Virtual Validation & Test Correlation of Wheel Using

Virtual Validation & Test Correlation of Wheel Using Abaqus Solver K. Mohammed Billal, Shankar V, Manimaran Krishnamoorthy, Narayana Balabhadruni, Rizwan Basha K and Anilkumar Nesarikar Chrysler India Automotive Pvt Ltd

Thomas Oery Chrysler Technology Center Abstract: The tire-wheel system is one of the most important subsystems of a ground vehicle. Different control, drive and resistance forces, created from the tire-ground interaction are carried and transferred to the vehicle by tire and wheel. The successful alloy wheel design must be able to support the vehicle weight, provide the vehicle control and stability, and transfer various forces and torques from road/tire interaction to a vehicle chassis / suspension system. The dynamic effects in terms of the wheel stiffness and internal damping characteristics during the impact loading conditions must be accounted in the model. In order to meet structural performance, the automotive industry has defined three major tests for the wheel which are Corner Fatigue Test (CFT), Radial Fatigue Test (RFT) and Impact Test. This paper explains how the Abaqus software is effectively used to validate the wheel and its correlation against the physical test values. Keywords: Wheel, Tire modeling, Wheel Impact, Corner Fatigue Test (CFT), Radial Fatigue Test (RFT), Wheel Stiffness, SAE J-175, Tire Stiffness, Hyperelastic.

1. Introduction The wheel is one of the critical components of the vehicle and it has to withstand the road loads and meet the safety requirements. In order to meet the structural performance, the automotive industry has defined three major tests for the wheel including impact test, radial fatigue test (RFT) and corner fatigue test (CFT). The impact damage on the wheel is evaluated in the Impact test, when the wheel hits a curb. In RFT test, the wheel and the tire are radially loaded against the constantly rotating drum, while in CFT, the wheel-disc structural characteristics are critical, the wheel is subjected to a constant rotating bending moment. In both the cases, the wheel has to complete the minimum number of the test cycles without any damage. By using the CAE simulation, the test timings and the cost of a wheel’s prototype development can be reduced significantly. The accuracy of CAE results majorly depends on parameters like tire modeling, simulation methods, load applications etc. This paper describes the tire representation, validation of tire model, methodology and test correlation of impact test, radial fatigue test and corner fatigue test.

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2. Tire Construction and Validation [1], [2] Tire plays a vital role as a medium to transfer the load from the loading drum to the wheel during radial fatigue test and it absorbs the energy during the impact test. The tire modeling is a complex task, which involves different components to be modeled properly with their respective material properties. Different components of tire were shown in Figure 1. The tire is constructed using hexahedral and beam elements. The hexahedral elements used to represent the tread, side wall and the bead wire. A net shaped beam element represents the body ply and beam element in the hoop direction represents the belts as shown in Figure 2. Steel is used for the bead wire and belt and polyester material is used for the body plies.

Figure 1. Tire Construction 2.1

Figure 2. Tire FE Model

Tire Vertical Stiffness Test (SAE J 2704) [3]

The SAEJ2704 is recommended practice, which describes the test method to determine the vertical force and deflection properties of a non-rolling tire. The setup consists of a fixture for mounting the inflated tire and wheel rim assembly at the rim hub and then a plate for a representing a flat simulated road surface, which would be used to apply normal force on the tire as shown in Figure 3.

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Figure 3. Tire Vertical Loading

Figure 4. Comparison of Tire F-D Curve

The force-deflection (FD) curve from the tire specification is used as reference for performing the analysis. Abaqus- Implicit solver is used to carry out the non-linear static analysis. This analysis is simulated in two steps: the first step for the tire inflation and the second step for the normal force loading on the tire. For loading, a rigid surface (road surface representation) is modeled using an analytical surface. In initial analysis, the CAE stiffness curve (FD Curve) was found deviating more with the tire vertical stiffness test curve. After by adjusting the rubber moduli, the CAE F-D curve matched with the tire test curve with 4% of deviation as shown in Figure 4.

3. Wheel Impact Test (SAE J 175) [4] The SAE J175 is recommended practice, which describes the minimum performance requirements, and the test procedures to evaluate the axial curb impact collision properties of all wheels, which is intended to use in passenger cars and light trucks. 3.1 SAEJ175 Test Set-Up The impact load is applied to the rim flange of a wheel-tire assembly. The wheel-tire assembly is mounted at an angle of 13º to the horizontal plane so that striker impacts the outer bead radius of the rim near the air valve hole. The striker impact face has to be at least 125mm wide and at least 375 mm long. Figure 5 shows the impact loading test machine set-up. The wheel and tire assembly were mounted on the wheel mount fixture and its dimensions were shown in Figure 6. Four natural rubber mounts were used in fixture to absorb the impact load and their hardness is equal to 50 shore. The vertical deflection in the wheel mount fixture should be 7.5mm ± 10% at the mid-span of the beam, when a vertical mass of 1000kg is applied at the center of wheel mount. All pivot joints in the fixture should be free to rotate.

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Figure 5. Impact Loading Machine [4]

Figure 6. Wheel Hub Fixture [4]

3.2 Laboratory Measurement The impact loading machine and the wheel hub mount were designed as per the SAE specifications. The wheel mount fixture is calibrated for the 7.5 mm vertical deflection. There were four strain gauges (A, B, C and D) mounted on top of the wheel spoke region and the two strain gauges (E and F) were mounted on the bottom of the wheel spoke region as shown in Figure 7. These mounting regions were selected from the initial CAE simulation. The strain gauge B and C have high strain limits.

Figure 7: Strain Gauge Locations 3.3 Validation of Wheel Mounting Fixture The wheel mounting fixture and the rubber mounts were modeled using hexahedral elements as shown in Figure 8. The revolute joint is used to represent the pivot joints. The hyper-elastic rubber material model is used for the rubber mounts. The links/interfaces within the fixture assembly and the striker- tire/wheel interfaces were modeled with appropriate contacts. The fixture is calibrated as per the SAE J175 standard. A non-linear static analysis is done for the vertical load of 1000Kg applied on the wheel mounting hub, and the vertical deflection is measured at the center of the SIMULIA India Regional User Meeting ‘14

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steel beam (Figure 8). From the CAE analysis, the vertical deflection at the center of the beam (7.3mm) is found to be well within the range of SAE standard of 7.5 mm ± 10% as shown in Figure 9.

Figure 8: Wheel Mount Fixture

Figure 9: Wheel Mount: Deflection

3.4 Wheel Impact Analysis ABAQUS-Explicit solver is used to carry out the nonlinear dynamic simulation using the following three sequential steps, Step I: Bolt preload: The bolt preload equivalent to the bolt tightening torque is applied for the first 10 millisecs. Step II: Tire inflation: The fully inflated tire pressure is applied inside the tire and wheel surface for the next 10 millisecs. Step III: Wheel Impact: As per SAE J-175 standard, the striker mass (615Kg) falls from 230mm height. In CAE, striker is kept at 54mm height. This height is calculated (from Equation 2), so that the impact loading occurs in correct timing sequence after bolt preload and the tire inflation. The initial velocity is calculated using Equation 1 and applied to the striker. The initial velocity (Vo) is calculated by equation,

Vo =

- (1) Where g = Acceleration due to gravity and h = Impact height.

The time (t) taken for impact is calculated by equation,

T=

- (2) Where g = Acceleration due to gravity and h = Impact height.

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3.4.1 Bolt Preload and Tire Inflation Simulation: In CAE simulations, the bolt preload will be done in a static process. Since the explicit process is used for this simulation, the bolt preload is simulated in dynamically [5]. Contacts are defined between the bolt, wheel and the fixture hub interfaces. A connector element is used to monitor the bolt force, the relative displacement between the bolt threads and the nut threads. The bolt force in the connector element is initially treated as a negative force to pull the bolt threads towards the nut threads as shown in Figure 10. After the bolt force reaches the magnitude of the desired bolt preload, as per the tightening torque, the connector element displacement is locked and the bolt load is removed. As the result, the applied bolt load is converted from a surface force to a selflimiting body force. By using this method, it is easy to incorporate the bolt preload into the subsequent dynamic simulations of tire inflation and the wheel impact. Figure 11 shows the time amplitude curve for the bolt preload and tire inflation.

Figure 10: Bolt Preload

Figure 11: Load Amplitude Curve

3.5 Wheel Impact Results - Discussion After the impact test, the wheel rim width is measured in the lab and found to be 203.4 mm, where the original length is 205.3 mm. From the CAE simulation, the value of the deformed rim width was found to be 203.9 mm, which is close to the lab measurement as shown in Figure 12. The impact load contribution between the wheel and tire are studied from the CAE simulation by monitoring the contact forces in the interface as shown in Figure 13. The tire contribution is 10% of the impact load, whereas the wheel contribution is 90% to the total impact load.

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Figure 12: Rim Width Measurement

Figure 13: Time Verses Contact Force

The bolt preload variations were monitored with the connector force during the impact as shown in Figure 14. The bolt preload decreased in the bolt 1 and 2, which is experienced the compression during impact. The bolt preload increased in bolt 4 and 5, which is subjected to tension. The bolt 3 experienced the minor variations, since it was located in the mid-plane along the loading direction.

Figure 14: Time Verses Blot Force From the laboratory impact test, the principle strains were measured at six locations A, B, C, D, E and F (refer Figure 7). During the impact test, the strain gauges A and E were damaged. In CAE model, the principal strains were measured in the appropriate locations in the wheel for B, C, D and F. Since locations B, C and D were on the top layer of the wheel spoke region, they went into tension during the impact and it experienced the maximum principal strain. The location E is at the bottom of the wheel spoke region went compression and it is experienced the minimum principal strain. From the test strain curve (refer Figure 16), it is observed that the first impact happened with the compression of the rubber mount, and then load was transferred to the wheel with the second impact. This phenomenon is captured closely in CAE simulation with accurate representation of the wheel mount fixture. Figure 15 shows the sectional view of the deformed SIMULIA India Regional User Meeting ‘14

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shape before the impact, and during impact. The principal strain value and the curve trend from CAE simulation correlated very well with the laboratory test for the location B, C, D and F as shown in Figure 17.

Figure 15: Wheel Impact – CAE

Figure 16: Test Strain Results – Loc B

Figure 17: Principal Strain Comparison – Test Vs CAE Results

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4. Radial Fatigue Test (SAE J 328) The SAE recommended practice is to establish minimum performance requirements and uniform procedures for fatigue testing of wheels intended for normal highway use on passenger cars, light trucks, and the multipurpose vehicles. 4.1 Radial Fatigue Test (RFT) Setup - SAE J-328 [6] Tire is mounted on the wheel and it is inflated to the test pressure. The wheel tire assembly is bolted to the adaptor prescribed and the bolts are tightened to the required torque. The wheel and the adaptor assembly is mounted on stationary fixture through the bearings. So the wheel assembly is free to rotate with respect to the fixture. A revolving driven drum is placed parallel to the wheel assembly as shown in Figure 18. The rotational axis of the drum and the wheel were parallel. The drum is pressed against the tire and it imparts a constant radial load on the wheel, and drives the wheel. As the wheel is rotated by the revolving drum, the wheel rim experiences the alternate bending load.

Figure 18: Radial Fatigue Test Setup [6] Radial fatigue loading machine is designed as per the SAE specifications. There were nine strain gauges mounted on the wheel rim regions and those locations were selected from the initial CAE simulation at zero degree (loaded opposite to the inflation hole). Four strain gauges were mounted at the section A, another four strain gauges mounted at the section B and the remaining one strain gauge is mounted at location ‘E’ as shown in Figure 19. The lab test is done in the static condition for zero degree, +15 degree and +30 degree as shown in Figure 20. The stress readings were recorded on the strain gauge after tire inflation and radial loading at three positions of the wheel.

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Figure 20. Wheel – Loading Positions

Figure 19. Strain Gauge Locations 4.2 Radial Fatigue – CAE Simulation

The radial fatigue test in static condition is simulated by applying the sequential load of the bolt preload, tire inflation and the radial load. Step 1: Bolt preload. The bolt preload equivalent to bolt tightening Torque: 150Nm is applied. Step 2: Tire inflation. The tire pressure of 35 PSI is applied inside the Tire and Wheel. Step 3: Radial Fatigue. The radial load is applied in static condition through the driven drum, which is constructed using the analytical surface. The analysis is done for zero degree, +15 degree, and +30 degree of wheel positions as shown in Figure 18.The radial load applied to the wheel is determined by using the following Equation 3, F

W K

- (3)

where, F = Maximum radial load (N) in Front or Rear axle Maximum of F (front/rear) is determined by using the following Equation 4, F ( front ) W ( front ) K (rear ) F (rear ) W (rear ) K (rear ) - (4)

where, W (front) = ½ of the max. Static load on the front axle K (front) = load factor (for aluminum, 2.5 for front and 2.25 for rear) W (rear) = ½ of the maximum static load on the rear axle SIMULIA India Regional User Meeting ‘14

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K (front) = load factor (for aluminum, 2.5 for front and 2.25 for rear)

4.4 Radial Fatigue – Results Discussion The measurement is done at two stages: the tire inflation loading and the radial loading. From the laboratory radial fatigue test (in static condition), the maximum principal stress, the minimum principal stress and Von-mises stress were measured on the nine strain gauges on wheel at two stages after the tire inflation and then at the wheel positions (zero degree, +15 degree and +30 degree). Figure 21 shows the tire deflection due to inflation and radial load. Figure 22 shows the rim deflection and it is observed that the more bending occurred at the strain gauge location A1/B1 and in testing also, the compressive stress is higher in these locations. At the strain gauge location A3/B3 the elongation is more than the bending, so the tensile stress is higher at these location. The Figure 22 shows the stress (Vonmises, Max. and Mini. Principle Stress) value comparison between the laboratory test results versus the CAE, after the tire inflation.

Figure 21. Tire deflection: Due to Tire Inflation (Scale 1:50) and Radial Load

Figure 22. Rim deflection (Scale 1:50) and Stress Comparison Test Vs CAE due to Tire Inflation Figure 23 and 24 shows the rim deformed shapes before and after the radial loading and the stress (Vonmises, Max. and Mini. Principle Stress) value comparison between the test and the CAE, after the radial loading at wheel 0°, +15° and +30° positions. The stress values and the directions (tensile and compressive components from Max. and Min. Principal Stress) in CAE are close to the test results for tire inflation and the radial loading at different wheel positions. SIMULIA India Regional User Meeting ‘14

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Figure 23. Rim deflection and Stress Comparison Test Vs CAE (Loading at 0°)

Figure 24. Stress Comparison Test Vs CAE (Loading at +15 and +30 Degree)

5. Corner Fatigue Test (SAE J 328) The corner fatigue test (CFT) simulates the loading condition of wheel in normal driving condition and the load is applied in the 90° as shown in Figure 25, as per SAE J328. The wheel is clamped at the outboard flange of the rim and a rigid moment arm is attached to the mounting surface of the wheel. A test load is applied on the moment arm to make a constant cyclic rotational bending moment. The wheel should withstand the target cyclic loading and it should not fail.

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Figure 25. Corner Fatigue – Test Setup [6] 5.1 Stiffness Evaluation using CFT Method The CAE model setup is shown in Figure 26. The wheel is model using tetra (aluminum wheel) or shell element (steel wheel). The moment arm is modeled using hexahedral elements and it is mounted with wheel using bolts. The test load is applied at the end of the moment arm at 15° apart and the cyclic stress values will be taken for the fatigue analysis. To evaluate the wheel lateral stiffness, the wheel is kept in the fixed positions and the load is applied in different locations and the deflection is measured at the tip of the moment arm. The simulation is done in the following steps, Step 1: Bolt preload. The bolt preload equivalent to bolt tightening torque. Step 2: CFT Load. The static load is applied for the required bending moment, which is calculated using the following relationship, M = P * L; - (5) Where M = Bending moment, Nm “P” is static load to be applied at a distance of “L” mm. 5.2 Stiffness Evaluation – Results Discussion In lab, different sizes of wheels are tested and the displacement measured at the moment arm. Similarly in CAE, wheels were analyzed and the stiffness is calculated using the moment arm displacement. The CAE results were close to the lab test values and comparison is shown in Figure 27.

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Figure 26. Corner Fatigue: CAE Model

Figure 27. Test Vs CAE Results

6. Conclusions This paper presents a methodology to simulate the wheel tests in CAE and following are the key challenges faced in virtual analysis, 1.

Wheel Impact Test: The CAE process captures the dynamic behavior of the tire-wheel system during and after the impact. The most critical points in the methodology are, the development of the FE models for tire, the wheel mounting fixture, and the bolt preload simulation using ABAQUS explicit scheme.

2.

Wheel RFT Test: The preliminary stress (compressive and tensile) values were predicted by the CAE simulation is close to the laboratory test (as per SAE J-328) and it gives more confidence while performing the fatigue life calculation. The most critical aspects of the methodology were; the Tire FE representation and the bolt preload simulation.

3.

Wheel CFT Test: The CFT simulation is a simple one and not much non-linearity’s involved in this analysis like tire and dynamic conditions. The CFT test method is used to evaluate the lateral stiffness of the wheel.

References 1. Mohammed Billal K, Vinothkumar S, Sabarinathan Srinivasan and Anilkumar Nesarikar, "Simulation and Test Correlation of Wheel Impact Test," SAE Technical Paper 2011-280129, 2011, doi:10.4271/2011-28-0129. 2. Mohammed Billal K, Thomas Oery, Taruvai Sankaran, R., and Anilkumar Nesarikar, A., "Simulation and Test Correlation of Wheel Radial Fatigue Test," SAE Technical Paper 201301-1198, 2013, doi:10.4271/2013-01-1198. 3. SAE J2704, Tire Normal Force/Deflection and Gross Footprint Dimension Test, SAE International, Surface Vehicle Recommended Practice, JAN2005.

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4. SAE J175, Wheel Impact Test procedure, Road Vehicles, SAE International, Surface Vehicle Recommended Practice, SEP2003. 5. Tsu-te Wu, “Structural Analyses of Fuel Casks Subjected to Bolt Preload, Internal Pressure and Sequential Dynamic Impacts”, 50th Annual INMM Meeting, 2009. 6. SAE International Surface Vehicle Recommended Practice, “Wheels - Passenger Car and Light Truck Performance Requirements and Test Procedures,” SAE Standard J328, Rev. Feb. 2005. 7. Kocabicak U, Firat M, “Numerical analysis of wheel cornering fatigue tests”, Engineering Failure Analysis, 2001. 8. Wang Liangmo, Chen Yufa, Wang Chenzhi, “Fatigue Life Analysis of Aluminum Wheels by Simulation of Rotary Fatigue Test”, Journal of Mechanical Engineering, 57(2011)1, 31-39. 9. ABAQUS / Explicit User’s Manual 6.10 Version, 2010

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