on
a rectangular plate [2]. A numerical verification of the method was performed by
randomly generating the impact locations and the force histories and then performing
forward calculations to obtain the corresponding strain responses. These responses
were then used as the input data for the identification purposes.
D. B. Marghitu (B)
Department of Mechanical Engineering, Auburn University, Auburn, AL 36349, USA
e-mail: marghitu@auburn.edu
D. Cojocaru
Department of Mechatronics and Robotics, University of Craiova, Craiova, Romania
© Springer Nature Switzerland AG 2021
N. Herisanu and V. Marinca (eds.), Acoustics and Vibration of Mechanical
Structures—AVMS 2019, Springer Proceedings in Physics 251,
https://doi.org/10.1007/978-3-030-54136-1_2
13
Friction Model
Dan B. Marghitu and Dorian Cojocaru
Abstract An analytical model for the impact of a rigid link in planar pure rotation
with a solid surface is developed. The free end of the link undergoes elastic and elastoplastic deformations during the compression phase of the impact. The restitution is
considered elastic with a permanent deformation. During the impact, a friction force
based on Benson model is employed. The differential impact equations are solved for
different initial impact incident angle and distinct values of the coefficient of kinetic
friction.
1 Introduction
An impact occurs in a very short interval of time in which the system has instantaneously change of velocities. Bhatt and Koechling analyzed the trace of the sliding
velocity at the contact point for a three-dimensional impact [1]. Flow patterns that
show the evolution of impact were defined. Also, three-dimensional parameters that
govern the defining equations for the sliding behavior of the contact point were identified. The qualitative behavior during impact was determined based on the region
which contains the parameters for a given impact configuration.
Yen and Wu proposed and verified experimentally a method to identify both the
impact location and the transverse impact force history from strain responses on
a rectangular plate [2]. A numerical verification of the method was performed by
randomly generating the impact locations and the force histories and then performing
forward calculations to obtain the corresponding strain responses. These responses
were then used as the input data for the identification purposes.
D. B. Marghitu (B)
Department of Mechanical Engineering, Auburn University, Auburn, AL 36349, USA
e-mail: marghitu@auburn.edu
D. Cojocaru
Department of Mechatronics and Robotics, University of Craiova, Craiova, Romania
© Springer Nature Switzerland AG 2021
N. Herisanu and V. Marinca (eds.), Acoustics and Vibration of Mechanical
Structures—AVMS 2019, Springer Proceedings in Physics 251,
https://doi.org/10.1007/978-3-030-54136-1_2
13