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Article

Machine Learning-Based Dynamic Modeling of Ball Joint Friction for Real-Time Applications

by
Kai Pfitzer
1,2,*,
Lucas Rath
2,3,
Sebastian Kolmeder
2,
Burkhard Corves
3 and
Günther Prokop
1,*
1
Chair of Automobile Engineering, TU Dresden, 01069 Dresden, Germany
2
BMW Group, Development Driving Experience, 80788 Munich, Germany
3
Institute of Mechanism Theory, Machine Dynamics and Robotics, RWTH Aachen, 52062 Aachen, Germany
*
Authors to whom correspondence should be addressed.
Lubricants 2025, 13(10), 436; https://doi.org/10.3390/lubricants13100436
Submission received: 24 June 2025 / Revised: 20 September 2025 / Accepted: 27 September 2025 / Published: 1 October 2025
(This article belongs to the Special Issue New Horizons in Machine Learning Applications for Tribology)

Abstract

Ball joints are components of the vehicle axle, and their friction characteristics must be considered when evaluating vibration behavior and ride comfort in driving simulator-based simulations. To model the three-dimensional friction behavior of ball joints, real-time capability and intuitive parameterization using data from standardized component test benches are essential. These requirements favor phenomenological modeling approaches. This paper applies a spherical, three-dimensional friction model based on the LuGre model, compares it with alternative approaches, and introduces a universal parameter estimation framework using machine learning. Furthermore, the kinematic operating ranges of ball joints are derived from vehicle measurements, and component-level measurements are conducted accordingly. The collected measurement data are used to estimate model parameters through gradient-based optimization for all considered models. The results of the model fitting are presented, and the model characteristics are discussed in the context of their suitability for online simulation in a driving simulator environment. We demonstrate that the proposed parameter estimation framework is capable of learning all the applied models. Moreover, the three-dimensional LuGre-based approach proves to be well suited for capturing the dynamic friction behavior of ball joints in real-time applications.
Keywords: ball joint friction; driving simulation; multidimensional friction model; LuGre model; LSTM; gradient-based optimization ball joint friction; driving simulation; multidimensional friction model; LuGre model; LSTM; gradient-based optimization

Share and Cite

MDPI and ACS Style

Pfitzer, K.; Rath, L.; Kolmeder, S.; Corves, B.; Prokop, G. Machine Learning-Based Dynamic Modeling of Ball Joint Friction for Real-Time Applications. Lubricants 2025, 13, 436. https://doi.org/10.3390/lubricants13100436

AMA Style

Pfitzer K, Rath L, Kolmeder S, Corves B, Prokop G. Machine Learning-Based Dynamic Modeling of Ball Joint Friction for Real-Time Applications. Lubricants. 2025; 13(10):436. https://doi.org/10.3390/lubricants13100436

Chicago/Turabian Style

Pfitzer, Kai, Lucas Rath, Sebastian Kolmeder, Burkhard Corves, and Günther Prokop. 2025. "Machine Learning-Based Dynamic Modeling of Ball Joint Friction for Real-Time Applications" Lubricants 13, no. 10: 436. https://doi.org/10.3390/lubricants13100436

APA Style

Pfitzer, K., Rath, L., Kolmeder, S., Corves, B., & Prokop, G. (2025). Machine Learning-Based Dynamic Modeling of Ball Joint Friction for Real-Time Applications. Lubricants, 13(10), 436. https://doi.org/10.3390/lubricants13100436

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