A general mechanical formulation of two-dimensional bristle friction models with a focus on the LuGre model and its dynamics

Concrete-concrete shear friction behavior under cyclic loading: Laboratory test, mathematical modeling, and code provisions

In this paper, we study hysteresis induced by friction in a simple mass-spring system and then in a dc servo motor experimental setup. The experimental setup is modeled and simulated using the Dahl, LuGre, and Maxwell-slip friction models. Comparison of the experimental and simulation results reveals that the LuGre model provides the best model of the testbed's friction-induced hysteresis.

In this article we recast the Dahl, LuGre, and Maxwell-slip models as extended, generalized, or semilinear Duhem models. We classified each model as either rate independent or rate dependent. Smoothness properties of the three friction models were also considered. We then studied the hysteresis induced by friction in a single-degree-of-freedom system. The resulting system was modeled as a linear system with Duhem feedback. For each friction model, we computed the corresponding hysteresis map. Next, we developed a DC servo motor testbed and performed motion experiments. We then modeled the testbed dynamics and simulated the system using all three friction models. By comparing the simulated and experimental results, it was found that the LuGre model provides the best model of the gearbox friction characteristics. A manual tuning approach was used to determine parameters that model the friction in the DC motor.

LuGre model has been widely used in dynamic friction modeling and compensation. However, there are some practical difficulties when applying it to systems experiencing large range of motion speeds such as the linear motor drive system studied in the paper. This paper first details the digital implementation problems of the LuGre model based dynamic friction compensation. A modified model is then presented to overcome those shortcomings. The proposed model is equivalent to LuGre model at low speed, and the static friction model at high speed, with a smooth transition between them. A discontinuous projection based adaptive robust controller (ARC) is then constructed, which explicitly incorporates the proposed modified dynamic friction model for a better friction compensation. Nonlinear observers are built to estimate the unmeasurable internal state of the dynamic friction model. Online parameter adaptation is utilized to reduce the effect of various parametric uncertainties while certain robust control laws are synthesized to effectively handle various modeling uncertainties for a guaranteed robust performance. The proposed controller is also implemented on an industrial linear motor driven gantry system, along with controllers with the traditional static friction compensation and LuGre model compensation. Extensive comparative experimental results have been obtained, revealing the instability when using the traditional LuGre model for dynamic friction compensation at high speed experiments and the improved tracking accuracy when using the proposed modified dynamic friction model. The results validate the effectiveness of the proposed approach in practical applications.

Adaptive robust control of linear motors with dynamic friction compensation using modified LuGre model

Control-oriented friction modeling of hydraulic actuators based on hysteretic nonlinearity of lubricant film

Regular evaluation and maintenance of skid resistance (friction) of highway and runway pavements is an essential task in improving transportation safety. Various measuring devices operating under different mechanisms have been developed for friction evaluation. Generally, there is a significant variation of friction measurements provided by different devices on the same surface, requiring reliable guidelines for comparison of devices. This paper presents the results of a study conducted to verify whether the LuGre model, an existing dynamic friction model composed of physically significant parameters, would satisfy the above need. A revised formulation which would enhance the applicability of the average lumped version of the LuGre model to model real-world dynamic friction problems is also presented. The original LuGre model was applied to two widely used pavement friction measuring devices; the locked wheel skid trailer and the dynamic friction tester (DFT). In the work presented here the characteristic equations for each device have been formulated based on the LuGre model. In addition an analytical treatment of the kinetics of the DFT is performed to facilitate the application of the LuGre model to the DFT. For each device, the LuGre model parameters were tuned to match a part of the field data collected during a field test carried out by the authors. It was seen that the obtained parameters are reasonably comparable with those reported in the literature. Moreover, the calibrated model equations were seen to predict the observed data that were not used in model fitting, with acceptable accuracy. The results obtained in this study clearly show that the LuGre model can be utilized as an efficient physically intuitive tool with possible applications in: (1) predicting the three-dimensional variation of friction (with wheel slip and traveling speed) as measured by selected friction measuring devices, (2) providing physical interpretations to friction data from different devices, (3) regular self-calibration of friction devices, and (4) comparing pavement friction measurements from different devices.

LuGre model has been widely used in friction modeling and compensation. However, the new friction regime, named prestiction regime, cannot be accurately characterized by LuGre model in the latest research. With the extensive experimental observations of friction behaviors in the prestiction, some variables were abstracted to depict the rules in the prestiction regime. Based upon the knowledge of friction modeling, a novel friction model including the presliding regime, the gross sliding regime and the prestiction regime was then presented to overcome the shortcomings of the LuGre model. The reason that LuGre model cannot estimate the prestiction friction was analyzed in theory. Feasibility analysis of the proposed model in modeling the prestiction friction was also addressed. A parameter identification method for the proposed model based on multilevel coordinate search algorithm was presented. The proposed friction compensation strategy was composed of a nonlinear friction observer and a feedforward mechanism. The friction observer was designed to estimate the friction force in the presliding and the gross sliding regimes. And the friction force was estimated based on the model in the prestiction regime. The comparative trajectory tracking experiments were conducted on a simulator of inertially stabilization platforms among three control schemes: the single proportional-derivative (PD) control, the PD with LuGre model-based compensation and the PD with compensator based on the presented model. The experimental results reveal that the control scheme based on the proposed model has the best tracking performance. It reduces the peak-to-peak value (PPV) of tracking error to 0.2 mrad, which is improved almost 50% compared with the PD with LuGre model-based compensation. Compared to the single PD control, it reduces the PPV of error by 66.7%.

The main contribution of this paper is an experimental validation and comparison of three different friction models for an electro-hydraulic servo system. The first is the well-kn own LuGre model which incorporates dynamic friction effects. The second model is based on a relatively recent publication by Yanada in 2008 [6], which incorporates liquid film thickness in the servo valve. The third model is a new contribution presented in this paper, where valve underlap and mass acceleration are combined with the LuGre model. The experimental results show that for hydraulic systems, the film thickness model is an improvement over the LuGre model, while the new model presented in this paper is an improvement over both the LuGre and the film thickness models. An accurate friction model is an important tool for reliability engineers when distinguishing maintenance related degradation from dynamic effects.

The LuGre model is widely used in the analysis and control of systems with friction. Recently, it has even been made available in the commercial multibody dynamics simulation software system Adams. However, the LuGre model exhibits well-known drawbacks like too low and force rate-dependent break-away forces, drift problems during sticking periods, and significant differences in non-stationary situations between the pre-defined friction law and the one produced by the LuGre model. In the present literature, these problems are supposed to come from the model dynamics or its nonlinear nature. However, most of these drawbacks are not simple side effects of a dynamic friction model but are caused in the LuGre approach, as shown here, by a too simple and inconsistent model of the bristle dynamics. Standard examples and a more practical application demonstrate that the LuGre model is not a “what you see is what you get” approach. A dynamic friction model with accurate bristle dynamics and consistent friction force is set up here. It provides insight into the physical basis of the LuGre model dynamics. However, it results in a nonlinear and implicit differential equation, whose solution will not be easy because of the ambiguity of the friction characteristics. The standard workaround, a static model based on simple regularized characteristics, produces reliable and generally satisfactory results but definitely cannot maintain a stick. The paper presents a second-order dynamic friction model, which may serve as an alternative. It can maintain a stick and produces realistic and reliable results.

Flow induced excitation forces in heat exchangers cause tube-support interactions. The long-term interaction is an important phenomenon which may cause fretting-wear of the tubes. Experimental tests of the interaction show the occurrence of stick-slip intermittent behavior in the tube response. Many factors are involved to precisely predict the interaction behavior including flow excitation forces, impact and friction forces. One of the explanations behind the intermittent stick-slip behavior may be interpreted by refinements in the conceptual choice of friction model and coefficient of friction. Therefore, among the factors above, the incorporated friction model plays an important role in the determination of the level of fretting-wear in the system. The friction model should satisfy two important criteria: the first important aspect is the strategy of the friction model to detect the cessation of sticking, the beginning of partial slipping and establishment of the sliding region. The second important aspect is defining a friction coefficient function for the entire system response to precisely represent the transient stick-slip regions. In the present work, the velocity limited friction model was compared with the LuGre model which is a rate dependent friction model. The effect of varying the break-away force and Stribeck effect on the stick-slip region was also investigated. Furthermore, the criteria to demarcate the stick-slip region in the LuGre model are discussed and a different method to incorporate the Stribeck effect and presliding damping in the Dahl friction model are proposed. Finally, a new hybrid spring-damper friction model inspired by the Cattaneo-Mindlin stress distribution in the contact region is proposed.

Fretting-wear is a common problem in different industries, especially when it comes to interactions between metallic components. Flow-induced excitation forces in heat exchangers for instance cause tube-support interactions. The long-term interaction is an important phenomenon, which may cause fretting-wear of the tubes. Experimental tests of the interaction show the occurrence of stick–slip intermittent behavior in the tube response. To precisely simulate the intermittent stick–slip behavior, it is crucial to refine the conceptual model of the coefficient of friction for the entire motion from absolute zero velocity to gross slip phase. The incorporated friction model plays an important role in the determination of the level of fretting-wear in the system. The friction model should satisfy two important criteria. The first important aspect is the strategy of the friction model to detect the cessation of sticking, the beginning of partial-slipping, and establishment of the sliding region. The second important aspect is defining a friction coefficient function for the entire system response to precisely represent the transient stick–slip regions. In the present work, the velocity-limited friction model was compared with the LuGre model, which is a rate-dependent friction model. The effect of varying the break-away force and Stribeck effect on the stick–slip region were also investigated. Furthermore, the criteria to demarcate the stick–slip region in the LuGre model are discussed, and a different method to incorporate the Stribeck effect and presliding damping in the Dahl friction model is proposed. Using the tangential stress distribution in the contact area, a new hybrid spring-damper friction model is developed. The model is able to estimate the elastic, plastic, and partial-slipping distances during the relative motion. The ability of the model to reproduce experimental tests is investigated in the present work.

Abstract. The micro stick-slip motion systems, such as piezoelectric stick-slip actuators (PE-SSAs), can provide high resolution motions yet with a long motion range. In these systems, friction force plays an active role. Although numerous friction models have been developed for the control of micro motion systems, behaviors of these models in micro stick-slip motion systems are not well understood. This study (1) gives a survey of the basic friction models and (2) tests and compares 5 friction models in the literature, including Coulomb friction model, Stribeck friction model, Dahl model, LuGre model, and the elastoplastic friction model on the same test-bed (i.e. the PE-SSA system). The experiments and simulations were done and the reasons for the difference in the performance of these models were investigated. The study concluded that for the micro stick-slip motion system, (1) Stribeck model, Dahl model and LuGre model all work, but LuGre model has the best accuracy and (2) Coulomb friction model and the elastoplastic model does not work. The study provides contributions to motion control systems with friction, especially for micro stick-slip or step motion systems as well as general micro-motion systems.

Hybrid pump-controlled asymmetric cylinder drive systems are implemented for energy saving purposes in applications that do not require fast responses. Under low-velocity and low-pressure conditions, the friction influence in the hybrid pump-controlled system is evident. Researchers have developed various models to describe friction. These friction models are implemented based on the relative motion of the contact surfaces, and they can be categorized into static friction and dynamic friction models. For example, dynamic friction models are suitable for simulating the friction in hydraulic cylinder seals under lubrication conditions. Among the dynamic models, the LuGre model can capture almost all static and dynamic friction behaviors at the macroscopic level; for example, stiction, the Stribeck effect, and hysteresis. Thus, the LuGre model is suitable for describing the friction in hydraulic cylinders. Because the friction force in the hydraulic cylinder is mainly from the cylinder seal and seal deformation occurs under pressure due to its flexibility, the friction in a hybrid pump-controlled hydraulic system is affected by the relative motion of the contact surfaces. Therefore, to investigate factors that affect the friction other than the relative motion of the contact surfaces, the friction behaviors of a hybrid pump-controlled hydraulic system are studied. Pressure difference and acceleration terms are introduced in the LuGre friction model, and the simulated friction results of the updated LuGre model are compared with the measured experimental results to validate the new friction model.

This paper presents two models based on the LuGre model for friction with consideration of thermal effects. In Model I, parameters in the LuGre model are considered as temperature dependent. In Model II, parameters in the LuGre model are considered as temperature independent; while a temperature-dependent function is added to the temperature-independent LuGre model. Both models are experimentally evaluated, which shows that both can effectively incorporate thermal effects but Model II has better accuracy. Since these models are developed in the context of the motion system, they should be readily incorporated in motion control algorithms for effective control of motion systems with friction if temperature rise is significant in these systems.