Dynamic simulation of mechanical systems can be performed using a multibody system dynamics approach. The approach allows to account systems of other physical nature, such as hydraulic actuators. In such systems, the nonlinearity and numerical stiffness introduced by the friction model of the hydraulic cylinders can be an important aspect to consider in the modeling because it can lead to poor computational efficiency. This paper couples various friction models of a hydraulic cylinder with the equations of motion of a hydraulically actuated multibody system in a monolithic framework. To this end, two static friction models, the Bengisu–Akay model and Brown–McPhee model, and two dynamic friction models, the LuGre model and modified LuGre model, are considered in this work. A hydraulically actuated four-bar mechanism is exemplified as a case study. The four modeling approaches are compared based on the work cycle, friction force, energy balance, and numerical efficiency. It is concluded that the Brown–McPhee approach is numerically the most efficient approach and it is well able to describe usual friction characteristics in dynamic simulation of hydraulically actuated multibody systems.

Real-world products and physics-based simulations are becoming interconnected. In particular, real-time capable dynamic simulation has made it possible for simulation models to run in parallel and simultaneously with operating machinery. This capability combined with state observer techniques such as Kalman filtering have enabled the synchronization between simulation and the real world. State estimator techniques can be applied to estimate unmeasured quantities, also referred as virtual sensing, or to enhance the quality of measured signals. Although synchronized models could be used in a number of ways, value creation and business model development are currently defining the most practical and beneficial use cases from a business perspective. The research reported here reveals the communication and collaboration methods that lead to economically relevant technology solutions. Two case examples are given that demonstrate the proposed methodology. The work benefited from the broad perspective of researchers from different backgrounds and the joint effort to drive the technology development towards business relevant cases.

A real-time multibody model of an off-road vehicle can be used to analyze the dynamics of tasks, such as loading and/or transferring material from deformable ground. This analysis requires an accurate description of the mechanics, hydraulic actuators, and the terrain. The objective of this paper is to introduce a novel, real-time capable, deformable terrain/soil model that can interact with the mechanics of a multibody system model and the dynamics of a hydraulics model. To this end, a tractor is modeled by using a semi-recursive multibody formulation based on velocity transformation. The hydraulic actuation of the tractor’s front-loader is modeled by using the lumped fluid theory. The tractor loads and transfers sand material from a deformable sand field (the ground), which is modeled by combining mesh-based and particle-based soil representation approaches for the real-time simulation of soil deformation. The work cycle of the tractor model follows a 3D maneuver that is used to load and transfer sand material. During the digging and dumping operations, the static sand field is converted into sand particles and vice versa respectively. For the presented work cycle, the real-time capability of the system is analyzed and determined. Furthermore, the dynamic actuator forces in the hydraulic cylinders are compared with the static actuator forces. The introduced real-time capable tractor simulation model can be utilized in product development and other product processes.

Electrification of non-road mobile machinery holds immense potential for reducing the high emissions and fuel consumption of such industrial machinery. Detailed real-time physics-based simulation models capable of comparing energy efficiencies of hybrid powertrains in realistic working conditions can aid the development of efficient mobile machinery. In this study, four system-level hybrid electric powertrain models have been developed and coupled with a detailed multibody dynamics-based tractor model in a co-simulation environment. The four models, differentiated by their topology and transmission design, are simulated in a virtual environment under the dynamic load conditions of a ploughing work cycle of the Deutsche Landwirtschafts-Gesellschaft powermix. The simulation results show that improvements of 9.7% and 9.2% in total energy consumption can be achieved by the two studied power-split configurations in the simulated work cycle compared to an automated manual transmission-based series powertrain. The double planetary gear-based power-split model achieved the highest energy recovery and lowest energy loss compared to the other models. The developed models are real-time capable, allowing a human operator to simulate customizable work cycles.

In multibody system dynamics, the equations of motion are often coupled with systems of other physical nature, such as hydraulics. To infer the real dynamical state of such a coupled multibody system at any instant of time, information fusing techniques, such as state estimators, can be followed. In this procedure, data is combined from the coupled multibody model and the physical sensors installed on the actual machine. This paper proposes a novel state estimator developed by combining a multibody model with an indirect Kalman filter in the framework of hydraulically driven systems. An indirect Kalman filter that utilizes the exact Jacobian matrix of the plant at position and velocity level is extended for hydraulically actuated systems. The structures of the covariance matrices of the plant and measurement noise are also studied. The multibody system, described using a semi-recursive formulation, and the hydraulic subsystem, described using lumped fluid theory, are coupled using a monolithic approach. As a case study, the state estimator is applied to a hydraulically actuated four-bar mechanism. The state estimator considers modeling errors in the force model because of its uncertainty in modeling. The measurements are obtained from a dynamic model which is considered as the ground truth, with an addition of white Gaussian noise to represent the noise properties of the actual sensors. The state estimator uses four sensor configurations with different sampling rates. For the presented case study, the state estimator can accurately estimate the work cycle and hydraulic pressures of the coupled multibody system. The results demonstrate the efficacy of the proposed state estimator.