Themenschwerpunkt: Simulation im Konsumgüterbereich

11Infoplaner 01/2010

Finite elements modeling provides an im-portant contribution to the developmentprocess at Audemars Piguet & Cie SA. Vir-tual prototyping is used to anticipate di-mensioning problems and therefore reducethe number of prototypes.

Amongst the wide range of componentsconstituting a bracelet watch, three keymechanisms are presented below as exam-ples where numerical simulation is usednowadays.

Optimization of a Date Mechanismwith ANSYS/LS-DYNAFigures 1a and 1b show the mechanismthat allows changing the date display every24 hours. This mechanism is composed ofthree main parts;

The mechanisms used in this study belong exclusively to

Audemars Piguet & Cie SA (www.audemarspiguet.com).

Pictures: Audemars Piguet & Cie SA

1. The display disc2. The trigger bloc (that stores

energy and transfers it to the display disc)

3. The jumper bloc (that brakes the display disc)

A cycle of this mechanism starts withthe loading of the trigger spring.When the date has to change, thecam blocking spring releases the pinand the potential energy stored in thetrigger spring rotates the cam and itsfinger that pushes a tooth of the dis-play disc. The resulting rotation of thedisplay disc is braked by the jumper

and its spring so that only one tooth passesthe jumper and therefore the date chan-ges by only one increment.

The complexity of this mechanism residesin the need of setting and balancing theway the energy is released by the triggerstring and the way the energy is dissipatedin the jumper bloc so that the date changeoccurs instantaneously to the eye (typical-ly within 0.015 s) but robustly enough sothat the display never jumps a date.

The geometrical shapes of the jumperspring, the jumper and the trigger springwere optimized with a three dimensional

Time for ANSYSDimensioning and Optimization of Flexible Watch Industry MechanicalComponents with ANSYS/LS-DYNA, ANSYS Workbench and optiSLang

Watch industry mechanisms involve a large number of high precision flexible pre-constrained mechanicalcomponents. Using traditional prototyping, the definition of non-deformed geometries for production is acostly manual iterative process. The use of non-linear finite elements modeling improves this process and thecoupling of the finite elements codes to a stochastic optimization toolbox like optiSLang makes it automaticand more robust.

Fig. 1a: Loaded date mechanism at time t=0.01s.

(display disc diameter = 12 mm

Fig. 1b: Zoom on the trigger bloc (cam diameter = 2.2 mm)

12 Infoplaner 01/2010

Themenschwerpunkt: Simulation im Konsumgüterbereich

dynamic model created with ANSYS/LS-DYNA (fig. 1). The calculated angularvelocity of the display disc (fig. 2) shows apositive acceleration of the disc by the trig-ger bloc (a-b), a sudden reversed accele-

ration when tooth 2 (fig. 1a) bounces onthe steep face of the jumper (b-c), a posi-tive acceleration again when tooth 1 tou-ches the jumper again (c-d) and a final sta-bilization between teeth 1 and 2 (d-e). Theloading moment of the trigger spring wasmeasured experimentally and is in goodagreement with the simulated values (fig.3). Furthermore, the pre-series mechanismthat was produced based on the designobtained with ANSYS/LS-DYNA has fulfil-led acceptance criteria and allowed laun-ching production without any further pro-totype.

Force Tuning of a Set Time Mechanismwith ANSYS Workbench and optiSLangFigure 4 shows the set time mechanismconnected to the pull-out button of awatch. The button actuates a winding shaftthat can be pulled up to its stop position;its rotation then allows time setting. Thewinding shaft is connected to the pull-out

ces set within 2% of the required valuewhile the maximum stress was 10% smal-ler than the value calculated with the in-itial geometry (fig. 5). The mechanism wasproduced and fulfilled expectations.

Robust Design Optimization of a Glass Driving Process with ANSYS Work-bench and optiSLangTightness between glass and watch-caseis ensured by a flexible joint (fig. 6). Theforce needed to remove the glass has tobe maximized whereas the force requiredto drive the glass should be minimized.Plastic deformations in the joint (fig. 7) aswell as stresses in the glass and watch-caseshould also be minimized.

piece via a pin. The pull-out piece can ro-tate on a fixed axis but is constrained bythe spring that pushes on a pin at its endand therefore sets its actuation moment.The maximum traction force on the win-

ding-shaft has to be 5N in order to ensurea good sensitivity when pulling with thefingers on the set time button. At the sametime, stresses in the spring have to remainbelow the yield strength.

A two dimensional parametric model ofthe spring and its non-linear frictionalcontact with the pin of the pull-out piecewas created with ANSYS Workbench andcoupled to optiSLang via the optiPlug in-terface. This allowed to run an automaticparametric optimization of the spring‘sshape based on eight geometrical inputparameters and three objectives:1.Set the traction force2.Set the pulling force3.Minimize structural stresses

The optimization algorithm chosen was anadaptive response surface method. After91 automatic design evaluations, the re-sulting design had traction and pulling for-

Fig.5: Spring initial shape (left) and tuned shape (right). The

pin of the pull-out piece is at the force inversion position

where stresses reach their maximum. The positioning and

angle of the two flat contact faces of the spring determine

the pull and push forces.

Fig. 2: Display disc angular velocity. A positive velocity means

a clockwise rotation on figure 1a.

Fig. 3: Comparison between simulated and measured trigger

bloc moments.

Fig. 4:

Set time mechanism

Themenschwerpunkt: Simulation im Konsumgüterbereich

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A quasistatic two dimensional axisymmetricparametric model was created with ANSYSWorkbench and coupled to optiSLang inorder to run three different analyses on themodel:

1.A sensitivity analysis2.A Pareto optimization3.A robustness analysis

Amongst a list of 16 geometrical inputparameters (dimensions of glass, joint andwatch body), the sensitivity analysis de-livered a list of 8 most important geome-trical dimensions. According to the statis-tical linear coefficient of importance cal-culated by optiSLang, these parameters de-termine 86% of the maximal withdrawalforce, 77% of the maximum glace stressand 65% of the joint maximum plasticstrain. In addition to the selection of asubset of most relevant parameters,the sensitivity analysis allowed togain understanding of the physi-cal system. For instance, the cor-relations between outputs canbe seen at a glimpse in theoptiSLang post processing.In this case, output va-lues that have to be mi-nimized (stresses andstrain) and the out-put value that hasto be maximized(removal force) arepositively correla-ted between eachother, which meansthat attempting to maxi-mize the force will also maxi-mize the stresses and strains.

In addition to this intuitive qualitative sta-tement, optiSLang delivered quantitativecorrelation values that helped defining ob-jective functions for the optimization.

Due to these output parameters correla-tions, a Pareto optimization with twoobjective functions was chosen; the firstobjective is a weighted function of theremoval force and of the difference bet-ween driving and removal force. The se-cond objective function is simply the sumof stresses in the watch-case and in theglass. After 209 design evaluations, theresult of this optimization, based on anevolutionary algorithm, is a Pareto frontwith designs that minimize both objectives(fig. 8). In this case, the choice of a best

design along this front is motivated by theneed to increase the force (move towardsthe left) while maintaining the stress lowenough (move down on the graph).

After having selected a candidate designon the Pareto front, a robustness analysiswas run for this design. Probability densi-ty functions were defined for each inputparameter, including material properties.The resulting output parameter probabili-ty density functions could then be inte-grated in optiSLang in order to get the pro-bability of being higher than a given stressthreshold. This failure probability givesquantitative information on whether thedesign is sufficiently robust or not. In thiscase, the failure probability of designnumber 203 was 20% for gold (inaccep-table) and negligible for steel (see 250 MPalimit on the probability density function offig. 8).