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A method of discretising the belt in a flat model of a belt transmission

Kubas K.

Archiwum Motoryzacji

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2017

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Vol. 78, nr 4

93--105

EN

The article presents a method of discretising a belt used in a transmission model with any number of pulleys and tensioning rollers and any direction of wrapping the pulleys or rollers. The positions of the discretising points are formulated in a global coordinate system. The method allows for arbitrary placement of pulleys and tensioning rollers. It also consequently allows to calculate the length of the belt, resulting from the geometry of the transmission, and the length of the belt, resulting from the coordinates of the discretising points that lie on its circumference. The method presented here allows to estimate the number of points that would provide satisfactory accuracy of the belt’s curvature surrounding the individual pulleys and rollers. In the paper presented comparison between two proposed ways of estimating. Designated points can be used as input data to analyse the belt dynamics with the belt modelled as rigid elements connected to one another by translational or rotational spring-damping elements.

2

A model for dynamic analysis of a 5pk belt transmission in dry or wet conditions

Kubas K.

Archiwum Motoryzacji

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2015

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Vol. 70, no. 4

75--96

EN

A belt transmission model with dry or partially wet belt models used for dynamic analysis has been presented in this paper. A two-dimensional discrete model was created, consisting of rigid elements connected with each other by means of longitudinal and torsional spring-damping elements (SDEs). The belt-pulley contact phenomena were described with the use of a model with appropriate stiffness and damping between the contacting surfaces and a simplified Threlfall friction model was used to describe the friction phenomenon. Motion of the transmission is triggered under the influence of torque loads applied on the pulleys. Calculations results are presented of reaction, contact and friction forces acting on dry and partially wet belt. Finally, an example of using the model to analyse the dynamics of a wet automotive belt transmission system driving the alternator and coolant pump has been presented.

3

A model for analysing the dynamics of belt transmissions with a 5pk belt

Kubas K.

Archiwum Motoryzacji

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2015

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Vol. 67, no. 1

61--82, 189--209

EN

A belt transmission model used for analysing the dynamics of such a transmission has been presented in this paper. A two-dimensional discrete model was adopted, consisting of rigid elements connected with each other by means of longitudinal and torsional spring-damping elements (SDEs). For the belt-pulley contact, a special contact model and a dry friction model were adopted. The belt-pulley contact phenomena were described with the use of a model with appropriate stiffness and damping between the contacting surfaces and a simplified Threlfall friction model was used to describe the friction phenomenon. The transmission motion caused by a force-type input or a kinematic input applied to transmission pulleys was examined. Results of determining the reaction forces developing in the belt and the normal and friction forces between the belt element and the pulley, arising from the driving and resistance torques on the pulleys, have been given as an example in the subsequent part of this article for the belt transmission adopted. Finally, an example of using the model to analyse the dynamics of an automotive belt transmission system driving the alternator and coolant pump has been presented.

PL

W pracy przedstawiono pewien model przekładni pasowej służący do analizy dynamiki. Przyjęto model dyskretny płaski pasa składający się ze sztywnych członów połączonych ze sobą wzdłużnymi i skrętnymi elementami sprężysto-tłumiącymi. W modelu tym, w chwili styku członu z kołem pasowym, przyjęto model kontaktu i model tarcia suchego. Do opisu zjawisk kontaktowych wykorzystano model z odpowiednią sztywnością i tłumieniem pomiędzy stykającymi się powierzchniami, natomiast do opisu zjawiska tarcia wykorzystano uproszczony model tarcia Threlfall’a. Ruch przekładni wywołany zostaje pod wpływem wymuszenia siłowego lub ruchowego założonego na kołach pasowych. W dalszej części przedstawiono wyniki sił reakcji w pasie oraz sił kontaktu i tarcia pomiędzy członem a kołem pasowym w przykładowej przyjętej przekładni pasowej, uzyskane pod wpływem działania założonych na koła momentów napędowego i oporu. Na zakończenie zaprezentowano przykładowe zastosowanie modelu do analizy dynamiki przekładni samochodowej napędzającej alternator i pompę płynu chłodniczego.