Dynamic Friction Model Research Articles

Dynamical friction and the evolution of black holes in cosmological simulations: A new implementation in OpenGadget3

Aims. We introduce a novel sub-resolution prescription to correct for the unresolved dynamical friction (DF) onto black holes (BHs) in cosmological simulations, to describe BH dynamics accurately, and to overcome spurious motions induced by numerical effects. Methods. We implemented a sub-resolution prescription for the unresolved DF onto BHs in the OpenGadget3 code. We carried out cosmological simulations of a volume of (16 comoving Mpc)3 and zoomed-in simulations of a galaxy group and of a galaxy cluster. We assessed the advantages of our new technique in comparison to commonly adopted methods for hampering spurious BH displacements, namely repositioning onto a local minimum of the gravitational potential and ad hoc boosting of the BH particle dynamical mass. We inspected variations in BH demography in terms of offset from the centres of the host sub-halos, the wandering population of BHs, BH–BH merger rates, and the occupation fraction of sub-halos. We also analysed the impact of the different prescriptions on individual BH interaction events in detail. Results. The newly introduced DF correction enhances the centring of BHs on host halos, the effects of which are at least comparable with those of alternative techniques. Also, the correction becomes gradually more effective as the redshift decreases. Simulations with this correction predict half as many merger events with respect to the repositioning prescription, with the advantage of being less prone to leaving substructures without any central BH. Simulations featuring our DF prescription produce a smaller (by up to ~50% with respect to repositioning) population of wandering BHs and final BH masses that are in good agreement with observations. Regarding individual BH–BH interactions, our DF model captures the gradual inspiraling of orbits before the merger occurs. By contrast, the repositioning scheme, in its most classical renditions, describes extremely fast mergers, while the dynamical mass misrepresents the dynamics of the black holes, introducing numerical scattering between the orbiting BHs. Conclusions. The novel DF correction improves the accuracy if tracking BHs within their hosts galaxies and the pathway to BH- BH mergers. This opens up new possibilities for better modeling the evolution of BH populations in cosmological simulations across different times and different environments.

A Novel Friction Compensation Method for Machine Tool Drive Systems in Insufficient Lubrication.

Friction is the dominant factor restricting tracking accuracy and machining surface quality in mechanical systems such as machine tool feed-drive. Hence, friction modeling and compensation is an important method in accurate tracking control of CNC machine tools used for welding, 3D printing, and milling, etc. Many static and dynamic friction models have been proposed to compensate for frictional effects to reduce the tracking error in the desired trajectory and to improve the surface quality. However, most of them focus on the friction characteristics of the pre-sliding zone and low-speed sliding regions. These models do not fully describe friction in the case of insufficient lubrication or high acceleration and deceleration in machine tool systems. This paper presents a new nonlinear friction model that includes the typical Coulomb-Viscous friction, a nonlinear periodic harmonic friction term for describing the lead screw property in insufficient lubrication, and a functional component of acceleration for describing the friction lag caused by the acceleration and deceleration of the system. Experiments were conducted to compare the friction compensation performance between the proposed and the conventional friction models. Experimental results indicate that the root mean square and maximum absolute tracking error can be significantly reduced after applying the proposed friction model.

Friction modeling from a practical point of view

AbstractRegularized static friction models have been used successfully for many years. However, they are unable to maintain static friction in detail. For this reason, dynamic friction models have been developed and published in the literature. However, commercial multibody simulation packages such as Adams, RecurDyn, and Simpack have developed their own specific stick-slip models instead of adopting one of the public domain approaches. This article introduces the fundamentals of these commercial models and their behavior from a practical point of view. The stick-slip models were applied to a simple test model and a more sophisticated model of a festoon cable system using their standard parameters.

Analysis of Fluid-Injection-Induced Seismicity Using a Dynamic Sliding Model Incorporating the Rate- and State-Dependent Friction Law

Summary Earthquakes can be triggered by fluid injection into underground formations. Fluid injection can cause large changes in the underground volume that exert stresses on nearby preexisting faults, leading to seismic activity. Assuming an increase in underground development activities in the future, our understanding of the mechanism underlying induced seismicity must be improved, and methods must be developed to properly assess the risk of seismic events. The objective of this study is to develop a seismicity prediction model that calculates the magnitude and timing of triggered earthquakes or seismic events occurring during various subsurface fluid injection activities. We developed an injection-induced seismicity analysis model that predicts the dynamic earthquake nucleation caused by changes in stress and pore pressure that occur during various subsurface activities. The governing equations consisting of the dynamic motion of the poroelastic spring-slider system, rate and state friction laws and pore pressure diffusion equation were solved using the embedded semi-implicit Runge-Kutta (SIRK) method. The dynamic sliding model was also incorporated into the finite element method (FEM) model, considering the variations in the stresses and pore pressures in the formation. A field case study was also conducted to compare the model results with typical microseismicity responses observed from hydraulic fracturing treatments in shale fields. Contrary to the popular understanding derived from Amonton’s law, the dynamic friction model revealed that a large normal stress on the fault leads to rapid sliding. A larger normal stress accumulates a large amount of elastic energy until it slips owing to fluid injection, nucleating large seismic waves. The poroelastic spring-slider model estimated reasonable microseismic magnitudes for hydraulic fracturing treatment but overestimated the time required to trigger a microseismic event under field conditions. To improve the analysis results, the poroelastic spring-slider model was coupled with a linear elastic FEM that considered the complex interplay of stress changes from hydraulic fracturing and the associated pore pressure variation in the formation. Compared with the field data, the coupled simulation model estimated a reasonable timing for the induced microseismic events when the increasing pore pressure during hydraulic fracturing penetrated deep into the formation. These findings suggest the existence of permeable natural fractures in the formation, which intensify early frictional sliding during treatment. The seismicity prediction model presented in this study simulates the magnitude and timing of seismic nucleation, helping to manage and mitigate the environmental impacts of induced seismicity during various subsurface development activities, such as oil and gas extraction, hydraulic fracturing, geothermal, and carbon dioxide sequestration. Moreover, the case study results imply that the time series of seismic events predicted by the model can be used to understand the possible fracture geometry and extent of fluid invasion for field applications. Key Terms and Phrases induced seismicity, subsurface fluid injection, rate- and state-dependent friction law, embedded semi-implicit Runge-Kutta method, finite element analysis

Friction Force Reduction Efficiency in Sliding Motion Under Tangential Vibrations of Elastic Support

Abstract The efficiency of reducing the friction force in sliding motion under the influence of forced vibrations of an elastic substrate significantly depends on the direction of these vibrations in relation to the sliding direction. This article presents a comparison of computational models developed by the authors to estimate the friction force in sliding motion under longitudinal and transverse tangential vibrations of the substrate. Fundamental differences between these models are discussed, and the results of comparative analyses of the impact of tangential vibrations on the friction force depending on their direction are presented. In the developed models describing the friction force, dynamic friction models of Dahl and Dupont and the so-called LuGre model were utilised. The analyses were performed as a function of the sliding velocity and two basic parameters of vibration, which are frequency f and amplitude u0. It has been shown that under longitudinal vibrations, the key parameter, which determines the occurrence of friction force reduction at a given driving velocity vd, is the amplitude va of vibration velocity. However, the level of this reduction cannot be determined unequivocally based on the value of this parameter alone since the identical value va can be obtained at different magnitudes of the frequency and amplitude of vibrations, and the reduction level is a nonlinear function of these parameters. The results of simulation analyses were verified experimentally.

Velocity and load dependent dynamic shock absorber friction at stationary conditions

When it comes to vehicle vertical dynamics, the characteristics of shock absorbers are of high importance. With the increasing use of active suspension systems, it becomes possible to adapt the hydraulic damping force to the road event, while the friction force is not controllable. As a result, friction becomes more relevant and can negatively affect passenger ride comfort. In many mechanical applications, it is observed that friction in lubricated sliding conditions is velocity and load dependent. In contrast, shock absorber friction, and therefore suspension friction, is commonly considered as quasi-static, i.e. characterised by a constant potential. Since the shock absorber is predominantly in motion over a wide velocity range, it is necessary to improve the understanding of friction characteristics especially in the dynamic domain. In this study, modified valve-free shock absorbers are presented that allow the observation of dynamic friction properties experimentally. As not covered by previous studies, the effect of side force (load) as a main parameter to increase friction is investigated. It is observed that its effect varies significantly with velocity and alters the stationary friction-velocity curve, also known as the Stribeck curve. In addition, the shape of the Stribeck curve depends strongly on the shock absorber's oil volume. These novel results emphasise a substantial, interdependent influence of load and velocity on the (elasto-)hydrodynamic properties of the dynamic shock absorber friction force, which was not identified in the literature. The dynamic friction force exceeds the quasi-static friction force multiple times, and also exceeds the hydraulic damping force for considerable side forces in the lower velocity range up to 60 mm/s. Consequently, the total shock absorber force under presence of side force is determined. The findings can be used to improve active suspension control or to improve vehicle simulation by enabling the parametrisation of dynamic shock absorber friction models.

Research on the influence factors of hydraulic oscillator on drag reduction efficiency in horizontal well drilling

The application of hydraulic oscillator can solve the problems of large friction and serious pressure support in the drilling process of extended reach well and long horizontal well, but the conventional hydraulic oscillator parameter setting is not reasonable, high pressure consumption, easy to make the ground machine pump overload operation and failure. Therefore, based on the LuGre dynamic friction model theory, a calculation model for the friction between drill string and rock wall under the condition of longitudinal oscillation is established, and the influence law of hydraulic oscillator oscillation parameters on drag reduction efficiency is studied. The results show that the change of oscillation intensity, oscillation frequency and oscillation amplitude can improve the drag reduction efficiency, and the increase trend of drag reduction efficiency is first increased and then decreased. The selection of each parameter has the optimal value. According to the analysis of orthogonal test results, it is found that the reduction degree of friction between drill string and borehole wall rock by each parameter is in the order of oscillation intensity, oscillation frequency and oscillation amplitude from the largest to the smallest.

Optimising pavement texture measurement resolution for accurate friction determination: a preliminary investigation

This study seeks to identify the most suitable pavement texture resolution for accurately representing friction properties, employing the Dynamic Friction Model (DFM). Friction and texture measurements were conducted on various pavement surfaces at resolutions ranging from 10 μm to 5000 μm. Results indicate that the optimal resolution for accurate representation is unexpectedly found to be 500 μm, aligning with the Microtexture/Macrotexture limit. This contradicts current trends emphasizing higher resolutions for pavement surface representation. The article provides a foundational exploration, prompting discussions and further investigations into determining the ideal resolution for characterizing pavement surfaces in the context of friction properties.

POSITION CONTROL OF ELECTRO-HYDRAULIC SERVO SYSTEM WITH FRICTION COMPENSATION

This work presents a model-based friction compensation technique and an integral adaptive backstepping controller to improve the position control of the electrohydraulic servo system. The controller design uses a continuous approximation of the LuGre friction model and the Lyapunov theory of nonlinear systems. The friction compensation enhances system performance, and comparison tests are conducted on a hydraulic servo test bench to validate the control strategy's tracking performance under various conditions. KEYWORDS: Electrohydraulic servo systems; Position control; Integral adaptive backstepping controller; LuGre dynamic friction model; Lyapunov theory; Friction compensation.

Effectiveness of Friction Force Reduction in Sliding Motion Depending on the Frequency of Longitudinal Tangential Vibrations, Sliding Velocity and Normal Pressure

Abstract The article presents the results of experimental research and simulation analyses of the influence of slip velocity, normal pressures and vibration frequency on the effectiveness of friction force reduction carried out in sliding motion in the presence of forced tangential vibrations. In experimental studies, changes in the driving force were measured during the slip of the upper body over the vibrating lower body. The direction of these vibrations was parallel both to the contact plane and to the direction of movement of the shifted body. The simulation tests were carried out in the Matlab/Simulink environment through the use of numerical procedures that were specially created for this purpose. Dynamic friction models considering the tangential compliance of contact and the phenomenon of pre-sliding displacement were used for calculations. The paper presents the designated values of the so-called coefficient of average friction force reduction in sliding motion for the following friction pairs: steel C45–steel C45, steel C45–cast iron GGG40 and steel C45–polytetrafluoroethy-lene PTFE (Teflon). The results of numerical analyses were in good agreement with those of experimental tests. A significant dependence of the level of average friction force reduction on the frequency of forced vibrations, sliding velocity as well as the kind of sliding pair material, and normal pressures was shown.

A Second-Order Dynamic Friction Model Compared to Commercial Stick–Slip Models

Friction has long been an important issue in multibody dynamics. Static friction models apply appropriate regularization techniques to convert the stick inequality and the non-smooth stick–slip transition of Coulomb’s approach into a continuous and smooth function of the sliding velocity. However, a regularized friction force is not able to maintain long-term stick. That is why dynamic friction models were developed in recent decades. The friction force depends herein not only on the sliding velocity but also on internal states. The probably best-known representative, the LuGre friction model, is based on a fictitious bristle but realizes a too-simple approximation. The recently published second-order dynamic friction model describes the dynamics of a fictitious bristle more accurately. It is based on a regularized friction force characteristic, which is continuous and smooth but can maintain long-term stick due to an appropriate shift in the regularization. Its performance is compared here to stick–slip friction models, developed and launched not long ago by commercial multibody software packages. The results obtained by a virtual friction test-bench and by a more practical festoon cable system are very promising. Thus, the second-order dynamic friction model may serve not only as an alternative to the LuGre model but also to commercial stick–slip models.

A new quasi-static friction model for the spherical hinge bearing in structural engineering

For most frictional issues in structural engineering, the classical friction law named after Coulomb is a reliable and convenient tool, but it cannot be used to predict a slippage-related quasi-static process due to the lack of relevant items. In this paper, based on some commonly used dynamic friction models, a new rate-independent friction model is proposed to describe a quasi-static frictional process in structural field, e.g., the motion of a spherical hinge bearing in a pedestrian bridge under reciprocal pedestrian and temperature loads. Most quasi-static processes happen at the pre-sliding regime when a friction contact tends to slide slightly before the Coulomb friction is reached. The well-known Dahl model, LuGre model, and other test-based dynamic models are surveyed, and their shortcomings in engineering use are summarized subsequently. The new model, the same as the Dahl model, is rate-independent, but adopts a more engineering-oriented form. On the basis, it can be easily applied on a finite element analysis by adjusting a built-in ideal elastoplastic model. Meanwhile, the accuracy has no obvious decrease according to a test-based comparison between the Dahl model and the new. The coefficient of stiffness deviation, defined as the deviation of the pre-sliding friction stiffness from the initial friction stiffness, is introduced into the new model, which makes the model possible to predict the energy dissipation at the pre-sliding regime and can be well explained by the asperity-based theory at microscopic level. The impacts from the curvature and the coverage of a contact on the coefficient of static friction are assessed by the finite element method. It is shown that the curvature has very few impacts while the coverage is highly positively related to the observed coefficient of friction. A friction test of a spherical hinge is then carried out to verify the new model. By data regression, the coefficient of stiffness deviation for the proposed model and the exponent for the Dahl model are identified as 0.492 and 2.272, respectively. A comparison of friction torque-slippage hysteresis loops shows both the Dahl model and the proposed model have good predication as the normal force is large enough and the proposed one is even better in some load cases. Finally, a brief application on a pedestrian bridge of the new model is introduced. It indicates that there will be some mechanical residuals when a spherical hinge is applied with a reciprocating load, but the residuals tend to be limited.

LuGre or not LuGre

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.

A novel dynamic dry friction model for applications in mechanical dynamical systems

This work presents a novel continuously differentiable, dynamic dry friction model, with dependence on normal contact force, slip velocity, and static and dynamic coefficients of friction. The state-of-the-art, Brown and McPhee friction model depends on transitional velocity, which is an empirical parameter. A limitation with this model is that there is no generic approach to select the optimal value for the transitional velocity for a certain application. The simulation results presented in this work highlight the sensitivity of friction force with transitional velocity in Brown and McPhee’s model to obtain smooth solutions, which are supportive in control system applications. It is because control systems require jitter-free signals in order to save costs on low-pass filters. The proposed model overcomes such empirical dependence on transition velocity through a combination of an iterative methodology and an empirical parameterization. In this article, a comprehensive analysis of the proposed friction model and the contributing parameters is carried out. The algorithm to implement the proposed friction model is elaborated. The proposed friction model is then simulated and compared against Brown and McPhee’s model. using a stick-slip benchmark problem. Furthermore, the proposed force model is applied to two spatial multibody systems formulated using index 0 tangent space differential-algebraic equations. The results demonstrate how the proposed friction model can be employed in dynamical mechanical systems. The independence on transitional velocity in the proposed friction model is observed to be effective for obtaining smooth solutions that make it suitable for control system applications.

Cylinder position control driven by pneumatic digital bridge circuit using a fuzzy algorithm under large stroke and varying load conditions

A digital bridge circuit based on the concept of independent metering control can enable the precise position control of a pneumatic cylinder, but large strokes and variable loads still cause challenges. To solve this problem, a piecewise on/off valve flow compensator and a composite friction observer were innovatively designed in this study, and they were combined with a multiple fuzzy intelligent algorithm to ensure the accuracy and robustness of pneumatic position control. Considering the starting and stopping delays and the response processes of on/off valves, a six-stage flow–duty ratio linearization relationship was proposed. Employing a parameter identification method, a static and dynamic composite friction model was presented. Then, a fuzzy PID controller was proposed, and a genetic algorithm was used to optimize the control parameters. Experiment results showed that, when focusing on a large stroke (250 mm) and varying loads (8.5–18.5 kg), for sinusoidal signal with amplitude of 150 mm and frequency of 0.125 Hz and the air supply pressure is 0.5 Mpa, the algorithm in this study could ensure that the steady-state step response error was less than 1% and the root mean squared error of the sinusoidal trajectory tracking was less than 3%.

An analytical approach to the stress relaxation behavior of a low temperature shape-memory fabric based on viscoelastic models

Shape-memory materials are a promising new class of smart materials with many applications such as strain sensors, artificial muscles, and smart breathing textiles. These materials are subjected to force and extension in situ. Thus, the time-dependent behavior of these materials can play an important role in their long-term performance. The present study was conducted to investigate the time-dependent behavior of a type of shape-memory fabric. Nanoclay-reinforced polylactic acid/thermoplastic polyurethane was used as the precursor. The yarn that was produced was highly twisted. The twisted yarn was then shaped into a coiled structure by mandrel annealing. This yarn was then used to produce knitted fabric. The fabric was examined under both cold (25 °C) and hot (50 °C) conditions. The fabric contracted in hot water in the course direction but did not show a significant contraction in the wale direction. It returned to its original width in cold water. This effect was observed repeatedly over several cycles. This shows that the knitted fabric composed of the precursor twisted-coiled yarn exhibited low-temperature actuation and reversible two-way shape-memory behavior. A value of %16 was calculated for the contraction stroke along the course direction. The stress relaxation behavior of the two-way shape-memory fabric was then studied and analyzed. For this purpose, four different viscoelastic models were considered: the standard linear model (a), Burgers model (b), Jeffrey model (c), and Kelvin-Voigt-Maxwell model (d). We used the curve fitting procedure to find the best fit to the experimental data based on the least-squares method. The results showed that the Kelvin-Voigt-Maxwell model (model d) exhibited a higher and more acceptable regression coefficient (R 2) than the other three models. The Jeffrey model showed the lowest regression coefficient (R 2), thus confirming that it is not suitable for explaining the relaxation behavior of the fabric. However, a limitation of Model (d) is that it is not in line with the experimental loading stage. To modify the model, we propose the replacement of the dashpot with a dynamic frictional element. The results indicate that the proposed dynamic friction model can eliminate the limitations of the dashpot body during the loading stage.

Numerical modeling and simulation of friction models for mechanical systems: A brief review

Friction is essential for the proper functioning of a mechanical system. On the other hand, friction has a dissipative nature which destroys useful energy and reduces the efficiency of a mechanical system. The analysis of friction is thus an interesting area of research as it is an essential factor that helps improve any machine's performance. However, friction analysis is not easy because it depends on many factors. Therefore, many researchers have proposed different models for effective friction analysis for different mechanical systems. In this paper, a brief review of existing literature on the proposed friction models for various kinds of mechanical systems is presented. The current research status for static and dynamic friction models is covered, and numerical modelling and simulation of various friction models are discussed. Features of the models are highlighted to reveal the importance of the past technique with suggestions on future directions in friction analysis.

A Two-Step Method for Dynamic Parameter Identification of Indy7 Collaborative Robot Manipulator.

Accurate dynamic model is critical for collaborative robots to achieve satisfactory performance in model-based control or other applications such as dynamic simulation and external torque estimation. Such dynamic models are frequently restricted to identifying important system parameters and compensating for nonlinear terms. Friction, as a primary nonlinear element in robotics, has a significant impact on model accuracy. In this paper, a reliable dynamic friction model, which incorporates the influence of temperature fluctuation on the robot joint friction, is utilized to increase the accuracy of identified dynamic parameters. First, robot joint friction is investigated. Extensive test series are performed in the full velocity operating range at temperatures ranging from 19 °C to 51 °C to investigate friction dependency on joint module temperature. Then, dynamic parameter identification is performed using an inverse dynamics identification model and weighted least squares regression constrained to the feasible space, guaranteeing the optimal solution. Using the identified friction model parameters, the friction torque is computed for measured robot joint velocity and temperature. Friction torque is subtracted from the measured torque, and a non-friction torque is used to identify dynamic parameters. Finally, the proposed notion is validated experimentally on the Indy7 collaborative robot manipulator, and the results show that the dynamic model with parameters identified using the proposed method outperforms the dynamic model with parameters identified using the conventional method in tracking measured torque, with a relative improvement of up to 70.37%.

Seismic analysis of landfill using advanced numerical approach considering material and contact nonlinearity

Seismic stability is of vital importance for municipal solid waste (MSW) landfills and this study proposes an advanced numerical approach considering material and contact nonlinearity for seismic analysis of landfill. The MSW is modeled as porous media through the u-p formulation and the bounding surface plasticity model based on the double-phase assumption is adopted. The dynamic friction model is applied to define the interface shear behavior so that the elastoplasticity and displacement-softening property of the liner interface can be well reflected. The advanced numerical method is validated through back analyses of soil column tests and centrifuge tests of landfills. The subsequent site-specific case study indicate that earthquake-induced sliding along the liner system is a typical failure mode of canyon landfill and the stability can be assessed based on the permanent displacement, which can also be roughly estimated with simplified semiempirical models by setting the yield coefficient as the residual friction coefficient of the liner interface.

Real-Time Torque Estimation of Automotive Powertrain With Dual-Clutch Transmissions

This article proposes a nonlinear observer for estimating a powertrain transmitted torque of vehicles equipped with dual-clutch transmissions. A new dynamical model of vehicle driveline is presented. It introduces a single characteristic state based on the dynamic friction model to scale the clutch torque capacity, which is available from the actuator position-to-torque map. Based on this model, the generated torque on the clutch disk can be effectively estimated in real time, and the sensitivity of the estimated value caused by high gain feedback can be reduced in the observer. Also, the engine torque uncertainty is estimated from the integrated driveline model. The Lyapunov-based analysis is presented to prove the convergence of the proposed observer. The effectiveness of the proposed method is shown by experimental validations on a test vehicle that allows for real measurements of the input shaft torque of transmission.