test and optimization of static and dynamical … and optimization of static and dynamical...

TEST AND OPTIMIZATION OF STATIC AND DYNAMICAL CHARACTERS FOR EXCAVATOR*

XUE Caijun Graduate Student

State Key Laboratory of CAD&CG

Zhejiang University

HangZhou, 310027, P.R.China

Email: [email protected]

QIU Qingying Associate professor


Zhejiang University



FENG Peien Professor


Zhejiang University



ABSTRACT

By the recent trend of high speed and efficiency, working

condition of a hydraulic excavator tends to be more

abominable, time varying and frequently with impact

accompanying and the structure of it is prone to be more

and more complex. Consequently, structural static and

dynamic synthetic performances are desired to be higher.

Furthermore, structural static and dynamic optimization

included in entire performance optimization plays a

significant role in complex mechanical system generalized

optimization. This paper puts forward a new method to

realize the structural static and dynamic collaborative

optimization of hydraulic excavator working equipment. The

mathematical model of static and dynamical optimization is

developed basing on finite element analysis and testing

results of static and dynamical characters of hydraulic

excavator working equipment. The paper introduces set-up

of testing system and presents the experiment results that

are used to validate the static finite element models and to

* This research is supported by the National 863 Program of China under Grand Number No. 2001AA412110 and the National Science Foundation of China under Grant Number No. 59635150.

update the dynamic finite element models. The optimum

results prove the present method efficient and effective.

1. INTRODUCTION

Vibration and shock easily result in crack and invalidity of

working equipment of hydraulic excavator, which is

designed with traditional static method. The way to change

this condition is to use dynamic method in analyzing and

designing. On the other hand, the dynamic characteristic

optimization of structures is a main aspect of the general

optimization of mechanical product just like the static

characteristic optimization [1]. Therefore, iteration of static

and dynamic analyzing and structure modifying is just the

general process of system optimization.

The paper puts forward a new method to realize the

collaborative optimization, including structural static

optimization and dynamic optimization of hydraulic

excavator working equipment. In order to meet the

demand of computing speed and computing accuracy, the

paper presents an improved structural optimization

modeling method based on finite element analysis and

testing results of static and dynamical characters.

The paper is organized as: First, the method of structural

static and dynamic collaborative optimization is

introduced in section 2. The experimental work and the

testing data processing result are presented in detail in

section 3. And then section 4 discusses finite element

modeling in our collaborative optimization system. Based

on the updated static and dynamic analyzing models the

optimization result is presented in section 5, and section 6

concludes the paper.

2. STRUCTURAL COLLABORATIVE OPTIMIZATION

Structural collaborative optimization aims to minimize the

structural weight under restriction of static stress, natural

frequency and dynamic stress. Structural optimization

with finite element analysis is typically complicated

processes, with information processing, problem solving

and decision-making. So, a multi-agent based structural

static and dynamic collaborative optimization system is

constructed, in which distributed and parallel computing

and data sharing can improve computing efficiency [2].

However, difficulties arise when several components and

parts will be analyzed on static and dynamic performance

at the same time during optimizing iterations because of

the fact of high finite element analysis cost. So, it is more

practical to use coarse-mesh finite element models, but

they can’t meet analyzing precision.

To overcome these difficulties, this paper put forward a

more promising strategy by integrating coarse-mesh

modeling and testing modeling. The finite element

analysis and optimization process is shown as Figure 1.

First, a group of coarse-mesh finite element models is

built at several critical working conditions. The

corresponding static analysis is used to find the boundary

load between assemblies, which is used to finish static

and transient finite element analysis for assemblies. The

corresponding modal analysis is used to identify the

structure’s dynamical characteristic. Then, based on static

and dynamic testing results the finite element models are

rebuilt or updated respectively. The ideal finite element

models are parameterized at next step. Parametric

models for structural finite element analysis are

demonstrated in Figure 2. Finally, the process for finite

element analysis is fully automatic by use of commercial

finite element analysis packages (MSC/NASTRAN).

Automation of geometry modeling, mesh generation,

analysis and post-processing is implemented by

programming in PCL language.

3. EXPERIMENTAL WORK

Our experimental work includes static testing and dynamic

testing. Since the static testing, which valuates static finite

element model, is relatively simple, only the dynamic testing

is discussed in this paper. Modal analysis is an experimental

method enabling studies of the dynamic behavior of

structures. This method describes the dynamics of any

vibrating system giving natural frequencies and natural

damping, as well as deformation patterns associated with

them. The first aim of the experiments presented in this

paper is to prove the accuracy of finite element models. And

another main aim is to find the important factors that

influence dynamic behavior of hydraulic excavator, based on

which coarse-mesh finite element is built.

3.1 EXPERIMENTAL TEST SET-UP

Figure 3 shows the set-up of the experimental system.

Mechanical Design Research Center of Zhejiang University

provides the tested hydraulic excavator, which is also used

to study planning and control technology of excavating robot

under unmanned condition. The dynamic testing was

finished during the rest time of the excavating robot team.

The testing system includes also supporting tires and the

experimental instruments such as modal hammer, force

transducer, amplifier, accelerometer, some data acquisition

instruments and a computer. Three data acquisition boxes

and one static and dynamic strain-measuring instrument are

used. The program provided with the strain measuring

instrument makes data process easier. The theory of testing

is showed as Figure 4. The tested hydraulic excavator body

was supported with elastic tires to simulate free-free

conditions as close as possible. A modal hammer was

used to excite the structure. Twenty-three nodes were

measured in three directions.

3.2 TESTING RESULT

A curve fitting method for modal parameters estimation was

used. The results of the modal analysis are listed for a

representative working gesture in Tables 1. In the second

column values of modal frequency is given. In the third

column the schematic mode shape is given.

Table 1 Value of modal frequency

Order Frequency (HZ) Mode shape

1 7.735

2 26.125

3 56.125

4 82.125

Table 1 show that the lowest natural frequency of the entire

model is in the order of magnitude 10 Hz. Table 2 shows

comparison between computing frequencies and testing

frequencies. A “Y” denotes a hydraulic cylinder is

considered in the computing model. The lowest natural

frequency of the entire model is far from the steel

component (boom, arm, and bucket) frequencies. Hence,

joints and hydraulic cylinders rather than boom, arm, and

bucket) dominate lower order natural frequencies of the

entire model.

Table 2 Comparison between computing frequencies and testing frequencies

Frequency (HZ) Order

Testing Y Y Y Y Y Y

1 7.735 42.254 22.999 7.197

2 26.125 70.039 42.549 26.747

3 56.125 -- 57.365 56.326

4 82.125 -- -- 89.912

4. FINITE ELEMENT ANALYSIS MODELLING OF THE

HYDRAULIC EXCAVATOR WORKING EQUIPMENT

The arm, boom and bucket of hydraulic excavator working

equipment are complex welded box structures of shells, otic

placodes and axile bushes, between which geometry

features such as aspect ratio of length and thickness, are

very different. Besides structural complexity, physical

complexity of hydraulic cylinders is another key factor for the

intensity distribution [3]. For different analyses, different

finite element analysis models should be employed because

of resource limits, result precision requirements and result

reliability requirements, which are incompatible but

important factors in the computation of the optimization

process.

All finite element models are showed as Figure 5.

Generally, the smaller the size of elements is, the more

accurate the analysis results are. Hence, a fine-mesh

model is commonly used in analysis of static stress. For

modal analysis, the global dynamic response of the

structure is of primary interest rather than the local

dynamic phenomenon, and even a fine-mesh model may

not accurately predict the dynamic response over a wide

frequency range due to local vibration modes [4]. In

addition, a fine-mesh model will cause large

computational time and storage space, which is contrary

to the optimization requirements. Transient analysis is

much more like static analysis from a precision point of

view, rather than modal analysis, which is a general

evaluation of system internal characteristics with a certain

extent of roughness.

5. STRUCTURAL OPTIMIZATION RESULT

Due to using coarse-mesh models for whole preliminary

static analysis and modal analysis, whole iteration time is

reduced by about thirty percent. Fourteen percent of

structural weight is reduced by structural static and

dynamical collaborative optimization. Part of structural

optimization result is showed as Figure 6. The upper part of

the figure shows that stress distribution of components is

more uniform. The low part of the figure shows that mode

shapes are equivalent to testing results and natural

frequencies can meet engineering demand.

6. CONCLUSION

The efficient way to develop complex engineering machine

with good structural static and dynamical performance is to

use collaborative optimization technology. The paper’s work

is proved a great sample in structural static and dynamical

collaborative optimization. In future work, the authors intend

to develop a more flexible system using intelligent

technology for wide applications.

ACKNOWLEDGMENTS

This research is supported by the National 863 Program of

China under Grand Number No. 2001AA412110 and the

National Science Foundation of China under Grant Number

No. 59635150.

REFERENCES

[1] Feng P., Qiu Q., Pan S., Qian Z., Wu J. Theoretical

Framework of the Generalized Optimization for

Mechanical Product. China Mechanical Engineering,

vol.11, No.1, pp.126~129, 2000.

[2] Feng P., Qian Z., Pan S., Wu J., Qiu Q. Research on

agent based structural static and dynamic collaborative

optimization. SCIENCE IN CHINA (Series E), vol.44,

No.5 pp.463-472, 2001.

[3] Qian Z., Xue C., Feng P., Pan S. A new method for

model updating. Proceedings of the 19th IMAC, pp.

362-367, 2001.

[4] Nefske, D.J.; Sung, S.H. 1996: Correlation of a

coarse-mesh finite element model using structural

system identification and a frequency response

assurance criterion. Proc. 14-th IMAC, pp. 597–602

Whole Simplified FimiteElement Modelling

Whole Static Analysis Whole ModalAnalysis

Whole ModalTesting

Testing Validation

boundary loadIdentification

Modal PeremeterIdentification

Whole ModalModel Updating

CollaborativeOptimizer

OptimizationModellingfor Boom

OptimizationResult Analysis

parameterizing parameterizing

OptimizationModelling

OptimizationModellingfor Arm

OptimizationModellingfor Bucket

FEAfor Boom

FEAfor Arm

FEAfor Bucket

Start

Stop

Figure 1: Process of structural static and dynamic collaborative optimization

Figure 2: Parametric model for structural finite element analysis

Figure 3: Experimental test set-up

Modal Hammer

Force Transducer

Amplifier

Amplifier

Accelerometer

Data acquisitioninstrument

Data analysissoftware

11 testing points

7 testing points

5 testing points

Figure 4: Testing principle

Coarse-mesh modal analysismodel for working equipment

static and transient analysis model forworking equipment

Fine-mesh static and transient analysis modelfor bucket, boom and arm

Figure 5: Finite element models

Stress distribution of components

Arm Boom Bucket

(1) (2) (3)

First three mode shapes of whole model

Figure 6: Structural optimization result of hydraulic excavator working equipment

test and optimization of static and dynamical … and optimization of static and dynamical...

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