virtual medical device optimization using abaqus · keywords: design optimization, optimization,...

2005 ABAQUS Users’ Conference 1

Virtual Medical Device Optimization using ABAQUS

Torben Strøm Hansen

Novo Nordisk A/S

Protein Delivery Systems – Device Research & Technology, Brennum Park DK-3400 Hilleroed, Denmark

In the development of medical devices, safety, robustness and reliability are crucial and have major priority. It is essential to be able to predict these device characteristics at the early development stages. Prediction and verification of the device functionality relied on iterative manufacturing and testing of hardware prototypes through many years. It still remains a challenge to provide prototypes with similar mechanical properties as those of the final components. Constitutive material behavior and frictional properties of the produced parts are usually different from those of the prototypes due to the nature of the manufacturing processes: Injection molding in running production versus the machining processes and simplified molding of the prototypes. This paper exemplifies how a virtual ABAQUS prototype including both non-linear instantaneous and viscoelastic polymer material response provides data that saved numerous prototype testing iterations. It will be shown how this model has been used in the process of mechanism optimization.

Keywords: Design Optimization, Optimization, Viscoelasticity, Polymer, Hyperelasticity, Dynamics, Creep

1. Introduction

1.1 Subject of the analyses

The FlexPen® is a multiple use pre-filled dial-a-dose insulin pen device. The pen is purely mechanically operated and designed for primarily domestic use by diabetics worldwide. The user interface aims at simplicity and ease of use. The user simply attaches a sterile needle to the device, sets the desired insulin dose followed by injection – typically in the abdomen. During the injection, the user depresses the push button as shown in Figure 1. It is of the outmost importance that the force required for this operation is limited as much as possible. Thus all mechanical subsystems interacting during the injection are optimized one by one. This paper deals with the Ratchet – Nut subsystem which by rotation of the Ratchet in the fixed Nut provides indexing of the dose and secures that no reverse flow through the needle occur.

2 2005 ABAQUS Users’ Conference

1.2 The analysis objective

During the medication injection, the Ratchet rotates in the Nut forcing oscillation of the Ratchet arms in the teethed Nut and thus bend like a tip loaded cantilever beam. This sequence creates audible clicks, enabling the user to hear the number of unit doses injected. To secure correct operation of the Ratchet, both arms are slightly pre-stressed in the teethed Nut so the tip of the arms will engage with the bottom of the tooth for each operation cycle. The cyclic forced deformation of the Ratchet arms (10 – 40 Hz) causes a time dependent stress response and a rippling reaction moment. Since this interaction is one of the major contributors to the overall dosing force of the FlexPen, it should be as limited and as predictable as possible. The existing design already has an optimized reaction moment at a given rotational velocity.

The objective is to optimize this Ratchet design further to make its mechanical operation less influenced by pen-injection velocity and storage time by limiting the viscous part of the stress response which will narrow the damping and stress relaxation.

2. Material characterization

2.1 Test approach

The Ratchet is manufactured by polymer injection molding in multi-cavity molds for high volume production. The selected material is an acetal copolymer grade (POM). As for many other technical polymers, the selected POM resin has both a non-linear steady state and a strain rate dependent stress response at large strains and cyclic loading. The inevitable hysteretic energy dissipation is most unwanted in the Ratchet design, since it has a damping effect on the action of the Ratchet arms in the Nut causing rotational velocity dependence. Figure 2 shows the hysteretic stress response of the POM grade when subjected to different triangular loading – unloading schemes. The hysteresis is caused by viscous dissipation which also occurs in the Ratchet arms during the cyclic displacement. Extensive material testing was consequently required to characterize the steady state and time dependent response. The course of the data generation and implementation was:

• Selection of applicable constitutive models for numerical implementation

• Define material test type, setup and test series

• Numerical implementation

• 1-element and multi element model vs. test data verification

A test setup using ISO 527 tensile bars mounted in a high speed Instron elastomer tensile test bench (Figure 3) was used. The bench was equipped with proper load cells, extensometers and a climatic chamber. The uni-axial approach is only valid if the Poisson’s ratio remains constant throughout the strain range specified in both compression and tension, which required a number of runs using dual extensometers for the sampling of the longitudinal and transversal straining. After verification of a constant Poisson’s ratio within the specified temperature, humidity and strain


range, the test series were defined. All the test series were performed at both room temperature and at elevated environmental conditions at each extreme of the product specification. For the non-linear steady state response in Figure 4, a low strain rate of 0.5 %/s was selected. For the relaxation measurement a strain rate of 150 %/s was used to quickly ramp the strain to a given level for the monitoring of the time dependent response of Figure 5.

2.2 Numerical implementation

For the steady state response a hyperelastic constitutive model was used. The uni-axial test data of Figure 4 were implemented by using *Uniaxial Test Data. By pre-processing the input file, those test data could be compared with data from several of the material models available in ABAQUS. Data from two optional models are plotted together with the test data in Figure 4. Best fit was obtained using a second order polynomial formulation with a predefined Poisson’s ratio:

*Hyperelastic, n=2, test data input, poisson=0.4.

The time dependent stress response was characterized by implementing the viscoelastic material model:

*Viscoelastic, time=PRONY

In ABAQUS, the Prony series represents the relaxation behavior of the bulk modulus and the shear modulus. Assuming similar relaxation of the two deformation modes, the terms of the Prony series were given by the values found from the uni-axial tensile test data by curve fitting. The Prony series representation can thus be written in terms of the time dependent modulus E(t) as:

−−= ∑=

−N

n

tPn

neeEtE1

/ )1(1)0()( τ

The test sample is subjected to a step strain similar to the peak strain of the Ratchet. The relative modulus e = E(t)/E(0) is plotted for the sampled relaxation data, and compared to the 1-term and the favoured 2-terms Prony parameters found from curve fitting in Figure 5. The 2-term series had a satisfactory fit. These parameters can also be provided by pre-processing test data in ABAQUS. Repeating the relaxation test for a number of strain levels, showed that the relaxation for this polymer is much strain level dependent: For high strain levels the relaxation became more dominant. Thus the Prony parameters had to be chosen from a given strain level relaxation test since the ABAQUS model is linear Viscoelastic. The peak strain relaxation results chosen for this analysis will cause overestimation of the mean stress relaxation of the time span of the analysis. Component reference testing has shown that the selected approach is applicable for relative comparison of different part versions.

3. Geometry optimization

It is now obvious that by reducing the peak strain level, both the unwanted viscous dissipation (damping of the Ratchet arms) and the stress relaxation (pen storage influence to the overall behavior of the Ratchet) can be reduced. The peak strain level of the flex arms of the Ratchet can be reduced by changing the geometry towards a prolonged shape without disturbing the reaction force vs. displacement characteristic of the Ratchet arms.


3.1 Room of improvement demarcation by problem simplification

The Ratchet arm was initially approximated by a simple cantilever beam as shown in Figure 6. The intention was to keep the compliance of the arm constant while reducing the peak strain causing the viscous dissipation. The relation between the beam compliance and the length and height of the beam can be derived from the Bernoulli equation for the vertical tip displacement uy and the resulting reaction Rf :

From EIlR

u fy 3

3

= the compliance proportionality can be derived as: 3

3

hl

Ru

f

y ≈

The relation between the peak strain εp of the beam and the length l, width w and height h of the beam can also be derived from the cantilever equation:

From EwhlRf

p 2

6=ε the peak strain proportionality is:

2hl

p ≈ε

Consequently strain reduction can be gained by increasing the length and height of the Ratchet arms by the same rate for fixed compliance values. A simple parametric optimization model was defined in the CAD integrated FE-code. A preliminary analysis indicated a significant peak strain reduction of 40 % by extending the length and width as shown in figure 7. The resulting geometry was transferred to ABAQUS for virtual validation of the stress relaxation and dynamic behaviour of the optimized design.

4. ABAQUS models

4.1 Quasi-static model for Ratchet arm relaxation analysis

The objective of this analysis was to evaluate the stress relaxation influence to the reaction force of the Ratchet arms when subjected to the assembly pre-stressing. A quasi-static model using the ABAQUS/Standard *Visco procedure allows time-dependent material response by implementation of explicit time integration. Both the *Viscoelastic and *Hyperelastic material models were implemented for this analysis. By applying a forced displacement similar to the assembly pre-stress to a rigid surface contacting the tip of one arm, the dissipated energy and reaction force can be monitored as a function of storage time and compared to the original design. Figure 7 shows the model and that the major part of the energy dissipation takes place in the early stage of the quasi instantaneous displacement. The reduction of the peak strain level has caused a reduction of 32% of the energy dissipation of Figure 8. The experimental verification setup is shown in Figure 9, where the forced displacement is applied by a probe attached to a tensile test bench. The effect of the relaxation to the pre-stress force can be monitored by sampling the load cell output.

4.2 Dynamic model for reaction moment of the improved design

The purpose of this analysis was to analyze the dynamic behavior improvement of the optimized Ratchet. When the Ratchet rotates in the Nut and the arms are displaced in a cyclic manner


causing interaction between inertia and elastic forces. Even though the strain energy share of the total energy is dominant at all times during the cycle, the kinetic energy can not be disregarded. ABAQUS/Explicit was chosen for the dynamic model depicted in Figure 10. The Ratchet was modeled as 3D solid and C3D10M tet meshed. The teethed Nut was modeled as analytical rigid. The discretization was refined until a strain gradient comparable with that of the quasi-static analysis was obtained. To impose the assembly pre-stress, artificial forces were imposed on each of the Ratchet arms in the first step and then released in the second step after turning the Ratchet-Nut contact surfaces on. The resulting impact would usually create substantial noise, but the viscoelasticity imposed an excellent damping which also helped to keep the reaction moment output signal stable at all times. From a prescribed rotational velocity, the resulting reaction moment was plotted (Figure 10). The reaction moment for both designs was almost identical, but the viscous dissipation plotted in Figure 11 differed between the two designs. The optimized design dissipated less energy than the original causing a reduced level of damping. The experimental test setup for the dynamic response for data verification is shown in Figure 12.

4.3 Implementation in the complete device model

After assessing the optimization impact to the rotational reaction moment of the Ratchet-Nut subsystem on component level, the Ratchet was implemented in an ABAQUS/Explicit full system model of the FlexPen. This model contains all interacting mechanical parts from the dosing button to the Ratchet and is used to quantify the contribution of each mechanical sub system to the overall dosing force applied by the user. By prescribing a forced displacement to the dosing button, the resulting translatory movement is transferred to a rotational movement of the Ratchet through a thread on a scale drum as shown in Figure 13. One second of the dosing operation was analyzed using limited mass scaling which only influences elements of stagnant parts. A mixture of analytical and discrete rigids together with elastic solids is used to save computational time. The reaction force caused by the forced displacement was chosen as the guiding qualification parameter of the system. Implementing the optimized Ratchet in this model verified that the dosing force plotted in Figure 14 had become less velocity dependent than with the original design.

5. Future model improvements and next step

Injection molded polymers are much influenced by the process parameters (injection pressure, packing pressure and thermal effects). As a consequence residual stresses and orthotropic material properties are inevitable in an injection molding process. Injection molding process analysis data transferal to ABAQUS would thus be an obvious next step. Pilot analyses have been defined for integration of Moldflow data in ABAQUS.

Many polymers such as the POM grade used for the Ratchet exhibit non-linear strain dependent viscoelasticity. Implementation of non-linear viscoelasticity in ABAQUS will significantly improve the relaxation prediction of large strain analyses such as this.

Machining and testing of the existing Ratchet has initially verified the impact of the design change. New injection molds based on the ABAQUS optimization analyses results are now being manufactured for production of samples for final validation.


6. Conclusion

Limiting the peak strain successfully decreased both the stress relaxation and viscous damping. Accordingly the pre-stress stability has been improved and the device injection velocity dependence substantially reduced. Both the quasi-static and dynamic analyses have provided core data for assessing the optimization impact. The hyperelastic and viscoelastic material models have been viable for characterizing the polymer material response in the relative assessment of dynamic Ratchet response and stress relaxation improvement from original to enhanced design. Using ABAQUS in the optimization procedure has directly led to a much improved design which could not have been achieved from traditional trial and error methods and has also saved numerous prototype manufacturing and test cycles. Using the knowledge gained in this study will enable Novo Nordisk to simulate large strain dynamic polymer component behavior much more accurately.

7. References

Brüeller, O.S. and Schmidt, H.H., “On the Linear Viscoelastic Limit of Polymers – Exemplified on PMMA” Polymer Engineering and Science, September 1979 vol. 19.

Kolberg, Raymond, “Mechanical Response of Beams of a Nonlinear Viscoelastic Material”, Polymer Engineering and Science, January 1995.

ABAQUS 6 Version 6.4 documentation


8. Acknowledgements

I would like to thank Lars P. Mikkelsen of Risø National Laboratory, Materials Research dept. for his contribution in both the test planning phase and on the test execution. The FlexPen team of Novo Nordisk has provided excellent reference test data on the different sub-systems of the pen. Furthermore Jan Granlund of ABAQUS Scandinavia has advised on model refinement and material model selections which is most appreciated.


9. Figures

Figure 1 The FlexPen and the selected sub system: The Ratchet – Nut

Push Button operated by the user

The Nut

The Ratchet

FlexPen®


Figure 2 The hysteresis of ramp loaded and unloaded polymer samples (POM) at different strain levels

Figure 3 Tensile testing using a high speed elastomer tensile test bench

ISO 527 tensile bar

T-extensometer

Ramp loaded samples At 0.5 kN/s


Figure 4 ABAQUS evaluation of steady state tensile test data (Polynomial and Ogden models) for the Hyperelastic model

Figure 5 Fitting of Prony series parameters of the Viscoelastic model to relaxation test data where the modulus e = E(t)/E(0) is plotted vs. time for


Figure 6 Equivalent Cantilever Beam approach

Figure 7 The static peak strain level of the original and optimized design

u y y

lx


Figure 8 ABAQUS Model for stress relaxation analysis

Figure 9 Experimental verification of the relaxation effect to the pre-stress force of the Ratchet arm

Optimized design

Original design

Probe attached to a tensile test bench


Figure 10 The Ratchet subjected to a prescribed rotation velocity of 8 radians per second and the resulting reaction moment

Figure 11 Viscous dissipation of the Ratchet during rotation of the original “X” and the optimized “O” design at 8 radians per second


Figure 12 Experimental verification of the dynamic response of the Ratchet. Forced rotation is applied by the bench and the reaction moment is sampled from a load cell

Figure 13 Full system model of the FlexPen for the analysis of the required dosing force

Housing modeled as elastic solid

Small diameter parts modeled as discrete rigid

Forced displacement imposed on an analytical rigid top surface


Figure 14 Full system reaction force response

virtual medical device optimization using abaqus · keywords: design optimization, optimization,...

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