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Author: Yeh-Liang Hsu, Chia-Chieh Yu, Shang-Chieh Wu, Ming Hsiu Hsu (2006-10-27); recommended: Yeh-Liang Hsu (2007-08-02)
Note: This paper is published in Proceedings of the I MECH E Part B Journal of Engineering Manufacture, Vol. 221, No. 3, March 2007, pp. 447-456.

Developing an automated design modification system for aluminum disk wheels

Abstract

Disc wheels intended for normal use on passenger cars have to pass three tests before going into production: the dynamic cornering fatigue test, the dynamic radial fatigue test, and the impact test. Fatigue prediction has been an important issue in the design of aluminum disc wheels. This paper presents an automated design modification system that integrates engineering analysis results and common redesign strategies of engineers with a fuzzy logic algorithm in order to provide effective strategies to reduce the failure probability in the fatigue test.

A probability model which provides quantitative information of “how likely the wheel is going to fail in the fatigue test” using simulation results is described first, followed by providing engineers’ common strategies for redesigning the wheels. Sensitivities of the strategies with respect to the probability of fatigue failures have been calculated to evaluate these strategies. A set of fuzzy rules on how to reduce the failure probability using these strategies is established, and an automated design modification system is constructed. Finally this system is validated using 3 real wheel design examples. Using this system, designers’ previous experience can be properly transformed and utilized by all designers.

Keywords: aluminum disk wheels; fatigue; probability model; fuzzy logic.

1.     Introduction

Wheels are one of the most critical components in automotive engineering. Their function is of vital importance to human safety. Disc wheels intended for normal use on passenger cars have to pass three tests before going into production: the dynamic cornering fatigue test, the dynamic radial fatigue test, and the impact test. Fatigue prediction has been an important issue in the design of aluminum disc wheels. Kocabicak and Firat developed numerical methods for the prediction of cornering fatigue tests for passenger car wheels [1, 2]. The correlation between the numerical simulation results and the cornering test results was good. Kaumle and Schnell also developed a technique for fatigue testing using a rapid-prototyping system, on which the fatigue behavior of the wheel can be tested [3]. Karandikar and Fuchs developed a computer-based system, including a CAD package, a finite element analysis program, and a fatigue life computation program, for predicting the fatigue life of wheels [4].

The randomness of fatigue prediction due to the inherent uncertainties in loading, manufacturing variability and material properties has been commonly recognized [5]. Probabilistic approaches are proposed to account for the uncertainties in fatigue prediction models for various industrial applications, such as the fatigue prediction of rolling bearings [6], the airframe fatigue test [7], and fatigue failure probability prediction of the vehicle axle of Shinkansen high-speed train [8], to name just a few.

The authors also presented a probability model for the prediction of fatigue failures of aluminum disc wheels, which intended to better link the prediction using simulation results with historical experimental data [9, 10]. In the previous work, finite element models of aluminum wheels were constructed to simulate the dynamic cornering fatigue test and dynamic radial fatigue test. The analysis results were compared with the historical experimental data, and a mathematical model was used to fit this data to construct the “failure probability contour.” This failure probability contour was then used to predict the failure probability of a new wheel. The failure probability contour can be updated when the number of historical experimental data increases. This probability model provides an excellent tool for the engineers to decide whether the wheel needs to be redesigned. The next question is, based on the prediction of the probability model, how to redesign the aluminum disk wheel.

When a wheel fails in the fatigue test, engineers in wheel manufactures often use their previous experiences to redesign the wheel according to the type of the wheel and the various failure phenomena in the fatigue test. Many researchers used fuzzy logic to help with the design decisions based on engineers’ experience in the product design stage. Deciu et al. proposed an integrated approach of configurable product design based on multiple fuzzy models. The transition from customer specifications into physical solutions is performed by the help of multiple fuzzy models [11]. Huang presented a fuzzy approach to model imprecise information and requirements of customers in modular product development; and to evaluate the design alternatives for designers [12]. Hsiao proposed a decision-making method by quantifying the correlations between human sensations and the physical characteristics of products using fuzzy logic analysis methodology to create products that satisfy the needs of customers [13]. From the researches discussed above, fuzzy logic seems to be a suitable approach to assist engineering decisions in the design stage when there is not enough quantitative, precise information.

This paper presents an automated design modification system that integrates engineering analysis results and engineers’ common redesign strategies with a fuzzy logic algorithm in order to provide effective strategies to reduce the failure probability.

Section 2 of this paper describes the probability model in detail. In Section 3, engineers’ common strategies for redesigning the wheels were collected. Sensitivities of the strategies with respect to the probability of fatigue failures were calculated to evaluate these strategies. In Section 4, a set of fuzzy rules on how to reduce the failure probability using these strategies was established, and an automated design modification system was constructed. This system was validated using three real wheel design examples in section 5. Finally the paper is concluded in section 6.

2.     The probability model for fatigue failure prediction of aluminum wheels

This section describes the four major steps for establishing the probability model for the fatigue failure prediction of aluminum wheels, using cornering fatigue test as an example.

(1)   Establishing the finite element model

The dynamic cornering fatigue test simulates the loading condition of the wheels in normal driving. Figure 1 shows a typical setup of the 90-degree loading method of cornering fatigue test, according to SAE J32 [14]. In the figure, the downside outboard flange of the rim is clamped securely to the test device, and a rigid load arm shaft is attached to its mounting surface. A test load is applied on the arm shaft to provide a constant cyclical rotation bending moment. After being subjected to the required number of test cycles, there shall be no evidence of failure of the wheel, as indicated by propagation of a crack existing prior to test, new visible cracks penetrating through a section, or the inability of the wheel to sustain load

Figure 1. Typical setup of 90 degree loading method of cornering fatigue [14]

Figure 2 shows the finite element model that simulates the cornering fatigue test. All degrees of freedom of the nodes on the downside outboard flange of the rim are fixed. The dynamic load is represented by 20 discrete loads that are 18 degrees apart.

Figure 2. The finite element model of a wheel

(2)   Interpreting the analysis results

Several different criteria are commonly used in predicting fatigue failure. For example, Goodman’s criterion can be expressed as follows [15]:

        Goodman’s criterion:                                                          (1)

where sm is the mean stress, sa is the stress amplitude, Se is the endurance limit, and Su is the ultimate strength of the material.

In the finite element model in Figure 2, the maximum and minimum Von Mises stresses of each node during the load cycle are extracted to obtain sm and sa. The top 1% nodes that are closest to the Goodman’s line, which have the greatest possibility to fail in the fatigue test, are plotted in Figure 3. The average (sm, sa) of these top 1% nodes is calculated to obtain (sm, sa)1% of the wheels. This (sm, sa)1% is used as the index to represent the wheel in fatigue prediction.

Figure 3. The top 1% nodes those are closest to the Goodman’s line

(3)   Fitting with historical experimental data

Finite element models of the 159 aluminum wheels, which were already physically tested by a local wheel manufacturer, were constructed to simulate the cornering fatigue test. The (sm, sa)1% for each wheel was calculated and plotted in Figure 4, where “o” and “´” represent whether the wheel actually passed or failed the cornering fatigue test.

Figure 4. The 159 historical experimental data of the cornering fatigue test

(4)   Constructing the failure probability contour

An algorithm was developed to construct the failure probability contour based on Figure 4 in the authors’ previous work [9]. Note that in Figure 4, historical data points towards the upper right corner are more likely to fail. Given a new data point (sm, sa)1%, a circle of radius r, which is centered on this new data point, is defined. The historical data points that fall in the circle are used to predict the failure probability of the new data point. The failure probability can be easily calculate as , where Nfail is the number of historical data points in the circle that actually failed, and Ntotal is the total number of historical data points in the circle.

While this is a straightforward way to calculate the failure probability of a new data point using historical test data, there is a practical problem of how to define the radius r. If r is large, the circle may be too big to adequately represent the new data point. If the radius r is small (or the historical data points are sparse in the neighborhood of the new data point), the number of historical data points in the circle will be too few to generate a meaningful probability value.

Therefore, instead of calculating failure probability directly from the historical data points that fall in the circle, a “probability contour” is drawn on the two-dimensional domain sm-sa first. To do this, the x(sm) and y(sa) axes of the 159 historical data points are normalized between 0 and 1, then this domain is divided into m´m rectangular grids. On each grid point, a circle of radius r=1/m, which is the length of the grid, is drawn. Then the failure probability of this grid point can be calculated from the historical data points that fall in this circle. Figure 5 shows the failure probabilities of the grid points for m=10.

MATLAB Handle Graphics

Figure 5. Failure probability on the grid points for m=10

The historical data points scatter along the diagonal of the sm-sa domain, and only the 24 grid points along the diagonal have failure probability figures. These probability figures are extrapolated to the whole domain in order to draw the failure probability contour. The extrapolation is done in an iterative manner, and the 24 original probability figures in Figure 5 remain fixed during the extrapolation.

Several assumptions are considered during the extrapolation. Grid points toward the upper right corner should have a higher failure probability. Therefore

                , if  and                        (2)

All probability figures generated during the process have to satisfy Equation (2). Moreover, since the probability value lies between 0 and 1, Equation (2) also implies

 and ,  if      (3)

 and ,  if       (4)

These two equations are also necessary when extrapolating the probability figures to the boundary of the domain.

Figure 6 shows the failure probability contour based on the 159 historical experimental data points. A new wheel can be simulated in the same way described in steps (1) and (2) to obtain its (sm, sa)1%, then the failure probability of this new wheel can be read directly from the failure probability contour. After obtaining the experimental test result, this wheel became a “historical experimental data.” The failure probability contour can then be updated to include this extra historical experimental data.

Figure 6. The failure probability contour

This probability contour provides quantitative information on “how likely a new wheel is going to fail” based on the historical experimental data. There is also a mechanism to update the failure probability contour to improve the prediction as the number of historical experimental data points increases.

3.     Redesign strategies for different types of wheels

From a series of interviews of several senior engineers in the local wheel manufacturer, it was concluded that engineers commonly use 5 redesign strategies when a new wheel fails in the fatigue test:

A.     Lathe spokes

B.     Modify the “x-factor”, which is the space of caliper clearance (or brake clearance) that can be reduced

C.     Raise the front surface of the center of the wheel

D.     Change the taper angle of the spoke

E.      Adjust the depth of the weight reduction hole

Figure 7 marks the positions of modifications on the wheel in these 5 common strategies. Basically, strategies A and D change the shape of the spoke, strategies B and C change the stiffness of the center of the wheel, and strategy E adjusts the depth of weight reduction holes. Table 1 lists the various discrete values for each strategy that are commonly used by the wheel manufacturer. More than one strategy can be used simultaneously when redesigning a wheel.

Table 1. The discrete values for each strategy that are commonly used by the wheel manufacturer

A: Lathe spokes

E: Adjust the weight reduction hole

A1: Decrease 2mm

E1: Decrease 2mm in depth

A2: Decrease 4mm

E2: Decrease 4mm in depth

B: Modify the “x-factor”

E3: Decrease 2mm in width

B1: Decrease 2mm

E4: Increase 2mm in depth

C: Raise the front surface of the center

E5: Increase 4mm in depth

C1: Increase 2mm

 

D: Change the taper angle of the spoke

D1: Increase

Figure 7. Five redesign strategies commonly used by wheel manufacturers

The geometry of the wheel also restricts the selection of different strategies. Table 2 shows three types of wheels with different number of spokes and therefore with different widths of spokes. Type 1 wheels have less than 5 spokes. The spokes are wide enough to contain a large weight reduction hole. Thus, strategy E is often used for Type 1 wheels. Type 2 wheels have 6-10 spokes, which are narrower than those of Type 1 wheels. Their weight reduction holes are smaller and cannot be redesigned freely. Type 3 wheels have many thin spokes and do not have any weight reduction holes. Thus, strategy E cannot be used at all.

Table 2. Three types of the wheel

Type

Wheel

1

1                   2                  3

2

1                  2

3

1

Six sample wheels (three of Type 1, two of Type 2, and one of Type 3) were chosen to test the effect of the 5 strategies using the failure probability model described in the previous section. The first column in Table 3 shows the initial failure probabilities of each wheel. The differences in failure probability (DP%) and in weight (DW%) after applying the strategies are listed. Note that in Table 3, some of the strategies are not effective in reducing the failure probability (DP%>0), and some others will increase the weight of the wheel (DW%>0).

Table 3. The change in failure probability and weight using redesign strategies A1~E5

 

 

A1

A2

B1

C1

D1

E1

E2

E3

E4

E5

Type 1-1

82.7%

DP%

-1.1

5.3

-20.8

-13.1

-1.4

-11.9

-49.4

-12.8

-10.4

0.9

DW%

-1.0

-1.7

0.9

2.1

0.2

0.5

1.2

0.4

-0.7

-1.2

Type 1-2

89.6%

DP%

5.1

-10.2

-10.1

-31.9

-17.1

-30.4

-36.4

-10.9

11.9

12.1

DW%

-0.5

-1.1

0.4

5.0

1.1

1.0

2.2

0.4

-1.1

-2.2

Type 1-3

58.2%

DP%

2.3

7.9

-18.4

-30.4

-7.3

-10.0

-191.

-10.7

16.8

54.2

DW%

-1.0

-1.7

0.8

1.8

0.5

0.3

0.9

0.3

-0.5

-1.2

Type 2-1

90.4%

DP%

-1.1

10.8

-17.7

-29.9

-12.7

-47.1

-57.3

-20.4

-4.9

-2.1

DW%

-0.5

-0.9

0.6

2.8

1.0

0.9

1.4

0.3

-0.4

-0.4

Type 2-2

63.1%

DP%

33.4

22.3

-15.9

-23.7

-6.3

NA

NA

NA

15.0

15.1

DW%

-1.0

-1.8

0.8

1.5

0.7

NA

NA

NA

-0.3

-0.5

Type 3-1

55.4%

DP%

-4.9

6.4

79.9

38.9

-36.8

NA

NA

NA

NA

NA

DW%

-1.4

-1.9

1.6

2.8

1.0

NA

NA

NA

NA

NA

In the simulations, Strategies B, D, and E1~E3 are effective in reducing the failure probability for all types of wheels (Strategies B and C have negative effects on Type 3-1 wheel), with an increase in their weights. On the other hand, Strategies A, E4 and E5 reduce the weight of the wheels, but have negative effects on failure probability. These strategies can be used when a wheel is over-designed.

Empirically, choosing an appropriate strategy to use often depends on the location of cracks occurred in the fatigue test. For example, if cracks occur near the spoke, the engineer will change the taper angle to increase the stiffness (Strategy D). Engineers may reduce the size of the weight reduction holes simultaneously. Similar idea can be used in choosing redesign strategies using the simulation results. For example, Figure 8 shows the simulated stress distribution of Type 1-1 wheel. High stress occurs at the end of the weight reduction hole near the x-factor. To reduce the failure probability, Strategy B (modify the x-factor) and Strategy E (adjust the weight reduction hole) can be effective. The simulation results also confirm that Strategies B1 and E2 can reduce the failure probabilities of Type 1-1 wheel significantly.

Figure 8. The stress contribution of the Type 1-1 wheel from simulations

From the discussion above, engineers should consider the probability of failure, type of the wheel (the width of the spokes, type of weight reduction hole), and location of high stress in the fatigue test simulation using the finite element model, and then manipulate these 10 redesign strategies (A1~E5) trying to reduce the probability of failure or to reduce the weight of the wheel. This decision process is integrated into a fuzzy-logic based automated system for redesigning the aluminum disk wheel.

4.     Developing the automated design modification system

Figure 9 shows the flowchart of the automated design system for redesigning the aluminum disk wheel developed in this research. An initial wheel design is simulated and both the high stress location and failure probability of the wheel are found by the probability model described in the previous section. The failure probability, the location of high stress, and the two statements (width of the spoke and size of the weight reduction hole) defined by the user are input to the fuzzy-logic engine.

Figure 9. The flowchart of an automated design modification system

There are two decision stages in the fuzzy-logic engines. First, the engine takes four inputs (the failure probability, the location of high stress, width of the spoke, and size of the weight reduction hole) and generates the locations of the wheel (such as spoke, reduction hole and center of the wheel) that need to be redesigned. In the second decision stage, the user defines the design restrictions of the wheel where the geometry cannot be redesigned. The fuzzy-logic engine takes the output from the first stage and design restrictions, and then maps to the 10 redesign strategies A1~E5. The output redesign strategies are then applied to the wheel and the procedure is repeated until the system indicates that no redesign is necessary.

Table 4 lists the linguistic terms of inputs. Figure 10 shows the membership function and linguistic terms of the failure probability. Typical triangle-shaped and trapezoid-shape membership functions are used. The linguistic terms of the failure probability is “very good” (0%-20%), “good” (10%-45%), “acceptable” (35%-60%), “bad” (45%-80%), and “very bad” (60%-100%).These values are determined by the experience of the senior engineers of the local manufacturer. From the experience of the local manufacturer, without careful computer simulations and predictions, 3~4 trials of making or revising the die are common for a new aluminum wheel until it can finally pass the fatigue test. These trials are also the major cause of the development cost and time.

Figure 10. The membership function of failure probability

Table 4. The linguistic terms of inputs

Four inputs

Failure probability

Width of spoke

Size of weight reduction hole

Location of high stress

Linguistic terms

Very good

Thin

None

Two sides of weight reduction

Good

Normal

Narrow and shallow

Near x-factor

Acceptable

Large

Wide and deep

Between two spokes

Bad

NA

Very bad

Given a predicted failure probability Pfail of a new wheel, the “expected value” of the number of trials of making and revising the die can be estimated. For example, if the failure probability of a new wheel Pfail=0.2, the chance for passing the fatigue test with just one trial is (1- Pfail). If the wheel does not pass in the first trial and is redesigned using the procedure described in this paper, the failure probability P’fail after redesign should be less than Pfail. The chance for passing the fatigue test with 2 trials is Pfail×(1- P’fail)Pfail, if the higher order terms are neglected for small Pfail. Therefore the expected value of the number of trials of making and revising the die is approximately 1×(1- Pfail)+2×Pfail=1.2, which is a very good number for the local wheel manufacturer. Therefore failure probability 0~20% is defined as “very good”.

Values of failure probability are mapped to the linguistic terms through membership functions in the fuzzification step. The other inputs are also mapped in the same way. After the crisp inputs are mapped to the linguistic terms, inference rules are applied to determine the output in the step 1 fuzzy engine. The rules are constructed from experienced engineers’ expertise, with help from computer simulation results listed in Table 3. These rules are written in following “IF-THEN” form, and Table 5 lists the linguistic terms of the outputs of the step 1 fuzzy engine.

Rule 1:    IF the failure probability is “Good”, THEN the geometry of spoke is “No change”, AND the geometry of weight reduction is “No change”, AND the geometry of the center is “No change”.

Rule 2:    IF the failure probability is “Very good”, AND the width of spoke is “Thin”, AND the size of weight reduction hole is “None”, AND the location of high stress is “Between two spokes”, THEN geometry of spoke is to “Reduce stiffness slightly”.

Rule 3:    IF the failure probability is “Very good”, AND the width of spoke is “Normal”, AND the size of weight reduction hole is “Narrow and shallow”, AND location of high stress is “Near x-factor”, THEN the geometry of weight reduction hole is to be “Enlarged slightly”.

………

Table 5. The linguistic terms of first step outputs

1st-step outputs

Geometry of spoke

Geometry of weight reduction hole

Geometry of the center

Linguistic terms

Reduce stiffness greatly

Enlarged greatly

No change

Reduce stiffness slightly

Enlarged slightly

Increase stiffness slightly

No change

No change

Increase stiffness greatly

Increase stiffness slightly

Reduced slightly

 

Increase stiffness greatly

Reduced greatly

In the system constructed in this research, there are 19 such rules in the first step fuzzy engine. These redesign rules are not generally true. They are specific to the production line of the local wheel manufacture. These rules are only useful (and confidential) to the local wheel manufacturer and thus are not listed here.

In the second decision step, the fuzzy-logic engine takes the output from the first step and adds the design restrictions, and then maps to the 10 redesign strategies A1~E5. The linguistic terms of design restrictions are “No restriction”, “x-factor cannot be changed”, and “Geometry of the center cannot be changed”. The rules in the step 2 fuzzy engine are as follows:

Rule 1: IF the geometry of spoke is to “Reduce stiffness slightly”, AND the geometry of weight reduction hole is “No change”, AND the geometry of the center is “No change”, AND design restrictions are “No restriction”, THEN “Lathe spoke 2mm”.

Rule 2: IF the geometry of spoke is to “Increase stiffness slightly”, AND the geometry of weight reduction hole is “No change”, AND the geometry of the center is to “Increase stiffness slightly”, AND design restrictions are “Geometry of the center cannot be changed”, THEN “Increase the taper angle is 3o”.

Rule 3: IF the geometry of spoke is to “Increase stiffness greatly”, AND the geometry of weight reduction hole is to be “Reduced greatly”, AND the geometry of the center is to “Increase stiffness slightly”, AND design restrictions are “x-factor cannot be changed”, THEN “Increase the taper angle is 3o”, AND “Raise the front surface of the center is 2mm”, AND “Decrease the weight reduction hole 4mm in depth”.

………

There are 14 such rules in the second step fuzzy engine. Again these redesign rules are specific to the production line of the local wheel manufacture, and thus are not listed here.

According to inputs and collected fuzzy rules, an automated design modification system generates a crisp output of redesigned strategies that is shown in Table 1. Engineers use this system to obtain the redesigned strategies A1~E5, and try to reduce the probability of failure and to prevent over design.

5.     Application examples

In this section, the automated design modification system is applied on three aluminum disk wheel design examples to validate the effectiveness of the system.

Case I

Table 6 shows the iteration results of Case I wheel. The initial failure probability of cornering fatigue simulation is 43.5%, which needs to be reduced further. The width of the spoke and size of the weight reduction hole of the wheel, and the failure probability and high stress location from the simulation are input to the automated design modification system. The system suggests strategy D1 (increase the taper angle of the spoke by 3o) to modify the wheel.

Table 6. The iterations results of Case I wheel

 

Cornering

Initial failure probability

43.5%

Initial weight

8.63 Kg

 

1st iteration: Using strategy D1 to redesign the wheel

 

Failure Probability

37.3%

Weight

8.77 Kg

 

2nd iteration: Using strategy D1 to redesign the wheel

 

Failure Probability

33.8%

Weight

8.82 Kg

 

As shown in Table 6, the failure probability reduces to 37.3% after the redesign strategy D1 is applied, and the weight of the wheel increases from 8.63kg to 8.77kg. This result is input to the system again, and the system suggests strategy D1 again. In the second iteration, the failure probability further reduces to 33.8%, but the weight of the wheel increases to 8.82 Kg.

In the 3rd iteration, the system suggests no design change. According to the suggestions by the automated design modification system, the taper angle of the initial wheel was increased by 6o. Later in a physical test, the modified design actually passed the cornering fatigue test.

Case II

Table 7 shows the iteration results of Case II wheel. The initial failure probability of cornering fatigue simulation is 80.3%, which needs to be reduced further. The width of the spoke and size of the weight reduction hole of the wheel, and the failure probability and high stress location from the simulation are input to the automated design modification system. The system suggests strategy C1 (raise in the front surface of the center by 2mm), D1 (increase the taper angle of the spoke by 3o), and E4 (increase in the depth of the weight reduction hole by 2mm) simultaneously to modify the wheel.

Table 7. The iterations results of Case II wheel

 

Cornering

Initial failure probability

80.3%

Initial weight

7.43 Kg

1st iteration: Using strategy C1, D1, and E4 to redesign the wheel

Failure Probability

51.3%

Weight

7.80 Kg

2nd iteration: Using strategy C1 to redesign the wheel

Failure Probability

26.4%

Weight

8.17 Kg

As shown in Table 7, the failure probability reduces to 51.3% after applying redesign strategies C1, D1, and E4. This result is input to the system again, and the system suggests strategy C1. In this second iteration, the failure probability further reduces to 26.4%.

In the 3rd iteration, the system suggests no design change. According to the suggestions by the automated design modification system, the front surface of the center of the initial wheel was increased by 4mm, the taper angle of the initial wheel was increased by 3o, and the depth of the weight reduction hole of the initial wheel was increased by 2mm. The modified design actually passed the physical test.

Case III

Table 8 shows the iteration results of Case III wheel. The initial failure probability of cornering fatigue simulation is 24.7%, and this wheel could be overly designed. The width of the spoke and size of the weight reduction hole of the wheel, the failure probability, and high stress location from the simulation are input to the automated design modification system. The system suggests strategy E4 (increase depth of the weight reduction hole by 2mm) to modify the wheel.

Table 8. The iterations results of Case III wheel

 

Cornering

Initial failure probability

24.7%

Initial weight

7.17 Kg

 

1st iteration: Using strategy E4 to redesign the wheel

 

Failure Probability

24.3%

Weight

7.10 Kg

 

2nd iteration: Using strategy E4 to redesign the wheel

 

Failure Probability

26.4%

Weight

7.03 Kg

 

As shown in Table 8, the failure probability reduces to 24.3% after redesign strategy E4 is applied, and the weight of the wheel reduces from 7.17kg to 7.10kg. This result is input to the system again, suggesting strategy E4. In the second iteration, the failure probability increases to 26.4%, but the weight of the wheel reduces to 7.03 Kg.

In the 3rd iteration, the system suggests no design change. According to the suggestions by the automated design modification system, and the depth of the weight reduction hole of initial wheel was increased by 4mm. The weight of the modified design is reduced by 0.14kg, and it also passed the physical test.

6.     Conclusions

Computer simulations are often used to predict the performance of a new product, but the results from computer simulation still have to be confirmed by physical testing. Therefore historical test results and engineers’ experience on how to modify the design are very valuable to manufacturers and should be systematically preserved and utilized.

This paper first presents a procedure that predicts the fatigue failure probability of aluminum disk wheels based on historical test data. Then an automated design modification system that integrates the engineering analysis results and engineers’ common redesign strategies with a fuzzy logic algorithm in order to provide effective strategies to reduce the failure probability of aluminum disk wheels is presented. This automated design modification system is constructed and validated using 3 real wheel design examples.

This automated design modification system is now being used in a local wheel manufacturer. The system provides effective design modification suggestions, which help the engineers to reduce the failure probability or reduce weight of the aluminum disc wheels. Using this system, historical test results and designers’ previous experience in how to modify the aluminum wheel to pass the fatigue test can be properly transformed and utilized by all designers.

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