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Contact mechanics and noise in gears
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, recent findings in the area of computational contact mechanics are applied to gear technology. The focus of this application is gear noise. One of the main goals is to calculate the so called transmission error, which is a measure that relates structural properties of a gear to gear noise.

Computational methodologies are developed in order to analyze different types of gear problems. The finite element method forms the basis for the developed models. In addition to the finite element models of the gear wheels, contact laws are used in order to simulate the contact between the gear flanks. These laws are Signorini's contact law and Coulomb's law of friction and by expressing them as B-differential equations the application of Pang's Newton method for B-differential equations is enabled.

The transmission error is calculated with good accuracy under both quasi-static and dynamic conditions. By incorporating Archard's wear law into the models, predictions of how wear affects the transmission error are made. It is found that wear can have a significant impact on gear noise.

It is shown that friction by no means can be neglected when calculating the transmission error. In the dynamic calculations of this thesis, friction always increases the dynamic transmission error. It is also concluded that the effect from friction becomes more significant if shaft and bearing stiffnesses are small.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2004. , 15 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 862
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-29071Local ID: 14325ISBN: 91-7373-896-4 (print)OAI: oai:DiVA.org:liu-29071DiVA: diva2:249883
Public defence
2004-03-18, Sal C3, C-huset, Linköpings Universitet, Linköping, 10:15 (Swedish)
Opponent
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2013-01-30
List of papers
1. Simulation of wear by use of a nonsmooth Newton method: a spur gear application
Open this publication in new window or tab >>Simulation of wear by use of a nonsmooth Newton method: a spur gear application
2001 (English)In: Mechanics of structures and machines (Print), ISSN 0890-5452, E-ISSN 1525-612X, Vol. 29, no 2, 223-238 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents a method for calculating wear between two elastic bodies in contact. Discrete representations of the bodies are obtained by the finite element method. Constitutive laws representing the behavior of the interacting surfaces are then added. These are Signorini's contact law, Coulomb's law of friction, and Archard's law of wear. By formulating Signorini's contact law and Coulomb's law of friction by means of projection equations, the complete formulation of a time increment of a quasistatic wear-friction evolution problem becomes a system of nonsmooth equations. A modification of Newton's method is applied to solve this system. The method is applied to a spur gear problem in a heavy truck transmission.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-47402 (URN)10.1081/SME-100104481 (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
2. Prediction of transmission error in spur gears as a consequence of wear
Open this publication in new window or tab >>Prediction of transmission error in spur gears as a consequence of wear
2001 (English)In: Mechanics of structures and machines (Print), ISSN 0890-5452, E-ISSN 1525-612X, Vol. 29, no 4, 431-449 p.Article in journal (Refereed) Published
Abstract [en]

The aim of this article is to investigate how the so-called transmission error in a gear develops in a wear process. A finite element procedure for calculating wear between two elastic bodies in contact is developed that includes constitutive laws, representing the behavior of the interacting surfaces. When treating a gear problem, large rotations must be included. This is done by analyzing a sequence of finite-element models along with an interpolation procedure. The constitutive laws of interacting surfaces are Signorini's contact law, Coulomb's law of friction, and Archard's law of wear. By formulating both Signorini's contact law and Coulomb's law of friction by means of projection equations, the complete formulation of a time increment of a quasistatic wear-friction evolution problem becomes a system of nonsmooth equations. Then, a modified Newton method is applied to solve this system. The transmission error can be found from the infinitesimal displacement field superposed on the rigid body configuration. Results from the simulations show that wear will increase the peak-to-peak value of the transmission error. This is most significant in a gear when some kind of modification of the gear flank is applied to minimize the transmission error in an initial state.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-47232 (URN)10.1081/SME-100107621 (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
3. A flexible multi-body approach for frictional contact in spur gears
Open this publication in new window or tab >>A flexible multi-body approach for frictional contact in spur gears
2004 (English)In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 278, no 3, 479-499 p.Article in journal (Refereed) Published
Abstract [en]

In the present paper, a large rotational approach for dynamic contact problems with friction is proposed. The approach is used for modelling a spur gear pair with shafts and bearings. The model is obtained by superposing small displacement elasticity on rigid-body motions, and postulating tribological laws on the gear flanks. The finite element method is used to model the elastic properties of the gear pair. Shafts and bearings are represented by linear springs. The tribological laws of the contact interface are Signorini's contact law and Coulomb's law of friction. An important feature of the approach is that the difficulties of impacting mass nodes are avoided. The governing equations of the model are numerically treated by use of the augmented Lagrangian approach. In such manner the geometry of the gear flanks are well represented in the numerical simulations. It is possible to study accurately the consequences of different types of profile modifications as well as flank errors. In this work, the dynamic transmission error is studied. For instance, it turns out that the effect from profile modification is less significant for the transmission error when frictional effects are included.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-22562 (URN)10.1016/j.jsv.2003.10.057 (DOI)1828 (Local ID)1828 (Archive number)1828 (OAI)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2017-12-13
4. Node-to-target formulation in finite element spur gear problems
Open this publication in new window or tab >>Node-to-target formulation in finite element spur gear problems
2005 (English)In: Mechanics based design of structures and machines, ISSN 1539-7734, E-ISSN 1539-7742, Vol. 33, no 1, 31-49 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, a quasistatic finite element model of a spur gear pair is developed. A node-to-target contact formulation is given, where calculations of initial gaps are based upon the actual geometry of the gear flanks rather than upon a contact node and a facet or a line segment. By using a special contact search algorithm, profile modifications and mounting errors are easily incorporated in the analysis. The problem, which also includes friction, is solved by using a nonsmooth Newton method. The static transmission error can be calculated with accuracy with a relatively small number of nodes along the gear flanks. Several examples are given in order to demonstrate the model.

Keyword
Contact, Finite element, Gears, Static transmission error
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-50338 (URN)10.1081/SME-200045797 (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-12

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