- Email: [email protected]
Evaluation of fatigue life of aluminum alloy wheels under radial loads
Engineering Failure Analysis 14 (2007) 791–800 www.elsevier.com/locate/engfailanal
Evaluation of fatigue life of aluminum alloy wheels under radial loads P. Ramamurty Raju a
a,*
, B. Satyanarayana b, K. Ramji b, K. Suresh Babu
a
Department of Mechanical Engineering, Sagi Rama Krishnam Raju Engineering College, Bhimavaram 534 204, Andhra Pradesh, India b Department of Mechanical Engineering, Andhra University, Vishakapatnam, Andhra Pradesh, India Received 12 November 2006; accepted 19 November 2006 Available online 17 January 2007
Abstract This paper is concerned with generation of S–N curve for aluminum alloy (Al) A356.2-T6 and estimation of fatigue life under radial fatigue load. The S–N curve is developed by conducting tests at different stress levels under constant amplitude loading. Tests are conducted on alloy wheels for fatigue life evaluation under radial loads. Finite element analysis (FEA) is carried out by simulating the test conditions to analyze stress distribution and fatigue life of the alloy wheels. It is observed from analysis that the prediction of fatigue life using FEA is found to be in close agreement with the corresponding experimental observations. An attempt has been made by conducting parametric study to suggest a suitable safety factor for reliable fatigue life prediction. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: S–N curve; Radial fatigue load; Fatigue life; Safety factor; Finite element analysis
1. Introduction In the fatigue life evaluation of aluminum wheel design, the commonly accepted procedure for passenger car wheel manufacturing is to pass two durability tests, namely the radial fatigue test and cornering fatigue test [1]. Since alloy wheels are designed for variation in style and have more complex shapes than regular steel wheels, it is difficult to assess fatigue life by using analytical methods. In general, the newly designed wheel is tested in laboratory for its life through an accelerated fatigue test before the actual production starts. Based on these test results the wheel design is further modified for high strength and less weight, if required. Grubisic and Fisher [2] have reported earlier in the literature that testing alone without the aid of stress analysis will not yield the optimum wheel design. Hsu et al. [3] described a probability based model for prediction of fatigue failure of aluminum disc wheels, which intended to better link the prediction of life using simulation results with historical data. Finite element models of 20 aluminum wheels *
Corresponding author. Tel.: 91 8816 225124. E-mail address: [email protected] (P.R. Raju).
1350-6307/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2006.11.028
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Nomenclature Su Sy e HB K F Fr
ultimate tensile strength yield strength elongation hardness acceleration test factor maximum tyre load radial load
which are already physically tested were constructed to simulate dynamic radial fatigue test. Their mean stress and stress amplitude during the fatigue loading cycles were calculated and plotted on a two dimensional plane. For a new wheel the failure probability of dynamic radial fatigue test can be read directly from this probability contour drawn from the test data. Gope [4] mentioned that a minimum of three specimens are required to predict the fatigue life using the log normal distribution. To the best of authors’ knowledge the research work carried out in this area is limited. The present work deals with estimating the fatigue life of aluminum alloy wheel by conducting the tests under radial fatigue load and comparison of the same with that of finite element analysis. Fatigue life prediction using the stress approach is mostly based on local stress, because it is not possible to determine nominal stress for the individual critical areas. The necessary material data for fatigue life prediction with the stress concept is the well known S–N curve. Therefore, S–N curves are required for each specimen which reflects the stress condition in the critical area of the component. To find out the fatigue properties of the aluminum alloy wheel material (A356.2-T6) for actual manufacturing conditions, fatigue test is conducted to generate S– N curve for which 43 specimens are machined from the spokes of alloy wheels and are tested using rotating bending fatigue test equipment. There are different loading methodologies for simulation of radial fatigue test. The dynamic nature of the tests is simulated using equivalent static load in the form of cyclic nature [5]. The results obtained by simulation of tests are compared with actual wheel tests performed. Since fatigue characteristics of a material depend upon several parameters from metallurgical aspects to manufacturing conditions, a safety factor should be considered. It is generally expected that there should be difference between experimental and analytical results. In order to correlate the experimental results with FEA, a parametric study is carried out by employing various safety factors and finally a reliable safety factor is suggested. Similarly the effect of loading angle along circumferential direction for applying radial load is also analyzed by performing parametric studies and finally a suitable angle is suggested. 2. Development of S–N curve To find the fatigue properties of aluminum alloy A356.2-T6 for actual manufacturing conditions, a test is carried out on specimens taken from the wheels. For all 43 identical specimens which are machined from the spokes of alloy wheels [6], rotary bending fatigue test is conducted according to Standards [7]. The schematic diagram of specimen geometry and dimensions are shown in Fig. 1. The wheels, from which specimens are machined, are manufactured at low pressure die casting followed by T6 heat treatment process. Table 1 shows six different stress levels at which test is conducted and the corresponding number of specimens that are tested at each level. The minimum number of specimens tested at each stress level is not less than 5. Curve fitting is done for all the specimens. The responses obtained at each stress level are checked for variation using lognormal distribution [4]. All the sets of responses at the six stress levels are found to be above 95% confidence level with an acceptance error of 5%. Fig. 2 shows the scattered points obtained from the rotary bending fatigue test. The S–N curve obtained from the curve fitting of the experimental data for the A356.2-T6 is presented in Fig. 3.
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Fig. 1. Rotating bending fatigue test specimen (All dimensions are in mm).
Table 1 Stress levels and specimen distribution S. No.
Stress (MPa)
No. of specimens tested
1 2 3 4 5 6
88 117 146 176 205 234
8 8 8 7 7 5
250
Stress, MPa
200 150 100 50 0 1.00E+04
1.00E+05
1.00E+06
1.00E+07
Cycles Fig. 2. Scattered points at different stress levels.
3. Material properties and manufacturing process for cast aluminum wheels One of the leading aluminum alloy for wheels in use today is AlSi7Mg, with the chemical composition shown in Table 2. The manufacturing of aluminum passenger car wheels is made up of low pressure die casting. The molten aluminum is kept in a gas tight heat insulated container from where it flows under mild pressure of approximately 70–100 kPa via a standpipe to escape through vent-holes, the molten aluminum enters the die without turbulence [8]. After solidification of the material in the die, the container is depressurized and the molten contents of the standpipe flow back into the container. The wheel is then sent for machining.
794
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Stress MPa
200
150
100
50
0 1.00E+04
1.00E+05
1.00E+06
1.00E+07
Cycles Fig. 3. S–N curve of A356.2 material.
Table 2 Chemical composition of AlSi7Mg (in %) Si
Fe
Cu
Mn
Mg
Zn
Ti
6.5–7.5
0.15
0.03
0.10
0.3–0.45
0.07
0.10–0.18
Mechanical properties: Following are the monotonic material data which were obtained from specimens taken from finished wheels. Ultimate tensile strength (Su): 250 MPa. Yield strength (Sy): 230 MPa. Elongation (e): 5%. Hardness (HB): 90.
4. Radial fatigue test layout A typical test setup according to standard [1] of the dynamic radial fatigue test is shown in the Fig. 4 equipped with a driven Rotatable drum. The drum axis is parallel to the axis of the test wheel which presents a smooth surface wider than the section width of the loaded test tyre section width. The test wheel and tyre provide loading normal to the surface of drum and in line radially with the center of test wheel and the drum. The test wheel is fixed to the hub by nuts with a suitable torque specified by vehicle or wheel manufacturer. The total weight of a car is balanced with a vertical reaction force from the road through the tyre. This load constantly compresses the wheel radially. While the car is running, the radial load becomes a cyclic load with the rotation of the wheel. Hence, the evaluation of wheel fatigue strength under radial load is an important performance characteristic for structural integrity. The wheel under test must complete the minimum number of test cycles prior to test termination. The test shall be terminated by loss of inflation pressure through a fatigue crack or the inability of the wheel to sustain the test load. There shall be no evidence of failure of the wheel as indicated, by propagation of crack existing prior to test or by new visible cracks penetrating through a section. Failure of the tyre or other parts of the test fixture does not require test termination but may result in damage to the wheel and test invalidation. According to the standards [1], a wheel should maintain structural integrity without any cracks or plastic deformation for more than 106 cycles under a radial load Fr, expressed by the following equation. Fr ¼ F K where K is acceleration test factor (K = 2.2) and F is the maximum tyre load in N.
ð1Þ
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Fig. 4. Layout of test setup of radial fatigue test.
Table 3 Radial fatigue test results Sample
Test results upto 1,000,000 cycles
Test results upto 2,500,000 cycles
1 2 3 4 5 6 7 8 9 10
Passed Passed Passed Passed Passed Passed Passed Passed Passed Passed
Failed Failed Failed Failed Failed Failed Failed Failed Failed Failed
Ten wheels have been tested on radial fatigue testing machine and results are presented in Table 3. The test is conducted in two stages. In the first stage, the wheel is inspected for first 106 cycles for visible cracks. If cracks are found, the test will be stopped, else it will be continued for next 1,500,000 cycles. After 2,500,000 cycles again the wheel is examined and is said to have passed the test if no cracks are found. 5. Radial fatigue test (RFT) results In the present tests, cracks started to initiate in between 1,050,000 and 1,300,000 cycles. All wheels are found to have cracks after 2,500,000 cycles. All the 10 wheels that are tested failed under the radial fatigue
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Fig. 5. Image showing cracks of failed wheel in RFT.
test. Fig. 5 shows the image of a failed wheel in radial fatigue testing. A visible crack can be seen in Fig. 5 starting from pocket edge fillet and propagating towards the other edge. 6. Finite element analysis The process of generation of finite element model to simulate dynamic radial fatigue test is described in the following sequel. Finite element modeling and analysis is carried out using a general purpose finite element software ANSYS. Element size of 5 mm is used for meshing the wheel model with 101,008 elements and 188,466 nodes. The wheel is glued to the base through the pitch circle diameter and all the degrees of freedom of the mounting face are constrained [9]. The test load of 33,630 N is applied as 18 discrete nodal point loads 10° apart over a span of 180° [5]. The load is distributed as a cosine function with in a central angle of 90° in a circumferential direction. The application of pressure on the rim is shown in Fig. 6. Along the line of contact between the tyre and road, the pressure will be maximum at 0° and decreases as the loading angle along circumferential direction increases and finally becomes zero at 90° [10]. The same is applicable due to symmetry over the other 90° of circumference. Fig. 7 shows the application of pressure with respect to the loading angle along circumferential direction over a span of 180°. Results obtained from strain gauge experiments [10] indicate that loading shape is in the form of a cosine function about a central angle of 40° from either side of the point of contact with the ground. This 40° angle is developed from the contact patch geometry of the tyre. Indicating that when the tyre is loaded there is flat at the point of contact with the ground, and the length of this patch is then converted to an
Fig. 6. Loading in the form of cosine function over 90°.
P.R. Raju et al. / Engineering Failure Analysis 14 (2007) 791–800
797
Pressure on rim in Pa
30000 25000 20000 15000 10000 5000 0 -100
-50
0 Circumferential Angle
50
100
Fig. 7. Pressure on rim vs. circumferential angle.
3.5E+06
Fatigue life in cycles
3.0E+06 2.5E+06
SF 1 SF 1.5 SF 2 SF 2.5
2.0E+06 1.5E+06 1.0E+06 5.0E+05 0.0E+00 40
50
60
70
80
90
100
Load angle in degrees Fig. 8. Load angle vs. fatigue life curves under variable safety factors.
angle swept by rim of the wheel. The analysis done using central angle of 40° did not prove to be accurate and a method proposed assumes the area in contact with the rim spans half of the tyre or 90° symmetrical about the point of loading. Based upon these results, since the angle of application of load in circumferential direction to which actual contact takes place cannot be decided exactly, analysis is carried out at different angles starting from 40° to 90° and the results are compared with those of the actual durability test performed in earlier experiment. The second step of analysis is carried out at different loading angle in circumferential direction starting from 0–40° to 0–90° with different safety factors 1, 1.5, 2 and 2.5. 7. Results and discussion The results obtained for different loading cases are shown in Figs. 8 and 9 for different safety factors. The variation of von Mises stress and life of the alloy wheel with respect to loading angle for different safety factors is shown in Figs. 8 and 9.
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von Mises stress in MPa
400 350 SF 1 SF 1.5
300
SF 2 SF 2.5
250 200 150 100 50 0
40
50
60
70
80
90
100
Load angle in degrees Fig. 9. Load angle vs. von Mises under variable safety factors.
From Fig. 8, it can be observed that for safety factor 1 and 40° circumferential loading, the life of the wheel is 424,812 cycles. As the circumferential angle increases from 40° to 70°, the life of the wheel increases to 3,277,860 cycles more and increases further up to 90° loading. From experimental results, the life of wheel lies in between 1,050,000 and 1,300,000 cycles. The change in life of the wheel by varying circumferential angle from 40° to 90° is much higher compared to experimental results. For safety factor 1.5, it can be observed that the life of wheel at 40° circumferential loading is 62,050 cycles and the life gradually increases to 3,277,860 cycles at 90°. It can also be observed that for safety factor 1.5, the life is more than the experimental results. For safety factor 2, it can be observed that the life of the wheel is less than 10,000 cycles at 40° circumferential loading and the life gradually increased to 1,213,400 cycles at 90° loading. It can be observed that results obtained from 90° circumferential loading with safety factor 2 are much closer to the experimental results. For safety factor 2.5, the life of alloy wheel is less than 10,000 cycles at 40° circumferential loading and 447,400 cycles at 90° loading, which shows that the safety factor 2.5 gives life much lesser compared to corresponding experimental results. Fig. 9 shows the variation of von Mises stress for different loadings and safety factors. From Fig. 9, it can be observed that for safety factor 1, the von Mises stress at 40° circumferential loading is 156.3 MPa and gradually decreases to 53.54 MPa at 90° circumferential loading. For safety factor1.5, von Mises stress is 234.5 MPa at 40° circumferential loading and 80.2 MPa at 90° loading. For safety factor 2, von Mises stress is 312.6 MPa at 40° circumferential loading and 107.8 MPa at 90° loading. The fatigue life of A356.2-T6 at 109 MPa is 1,213,400, which is much closer to the experimental results. For safety factor 2.5, the von Mises stress is 390 MPa at 40° circumferential loading and 133.8 MPa at 90° loading. 7.1. Test results under radial load along circumferential direction of 0–90° with safety factor 2 Fig. 10 shows maximum stress distribution at the spoke of the wheel when loaded radially over the span of 0–90° in circumferential direction symmetrically over the path of contact on both sides with a safety factor 2. From Fig. 10, it can be observed that maximum stress location is at the ends of the spoke connecting to mounting face and the value is 108.8 MPa. Fig. 11 shows maximum and minimum distribution at the spoke of the wheel when loaded radially over the span of 0–90° in circumferential direction symmetrically over the path of contact on both sides with a safety factor 2. From Fig. 11, it can be observed that the minimum life of 1,213,400 cycles is at the spoke pocket area. This minimum life area is considered to be the sensitive point with in the wheel where it is more likely to fail.
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Fig. 10. Stress distribution plot showing max. and min. stress locations.
Fig. 11. Life distribution plot showing the locations of max. and min. life.
8. Conclusions Development of S–N curve for aluminum alloy (Al) A356.2-T6 and fatigue life evaluation for wheels made of alloy under radial fatigue load is presented. The S–N curve is developed by conducting tests at different stress levels under constant amplitude loading. Finite element analysis is carried out by simulating the test conditions to analyze stress distribution and fatigue life of the alloy wheels. An attempt has been made by conducting parametric study to suggest a suitable safety factor for reliable fatigue life prediction. The following conclusions are drawn based on the comparison of the results obtained from the tests and the FEA: 1. The location of crack initiation in both the laboratory test and FEA is found to be the same. 2. The S–N curve approach for predicting the fatigue life of alloy wheels by simulating static analysis with cyclic loads is found to converge with experimental results.
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3. The predicted fatigue life using FEA is found to be in close agreement with the corresponding experimental observations 4. Safety factors for fatigue life and radial load are suggested by conducting extensive parametric studies. 5. The proposed safety factors will be useful for manufacturers/designers for reliable fatigue life prediction of similar structural components subjected to radial fatigue load.
References [1] JIS D 4103. Japanese Industrial Standard. Disc Wheel for Automobiles. 1989. [2] Grubisic V, Fischer G. Automotive wheels, methods and procedures for optimal design and testing. SAE Technical Paper Series 830135; 1984:1.508–1.525. [3] Hsu YL, Wang SG, Liu TC. Prediction of fatigue failure of aluminum disc wheel using the failure probability contour based on historical test data. J Chin Inst Industrial Eng 2004;21(6):551–8. [4] Gope PC. Determination of minimum number of specimens in S–N testing. J Eng Mater Technol 2002;124:421–7. [5] Kerr S, Russell DL, Patel US, Bishop NWM. FE-based wheel fatigue analysis using MSC. Fatigue. Proceedings of the 1st MSC worldwide automotive conference, Munich, Germany: 1999. [6] David Gerken T, Rick Neal. Squeeze cast (SCPM) light weight aluminum front knuckle case study. International Congress and Exposition. Detroit, Michigan; 1999. [7] IS: 5075 INDIAN STANDARD. Method of rotating bending fatigue testing of metals 1985. [8] Fischer G, Grubisic V. Cast aluminum wheels and buses – testing and evaluation. SAE Technical Paper Series 841705; 1985;6.1051– 6.1062. [9] Hsu YL, Hsu MS. Weight reduction of aluminum disc wheels under fatigue constraints using a sequential neural network approximation method. Computers Ind 2001;46(2):61–73. [10] John Stearns C. An investigation of stress and displacement distribution in a aluminum alloy automobile rim. A Dissertation Presented to the Graduate Faculty of the University of Akron, Ohio; 2000.
Evaluation of fatigue life of aluminum alloy wheels under radial loads P. Ramamurty Raju a
a,*
, B. Satyanarayana b, K. Ramji b, K. Suresh Babu
a
Department of Mechanical Engineering, Sagi Rama Krishnam Raju Engineering College, Bhimavaram 534 204, Andhra Pradesh, India b Department of Mechanical Engineering, Andhra University, Vishakapatnam, Andhra Pradesh, India Received 12 November 2006; accepted 19 November 2006 Available online 17 January 2007
Abstract This paper is concerned with generation of S–N curve for aluminum alloy (Al) A356.2-T6 and estimation of fatigue life under radial fatigue load. The S–N curve is developed by conducting tests at different stress levels under constant amplitude loading. Tests are conducted on alloy wheels for fatigue life evaluation under radial loads. Finite element analysis (FEA) is carried out by simulating the test conditions to analyze stress distribution and fatigue life of the alloy wheels. It is observed from analysis that the prediction of fatigue life using FEA is found to be in close agreement with the corresponding experimental observations. An attempt has been made by conducting parametric study to suggest a suitable safety factor for reliable fatigue life prediction. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: S–N curve; Radial fatigue load; Fatigue life; Safety factor; Finite element analysis
1. Introduction In the fatigue life evaluation of aluminum wheel design, the commonly accepted procedure for passenger car wheel manufacturing is to pass two durability tests, namely the radial fatigue test and cornering fatigue test [1]. Since alloy wheels are designed for variation in style and have more complex shapes than regular steel wheels, it is difficult to assess fatigue life by using analytical methods. In general, the newly designed wheel is tested in laboratory for its life through an accelerated fatigue test before the actual production starts. Based on these test results the wheel design is further modified for high strength and less weight, if required. Grubisic and Fisher [2] have reported earlier in the literature that testing alone without the aid of stress analysis will not yield the optimum wheel design. Hsu et al. [3] described a probability based model for prediction of fatigue failure of aluminum disc wheels, which intended to better link the prediction of life using simulation results with historical data. Finite element models of 20 aluminum wheels *
Corresponding author. Tel.: 91 8816 225124. E-mail address: [email protected] (P.R. Raju).
1350-6307/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2006.11.028
792
P.R. Raju et al. / Engineering Failure Analysis 14 (2007) 791–800
Nomenclature Su Sy e HB K F Fr
ultimate tensile strength yield strength elongation hardness acceleration test factor maximum tyre load radial load
which are already physically tested were constructed to simulate dynamic radial fatigue test. Their mean stress and stress amplitude during the fatigue loading cycles were calculated and plotted on a two dimensional plane. For a new wheel the failure probability of dynamic radial fatigue test can be read directly from this probability contour drawn from the test data. Gope [4] mentioned that a minimum of three specimens are required to predict the fatigue life using the log normal distribution. To the best of authors’ knowledge the research work carried out in this area is limited. The present work deals with estimating the fatigue life of aluminum alloy wheel by conducting the tests under radial fatigue load and comparison of the same with that of finite element analysis. Fatigue life prediction using the stress approach is mostly based on local stress, because it is not possible to determine nominal stress for the individual critical areas. The necessary material data for fatigue life prediction with the stress concept is the well known S–N curve. Therefore, S–N curves are required for each specimen which reflects the stress condition in the critical area of the component. To find out the fatigue properties of the aluminum alloy wheel material (A356.2-T6) for actual manufacturing conditions, fatigue test is conducted to generate S– N curve for which 43 specimens are machined from the spokes of alloy wheels and are tested using rotating bending fatigue test equipment. There are different loading methodologies for simulation of radial fatigue test. The dynamic nature of the tests is simulated using equivalent static load in the form of cyclic nature [5]. The results obtained by simulation of tests are compared with actual wheel tests performed. Since fatigue characteristics of a material depend upon several parameters from metallurgical aspects to manufacturing conditions, a safety factor should be considered. It is generally expected that there should be difference between experimental and analytical results. In order to correlate the experimental results with FEA, a parametric study is carried out by employing various safety factors and finally a reliable safety factor is suggested. Similarly the effect of loading angle along circumferential direction for applying radial load is also analyzed by performing parametric studies and finally a suitable angle is suggested. 2. Development of S–N curve To find the fatigue properties of aluminum alloy A356.2-T6 for actual manufacturing conditions, a test is carried out on specimens taken from the wheels. For all 43 identical specimens which are machined from the spokes of alloy wheels [6], rotary bending fatigue test is conducted according to Standards [7]. The schematic diagram of specimen geometry and dimensions are shown in Fig. 1. The wheels, from which specimens are machined, are manufactured at low pressure die casting followed by T6 heat treatment process. Table 1 shows six different stress levels at which test is conducted and the corresponding number of specimens that are tested at each level. The minimum number of specimens tested at each stress level is not less than 5. Curve fitting is done for all the specimens. The responses obtained at each stress level are checked for variation using lognormal distribution [4]. All the sets of responses at the six stress levels are found to be above 95% confidence level with an acceptance error of 5%. Fig. 2 shows the scattered points obtained from the rotary bending fatigue test. The S–N curve obtained from the curve fitting of the experimental data for the A356.2-T6 is presented in Fig. 3.
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Fig. 1. Rotating bending fatigue test specimen (All dimensions are in mm).
Table 1 Stress levels and specimen distribution S. No.
Stress (MPa)
No. of specimens tested
1 2 3 4 5 6
88 117 146 176 205 234
8 8 8 7 7 5
250
Stress, MPa
200 150 100 50 0 1.00E+04
1.00E+05
1.00E+06
1.00E+07
Cycles Fig. 2. Scattered points at different stress levels.
3. Material properties and manufacturing process for cast aluminum wheels One of the leading aluminum alloy for wheels in use today is AlSi7Mg, with the chemical composition shown in Table 2. The manufacturing of aluminum passenger car wheels is made up of low pressure die casting. The molten aluminum is kept in a gas tight heat insulated container from where it flows under mild pressure of approximately 70–100 kPa via a standpipe to escape through vent-holes, the molten aluminum enters the die without turbulence [8]. After solidification of the material in the die, the container is depressurized and the molten contents of the standpipe flow back into the container. The wheel is then sent for machining.
794
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Stress MPa
200
150
100
50
0 1.00E+04
1.00E+05
1.00E+06
1.00E+07
Cycles Fig. 3. S–N curve of A356.2 material.
Table 2 Chemical composition of AlSi7Mg (in %) Si
Fe
Cu
Mn
Mg
Zn
Ti
6.5–7.5
0.15
0.03
0.10
0.3–0.45
0.07
0.10–0.18
Mechanical properties: Following are the monotonic material data which were obtained from specimens taken from finished wheels. Ultimate tensile strength (Su): 250 MPa. Yield strength (Sy): 230 MPa. Elongation (e): 5%. Hardness (HB): 90.
4. Radial fatigue test layout A typical test setup according to standard [1] of the dynamic radial fatigue test is shown in the Fig. 4 equipped with a driven Rotatable drum. The drum axis is parallel to the axis of the test wheel which presents a smooth surface wider than the section width of the loaded test tyre section width. The test wheel and tyre provide loading normal to the surface of drum and in line radially with the center of test wheel and the drum. The test wheel is fixed to the hub by nuts with a suitable torque specified by vehicle or wheel manufacturer. The total weight of a car is balanced with a vertical reaction force from the road through the tyre. This load constantly compresses the wheel radially. While the car is running, the radial load becomes a cyclic load with the rotation of the wheel. Hence, the evaluation of wheel fatigue strength under radial load is an important performance characteristic for structural integrity. The wheel under test must complete the minimum number of test cycles prior to test termination. The test shall be terminated by loss of inflation pressure through a fatigue crack or the inability of the wheel to sustain the test load. There shall be no evidence of failure of the wheel as indicated, by propagation of crack existing prior to test or by new visible cracks penetrating through a section. Failure of the tyre or other parts of the test fixture does not require test termination but may result in damage to the wheel and test invalidation. According to the standards [1], a wheel should maintain structural integrity without any cracks or plastic deformation for more than 106 cycles under a radial load Fr, expressed by the following equation. Fr ¼ F K where K is acceleration test factor (K = 2.2) and F is the maximum tyre load in N.
ð1Þ
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795
Fig. 4. Layout of test setup of radial fatigue test.
Table 3 Radial fatigue test results Sample
Test results upto 1,000,000 cycles
Test results upto 2,500,000 cycles
1 2 3 4 5 6 7 8 9 10
Passed Passed Passed Passed Passed Passed Passed Passed Passed Passed
Failed Failed Failed Failed Failed Failed Failed Failed Failed Failed
Ten wheels have been tested on radial fatigue testing machine and results are presented in Table 3. The test is conducted in two stages. In the first stage, the wheel is inspected for first 106 cycles for visible cracks. If cracks are found, the test will be stopped, else it will be continued for next 1,500,000 cycles. After 2,500,000 cycles again the wheel is examined and is said to have passed the test if no cracks are found. 5. Radial fatigue test (RFT) results In the present tests, cracks started to initiate in between 1,050,000 and 1,300,000 cycles. All wheels are found to have cracks after 2,500,000 cycles. All the 10 wheels that are tested failed under the radial fatigue
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Fig. 5. Image showing cracks of failed wheel in RFT.
test. Fig. 5 shows the image of a failed wheel in radial fatigue testing. A visible crack can be seen in Fig. 5 starting from pocket edge fillet and propagating towards the other edge. 6. Finite element analysis The process of generation of finite element model to simulate dynamic radial fatigue test is described in the following sequel. Finite element modeling and analysis is carried out using a general purpose finite element software ANSYS. Element size of 5 mm is used for meshing the wheel model with 101,008 elements and 188,466 nodes. The wheel is glued to the base through the pitch circle diameter and all the degrees of freedom of the mounting face are constrained [9]. The test load of 33,630 N is applied as 18 discrete nodal point loads 10° apart over a span of 180° [5]. The load is distributed as a cosine function with in a central angle of 90° in a circumferential direction. The application of pressure on the rim is shown in Fig. 6. Along the line of contact between the tyre and road, the pressure will be maximum at 0° and decreases as the loading angle along circumferential direction increases and finally becomes zero at 90° [10]. The same is applicable due to symmetry over the other 90° of circumference. Fig. 7 shows the application of pressure with respect to the loading angle along circumferential direction over a span of 180°. Results obtained from strain gauge experiments [10] indicate that loading shape is in the form of a cosine function about a central angle of 40° from either side of the point of contact with the ground. This 40° angle is developed from the contact patch geometry of the tyre. Indicating that when the tyre is loaded there is flat at the point of contact with the ground, and the length of this patch is then converted to an
Fig. 6. Loading in the form of cosine function over 90°.
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Pressure on rim in Pa
30000 25000 20000 15000 10000 5000 0 -100
-50
0 Circumferential Angle
50
100
Fig. 7. Pressure on rim vs. circumferential angle.
3.5E+06
Fatigue life in cycles
3.0E+06 2.5E+06
SF 1 SF 1.5 SF 2 SF 2.5
2.0E+06 1.5E+06 1.0E+06 5.0E+05 0.0E+00 40
50
60
70
80
90
100
Load angle in degrees Fig. 8. Load angle vs. fatigue life curves under variable safety factors.
angle swept by rim of the wheel. The analysis done using central angle of 40° did not prove to be accurate and a method proposed assumes the area in contact with the rim spans half of the tyre or 90° symmetrical about the point of loading. Based upon these results, since the angle of application of load in circumferential direction to which actual contact takes place cannot be decided exactly, analysis is carried out at different angles starting from 40° to 90° and the results are compared with those of the actual durability test performed in earlier experiment. The second step of analysis is carried out at different loading angle in circumferential direction starting from 0–40° to 0–90° with different safety factors 1, 1.5, 2 and 2.5. 7. Results and discussion The results obtained for different loading cases are shown in Figs. 8 and 9 for different safety factors. The variation of von Mises stress and life of the alloy wheel with respect to loading angle for different safety factors is shown in Figs. 8 and 9.
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von Mises stress in MPa
400 350 SF 1 SF 1.5
300
SF 2 SF 2.5
250 200 150 100 50 0
40
50
60
70
80
90
100
Load angle in degrees Fig. 9. Load angle vs. von Mises under variable safety factors.
From Fig. 8, it can be observed that for safety factor 1 and 40° circumferential loading, the life of the wheel is 424,812 cycles. As the circumferential angle increases from 40° to 70°, the life of the wheel increases to 3,277,860 cycles more and increases further up to 90° loading. From experimental results, the life of wheel lies in between 1,050,000 and 1,300,000 cycles. The change in life of the wheel by varying circumferential angle from 40° to 90° is much higher compared to experimental results. For safety factor 1.5, it can be observed that the life of wheel at 40° circumferential loading is 62,050 cycles and the life gradually increases to 3,277,860 cycles at 90°. It can also be observed that for safety factor 1.5, the life is more than the experimental results. For safety factor 2, it can be observed that the life of the wheel is less than 10,000 cycles at 40° circumferential loading and the life gradually increased to 1,213,400 cycles at 90° loading. It can be observed that results obtained from 90° circumferential loading with safety factor 2 are much closer to the experimental results. For safety factor 2.5, the life of alloy wheel is less than 10,000 cycles at 40° circumferential loading and 447,400 cycles at 90° loading, which shows that the safety factor 2.5 gives life much lesser compared to corresponding experimental results. Fig. 9 shows the variation of von Mises stress for different loadings and safety factors. From Fig. 9, it can be observed that for safety factor 1, the von Mises stress at 40° circumferential loading is 156.3 MPa and gradually decreases to 53.54 MPa at 90° circumferential loading. For safety factor1.5, von Mises stress is 234.5 MPa at 40° circumferential loading and 80.2 MPa at 90° loading. For safety factor 2, von Mises stress is 312.6 MPa at 40° circumferential loading and 107.8 MPa at 90° loading. The fatigue life of A356.2-T6 at 109 MPa is 1,213,400, which is much closer to the experimental results. For safety factor 2.5, the von Mises stress is 390 MPa at 40° circumferential loading and 133.8 MPa at 90° loading. 7.1. Test results under radial load along circumferential direction of 0–90° with safety factor 2 Fig. 10 shows maximum stress distribution at the spoke of the wheel when loaded radially over the span of 0–90° in circumferential direction symmetrically over the path of contact on both sides with a safety factor 2. From Fig. 10, it can be observed that maximum stress location is at the ends of the spoke connecting to mounting face and the value is 108.8 MPa. Fig. 11 shows maximum and minimum distribution at the spoke of the wheel when loaded radially over the span of 0–90° in circumferential direction symmetrically over the path of contact on both sides with a safety factor 2. From Fig. 11, it can be observed that the minimum life of 1,213,400 cycles is at the spoke pocket area. This minimum life area is considered to be the sensitive point with in the wheel where it is more likely to fail.
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Fig. 10. Stress distribution plot showing max. and min. stress locations.
Fig. 11. Life distribution plot showing the locations of max. and min. life.
8. Conclusions Development of S–N curve for aluminum alloy (Al) A356.2-T6 and fatigue life evaluation for wheels made of alloy under radial fatigue load is presented. The S–N curve is developed by conducting tests at different stress levels under constant amplitude loading. Finite element analysis is carried out by simulating the test conditions to analyze stress distribution and fatigue life of the alloy wheels. An attempt has been made by conducting parametric study to suggest a suitable safety factor for reliable fatigue life prediction. The following conclusions are drawn based on the comparison of the results obtained from the tests and the FEA: 1. The location of crack initiation in both the laboratory test and FEA is found to be the same. 2. The S–N curve approach for predicting the fatigue life of alloy wheels by simulating static analysis with cyclic loads is found to converge with experimental results.
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3. The predicted fatigue life using FEA is found to be in close agreement with the corresponding experimental observations 4. Safety factors for fatigue life and radial load are suggested by conducting extensive parametric studies. 5. The proposed safety factors will be useful for manufacturers/designers for reliable fatigue life prediction of similar structural components subjected to radial fatigue load.
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