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SAE TECHNICAL
PAPER SERIES
2007-01-1206
Strength Prediction and Correlation of Tow Hook
Systems using Finite Element Analyses
Michael Guo, Rana Sanghera and Shujath Ali
DaimlerChrysler Corporation
Reprinted From: Load Simulation & Analysis in Automotive Engineering, 2007
(SP-2107)
2007 World Congress
Detroit, Michigan
April 16-19, 2007
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ABSTRACT
In this paper, tow hook systems and their functional objectives are briefly introduced. General analysis considerations in strength prediction of a tow hook system are described. These considerations contain nonlinear, clamping and material property simulations. Connections and loading simulation of a tow hook system model are discussed in details. A correlation example of a tow hook system is illustrated.
This study shows that detailed modeling of a tow hook system is a fundamental requirement for accurate strength prediction and good correlation between finite element analysis and testing.
INTRODUCTION
Tow hooks’ primary function is to withstand towing loads. Tow hooks are attached to supporting structure by bolt or weld connections and have to meet certain strength and impact requirements. A tow hook system consists of tow hooks and related attachment structure. If tow hooks are bolted to the attachment structure, clamp load, slippage and bolt strength should be considered in design. Strength requirements of tow hook systems normally cover performance under extreme towing loads. Thus strength prediction of a tow hook system is typically a nonlinear analysis and finite element analysis (FEA) is an appropriate tool for the application.
Proper assumptions applied in a FEA model can simplify analyses dramatically while still retaining enough accuracy and reliability. What are the significant details that need to be modeled, how to simplify the analyses, and how well the FEA can predict the structure performance are frequently asked questions.
Unexpected separation of a tow hook or the attached structure from the vehicle during towing application may result as a safety concern. Therefore accuracy and
reliability of strength predictions of tow hook systems are very critical, and correlation of the predictions to testing provides the corroboration.
Based on many years of FEA, testing and design experience, a detailed modeling approach in strength prediction of tow hook systems is studied and described in this paper. Accuracy and reliability of the prediction are verified by a correlation example.
TOW HOOKS AND TOW HOOK SYSTEMS
Tow hooks are key structural components designed to withstand towing loads without affecting impact performance, and are classified as front tow hooks, rear tow hooks, and front and rear tow eyes (for export vehicles), etc.
A tow hook system is an assembly consisting of tow hooks and an attachment structure. The attachment structure includes the support structure and the parts which attach the tow hooks to the support structure. Rail tip, tip plate, bumpers and fasteners are common attachment structure members (Fig. 1). According to different frame, bumper and unitized body designs, there are some other special attachment structural members as well.
Generally speaking, a tow hook design is a tow hook system design. Correspondingly, a strength analysis of a tow hook is that of a tow hook system.
FUNCTIONAL OBJECTIVES AND LOAD CASES
Structurally, there are two types of functional objectives for tow hook systems: to sustain required towing loads, and not to degrade impact performance. The former requires that tow hook systems have sufficient strength, and the latter requires that tow hook systems have sufficient flexibility and compliance so that not to fire airbags too early or change the impact mode of the vehicle. Only the former is influenced by the strength analyses.
2007-01-1206
Strength Prediction and Correlation of Tow Hook Systems
using Finite Element Analyses
Michael Guo, Rana Sanghera and Shujath Ali
DaimlerChrysler Corporation
Fig. 1 A TOW HOOK SYSTEM
Each tow hook and the attachment structure should be capable of towing a fully loaded vehicle or a comparable vehicle out of a muddy ditch. The detailed structure requirements are as follows:
x Under a towing load that is more commonly experienced, the tow hook and the attachment structure should not result in a visible permanent set.
x Under an extreme towing load, the tow hook and the attachment structure should not separate.
x Each tow hook and the attachment structure should be able to support the towing loads applied as straight and angular pulls. The angular pulls include upward, downward, inboard and outboard pulls, Fig. 2. The towing angle is determined based on the maximum possible angle allowed by other parts of the vehicle such as fisher or bumper beam.
Normally the towing angle is of 20 or 30 degrees.
(a) Straight, Inboard and Outboard Pulls
(b) Straight, Upward and Downward Pulls Fig. 2 TOWING LOAD CASES
GENERAL ANALYSIS CONSIDERATIONS
A static testing is generally carried out to evaluate strength performance of tow hook components or tow hook systems. The FEA model simulating the test needs to represent the tested prototype.
Nonlinear analyses, including nonlinear material, nonlinear boundary and nonlinear geometry, should be conducted because of the following reasons:
x Nonlinear material property can provide more accurate information to identify a) if the structure has yielded under the commonly experienced towing loads and the quantity of permanent set levels. b) if separation will occur under the extreme loads.
x Nonlinear boundary/contact is critical when a tow hook system is analyzed because components are in contact to each other under Straight Outboard Inboard Pulling angle Upward pull Downward pull Pulling angle Bumper beam Tow hook Bumper bracket Tow hook
reinforcement Rail tip Spacer Bolts Bumper bracket Tow hook reinforcement Bolt, Connecting tow hook, tip plate, bumper bracket and tow hook reinforcement Rail tip Bolts, connecting tow hook reinforcement, bumper bracket and rail tip Tow hook Tip plate
clamp loads from the fasteners and under the different towing load cases.
x Nonlinear geometry consideration is necessary when a tow hook system is analyzed since the system normally has a large deformation, especially under the extreme towing loads. Clamping simulation of bolted connection usually is essential as stress performance and slippage of the connected structure components will directly influence the whole system performance. A clamping load generates local high stress, and slippages of components result in permanent set1 to 3.
MODEL MESH
In a tow hook system model, tow hooks should be meshed using solid elements and all the other parts using shell elements. Second order tetra mesh is acceptable but hexa element dominated mesh is recommended for the tow hooks. To capture accurate stress levels, it is recommended that thin skin of shell elements be included on the surface of solid elements. In a tow hook component model where fasteners need to be included and modeled in detail, both the tow hook and fasteners should be meshed using solid elements. In a FEA model where contact simulation between components is critical, such as the assembly in Fig. 1, hexa element dominated solid mesh is recommended. If a component includes both solid and shell mesh, the ‘T’ connection transition is recommended between the solid and shell elements.
A refined and better quality mesh should be developed at stress critical areas, such as bolt holes and contact areas.
MODEL CONNECTIONS
If analysis is focused on strength of a tow hook and the attached structure, special attention should be given to the tow hook connection/joint to the attached structure. Detailed fastener/joint modeling is required. This includes all major features and clamp loads of the bolt joint. The rigid connection, when used to represent fastener, artificially reinforces the bolt hole area and results in lower stresses around the bolt hole. In reality, however, the bolt hole area could be a strength concern. Fig. 3 shows an example of a tow hook base plate with different connections. Significantly different stress values and distributions are obtained under the same loading conditions.
If the analysis is focused on performance of the support structure, front/rear frame for example, rigid connections simplify the model and analysis extensively.
MATERIAL MODELING
Tow hooks are normally made from conventional ductile cast iron. Sometimes other materials, such as forged steel and Austempered Ductile Iron (ADI), are also employed.
(a) Rigid Connections
(b) Detailed Bolt Connections
Fig. 3 EFFECT OF TOW HOOK CONNECTIONS Plasticity of material should be simulated for every structural member in the model. Full and smooth stress-strain curves are needed to ensure convergence when high degree of material nonlinearity is involved. Tested material properties are highly recommended.
Rigid connections
Detailed bolt connections
The max von Mises stress: 510.0 MPa.
The max von Mises stress: 284.0 MPa.
LOADING AND BOUNDARY CONDITIONS
A towing load should be simulated using concentrated load, and it is distributed on a set of nodes by using a RBE3 element. The area of the loaded nodes should represent a strap, a chain or some other hook. The loading location should correctly represent the way the towing load actually acts on the hook.
If a tow hook as shown in Fig. 4 is analyzed, for example, the possible loading approaches and the appropriate simulations should be considered in details. If the hook is loaded by a strap, the strap should be applied around the uvula and act either on upper or lower of the hook surface. As the strap is put on the upper surface of the hook, it generates the worst load case for downward angular pull. As the strap is put on lower surface of the hook, it generates the worst load case for upward angular pull. Even for straight forward pull, according to the attachment structure, the strap on upper or lower hook surface results in different actions to the attachment structure.
In both cases that the strap acts on upper and lower surface of the hook, offset from the surface to the center of strap should be included in towing load simulation in the FEA model, F1 in Fig. 4. If the load is simply applied
at middle depth of the hook, significant stress difference will be created as the same magnitude of load is applied, Fig. 5.
Fig. 4 LOADING LOCATIONS
If the tow hook in Fig. 4 is loaded by another open hook which is tied by a chain, the loading point will be either inboard or outboard of the uvula, F2 in Fig. 4. Loading at
outboard location generates the worst load case for inboard angular pull, while loading at inboard location generates the worst load case for outboard angular pull. For either loading at inboard or outboard location, the
loading point should be (a) at lower rear corner of the hook for upward angular pull; (b) at upper rear corner of the hook for downward angular pull; (c) both upper and lower rear corners of the hook for straight forward pull. Residual deflection/permanent set of a tow hook system can be captured by unloading the applied load in the analysis.
(a) Loading with Offset
(b) Loading without Offset
Fig. 5 EFFECT OF LOADING LOCATIONS
CORRELATION EXAMPLES 4
The model, loading and boundary conditions of a tow hook system are shown in Fig. 6.
Offset
F1
F2
Offset
Loaded 5 mm above the top surface of the hook The max von Mises stress: 895.0 MPa
Loaded at middle depth of the hook The max von Mises stress: 447.0 MPa
Fig. 6 MODEL, LOADING AND BOUNDARY CONDITIONS 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Displacement Ratio L oad Rat io FEA TEST
(a) Straight Pull
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Displacement Ratio L oad Ra ti o FEA TEST (b) Upward Pull 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Displacement Ratio Lo ad R a ti o FEA TEST (c) Downward Pull 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Displacement Ratio L oad Rat io FEA TEST (d) Inboard Pull 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Displacement Ratio Lo ad Ra ti o FEA TEST
(e) Outboard Pull
Fig. 7 LOAD VERSUS DISPLACEMENT CURVES Loading
Constraints of all DOFs.
The correlations of load versus displacement curves of the tow hook system under all the required towing load cases are illustrated in Fig. 7. The solid curves represent FEA results and the dash curves represent testing results. The unloading testing results in the straight and outboard pull cases are not available.
In this case, the FEA predictions were available prior to the testing. Since all the required details were included, the simulation predictions compared reasonably well with the test results.
The FEA exhibits somewhat stiffer behavior, and lower permanent set values than the testing. The reason is that the measured displacements from testing include the deflections resulting from tightening of the specimen, the fixture, the chain and the opened hook that connects the tested hook to the actuator.
CONCLUSIONS
A detailed FEA modeling with nonlinear considerations, clamped joints, and loading conditions is extremely important for strength prediction and correlation of a tow hook system. Once model is developed with reasonable details, it can predict results that would correlate quite closely with the physical testing.
REFERENCES
1. Guo, M., Bhandarkar, R. and Lin, B., “Clamp Load Consideration in Fatigue Life Prediction of A Cast Aluminum Wheel Using Finite Element Analysis”, SAE 2004-01-1581, 2004.
2. Guo, M. and Ali, S., “Study on Simplified Finite Element Simulation Approaches of Fastened Joints”, SAE 2006-01-1268, 2006.
3. Guo, M., Lin, B., Ali, S. and Sanghera, R., “Finite Element Analyses of Fastened Joints in Automotive Engineering”, SAE 2007-01-1204, 2007.
4. National Technical Systems, “Ultimate Pull Testing of JK Towing Attachment Systems”, Report D004721, 2005.
ACKNOWLEDGEMENT
The author would like to acknowledge the support from the following DaimlerChrysler employees: Alan McGowan, Arun Natesan, Hamid Keshtkar and John Johnson.
CONTACT
Dr. Michael Guo, CIMS 514-20-10,
14250 Plymouth Road, Detroit, MI 48227-6027, USA. mg152@dcx.com
