Simulating Nonlinear Materials under Centrifugal Forces by using Intelligent Cross-linked Simulations

*Corr. Author’s Address: Department of Engineering Design and CAD, University of Bayreuth, 95440 Bayreuth, Germany, konstruktionslehre@uni-bayreuth.de 531 Simulating Nonlinear Materials under Centrifugal Forces by using Intelligent Cross-linked Simulations Hackenschmidt, R. ‒ Alber-Laukant, B. ‒ Rieg, F. Reinhard Hackenschmidt*, Bettina Alber-Laukant, Frank Rieg University of Bayreuth, Department of Engineering Design and CAD, Germany


INTRODUCTION
Classical claw couplings (Fig. 1) are flexible and designed for positive torque transmission.They are fail-safe.Operational vibrations and shocks are efficiently dampened and reduced with the use of an elastomeric insert element to be located between metal parts.The two congruent coupling halves with concave claws on the inside are peripherally offset in relation to one another by half a pitch.

Fig. 1. Standard Claw coupling
To broaden the clutches technical field of application for up to 40,000 rpm high-speed rotating drive-trains, the question of material distortion both under centrifugal / torque and compression load has to be investigated.To avoid costly hardware experiments, the development of an effective simulation solution, also transferable to a wide range of couplings with different nominal torques had top priority.
As the use of a variety of different computer-aided tools (CAx-tools) e.g. for strength of material and manufacturing simulations is necessary for a useful outcome, the methodical approach based on Intelligent CROss-linked Simulations (ICROS) was chosen to optimize the virtual simulation process chain as presented in subsequent sections of this paper.

RELATED RESEARCH
Product development as a whole consists of many sub-processes that have to be performed in specific order.These processes are also iterative and linked to certain product-specific data.By a detailed analysis of these processes, their functionalities and complex interactions can be uncovered.There were many attempts to improve the product development processes in industry, from traditional phase-gate approach [1] to more efficient set-based concurrent engineering [2].
In order to achieve a better organisation and an efficient use of available product development, computer-aided tool, the Artificial Intelligence (AI), has been extensively applied [3] to [5], along with other multi-criteria analyses [6] and [7].
Despite all the proven benefits of modern engineering software, one of the main problems existing today in the development process is the Babylonian-like system variety and complexity.On the one hand, as discussed in [8], the conflicts in-house use of multiple systems, programs and simulation tools may lead to coordination problems.
On the other hand, the complexity of global supplier structures with their own simulation systems also creates significant handling problems (Fig. 2).
When designing complex products, often various special analysis tools need to be applied [10].Moreover, sometimes even different shape models representations are needed to perform the analysis [11].In addition, the existing sequence of simulation tools does not adequately model fibre reinforced polymer parts [12].
Depending on their relations single subprocesses can be composed to complete processchains up to adequate support during the post-processing phase by the use of e.g.intelligent rule-based consultative system [13].
It can be concluded that the achievement of adequate coordination of multiple simulation programs still represents a bottleneck in the product development process.

ICROS
To ensure a reliable accomplishment of product development by using multiple simulation programs ICROS recommends to organize the procedural method following the widespread four step engineering design approach according to Pahl/Beitz [14] or the VDI 2221 [15].This basic approach only has to be adapted from product design in a way that it can support process design [16]: Fig. 2. Complex simulation tool environment [9] Simulating Nonlinear Materials under Centrifugal Forces by using Intelligent Cross-Linked Simulations A detailed discussion about the application of methods, processes and instruments is made in advance.This approach stimulates the use of adequate virtual design tools already in the early phase of the overall process.
In the same way, it also determines the criteria and information that has to be carried along the way through all the design and simulation steps.With qualified information about the simulations needed and the CAxsoftware available decisions about either reserving capacities in the in-house CAE-department or the necessity for contacting external service providers, is facilitated.This is fundamental for developing generic simulation process chains, and also for the outline of a project-based workflow and timeline.
Detailed decisions about programs, operating systems and adequate hardware have to be made under the viewpoint of necessary functionality and existing system environment.It is fundamental to know the detailed program capacity and coverage of internally available or even externally used programs.If, for example, a part out of a material with non-linear behaviour has to be developed, the simulation tool needs to be able to cope with inhomogeneous material.
The results of the examinations have to be fixed to all necessary details, in corresponding worksheets.This ranges from correct exportand import-formats, including corresponding settings, to detailed support in order to resolve interdependencies of results or design tasks.These should be provided on an effective level of granularity to take account of software-and userspecific circumstances.They can be combined to form a holistic environment, which is used in this specific development task.The abstraction to a generalized and certifiable process chain later on is easily possible.
This will lead to a dramatic improvement in coping with challenging tasks, especially in today's multinational and complex relations between customers and tiers.The precise analysis of the main tasks to be performed in this complex development process determines that especially the simulation phase itself has to be supported by documents that help the designer to choose the right simulation features or, if experienced designers are involved, represent special topics seldom used or critical (Fig. 3).In this way, also internal regulations or legal restrictions can be provided on the spot after a full ICROS-schema is developed.The design of a claw coupling with elastomeric damping elements is a challenging task, especially if high speed rotational frequencies are claimed for its application.Without doubt, the specification list according to Pahl/Beitz [14] is a basic prerequisite for the engineering task as here all the technical needs have to be defined.
The discussed clutch application assumes mainly correct dimensioning of the polymer part.Hence, there is a need for adequate computeraided simulation tools to predict the material behaviour.
As polymers are widely non-linear in their characteristics, in the first ICROS step the variety of software to be considered has to be selected.Table 1 shows a representative list.The list has to be verified and completed by other necessary programs to meet all requirements in regard to all the simulation needs.In the second ICROS step the simulation program requirements for the entire simulation chain were discussed and fixed for all the necessities of the project: • centrifugal force load calculation, • mould injection behaviour, • displacement simulation, • die casting mould machining.
This leads to a well-defined list of programs (Table 2), which are of course adjustable and adaptable due to the companies' standards and prerequisites.

Fig. 4. Standard process workflow for polymer simulation processing
A typical simulation program flow suggestion for such an engineering design problem can be found in ICROS´standardized workflow diagrams and has to be adapted to the concrete task in the third ICROS step (Fig. 4).
The classical approach along the ICROS path with modelling the clutch in the 3D-CAD system followed by a linear FEM calculation under high rotation speed (28,000 rpm) plus torque load (60 Nm) of the charged insert-clutchcontact areas lead to fundamental results (Fig. 5).

Fig. 5. First simulation results
Firstly, due to the rotation load, the displacement areas show significant radial deformation of the elastomeric insert.Secondly, the torque burdened areas are partially disabled in their distortion; that is the reason why the appropriate regions differ from the others.These results represent the reality very well in principle, but unfortunately the absolute figures as seen in Table 3 are some order of magnitudes too high as compared with a physical high speed test on a specially developed high speed test bench.Here, it was a great challenge to measure the radial polymer deformation values at the clutch while rotating up to 40,000 rpm.It was realized by the use of a light beam in combination with a highly sensitive photo cell, delivering the strength Simulating Nonlinear Materials under Centrifugal Forces by using Intelligent Cross-Linked Simulations of current according to the real deformation peak of the elastomeric element.Not only maximum but also enduring distortion and time dependent creeping effects could be measured very precisely.

Fig. 6. High-speed test bench
To ensure reliable simulation results, it was found that the use of linear material parameters determined out of standard pulling tests as provided e.g. by the producer of elastomeric materials, do not fit the real material values.The explanation lies in the specific material behaviour: For reasons of expense, thermoplastic elastomers (TPE) are used.These materials are either copolymers or physically mixed polymers.
Compared to common thermoset elastomers with chemical bonding these special thermoplastic elastomer blends have physically cross linking depending on their hard/soft segmentation of the blend components (see Figs. 7a and b).Therefore, by room temperature and moderate forces they act like real elastomers only with the help of semi crystalline agglomerations and the resulting van der Waals forces.
The properties lie between both materials thermoplastic and elastomers (see Fig. 7c).
In spite of elastomers the production of TPE is quite simple owing to the use of standard injection moulding processes (Fig. 8).Nevertheless, the most important difference between thermoset elastomers and thermoplastic elastomers is the type of the cross-linking bond in their structures.The cross-linking mechanism of TPE strongly depends on the fabrication process and differs substantially.The behaviour cannot be simulated in its complexity.To ensure that TPE´s behaviour is neither linear elastic nor viscoelastic, an additional simulation with a hyperelastic material model was done which produced more realistic results but they did not fit the above pattern at all.The chosen material model is a hyper elastic model of Ogden which depends on the principle stretch ratios λ i .
and α i , μ i , D i are to be determined from experimental test data [17].Additionally, known hardening effects of elastomeric parts under pressure load [18] led to a conclusion that for the investigated clutch part, a specific determination of the material parameters is indispensable.

Fig. 8. Insert mould process simulation results
Hence, a part specific pulling rig was developed for the use on a standard Zwick testing machine (Fig. 9).

Fig. 9. Insert pulling rig
The resulting material parameters served as mapping basis for the FEM model in an adequate non-linear FEM tool.The comparison of the results shows that the simulation data are very close to the measured reality, leading to the manufacturing approval of the mould forms and materials procurement.It should be stated that some additional improvement loops on behalf of the geometrical attributes of the clutch and insert geometry were also performed.Conducting thoroughly this fourth ICROS step results in the development of a detailed simulation workflow plan perfectly suitable for the task (Fig. 10).

Fig. 10. ICROS high-speed simulation workflow overview
The findings of this specific task according to the simulation tool needs and interactions are added to the general ICROS case database and can be used for related virtual development tasks.

Simulating Nonlinear Materials under Centrifugal Forces by using Intelligent Cross-Linked Simulations
To face these challenges, engineers should have direct contact to the best practices for their current simulation step [19].Ideally, it is essential to provide them with the necessary information according to their respective design experience without constraining their creativity.This case sensitivity could be managed with the help of AI (Fig. 11).

RESULTS AND CONCLUSIONS
Due to the requirement of being able to handle centrifugal forces and distortions resulting from a very high rotating speed applied on nonlinear elastomer, the finding of an optimized virtual simulation tool dedication was investigated.It could be pointed out that material properties can be mapped and scaled to a computer model by a skilled combination of virtual product design and prototype testing using the ICROS method presented.
With the help of adequate methods like AI it should even be possible to come to an automatic case covering detection system to effectively support engineer in developing processes.

•
First step: Clarification and specification of task and simulation needs.• Second step: Conceptual design of the simulation needs.• Third step: Design of the simulation scenario.• Fourth step: Development of a suitable simulation environment.

Fig. 3 .
Fig. 3. Required input data / generated output data for simulation processes

Fig. 7 .
Fig. 7. Conformation and properties of thermoplastic elastomers and thermoset elastomersDifferent material models like Mooney Rivlin, Neo Hooke, Yeoh, Ogden, Marlow or Arruda-Boyce are suitable to deal with the problem.The chosen material model is a hyper elastic model of Ogden which depends on the principle stretch ratios λ i .

Table 1 .
Software selection list excerpt for polymer mechanical stability calculation

Table 2 .
Overall software selection list excerpt

Table 3 .
Simulation vs. experimental results