Friction Modeling and Compensation in Mechanical Systems

Friction is a pervasive nonlinearity in mechanical systems, arising at interfaces from the microscale asperities of surfaces and manifesting in macroscopic performance degradation, wear and control challenges. Accurate modelling of friction phenomena—encompassing static stiction, kinetic friction, velocity‐dependent behaviour and hysteresis—is essential for predicting system response in fields as diverse as automotive suspensions, precision manufacturing, robotics and aerospace actuation. Classical approaches such as Coulomb and viscous friction models capture basic resistance, while more advanced representations (for example the LuGre model) include internal state variables to account for pre-sliding displacement and the Stribeck effect. Experimental characterisation has revealed that factors such as load, velocity, lubrication state and temperature interact in complex ways, producing phenomena such as stick-slip oscillations and dynamic friction peaks that exceed quasi-static levels. Compensation strategies have evolved in parallel, ranging from feedforward friction observers and adaptive control laws to hybrid sliding-mode and neural network schemes that estimate and counteract nonlinear friction torques in real time. By integrating refined models with robust control algorithms, modern systems achieve higher tracking accuracy, reduced wear and extended lifetime, bolstering industrial productivity and vehicle comfort while enabling ever finer motion resolution in emerging micro- and nano-scale devices.

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An experimental study of hydraulic shock absorbers has demonstrated that dynamic friction forces can be several times larger than their quasi-static counterparts and strongly depend on both side-load and velocity. By employing valve-free test elements, researchers mapped out modified Stribeck curves under varying oil volumes and loads, revealing that dynamic friction peaks can exceed hydraulic damping forces at low speeds and substantial side-forces. These findings underline the need to incorporate velocity- and load-dependent friction terms into active suspension control algorithms and vehicle simulation platforms.

A comprehensive review of friction nonlinearity in electro-hydraulic servo systems has consolidated recent advancements in model selection and parameter identification. The analysis contrasts conventional friction models, highlights modern inversion techniques for hysteresis and backlash, and evaluates compound control strategies such as model-free observers combined with model-based compensation. Key outcomes include guidelines for choosing friction models based on application bandwidth, and recommendations for integrating genetic-algorithm-based tuning of extended state observers in industrial servo drives.

In the domain of robotic manipulators, an adaptive control scheme combining fast integral terminal sliding-mode control with a robust exact differentiator and a neural network-based friction estimator has been shown to deliver finite-time convergence and high-precision trajectory tracking. The feedforward neural network is trained online to approximate the unobservable dynamic friction state within a LuGre framework, while the sliding-mode component ensures robustness to unexpected disturbances. Simulation results for multi-degree-of-freedom arms report sub-millisecond settling times and overshoots below 1.5 per cent, illustrating the effectiveness of data-driven compensation embedded within rigorous stability proofs.

Friction Modeling and Compensation in Mechanical Systems publication trend

The graph below shows the total number of articles in friction modeling and compensation in mechanical systems across all publications each year (not limited to Nature Index journals).

Technical terms

Stribeck curve: A plot of friction force versus sliding velocity that shows a characteristic drop from static to kinetic friction before rising again due to viscous effects.

LuGre model: A dynamic friction model incorporating an internal state variable to capture pre-sliding displacement, hysteresis and the Stribeck effect.

Stick-slip motion: An oscillatory phenomenon where contact surfaces alternately stick and slip, often causing unwanted vibrations and noise.

Extended state observer (ESO): A control observer that estimates both system states and unmodeled disturbances, such as friction torques, to improve compensation.

Sliding-mode control: A robust control method that forces system trajectories onto a predefined sliding manifold, offering insensitivity to bounded uncertainties.

References

1. Velocity and load dependent dynamic shock absorber friction at stationary conditions. Tribology International (2024).
2. A Review of Key Technologies for Friction Nonlinearity in an Electro-Hydraulic Servo System. Machines (2022).
3. Adaptive FIT-SMC Approach for an Anthropomorphic Manipulator With Robust Exact Differentiator and Neural Network-Based Friction Compensation. IEEE Access (2022).