Dariusz Grzelczyk

MODELING AND ANALYTICAL/NUMERICAL ANALYSIS OF WEAR PROCESSES IN A MECHANICAL FRICTION CLUTCH

This work is devoted to modeling and the analytical/numerical analysis of tribological processes occurring on the contact surface of shields of a mechanical friction clutch. Although the considered problems have been already studied earlier, however, simplified mathematical models have been used and applied. Unlike previous works, our work takes into account elasticity and wear properties of material of shields rubbing themselves. A general nonlinear differential model of wear is considered, as well as a wear model in the integral form taking into account gradual decrease of speed of wear of shields as a result of abrasive adapting to each other in the process of the exploitation. Equations modeling contact pressure on the contact surface of shields are derived and they yield the contact pressure and the wear of the shields. An analytical/numerical analysis is carried out with the qualitative and quantitative theories of differential and integral equations, including Laplace transformation. Many interesting results are obtained, illustrated and discussed. The presented results can be widened and used in other disciplines of the science, for instance, in physics of solids or biomechanics of various human joints.

MODELING AND ANALYSIS OF THERMAL PROCESSES IN MECHANICAL FRICTION CLUTCH — NUMERICAL AND EXPERIMENTAL INVESTIGATIONS

Thermal processes occurring in the mechanical clutch or brake systems have a great influence on the strength of elements of these systems as well as on their dynamics. The contact problems exhibited by such systems include heat generated by dry friction contact surfaces. The contact dynamics in general depends on many system parameters, and it attracted attention of many researches focused on analysis of the mentioned phenomena in different kinds of mechanical systems like clutches, brakes, and others. In this work a mathematical model describing the processes of heat generation and its propagation in the mechanical friction clutch is presented. The presented model takes into account the unequal distribution of flux density of produced heat in the clutch, the thermal conductivity of materials of friction linings, and the heat transfer between the friction linings of clutch and its environments. The analyzed object is described by a set of algebraic linear homo- and heterogeneous equations, and it is derived using a computer numerical method. Many interesting numerical and experimental results are obtained, illustrated and discussed. Presented numerical results coincide with experimental data.

Wear Processes in a Mechanical Friction Clutch: Theoretical, Numerical, and Experimental Studies

Mathematical modeling, theoretical/numerical analysis, and experimental verification of wear processes occurring on the contact surface of friction linings of a mechanical friction clutch are studied. In contrast to many earlier papers we take into consideration wear properties and flexibility of friction materials being in friction contact. During mathematical modeling and numerical simulations we consider a general nonlinear differential model of wear (differential wear model) and a model of wear in the integral form (integral wear model). Equations governing contact pressure and wear distributions of individual friction linings, decrease of distance between clutch shields, and friction torque transmitted by the clutch are derived and compared with experimental data. Both analytical and numerical analyses are carried out with the qualitative and quantitative theories of differential and integral equations, including the Laplace transform approach to ODEs. We show that theoretical results and numerical simulations agree with the experimental data. Finally, a numerical analysis of the proposed mathematical models was carried out in a wider range of parameters of the considered system.

Kinematics, Dynamics and Power Consumption Analysis of the Hexapod Robot During Walking with Tripod Gait

The paper is focused on the kinematic, dynamic and power consumption analysis of the constructed prototype of the hexapod robot walking with tripod gait on a flat and hard ground. The movements of the robot legs are controlled by different well known oscillators working as central pattern generators (CPGs). The mentioned models, as well as those proposed in our previous paper, are employed and compared from the viewpoint of fluctuations of the robot gravity center both in vertical and movement direction, contact forces between the robot legs and the ground as well as energy demand of the whole robot during walking process. Time histories of the key kinematic and dynamic quantities describing locomotion of the robot are numerically studied and experimentally verified. Power consumption of the whole robot is experimentally investigated based on the current consumption in the applied servo motors which drive the robot legs. We show that the proposed CPG model is more efficient regarding acceleration/decelera...

On the Hexapod Leg Control with Nonlinear Stick-Slip Vibrations

In the paper the control problem of the six-legged walking robot is studied. In order to find the relationship between commonly used by insects gaits (trajectory of the foot point) and stable trajectory of mechanical systems, at first we analyse various previous papers and the gaits of the real insects. For control the motion of the tip of the robot leg a nonlinear mechanical oscillator describing stick-slip induced vibrations further referred as central pattern generator (CPG) has been proposed. The advantages of the proposed model has been presented and compared with other previous applied mechanical oscillators. The possibility of control of the tip of the robot leg via changing parameters characterized oscillator working as a CPG has been discussed. Time series of the joints and configurations of the robot leg during walking are presented. The obtained numerical solutions indicate some analogies between the characteristics of the simulated walking robot and animals found in nature. Moreover, some aspects of an energy efficiency analysis (in order to reduce the energy costs) are discussed for the analysed system and the whole hexapod robot. In particular, we discuss the interplay of the proposed gait patterns and the system energy cost.

Kinematic and dynamic simulation of an octopod robot controlled by different central pattern generators

The goal of the study was to perform both kinematic and dynamic simulation of an octopod robot walking on a flat and hard surface. To drive robot legs, different non-linear mechanical oscillators were employed as central pattern generators. Aside from using some well-known oscillators, a new model was proposed. Time series of robot’s kinematic and dynamic locomotion parameters were computed and discussed. Displacement and velocity of the centre of gravity of the robot, ground reaction forces acting on the robot legs, as well as some aspects of energy consumption of a walking robot were analysed to assess the central pattern generators. The obtained kinematic and dynamic parameters showed some advantages of the applied generator. In particular, the gait of the robot was most stable when the robot was driven by the proposed central pattern generator model.

A 3-Link Model of a Human for Simulating a Fall in Forward Direction

In this study we consider a 3-link biomechanical model of a human for simulating a forward fall. Individual segments of the human body are modelled as rigid bodies connected by the rotary elements which correspond to the human joints. The model implemented in Mathematica is constructed based on a planar mechanical system with a non-linear impact law modelling the hand-ground contact. Due to kinematic excitation in the joints corresponding to the hip and the shoulder, the presented fall model is reduced to a single-degree-of-freedom system. Parameters of the model are obtained based on the three-dimensional scanned human body model created in Inventor, while its kinematics (time histories of the angles in hip and shoulder joints) are obtained from the experimental observation with the optoelectronic motion analysis system. Validation of the model is conducted by means of comparing the simulation of impact force with experimental data obtained from the force plate. Finally, the obtained ground reaction forces can be useful in further studies, as a load conditions, for finite element analysis of the numerical model of the human upper extremity.

Reflectance and Transmittance of Cholesteric Liquid Crystal Sandwiched Between Polarizers

In this paper we calculated reflection and transmission coefficients of the electromagnetic radiation (light) incident on the cholesteric liquid crystal sandwiched between two isotropic optical media and a pair of polarizers. To model optical phenomena (i.e. propagation and interference of the light waves) in liquid crystal, we applied the 4 × 4 matrix method. As a result of the performed computer simulation, we obtained some interesting reflection/transmission spectra and polar plots for different parameters of the considered system and arbitrary incident monochromatic light. The illustrated and discussed results can be useful for understanding different optical systems, especially liquid crystal displays. Moreover, the applied mathematical approach can be potentially used for modelling of more advances contemporary optical systems, i.e. photonic crystals.

Hydraulically Driven Unit Converting Rotational Motion into Linear One

The contribution concerns a unit which can be implemented in driving hand prostheses, surgical manipulators and other equipment, the operation of which is based on linear motion. The state-of-the-art research presents several medical devices usually driven by means of electric or hydraulic, complex elements. The primary purpose of this work is to provide a solution that, due to simplicity of its design, will be an alternative to existing expensive devices. Simultaneously, the goal of the efforts is to ensure high precision and repeatability of linear movement. The proposed device comprises two hydraulic actuators driven by a stepper motor. Apart from presenting the design of the unit, the following work comprises description of modelling of the unit operation supplemented with presentation of the constructed prototype and results of initial experimental evaluation. Eventually, conclusions are drawn, pointing several amendments which are recommended for implementation in the future work.