Mechanics Research Communications 111 (2021) 103644 Contents lists available at ScienceDirect Mechanics Research Communications journal homepage: www.elsevier.com/locate/mechrescom On the interaction between rigid discs and rotating damped contact elements Hugo Heidy Miyasato ∗ , Vinícius Gabriel Segala Simionatto, Milton Dias Junior School of Mechanical Engineering, Department of Integrated Systems, University of Campinas - UNICAMP, Rua Medeleyev, 200, 13083-860, Campinas, SP, Brazil a r t i c l e i n f o Article history: Received 7 September 2020 Accepted 30 November 2020 Available online 4 December 2020 Keywords: Viscous damping Friction Instability a b s t r a c t Minimal models involving rigid discs have been studied due to brake squeal and clutch squeal/eek. In this work, a rotating contact element with viscous damping characteristic is developed. It induces additional circulatory effects to the system and the results indicate that stability becomes much more intricate to determinate, involving the rotating speed of the moving element. © 2020 Elsevier Ltd. All rights reserved. 1. Introduction Friction induced vibration is an important subject of in many fields of application, such as automotive brakes [1], and has a vast literature. A timeline discussing the friction force models as well as multibody representations were extensively reviewed by Ibrahim [2,3]. Stick-slip [4] may lead to self-excited vibrations if the dy- namic friction coefficient decreases with the sliding speed. Unsta- ble behavior can occur when there is a high slip speed and con- stant friction coefficient due to mode coupling [5]. Hoffmann and Gaul [6] concluded that the increase of the damping amount may not lead to stabilization of those systems. The physical distribution of the damping throughout the system was another important fac- tor to characterize the stability boundaries [7]. Minimal brake squeal models were reviewed in von Wagner et al. [8], where a new model with two degrees-of-freedom (DOF) was also developed. The rotor was represented as a rigid disc and the breaking pads were carefully included as fixed contact ele- ments without mass. Many subsequent works unfolded from this research, each one exploring and including new features to the representation. Smart pads with a circular path were included for squeal control in [9], in-plane movements of the pads are found on [10], and Stender et al. [11] has recently studied the influence of a temperature-dependent friction coefficient. External damp- ing should be taken into account with caution for these systems. Spelsberg-Korspeter et al. [12], Whener et al. [13], and Karev and Hagerdorn [14] studied the parametric excitation that emerges on ∗ Corresponding author. E-mail address: hugohm@fem.unicamp.br (H.H. Miyasato). the system due to mountings that are not positioned on the local coordinate frame. Damping properties induced by friction were im- portant contributions from Ref. [8]. Due to linearization, those ef- fects were represented by coefficients which were directly depen- dent on the friction coefficient, but inversely proportional to the rotor’s rotating speed. Findlin et al. [15] mentions that those find- ings can be credited to earlier results from Hochlenert [16]. More recently, Mercier et al. [17] studied a rotor with a friction interface and such terms also played a role on its response. Hagedorn et al. [18] introduced viscous damping in the contact elements from von Wagner et al. [8]. As a result, the linearized representation involves skew-symmetric matrices (gyroscopic and circulatory) and another branch of research regarding its stabi- lization has been developed since then [19,20]. The rigorous in- clusion of new elements at the formulation stage was very im- portant for the models, given that each new feature introduced forces/moments that were not predicted with the application of structural/proportional damping. Nevertheless, for all mentioned brake models [8–11,18], the con- tact elements did not have a rotating movement. Friction played a crucial role on the excitation of clutch squeal/eek [15,21–26]. Here, most of the minimal models involved the contact between two rotating elements. Hervé et al. [24] con- sidered the interaction between the clutch disc and engine fly- wheel. According to Fidlin [22], Fidlin et al. [15], and Hervé et al. [23,24], damping was another important factor for the phe- nomenon. Hervé et al. [23,24] extended the ideas from Ref. [7] by determining the stability boundaries on the system involving circu- latory forces and the gyroscopic effects. Friction induced damping is represented in Refs. [15,24] by terms that are inversely propor- tional to the relative angular speed. https://doi.org/10.1016/j.mechrescom.2020.103644 0093-6413/© 2020 Elsevier Ltd. All rights reserved.