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Static Model of a Snowboard Undergoing a Carved Turn: Validation by Full‑Scale Test

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Static Model of a Snowboard Undergoing a Carved Turn: Validation by Full‑Scale Test Sports Engineering (2019) 22:15 https://doi.org/10.1007/s12283-019-0307-4 ORIGINAL ARTICLE Static model of a snowboard undergoing a carved turn: validation by full‑scale test Benoit Caillaud1 · Robert Winkler1 · Michael Oberguggenberger2 · Marc Luger3 · Johannes Gerstmayr1 Published online: 5 July 2019 © The Author(s) 2019 Abstract The purpose of this study was to defne a method for the validation of a numerical model representing a snowboard structure undergoing the conditions of a carved turn. A static load bench was developed to expose a snowboard to in-situ conditions. The deformed shape of the structure was measured with the use of retro-refective markers, whose positions in space were tracked by six cameras and determined by triangulation. The experimental set-up was idealized in a fnite element model, representing the composite structure and the loading environment. The model was validated by comparing the measured and computed displacement felds. The congruence between the two deformed surfaces was expressed by statistical means and constitutes the target function for optimization frameworks. Additionally, the contact pressure at the ground interface was experimentally assessed with the use of pressure measurement tape and compared with the numerical predictions. Keywords Snowboarding · Carving turn · FEM · Test validation · Contact pressure · Composite structure 1 Introduction Structural analysis applied to thin-walled structures has been widely used in the past, especially in the aerospace indus- * Benoit Caillaud try. Nonlinear investigation methods applied to composite [email protected] materials have been widely documented [1], and automa- http://www.uibk.ac.at/mechatronik/mekt/ tion techniques have made them afordable yet applicable Robert Winkler to other industrial sectors [2]. Regardless of the applica- [email protected] http://www.uibk.ac.at/mechatronik/mekt/ tion, the reliability of the numerical representations must be assessed through a stringent validation procedure, to control Michael Oberguggenberger [email protected] the quality of the engineering solutions. The development http://www.uibk.ac.at/techmath/ of sports equipment, and more particularly composite snow- Marc Luger board structures, is taken here as an illustration of how the [email protected] manufacturing environment can be numerically represented http://www.uibk.ac.at/mti/ by creating a ‘digital twin’ of the product. Johannes Gerstmayr Previous research on the behavior of snowboard struc- [email protected] tures have proposed models to represent the stifness at rest http://www.uibk.ac.at/mechatronik/mekt/ [3, 4]. In addition, analytical simulations of the dynamics of 1 Faculty of Engineering Sciences, Department a carved turn have been developed [5] and extensive knowl- of Mechatronics, University of Innsbruck, Technikerstraße edge is available to represent the on-snow conditions [6]. In 13, 6020 Innsbruck, Austria these aforementioned studies, the validation of the numerical 2 Faculty of Engineering Sciences, Unit of Engineering models consisted of comparing scalar values of the maxi- Mathematics, University of Innsbruck, Technikerstraße 13, mum displacements under bending and torsional loading 6020 Innsbruck, Austria independently. However, this approach is insufcient since it 3 Faculty of Engineering Sciences, Unit of Material does not guarantee the validity of the entire defected shape. Technology, University of Innsbruck, Technikerstraße 13, Furthermore, it does not account for combined problems 6020 Innsbruck, Austria Vol.:(0123456789) 15 Page 2 of 11 B. Caillaud et al. including contact formulations, as required in the present 2.2 Specimen investigated investigation. The conditions of a carved turn have been pre- viously investigated to qualify the interface loads [7] and the The prototype consisted of a simplifed snowboard structure behavior of a snowboard set on a carving angle [8]. Based manufactured according to the current industrial standards on this work, the present paper proposes a methodology to [9]. The structure featured a 5.55 mm constant thickness validate a mathematical model by comparing the global dis- wood core made out of ash ( 60 mm-wide strip along the placement felds. length of the snowboard, centered in the width) and poplar (remaining area), sandwiched between two composite skins made out of epoxy reinforced fberglass (each 0.665 mm 2 Experimental set‑up thick). The stacking sequence and corresponding fber ori- entations are shown in Sect. 3.2. The snowboard geometry To simulate the loading conditions occurring on a snow- was defned as symmetric twin-tip (two planes of symme- board during a carved turn, a static load bench was devel- try: xz-plane and yz-plane) and the sidecut had a constant oped and measurements of deformations were performed on radius of 7.05 m . The prototype’s geometrical parameters a simplifed snowboard structure. The experimental set-up are reported in Table 1 and illustrated in Fig. 1. is described within this section. 2.3 Static load bench 2.1 Local coordinate system and conventions The test bench developed in-house is represented in Fig. 2. The local coordinate system relative to the snowboard (O xyz ) It consisted of two independent structural profles (d) con- is defned as Cartesian (Fig. 1), such that the origin is posi- nected to the snowboard binding inserts via six screws each. tioned half-way between the centers of the binding loca- Each profle was equipped with a support beam (i) that could tions ( BR and BF ), and coincident with the horizontal plane be loaded with weight rings (j). The position of the weight (H), averaged from the four contact point locations ( Pi with rings was adjusted along the support beams to bring the ◦ ◦ i = 1, … ,4 ) on the bottom surface side of the snowboard. system to the desired tilt angle, ranging from 40 to 60 . The The lines P1P2 and P3P4 are referred to as ‘contact limits’. angular position was measured via the reference profles (e). The z-axis is normal to the plane (H), with the positive direc- The contact took place between the edge of the snowboard tion pointing towards the top surface of the snowboard. The and a rigid, fat contact plate (g) made out of 1.5 mm thick global x-axis runs along the length of the snowboard, defned aluminum. as the projection of BRBF onto (H). The y-axis runs across Once the weights were in position, the angular position the width according to the right-hand rule. As a convention, of the system was set with a threaded rod (c) and adjustment the front tip of the snowboard (referred to as ‘nose’) points screws (a) until static equilibrium was achieved. Thus, the towards the positive x, whereas the rear tip (referred to as threaded rod was no longer transmitting neither axial nor ‘tail’) points towards the negative x. The present conventions bending load. and reference systems are used throughout this paper unless A schematic representation of the forces and moments mentioned otherwise. applied to the snowboard is shown in Fig. 3. The application point of the input force P is represented at the center of the (a) ‘tail’ z ‘nose’ Table 1 Geometrical parameters of the specimen P O x P 1,2 2,3 (H) Parameter Abbreviation Value LC Total length L 1580 mm (b) L 1100 mm Contact length C y P2 P4 WN 291 mm BR BF Nose width W 248 mm O x Waist width W W 291 mm P1 P3 Tail width T hC 0 mm WW Camber height WT R WN h 34 mm Nose tip height F L h 28 mm Tail tip height R Sidecut radius R 7.05 m Fig. 1 t 6.88 mm Local coordinate system relative to the snowboard and conven- Total thickness T tions. a Front view. b Top view Page 3 of 11 15 Static model of a snowboard undergoing a carved turn: validation by full-scale test (a) adjustment screws interface, equal to the y-component of the input force P and (b) wall mounting proportional to the sine of the tilt angle : P = R = P () y y sin (1) This loading condition including the extra force component (c) threadedrod (j) weight rings is correspondingly regarded for the numerical representation of the experiment and throughout this paper. The impacts on (d) structural (i) support the validation procedure are discussed in Sect. 6. profiles beam 2.4 Measurement strategy (e)reference profile A motion tracking system (Vicon [10] and Vero v2.2 cam- eras) was used to capture the deformed shape of the struc- (f) snowboard ture. The measurement process consisted of positioning y spherical retro-refective markers on the top surface of the O x snowboard (such that they did not contribute to a stifen- ing of the structure) and measuring their position in space (h) connecting interfaces by triangulation, with the use of six cameras (see Fig. 4). (g) contactplate The absolute positioning error of the measurement system is reported to be 0.15 mm for static measurements [11]. Fig. 2 CAD model of the static load bench Due to the relatively small curvature of the deformed structure, the direct measurements of the marker positions were assumed to represent the deformation of the mid- −5 −1 z surface of the laminate ( max ≈ 5 × 10 mm leading to P ∼ 0.06 % positioning error). The angular positions of the y front and rear bindings with respect to the horizontal plane R were measured during the experiment via the reference pro- fles (see Fig. 2), on which extremities two Vicon markers were positioned. M Rz 2.5 Evaluation scheme θ Ry The reference stance (distance between both bindings) was set to s = 600 mm for the present measurements. Sym- Fig. 3 Schematic 2-D representation of the external forces and metrical loading conditions were defned: the total loading moments applied to the snowboard (side view).
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