Properties of the Dahl Model Applied to Modelling of Static Friction in Closed-Loop Kinematic Chains

Wojtyra, Marek

doi:10.1007/978-3-319-33714-2_11

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…In each case, it was shown that rigid-body models of multibody systems offer no means to credibly predict friction forces in the stiction regime and its vicinity. Note that most recent studies show that similar effects are observed also for the Dahl model [42].…”

Section: Discussionsupporting

confidence: 74%

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Wojtyra

2016

Multibody Syst Dyn

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Problems with uniqueness and high parametric sensitivity of the solution of equations of motion, encountered in the static friction regime, are addressed. Friction in joints of a multibody system with closed-loop kinematic chains is discussed. Three different models of friction are studied: the discontinuous Coulomb model with stiction regime represented in terms of additional constraints; the approximate Coulomb model, smoothed in the vicinity of zero relative velocity; and the LuGre model with presliding displacements represented in terms of auxiliary state variables. Firstly, a rigid body model is investigated. It is shown that in the case of constraint addition approach, problems with uniqueness of solution emerge in the static friction regime. In the case of continuous models of friction, the solution in the stiction regime and its vicinity is highly sensitive to some hardly measurable or arbitrarily chosen parameters of the model of friction. Origins of nonuniqueness and high sensitivity are investigated, and the questionable credibility of the stiction regime simulation results is discussed. Secondly, a simplified model of body and joint elasticity is introduced to investigate the impact of flexibility on the mechanism frictional behavior. It is shown that taking the flexibility into consideration may eliminate the uniqueness and sensitivity problems. Moreover, the quantities that represent flexibility may be regarded as the key factors influencing the results of stiction regime simulation. Five examples are provided to illustrate the presented considerations.

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Section: Discussionsupporting

confidence: 74%

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Wojtyra

2016

Multibody Syst Dyn

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“…These models are data-driven ones that do not consider physical sources of actuator-based hysteresis, and they can be approximately classified into general mathematics-based models, differentialbased models and operator-based models. General mathematics-based models fit hysteresis loops by testing common mathematical functions such as polynomial functions, exponential functions or trigonometric functions [14,15]; Differential-based models adopt nonlinear differential equations to display the hysteresis, such as Dahl model [16], Duhem model [17], Bouc-Wen [18] model and LuGre model [19]. Although differential-based models provide several advantages like compact structures and easy-to-use controller design, these models have difficulties in identifying complex parameters.…”

Section: Introductionmentioning

confidence: 99%

A novel hysteresis modelling method with improved generalization capability for pneumatic artificial muscles

Zhang

Gao

Yang

et al. 2019

Smart Mater. Struct.

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A pneumatic artificial muscle (PAM) consists mainly of an inner elastomeric bladder surrounded by a braided shell. Due to the special geometric structure, PAMs are subject to the typical drawbacks of a highly-asymmetric hysteresis-based nonlinear system. This paper presents a D-extended un-parallel Prandtl–Ishlinskii model (D-EUPI) model for modelling the asymmetric hysteresis of PAMs, which is a deep learning-based model combining a modified EUPI model and a convolution neural network (CNN). Compared with the existing phenomenological hysteresis models, the proposed model has good generalization capability, meaning that not only can it be suitable for trained data, but also can accurately predict the PAM displacement corresponding to input pressure independent of trained data. We investigate the influences of input frequency and amplitude on the inherent hysteresis characteristics of PAMs via experiments. The experiments reveal that the asymmetric hysteresis of the PAM is quasi-rate independent but dependent on its input amplitude for the low frequency range in this study. Furthermore, the D-EUPI model is trained and tested based on the experimental data. The results show that the D-EUPI model is effective in predicting the hysteresis of PAMs over a wide range of input amplitudes. And the D-EUPI model has better performance in modelling complex multi-loop hysteresis by comparison with the EUPI model and the CNN model.

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“…In recent studies [7,8] it was shown that problems with uniqueness of solution may be experienced when closed-loop mechanisms without redundant constraints are modeled and simulated. The investigation was focused on the stiction phase and its neighborhood, when the relative joint velocities are null or close to zero.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Static Friction in Closed-Loop Kinematic Chains with Multiple Degrees of Freedom—A Study of Uniqueness and Parametric Sensitivity Problems

Wojtyra

2018

ROMANSY 22 – Robot Design, Dynamics and Control

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Problems with uniqueness and high parametric sensitivity of solution of equations of motion, encountered in the static friction regime, are addressed. Friction in joints of a multiple degree of freedom closed-loop kinematic chains is discussed. Two different models of friction are studied: the discontinuous Coulomb model with stiction regime represented in terms of additional constraints and the approximate Coulomb model, smoothed in the vicinity of zero relative velocity. Origins of non-uniqueness and high sensitivity are investigated; the questionable credibility of the stiction regime simulation results is pointed out. Two examples are provided to illustrate the discussed issues.

show abstract

Properties of the Dahl Model Applied to Modelling of Static Friction in Closed-Loop Kinematic Chains

Cited by 4 publications

References 13 publications

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

Modeling of static friction in closed-loop kinematic chains—Uniqueness and parametric sensitivity problems

A novel hysteresis modelling method with improved generalization capability for pneumatic artificial muscles

Modeling of Static Friction in Closed-Loop Kinematic Chains with Multiple Degrees of Freedom—A Study of Uniqueness and Parametric Sensitivity Problems

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