Reliability analysis of dynamicaly loaded systems.

Karaulova, Tatyana ; Preis, Irina ; Marquis, Gary 等

Abstract: The attempt to develop the tool for dynamic system analysis taking into account various effective factors was undertaken. The approach evaluates reliability of a complex mechanical system by presenting it in forms of various analytical models using loading spectrum representation. The forestry forwarder has been selected as a prototype of the dynamic system.

Key words: dynamic system analysis, process model, MBD, system reliability.

1. INTRODUCTION

System reliability assessment and prediction has become an increasingly important aspect on the different operating stages of a process. Efficient system reliability assessment techniques need to be developed for complicated systems with multiple components and multiple failure mechanisms in order to ensure adequate performance under uncertain and extreme demands (Leangsuksun et. al., 2003).

Reliability studies of complex dynamic systems require using powerful research tools such as Multibody Dynamics (MBD), Finite Element Analysis (FEA) and others. The forecasting of system reliability based on the process modelling is effective and convenient. Modelling and simulation of load processes for fatigue analysis is an important issue in reliability and engineering design in, for example, vehicles manufacturing.

The majority of reliability modelling approaches is based on statistical methods such as reliability block diagrams and fault trees. However, many intricate system dependencies cannot be adequately represented by these methods. Instead, continuous Markov chain models may be used to handle these kinds of system dependencies.

The present report introduces the solution logic consisting of the following steps:

* The process model used to describe the work cycle of the system. Results of the model simulation denote the duration of loads applied for every item under consideration.

* The process diagram lashed with the plot of mechanical loading spectra for considered parts or nodes of the system in time domain.

* The major external factors influencing the reliability are studied using the process model.

2. SYSTEM DISCRIPTION

The forestry forwarder has been selected as a prototype of the dynamic system. The external factors present an interest for the system reliability assessment.

The system under consideration operates under complicated service (static loading, fatigue loading, wear, impacts etc.), and environmental (ground surface, weather, wind, illumination etc.) conditions. The human factors (skills, health state, level of concentration etc.) also affect the system operations. These conditions relate to so called live loads and are to be modelled. The design and analysis of machines and structures requires the identification of service factors, which include loads and their quantification. The following types of load are important (Roa, 1992):

* Dead load or gravity load, i.e. the weight of the machine or structure with all permanent attachments. The dead load is usually described by normal distribution with a coefficient of variation of 0,1.

* Live loads, which consist of weight of personnel, i.e. portable load. Since these loads vary in time and space the establishing of the random variability of these loads is a difficult task.

* Wind loads.

Since considering of all loading spectra of complex mechanism transporting the logs is complicated, definite service loads in critical structural cross sections (arm of the crane) were taken as modelled loads. It should be also noticed that applied loading spectra would change noticeably if environmental and human factors were also taken into account.

3. ANALYSIS APPROACHES AND METHODS

Each analysis method has a definition, a discipline, and may be used in various ways. The definition contains the concepts, motivation, and the theory of the method.

Many system analysis and engineering methods use graphical syntax to provide visualization of collected data as unambiguously displayed key information. The method may be used separately or as incorporated to a group of methods.

A model can be characterized as an idealized system of objects, properties, and relations designed in certain relevant respects within a particular structure to imitate the character of a given real-world system.

The power of a model comes from its ability to simplify the real-world system it represents, and to predict certain facts about that system with corresponding facts within the model. Figure 1 presents approaches for reliability analysis implementation.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

For the process modelling several standards (UML, IDEF etc.) may be used. Here the structural analysis method has been adopted as standard modelling language to describe system behaviour and its aspects.

The simulation model of the process is shown in Figure 2 where the process diagram is combined with the loading spectrum in time domain. The variable amplitude service loading is given as a real service loading spectra. These spectra, however, could be taken from MBD simulation as output data or even generated by Matlab or Simulink mathematical software using Markov chains.

When considering variable amplitude loading the primary problem is computing the expected rainflow count and the expected damage using given random load model. In this case Markov chains have been found very useful in describing real loads (Rychlik, 1987).

As one can see from Figure 2 the process simulator applies statistical distribution functions of duration logic (DL) for each act of the process (Log Normal L(a,b), where a=mean of the normal, b=standard deviation of the normal).

Since the process has duty cycle described as the log transfer, one deals with the service loading spectra and the reliability of the system during this cycle. The results of preliminary process simulation (Figure 3) showed that the percentage of service loads applied to the working arm of crane acting during complete duty cycle is 36.94%.

[FIGURE 3 OMITTED]

5. SYSTEM RELIABILITY

It has been claimed that fatigue is responsible for at least 80% of all mechanical failures. The system reliability, therefore, is connected to the lifetime of the system components. The reliability is presented in Figure 4 by damage accumulation according to the Miner's rule.

The reliability prediction connected to the system damage accumulation is known in form of equation (1) (Carter, 1986):

[FIGURE 4 OMITTED]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where S(s) and L(s) are strength and load distribution functions respectively, and kt--time dependent function.

The parameter kt has to be taken as time variable according to the simulation output data. Damage accumulation is calculated as the amount of load cycles, i.e. their repetitions during service life.

Following the above-mentioned approach the reliability is measured by the system's mean time to failure (MTTF). The mean time to failure MTTF of a system is the expected time until the occurrence of the first system failure. Given the system reliability R(t), the MTTF can be computed with equation (2) (Leangsuksun et. al., 2003):

MTTF = [[integral].sup.x.sub,0] R(t)dt (2)

Further analysis is based on the Markov's method, which is a powerful tool in reliability, maintainability, and safety (RMS) engineering. Markov's chains are commonly used to study the reliability of complex systems. Markov's analysis provides means for analysing the RMS of systems with strong dependencies between components. Other analysis methods, such as, for example, fault tree analysis method, often assume independent character of components. Used separately, these methods may lead to optimistic prediction for the system reliability and safety parameters (Fuqua, 2003).

6. CONCLUSIONS

The present report introduces the preliminary assessment of the reliability of dynamically loaded systems. The proposed solution brings together benefits of different methods of reliability assessment: starting from technologies of data acquisition, accumulation, analysis and visualization, it ends with the complex stress and fatigue analysis.

7. REFERENCES

Leangsuksun, C., Song, H., Shen, L. (2003) Reliability Modeling Using UML. Software Engineering Research and Practice 2003, pp. 259-262

Rao, S. S. (1992)--Reliability Based Design. ISBN 0-07-051192-6 McGraw-Hill, Inc. New York

Carter, A. D. (1986) Mechanical Reliability ISBN 0-333-40586-2, MACMILLAN, London: pp. 49-51

Rychlik, I. (1987) A New Definition of the Rainflow Cycle Counting Method. Int J Fatigue, 9, pp. 119-121

Fuqua, N. B. (2003) The Applicability of Markov Analysis Methods to reliability, Maintainability, and Safety, START.