Stick-slip motion in one-dimensional continuous systems and
in systems with several degrees of freedom
Citation for published version (APA):
Andersson, I. (1981). Stick-slip motion in one-dimensional continuous systems and in systems with several degrees of freedom. Wear, 69(2), 255-256. https://doi.org/10.1016/0043-1648(81)90249-0
DOI:
10.1016/0043-1648(81)90249-0 Document status and date: Published: 01/01/1981 Document Version:
Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.
• The final author version and the galley proof are versions of the publication after peer review.
• The final published version features the final layout of the paper including the volume, issue and page numbers.
Link to publication
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:
www.tue.nl/taverne
Take down policy
If you believe that this document breaches copyright please contact us at:
openaccess@tue.nl
providing details and we will investigate your claim.
Wear, 69 (1981) 255 - 256
0 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
255
Short Communication
Stick-slip motion in one-dimensional continuous systems and in systems with several degrees of freedom
I. ANDERSSON
Department of Mechanical Engineering, W-hoog 04.101, Technische Hogeschool Eindhoven, Postbus 513, 5600 MB Eindhoven (The Netherlands)
(Received December 15, 1980)
Stick-slip is the name for a vibration phenomenon characterized by a jerky motion in systems that are required to perform uniform sliding at, in most cases, low sliding velocities. This jerky motion is caused firstly by the dependence of the frictional force on the sliding velocity and secondly by the elastic and damping properties of the system. There are many cases where this stick-slip motion can be seen; one of the most investigated examples is the feeding mechanism in machining processes. More trivial examples are the bow sliding on a string of a violin, the chalk sliding on a chalkboard, and squealing brakes. Another example is long moving assembly lines in factories, where stick-slip motion sometimes occurs.
The first examples above can be analysed using a theory with one degree of freedom. The critical feed velocity for the stick-slip problem with one degree of freedom has been presented in an appendix of a thesis by Andersson [ 11, and references to more detailed papers on this subject are given in the historical survey included in the thesis.
For the assembly line problem, however, it is not correct to use a one degree of freedom theory; the system must be treated as one with several degrees of freedom or as a continuous system. Because of the sometimes rather complicated relation between the frictional force and the sliding velocity this problem has certain similarities to the non-linear wave propaga- tion problem.
The one-dimensional continuous system is discretized by the finite difference technique, and a solution common to this system and to systems with several degrees of freedom has been given [ 11. The motion of these systems was calculated numerically by the Runge-Kutta method. The stored energy and the power flow were analysed during the calculated motion and were used in the iterative calculation of the critical feed velocity. Different frictional force models suggested by other workers were used in the calcula- tions. Quantitative results for various values of the parameters and different frictional force models were presented in nondimensional form.
256
For continuous systems or for systems with several degrees of freedom that are subjected to stick-slip motion, the methods for preventing stick-slip are the same as those for systems with one degree of freedom, i.e. increased stiffness, increased damping or decreased difference between static and kinetic friction, where the decreased difference between the types of friction is best achieved by using lubricants doped with polar additives.
1 I. Andersson, Ph.D. Thesis, Chalmers University of Technology, 1980 (available from Division of Machine Elements, Chalmers University of Technology, 412 96 Gijteborg, Sweden).
