The ability to test field service conditions in dangerous work areas and simulate these conditions leads to optimized load bearing structures in automotive and allied applications. For better safety of a driver or operator, mining, agricultural and self-propelled machines are equipped with protective structures
AdvanSES provides experimental test facilities to conduct FOPS tests on automotive and construction related machinery.
FOPS ANALYSES CONDITIONS
FOPS stands for Falling Object Protective Structure. FOPS are protective devices structure designed to protect operators from items that may fall on a vehicle or machinery when it is being operated. The recognized standard to define the performance requirements for FOPS is ISO 3449 Earth moving machinery – Falling object protective structures. This standard is referenced in other standards for machineries in general also. ISO 3449:2005 specifies laboratory tests for measuring the structural characteristics of, and gives performance requirements in a representative test for, falling-object protective structures (FOPS) intended for use on ride-on earth-moving machines as defined in ISO 6165. It is applicable to both FOPS supplied as an integral part of the machine and those supplied separately for attachment onto the machine.
There are two (2) different levels of FOPS – Level 1 & Level 2.
ISO 3449 states the following –
Level I impact protection – Impact strength for protection from small falling objects (e.g. bricks, debris, small rocks) encountered in operations such as highway maintenance, and construction site services. Level II impact protection – Impact strength for protection from heavy falling objects (e.g. boulders, rocks) for machines involved in site clearing, mining and overhead demolitions.
Level I – withstands 1,365 joules (45kgs Fall at 3.1m drop)
Level II – withstands 11,600 joules (227 kgs Fall at 5.2m drop)
According to the standard, the weight is let to fall freely onto the vehicle cabin roof ceiling from a definite height. The weight is made of steel or cast steel with a cylindrical or spherical shape. The height of free fall in correlation with the mass of the weight has to provide the impact energy. The levels of energy depend on purpose of the structure. In the current project virtual testing has been carried out for the FOPS using the commercial software package Abaqus®.
Figures show the impactors and striker geometry prescribed in the standard for evaluating the vehicle structure.
Contact us for a discussion on your FOPS and ROPS testing and analysis requirements.
Quality control refers to the process of systematically detecting errors in the laboratory testing results to ensure both that the accuracy and reliability of test results are maintained and best possible testing results are supplied to customers. Unreliable and inaccurate testing results can result in faulty failures, degraded field performance of engineering materials and products. it is therefore of great importance to ensure all results provided are accurate, reliable and consistent.
Alfort and Beaty define quality control as;
“Quality control is the mechanism by which products are made to measure up to the specifications determined from the customer’s demands and transform into sales, engineering and manufacturing requirements. It is concerned with making things right rather than discovering and rejecting those made wrong. Quality control is a technique by means of which products of uniform acceptable quality are manufactured.”
A mechanical and materials testing laboratory tests all kinds of materials at all stages of product engineering, from the raw material stage to performance characterization and durability testing of finished ready to market products.
The range and types of instruments to test these materials and product range from simplest to complex. Instruments such as density meter and hardness meters are the simple instruments, while SEMs, fatigue test benches, high strain rate equipments etc., are complex instruments that also have a significant learning curve. Only qualified engineers and analysts would be conducting the tests with the help of calibrated instruments to make sure that the data obtained is reliable and accurate.
Achieving quality in a mechanical and materials testing laboratory requires the use of many tools, instruments and machinery. These include UTMs, hardness meters, fatigue testing rigs, and also various custom made test benches. An established maintenance schedule, calibration, quality assurance program, training and quality control are pre-requisites. Calculations and maintenances of QC Statistics for systematic analysis of historical standard deviations, covariances, uncertainty calculations etc., is also required.
Data Integrity
Data integrity refers to completeness, consistency and accurateness of the raw data generated in the testing laboratory during the course of its work. It means that the raw data has to be reliable, consistent and accurate and that no modifications, changes or deletions cannot be caried out by any person or machine.
Raw data in the quality control laboratory can be generated by testing machnes, DAQ systems, and computer systems as well as by laboratory staff as paper records and reports. Ensuring integrity of data starts from the proper design of the procedural documents, level of access provided to authorized persons, physical reliablility of the infrastructure and training of laboratory personnel. An appropriately designed procedure is uniquely named and numbered has sufficient leeway for records to be stored comfortably digitally and physically and distribution are strictly controlled at all levels.
Having established all the QC standard protocols at AdvanSES, we take pride in our work and our protocols are available for audit at any time.
Non-linear Viscoelastic Dynamic Properties of Polymer, Rubber and Elastomer Materials
Static testing of materials as per ASTM D412, ASTM D638, ASTM D624 etc can be categorized as slow speed tests or static tests. The difference between a static test and dynamic test is not only simply based on the speed of the test but also on other test variables em- ployed like forcing functions, displacement amplitudes, and strain cycles. The difference is also in the nature of the information we back out from the tests. When related to poly- mers and elastomers, the information from a conventional test is usually related to quality control aspect of the material or the product, while from dynamic tests we back out data regarding the functional performance of the material and the product.
Tires are subjected to high cyclical deformations when vehicles are running on the road. When exposed to harsh road conditions, the service lifetime of the tires is jeopardized by many factors, such as the wear of the tread, the heat generated by friction, rubber aging, and others. As a result, tires usually have composite layer structures made of carbon-filled rubber, nylon cords, and steel wires, etc. In particular, the composition of rubber at different layers of the tire architecture is optimized to provide different functional properties. The desired functionality of the different tire layers is achieved by the strategical design of specific viscoelastic properties in the different layers. Zones of high loss modulus material will absorb energy differently than zones of low loss modulus. The development of tires utilizing dynamic characterization allows one to develop tires for smoother and safer rides in different weather conditions.
Figure Locations of Different Materials in a Tire Design
The dynamic properties are also related to tire performance like rolling resistance, wet traction, dry traction, winter performance and wear. Evaluation of viscoelastic properties of different layers of the tire by DMA tests is necessary and essential to predict the dynamic performance. The complex modulus and mechanical behavior of the tire are mapped across the cross section of the tire comprising of the different materials. A DMA frequency sweep
test is performed on the tire sample to investigate the effect of the cyclic stress/strain fre- quency on the complex modulus and dynamic modulus of the tire, which represents the viscoelastic properties of the tire rotating at different speeds. Significant work on effects of dynamic properties on tire performance has been carried out by Ed Terrill et al. at Akron Rubber Development Laboratory, Inc.
Non-linear Viscoelastic Tire Simulation Using FEA
Non-linear Viscoelastic tire simulation is carried out using Abaqus to predict the hysteresis losses, temperature distribution and rolling resistance of a tire. The simulation includes several steps like (a) FE tire model generation, (b) Material parameter identification, (c) Material modeling and (d) Tire Rolling Simulation. The energy dissipation and rolling re- sistance are evaluated by using dynamic mechanical properties like storage and loss modu- lus, tan delta etc. The heat dissipation energy is calculated by taking the product of elastic strain energy and the loss tangent of materials. Computation of tire rolling is further carried out. The total energy loss per one tire revolution is calculated by;
Ψdiss = ∑ i2πΨiTanδi, (.27)
i=1
where Ψ is the elastic strain energy,
Ψdiss is the dissipated energy in one full rotation of the tire, and
Tanδi, is the damping coefficient.
The temperature prediction in a rolling tire shown in Fig (2) is calculated from the loss modulus and the strain in the element at that location. With the change in the deformation pattern, the strains are also modified in the algorithm to predict change in the temperature distribution in the different tire regions.
Polymeric rubber components are widely used in automotive, aerospace and biomedical systems in the form of vibration isolators, suspension components, seals, o-rings, gaskets etc. Finite element analysis (FEA) is a common tool used in the design and development of these components and hyperelastic material models are used to describe these polymer materials in the FEA methodology. The quality of the CAE carried out is directly related to the input material property and simulation technology. Nonlinear materials like polymers present a challenge to successfully obtain the required input data and generate the material models for FEA. In this brief article we review the limitations of the hyperleastic material models used in the analysis of polymeric materials.
Theory:
A material model describing the polymer as isotropic and hyperelastic is generally used and a strain energy density function (W) is used to describe the material behavior. The strain energy density functions are mainly derived using statistical mechanics, and continuum mechanics involving invariant and stretch based approaches.
Statistical Mechanics Approach
The statistical mechanics approach is based on the assumption that the elastomeric material is made up of randomly oriented molecular chains. The total end to end length of a chain (r) is given by
Where µ and lm are material constants obtained from the curve-fitting procedure and Jelis the elastic volume ratio.
Invariant Based Continuum Mechanics Approach
The Invariant based continuum mechanics approach is based on the assumption that for a isotropic, hyperelastic material the strain energy density function can be defined in terms of the Invariants. The three different strain invariants can be defined as
I1 = l12+l22+l32
I2 = l12l22+l22l32+l12l32
I3 = l12l22l32
With the assumption of material incompressibility, I3=1, the strain energy function is dependent on I1 and I2 only. The Mooney-Rivlin form can be derived from Equation 3 above as
With C01 = 0 the above equation reduces to the Neo-Hookean form.
Stretch Based Continuum Mechanics Approach
The Stretch based continuum mechanics approach is based on the assumption that the strain energy potential can be expressed as a function of the principal stretches rather than the invariants. The Stretch based Ogden form of the strain energy function is defined as
where µiand αi are material parameters and for an incompressible material Di=0.
Neo-Hookean and Mooney-Rivlin models described above are hyperelastic material models where, the strain energy density function is calculated from the invariants of the left Cauchy-Green deformation tensor, while in the Ogden material model the strain energy density function is calculated from the principal deformation stretch ratios.
The Neo-Hookean model, one of the earliest material model is based on the statistical thermodynamics approach of cross-linked polymer chains and as can be studied is a first order material model. The first order nature of the material model makes it a lower order predictor of high strain values. It is thus generally accepted that Neo-Hookean material model is not able to accurately predict the deformation characteristics at large strains.
The material constants of Mooney-Rivlin material model are directly related to the shear modulus ‘G’ of a polymer and can be expressed as follows:
G = 2(C10+ C01) …………………………….…(6)
Mooney-Rivlin model defined in equation (4) is a 2nd order material model, that makes it a better deformation predictor that the Neo-Hookean material model. The limitations of the Mooney-Rivlin material model makes it usable upto strain levels of about 100-150%.
Ogden model with N=1,2, and 3 constants is the most widely used model for the analysis of suspension components, engine mounts and even in some tire applications. Being of a different formulation that the Neo-Hookean and Mooney-Rivlin models, the Ogden model is also a higher level material models and makes it suitable for strains of upto 400 %. With the third order constants the use of Ogden model make it highly usable for curve-fitting with the full range of the tensile curve with the typical ‘S’ upturn.
Discussion and Conclusions:
The choice of the material model depends heavily on the material and the stretch ratios (strains) to which it will be subjected during its service life. As a rule-of-thumb for small strains of approximately 100 % or l=2.0, simple models such as Mooney-Rivlin are sufficient but for higher strains a higher order material model as the Ogden model may be required to successfully simulate the ”upturn” or strengthening that can occur in some materials at higher strains.
REFERENCES:
ABAQUS Inc., ABAQUS: Theory and Reference Manuals, ABAQUS Inc., RI, 02
Attard, M.M., Finite Strain: Isotropic Hyperelasticity, International Journal of Solids and Structures, 2003
Bathe, K. J., Finite Element Procedures Prentice-Hall, NJ, 96
Bergstrom, J. S., and Boyce, M. C., Mechanical Behavior of Particle Filled Elastomers,Rubber Chemistry and Technology, Vol. 72, 2000
Beatty, M.F., Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers and Biological Tissues with Examples, Applied Mechanics Review, Vol. 40, No. 12, 1987
Bischoff, J. E., Arruda, E. M., and Grosh, K., A New Constitutive Model for the Compressibility of Elastomers at Finite Deformations, Rubber Chemistry and Technology,Vol. 74, 2001
Blatz, P. J., Application of Finite Elasticity Theory to the Behavior of Rubber like Materials, Transactions of the Society of Rheology, Vol. 6, 196
Kim, B., et al., A Comparison Among Neo-Hookean Model, Mooney-Rivlin Model, and Ogden Model for Chloroprene Rubber, International Journal of Precision Engineering & Manufacturing, Vol. 13.
Boyce, M. C., and Arruda, E. M., Constitutive Models of Rubber Elasticity: A Review, Rubber Chemistry and Technology, Vol. 73, 2000.
Srinivas, K., Material Characterization and FEA of a Novel Compression Stress Relaxation Method to Evaluate Materials for Sealing Applications, 28th Annual Dayton-Cincinnati Aerospace Science Symposium, March 2003.
Srinivas, K., Material Characterization and Finite Element Analysis (FEA) of High Performance Tires, Internation Rubber Conference at the India Rubber Expo, 2005.
Design Development and Finite Element Analysis (FEA) of Torque Arm Bush Mount for Heavy Truck Applications
Abstract:
A Torque Arm Bush is a metal-elastomer bonded component that forms an integral part of a heavy truck bogie or suspension system. Many different designs exist in the market today and each one with its own unique geometry, material and load application conditions. This analysis demonstrates the hyperelastic material characterization testing, material constant generation and FEA on the component to predict the service performance.
Methodology:
The physics involved in the simulation are complex and can be summarized as follows:
Elastomer performance is markedly non-linear.
Loading conditions like axial, radial, conical, torsional must be defined in multiple steps as per the service conditions and loading cycles.
Large strain deformation with contacts
Figure 1: Hyperelastic Material Characterization Testing Figure 2: FEA Model of the Torque Arm Bush Mount Assembly
Approach:
Material Study and Characterization to understand static and dynamic material properties.
Develop material constants and design concepts based on load-deflection and performance characteristics.
Use Finite Element Analysis (FEA) to optimize the design and understand FMEA.
Provide assembly modeling & drawings for prototype manufacturing.
Figure 4: Deformed Shape and Stress-Strain Distribution in the Torque Arm Bush Mount
Results and Discussion:
The principal deformation modes of a heavy duty suspension component were modeled in Abaqus using hyperelastic analysis. High stresses were noted along the curvature locations in the design under conical deformations and confirmed by fatigue testing. This locations were identified as ‘hot-spots’ and are fatigue-critical locations. The geometrical and material parameters were optimized to better mitigating the stresses and reduce the fatigue failures.
References:
Dassault Systemes, Abaqus theory and reference manuals
Yunhi, Yu, Nagi G Naganathan, Rao V Dukkipati, A literature review of automotive vehicle engine mounting systems, Mechanism and Machine Theory Volume 36, Issue 1, January 2001.
Srinivas, K., Material Characterization And CAE For Non-Metallic Materials & Manufacturing Processes, SAE Symposium on CAE Applications for Automotive Structures, Detroit, November 2005.
Technicals:
Advanced Softwares like Abaqus, Static testing machines are available in-house and design iterations can be carried out on the fly.
Full material characterization capabilities of polymeric materials for FEA
Capabilities for fatigue durability testing In-house.
Advanced material testing facilities like DMA, DSC, TGA and TMA also available.
