Limited life design of auto drive axle housing based on CAE

Limited Life Design of Auto Drive Axle Housing Based on CAE

Zheng Yanping He Haibo Xu Xiaomei

Department of Vehicle Engineering

College of Automobile and Traffic Engineering, NJFU

Nanjing, China

E-mail:zhengyp@https://www.360docs.net/doc/1c6630316.html,

Fang Minxia

College of Aerospace Engineering and Mechanic

Tongji University Shanghai, China

Abstract—In this paper, by combining mechanical probabilistic fatigue analytical theory with automobile vibration theory and u sing CAD/CAE method, the correct finite element vibration analytical model for au to drive axle hou sing was established and its analytical load was determined. At the same time, based on the fatigue analysis of finite element, the limited life design technological flow and method of au to drive axle hou sing were proposed and the feasibility of the method was testified by an example. The most typical random vibration for vehicles in motion was cau sed by u neven road and in this paper the random dynamic load caused by road roughness and the static load of fu lly loaded vehicle was taken as the analytical load using for verifying the limited life of auto drive axle ho u sing. This method had some credibility and practicality when the actu al working load cou ld not be obtained and it laid fou ndation for the realization of the lightweight design of the auto drive axle housing and improved the related vehicle performance.

Keyword-Automobile; FEM; CAD/CAE; Drive A x le Housing; Fatigue Life Assessment; Limited Life

I.INTRODUCTION

According to the obtaining documents, many developed countries pay more attention to the research of limited life about mechanical components [1,2,6,7], but it is hard for our country to design the limited life of automotive components [3,4]. Since the most typical random vibration in vehicle is caused by uneven road when driving [5], in the paper the full auto vibration causes by uneven road is used as fatigue load and combining with the theory of fatigue life and auto vibration about mechanical components the auto drive axle housing is taken as the research object. By utilizing ANSYS software and designing by the way of CAD/CAE the limited life design method for automotive drive axle housing is proposed. II.

LIMITED LIFE DESIGN METHOD FOR AUTOMOTIVE

DRIVE AXLE HOUSING BASED ON CAE

The automotive drive axle housing is the main load-bearing component in vehicle. The design ideas for limited life of automotive drive axle housing by utilizing ANSYS software are: firstly build the correct finite element vibration analytical model, then determine the analytical load and apply the analytical theory of probabilistic fatigue based on the result of fatigue analysis by the way of CAE, then proceed the design for limited life of drive axle housing.

And the design flow is showed in Figure1.

Figure 1. Driving axle housing design flow of limited life

A.Establishment of Vibration Analytical Model for Automotive Drive Axle Housing

When driving the automotive vibration caused by uneven road make force between wheels and ground. The force changed continuously and the changes have relations with road shape and its unevenness measurement, inertial and elastic property of related automotive components. Based on the analytical theory of automotive vibration, we can simplify the complicated automotive vibration model according to the requirement of the problem to be analyzed and assuming that the wheels are in touching with the road all the times and the stiffness and the damp are linear separately to the corresponding displacement and velocity.

For the study of the limited life of auto drive axle housing, the drive axle housing should be considered as elastic entity when building model. And at the same time the suspension, vehicle body and wheels components related to the drive axle housing should be taken into account and the complete load-bearing system of drive axle housing including the position of actual load acting and restraining was constructed.

To check the correctness of three-dimensional solid model for auto drive axle housing, the mass of drive axle

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2010IEEE

entity should be calculated and the modal of it should be analyzed. At the same time through experiment the actual mass, the natural frequency and the vibration mode of drive axle housing could be measured and in accordance with the experimental result the mode built should be modified to make sure that both the mass and stiffness of the model are correct.

B.Load-Bearing Analysis of the Auto Drive Axle Housing

The load-bearing of drive axle housing when driving can be divided into two parts: the static load and the random dynamic load. In this paper we research the full auto vibration caused by uneven road. Then the static load carried by drive axle housing is just the static load the full auto carried and the automotive vibration load caused by uneven road is taken as the random dynamic load. When we research the random dynamic load the road power spectral density is applied to describe the statistical character of road roughness, which is used as input load. In accordance with automotive theory, some kind of the road power spectral density S q (n) is applied to the

calculation by the conversion of spatial frequency n and

time frequency f and then in the light of the relationship

between the power spectral density S q′(f ) and the displacement power spectral density S q (f ) according to the

vertical velocity of roughness q′(t)dq(t)/dt based on the time-frequency, the formula was given by :

S q′(f

)(2πf )2S q (f )=4π2S q (n 0)n 02V (1) In formula (1) when vehicle speed is fixed the amplitude of velocity power spectral density S q′(f) is considered as white noises within the whole frequency range. The velocity spectrum is usually adopted as road input spectrum for short. C.Finite Element Analysis of Random Vibration

Automotive random vibration caused by random load

which is caused by road roughness has uncertainty but we

can study the law of it by the way of probabilistic method.

The random vibration process is the stochastic process in

mathematics and when we describe the stochastic process in

the frequency area the statistical characteristic of random

vibration process in various frequencies can mainly be

represented by the power spectral density function which is

the measurement of mean square of stochastic process. With

power spectral density analysis in ANSYS software, it can

obtain the relation curve between power spectral density and

frequency about all nodes and 1σ stress value (standard

deviation) distribution of all nodes on the structure. Here 1σ

stress value actually means: when the auto drive axle

housing was under random load, the probability of stress

value between -1σ~1σ on the node is 68.3% or with 68.3%

of the time in stochastic process the stress value is in the

range -1σ~1σ.

It is worthy to notice that 1σ stress value based on

ANASYS software is the calculation of power spectral

density analysis by assuming the mean value was zero but in

the random vibration process the actual stress mean value of

auto drive axle housing is the stress value under static

analysis of fully loaded vehicle.

D.Limited Life Design Based on CAE

The calculation of the finite element random vibration based on CAE is the basis of limited life analysis. In this paper the Steinberg 3 interval method based on random vibration results and Miner linear cumulative damage rule are applied to the fatigue calculation because it is hard to calculate the fatigue life when the force process of auto drive axle housing is stochastic process and not the process with fixed amplitude. Much measuring results demonstrate

that both road random input and vehicle vibration response basically conform to the normal distribution. According to the Steinberg 3 interval method theory based on the normal distribution with 68% of the time in stochastic process the stress value is between -1σ~1σ;with 95.4% of the time the stress value is between -2σ~2σ;with 99.73% of the time the stress value is between -3σ~3σ. When the Miner rule is applied to the fatigue calculation the stress can be divided into three grades and at the same time by assuming the stress value will not more than 3σ within 0.27% of the time. Overall damage is calculated by: D=n 1σ/N 1σ+ n 2σ/N 2σ+n 3σ/N 3σ 2Where n k is the actual cycle count when the stress level is less than or equal to k (k=1σ, 2σ, 3σ). N k is the permissible cycle count through fatigue life curve when the stress level is k.

According to the calculation of random vibration with

1σ stress and the static calculation the node with greater

stress on the drive axle housing is selected out as the

research object. Its 1σ stress level value is the sum of static stress value and 1σ stress calculation and its statistical vibration average frequency f equals to the value of stress speed dividing stress. As the auto drive axle housing is the

load-bearing component in vehicle, the limited life time of auto drive axle housing T is slightly greater than vehicle

scrap time. In the national mandatory retirement standard, it

can find compulsory scrap mileage traveled of various

vehicles S and the limited life time T is calculated by T=S/V

where V is the vehicle average driving speed. Therefore

there are the following equations.

n 1σ=0.6831fT

n 2σ=0.271fT

n 3σ=0.0433fT

In the light of S-N curve for material in the Volume 2 of

Handbook of Mechanical Design and by reckoning related

component size in stress concentration factor of drive axle

housing one can get the following conclusions.

1σ stress level is respond to N 1σ

2σ stress level is respond to N 2σ

3σ stress level is respond to N 3σ

It gets the value of D by inputting above data into the

calculation formula of overall damage. If the value of D is

greater than 1 the disruption occurred when it can’t meet the

design requirements of limited life of drive axle housing; if

the value of D is less than 1 there is no damage to auto drive

axle housing even the discharge time is exceed design time

of limited life. According to the calculation of D the

designer can make the value of D less slightly than 1 by

adjusting the structure and the size of auto drive axle housing and get the aim of limited life design.

III.

C ALCULATION EXAMPLE

Some kind of truck integral drive axle housing, which is stamped and welded by 09SiVL steel plate, is selected as the object for calculation in this paper. During foundation of finite element model for drive axle housing, it needs to simplify the drive axle housing solid firstly and then builds solid model with UG software and finally exports the model into the finite element analysis software ANSYS.

To check the correction of the finite element model built for auto drive axle housing, the calculating and experimental mass and stiffness of drive axle housing are compared. Both the calculating and experimental natural frequency is shown in TABLE I. The relative error caused by simplification of finite element model and experimental error is within permissible range of 0.25%~22.2%. The first order shape mode of finite element model is identical with experimental shape mode shown in Figure 2. By inputting the mass density of drive axle housing in software simultaneously, it calculates the drive axle housing mass is 60kg and the actual measurement mass of drive axle housing is 58kg. They are slightly coincident with each other and the relative error is only 3.4%. So it can be approved in both mass and stiffness that the finite element model built for drive axle housing is slightly coincident with the solid about mechanical vibration and it is feasible to perform the dynamic analysis with the built model.

TABLE I. FREQUENCY COMPARISON OF CALCULATION

AND EXPERIMENT Frequency Set

Calculating Result(H Z )

Experimental Result(H Z )

Relative Error (%)

1 147.93 147.55 0.25

2 249.6 292.37

14.6

3 394.67 466.60 15.3

4 399.49 513.4

5 22.2

5 607.85 625.21 2.8 (a) Calculating picture

(b) Experimental picture

Figure 2. Pictures of first order mode shape

During founding the vibration model for structure, the vibration of two points on vehicle body above front axle and

rear axle is almost independent since the value of truck suspension-mass distribution parameter nearly equals to 1. Based on the vehicle vibration model of two degree and two-mass system and regarding drive axle housing as flexible entity, it gets that the equivalent mass of suspension above rear axle m 2 is m[a/ (a+b)](where “m” is the vehicle suspension-mass; “a” is the horizontal distance between front axle and center-of-mass axis; “b” is the horizontal distance between rear and center-of-mass axis) when the elastic deformation of vehicle body in model is neglected.Based on the above finite element model for drive axle housing, the model for vehicle suspension is built. Since the truck use leaf spring, the rod with large rigidity which has the same length as leaf spring is built on both right and left spring seat, and the spring element is founded at the end of the rod, and the rigidity and damp of vehicle suspension should be input. The plate with thickness of 10mm is built above the suspension instead of the rigid vehicle body. The equivalent suspension-mass m 2 corresponding to full automotive should be input in form of mass density. The spring elements are used to take instead of the tires and their rigidity and damp should be input. The completed finite element vibration model for driving axle housing is shown in Figure 3. There are 11945 nodes and 37910 elements in all on the model.

Figure 3. Finite element vibration model of driving axle housing

Vehicle speed V is usually between 10-30m/s. In this paper the vehicle speed is 20m/s (72km/h) and the

geometrical mean of irregularity factor S q (n 0) of typical general road (grade D) is 1.024×10-3m 3. The velocity power spectral density S q′(f) can be calculated as 8.077×10-3 m 2

/s by inserting the above data into formula 1.

The actual load value on rear axle housing is 4.5 tons when the vehicle is fully loaded.

In order to calculate the fatigue life, it needs to analyze 1σ stress value of drive axle housing. The distribution of calculation of finite element is shown in Figure 4.

Figure 4. Distribution of 1σ stress of drive axle housing

Distribution of 1σ stress demonstrates that the maximum 1σ stress value appears on the location of constraint points

and the location can stress concentration caused by the restrain. If the stress concentration effort is neglected the area with larger 1σ stress value located at upper and lower surfaces of medial and lateral side of the leaf spring seat and the lower surfaces in the middle of auto drive axle housing. It is the area with lighter color in Figure 4.

It is worthy to notice that 1σ stress value based on ANASYS software is the calculation of power spectral density analysis by assuming the mean value is zero but in the random vibration process the actual stress mean value of the auto drive axle housing is the stress value under static analysis of fully loaded vehicle.The larger stress value is distributed at upper and lower surfaces of medial and lateral side of the plate steel seat [8,9]. The related static calculation of finite element of auto drive axle housing has already come to maturity and it’s no need to go into details [10,11].

According to the calculation of random vibration with 1σ stress and the static calculation about auto drive axle housing the node 2823 with larger stress, which locates at upper surface of lateral side of the left leaf spring, is selected out as research object. The 1σ stress value of that node is 79.3MPa and the static stress value is 69.8MPa. Its statistical vibration average frequency f is the value of stress speed dividing stress. In the national mandatory retirement standard the mandatory retirement mileage of truck is 600,000 kilometers. In this paper the vehicle speed is 20m/s and T=3E7s where “T” is the limited life of axle housing. Then there are following equations.

n1σ=0.6831fT=8.144E5

n2σ=0.271fT=3.231E5

n3σ=0.0433fT=5.162E4

In the light of S-N curve for material in Volume 2 of Handbook of Mechanical Design and by reckoning related component size in stress concentration factor of drive axle housing it can get:

1σ stress level is respond to N1σ=+∞

2σ stress level is respond to N2σ=9.01E5

3σ stress level is respond to N3σ=3.381E4

By inputting above data into the calculation formula of overall damage, it gets D=1.8856>1.

Calculation demonstrates that the axle housing designed will show fatigue breakage within 600,000 kilometers mileage when the vehicle moves with a constant speed 20m/s on general road. The result is consistent with the actual fatigue bench test of axle housing which can’t meet the requirement, but the requirement for limited life designed of components can be meet by the modification construction and size.

Since lacking of statistical data the adverse driving condition selected as the driving cycle for calculation has some different with actual driving condition and the aim of this paper is to check the feasibility of the method proposed.

IV.C ONCLUSION

?Combining with analytical theory of probabilistic fatigue and vehicle vibration theory the design

method for limited life of auto drive axle housing is

proposed in the paper and the method proposed is

verified as a feasible method by an example.

?When vehicle moves with full load, the basic load acting on auto drive axle housing is made up of the

random dynamic load caused by road roughness and

the static load, and it is utilized as the load for the

drive axle housing analysis to calculate and check

the limited life in this paper. With the variety of the

driving condition under the condition of lack of the

actual vehicle driving load, the method proposed in

the paper has some credibility and practicality and it

lays the foundation for lightweight design of

automotive drive axle housing and improves of the

related vehicle performance.

A CKNOWLEDGEMENT

This project is sponsored by the 10th Five-Year talent project of Nanjing Forestry University (NO.163040014) and the Specific Industrial Technology Innovation of Shanghai (NO.07XI2-014)

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