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Measurement of Contact Force–Deformation curves of colliding two identical spheres
Publikationstyp
Journal Article
Date Issued
2023-06-01
Sprache
English
Institut
Journal
Citation
Experimental Mechanics: (2023)
Publisher DOI
Scopus ID
Publisher
Springer
Peer Reviewed
true
Background
The contact force–deformation relation between two spheres is one fundamental property which determines the mechanical response of the colliding bodies. In general, collisions of solid spheres occur in a very short time, so a highly accurate and a non-contact measurement method is required.
Objective
In this study, a concept for the experimental determination of contact force–deformation curves of two colliding spheres is presented. Thereby two identical steel spheres collide by using a pendular setup and the sphere's velocities are measured by Laser Doppler Vibrometers (LDVs).
Methods
The displacements are obtained by integrating the velocity with time and the accelerations are obtained by differentiating the velocity with time. From these values, the deformation and the contact forces can be calculated. Then, the elastic results are compared with the Hertzian theory of impact and experiments are conducted with elasto-plastic spheres.
Results
Although the deformations are in good agreement with these analytical values, the influence of numerical differentiation is observed in the contact force. However, it is shown that the elastic contact force–deformation curve of two colliding spheres can be obtained with reasonable accuracy by using LDVs. For elasto-plastic spheres the coefficient of restitution became smaller than for the purely elastic case, and the force–deformation curve with hysteresis are measured.
Conclusions
The results of this study are considered to be reasonable as far as comparisons with those for elastic collisions. Therefore, more detailed verification by numerical analysis, such as finite element analysis, is desirable.
The contact force–deformation relation between two spheres is one fundamental property which determines the mechanical response of the colliding bodies. In general, collisions of solid spheres occur in a very short time, so a highly accurate and a non-contact measurement method is required.
Objective
In this study, a concept for the experimental determination of contact force–deformation curves of two colliding spheres is presented. Thereby two identical steel spheres collide by using a pendular setup and the sphere's velocities are measured by Laser Doppler Vibrometers (LDVs).
Methods
The displacements are obtained by integrating the velocity with time and the accelerations are obtained by differentiating the velocity with time. From these values, the deformation and the contact forces can be calculated. Then, the elastic results are compared with the Hertzian theory of impact and experiments are conducted with elasto-plastic spheres.
Results
Although the deformations are in good agreement with these analytical values, the influence of numerical differentiation is observed in the contact force. However, it is shown that the elastic contact force–deformation curve of two colliding spheres can be obtained with reasonable accuracy by using LDVs. For elasto-plastic spheres the coefficient of restitution became smaller than for the purely elastic case, and the force–deformation curve with hysteresis are measured.
Conclusions
The results of this study are considered to be reasonable as far as comparisons with those for elastic collisions. Therefore, more detailed verification by numerical analysis, such as finite element analysis, is desirable.
DDC Class
600: Technik
620: Ingenieurwissenschaften