## 1 Introduction  
Generally, mechanisms in the mechanical engineering industry consist of components in contact with one another. If a suitable combination of relative surface contact speed, load and viscosity is achieved, hydrodynamic lubrication occurs. Hydrodynamic forces differ from dry contact forces [1]. The magnitude of hydrodynamic forces depends not only on the relative speed of the contact surfaces and the load, but also on the properties of the lubricant and the shape of the gap between the contact surfaces. There are applications where the hydrodynamic forces are small enough to cause significant deformation to the contact bodies; thus, affecting the hydrodynamic effect. Such cases include high-speed journal bearings and pad bearings. Contrarily, there are applications where the hydrodynamic forces are so great that they significantly affect the shape of the contact bodies, thereby affecting the distribution of the hydrodynamic pressure. This case of hydrodynamic lubrication is called elastohydrodynamic lubrication (EHL). Typical examples of EHL include rolling bearings, low-speed journal bearings and gear wheels. In some cases, deformation of the contact bodies is required to create a hydrodynamic phenomenon, thereby allowing for the correct function of the component, e.g., lip seals, piston rings and pistons of an internal combustion engine. The dynamics of mechanical systems are typically solved using the theory of multi-body dynamics (MBD). Industrial companies tend to use commercial MBD solvers rather than their in-house programs. Over decades of use of MBD systems, these companies have built proven solutions to solve specific issues they encounter. However, at present, to maintain their existence, they are pressured to push their products to the limits of possibility (companies operating in the automotive industry are a typical example). This also relates to the improvement of the development cycle, which is often based on computational modelling and subsequent experimental testing. When dealing with the dynamics of mechanical systems, companies are forced to expand their MBD simulations to include additional physical phenomena, creating multiphysical problems. In other words, the MBD models that use the basic solution of hydrodynamic lubrication must be extended with a more detailed EHL to uncover a gap in the design. Linking an EHL and an MBD simulation is a typical coupled simulation problem. A detailed classification and historical overview of coupled simulations has been presented by [PERSON] et al. [2]. One way to create an MBD model with EHL is to use a separate integrator for each subsystem. This is a weak-coupled co-simulation between the MBD software and another fluid dynamics program. During co-simulation, each subsystem solver conducts the integration of its states interacting with its environment only at communication points in which coupling variables are exchanged. This may be the root cause of unstable integration. [PERSON] et al. [3] presented a methodology to determine a stable configuration for computationally efficient non-iterative co-simulations, which are often found in real-time applications. Their work addresses multiphysical issues in the context of the simulation of machinery. [PERSON] et al. [4] used a combination of higher-order approximation for interpolation/extrapolation of the coupling variables. They used relaxation techniques to avoid artificial oscillations in the Lagrange multipliers of the kinematic differential equations. [PERSON] and [PERSON] [5] applied co-simulation to calculate a squeeze-film damper designed to dampen the outer ring of the ball bearing of the jet engine. In this scenario, the dynamics were solved in MSC Adams, while the damper lubrication was calculated in MATLAB/Simulink. Similarly, [PERSON] and [PERSON] [6] co-simulated an electric power steering control system and a full-vehicle dynamic model in an MBD system. [PERSON] et al.