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A. Freddi*, A. R. Gradassi**, G. Olmi**, D.Croccolo***, V. Ciavatti***

* Ordinary Professor of Experimental Mechanics –DIEM – Department of Mechanical Engineering –

Bologna University.** Graduated at Bologna University.

*** DIEM – Department of Mechanical Engineering –Bologna University.

/1032547698;:<4>=Object of this work is to project and construct a six –degree of freedom loading cell, which can be used tomeasure the forces and the moments transmitted by thefeet of the skier to the skies.In order to find the best solution to the problem that hasbeen posed we have analysed and tested two possibleconfigurations. Both of them have in common the useof a certain number of strain gage sensors collocatedbetween two aluminium plates, and the samedimensional constraints: the loading cell must becontained in the space which would be occupied byanti-vibrating plates. The first is based upon an ideacontained in a German text [2], while the second iscompletely original and distinguishes itself for itsgreater compactness. The uses of such dynamometersare connected to tests on the field and release testsexecuted in laboratory, and regulated by national andinternational standards which guarantee the security ofski – bindings (in particular ISO 9462).?A@ 69254B2DC;E F�4 @ C;G =The first generation transducer employs seven sensorswhich can be charged only along a particular direction,so that they are not solicited when the direction of the

force is different. In other words it can be said that anyof these members works as a fixed beam, solicited by aforce always maintaining the same direction and actingin two diametrically opposite points. The productbetween the force and its arm furnishes the bendingmoment soliciting the beam. Consequently tensionsand strengths can be calculated, in particular the lastones can be easily measured by employing straingages. In order to assure the transmission of the forcesfrom the aluminium plates to the sensors and totransform them in punctual ones, we have employedforks that could contain the ends of the beams. It canbe observed that every fork realizes a mechanicalconstraint along only one direction, leaving inferiorand superior plates free to a relative movement alongany other axis. Among the seven sensors, four canmeasure as many vertical forces and two as manytransverse forces. The last one can reveal the presenceof a longitudinal load due to the slope of the piste.Knowing the entity of these forces and the distancesbetween the sensors, i.e. the arms of rolling andforward bending moments and of torsion, it is possibleto calculate torques values. As far as gaugesconnections are concerned, it can be added that wehave employed seven half bridges, which guarantee agood resolution and a natural compensation ofstrengths due to thermal effects. A calibration test hasbeen executed for each sensor in the DIEM laboratory,so that it was possible to obtain the functionsexpressing the relationships between strengths signalsand forces soliciting the beams, on which stain gaugesare glued. The grade of precision of the regression linesemployed to approximate the distributions of dates is99,9÷100%, which indicates the good linearity ofmeasures.H�I9:9C;G3JKCL6 @NM;@ G38;E 2DC;E F�4 @ C;G =The second generation transducer has been projectedafter the execution of several tests on the field, and inparticular release ones. These experimentations have

taken place at Passo SanPellegrino (Trento, Italy), thankto the collaboration of theNordica – Benetton personnel,with the use of the firstgeneration loading cell. Duringthese tests it has been possibleto individuate the forces andtorques the new dynamometerwould be called to measure andsustain during its life. On onehand it was important to satisfyobvious safety requirements, onthe other it was necessary to

avoid

projecting sensors characterized by an excessivethickness, which would cause a decrease in sensitivity.Once we had the diagrams representing the valuesassumed by the forces and torques transmitted by thetester to the ski, we had to decide how to use thesedates. The following step was to make the firstdesigning choice, concerning the use of four modularsensors which could be solicited by forces directedalong the three spatial directions. Two of them wouldbe collocated forward and the others backward, so thatthe sensors forming each couple would be side by side.An important aspect would be to assure a sufficientlength for torques arms, in order to improvemeasurement precision, and to avoid any negativeinfluence on skiing, or risk of injuries for the tester.

After making this choice it was necessary to elaboratethe experimental dates, calculating longitudinal,transverse and vertical forces soliciting the foursensors. In order to take advantage from themodularity, each sensor has been realized employing acyclic productive process, with the use of the same fileapplying an electroerosion machine. A high resistancesteel has been chosen as material for the constructionof the sensors, to reduce the thickness of beamelements we would employ. A particular attention hasbeen dedicated to the individuation of the mostopportune design of the sensors. The load section ischaracterized by the presence of a threaded hole and of

a lightly cambered surface.Strain gauges are glued in threezones, which are particularsensitive to vertical, longitudinaland transverse solicitation. It canbe noticed that the electric wiresconnecting strain gages to thedata acquirer easily pass throughthe rounding and the lighteningengraving. Four threaded holesguarantee the coupling betweensensors and inferior plates.Belleville washers are collocatedunder the heads of the screwsrealizing the coupling betweensensors and superior plates andallow the screw stems to tilt, sothat, in presence of a verticalforce, sensors can buckle in an

isostatic way. Other washers prevent sensors superiorsurfaces from getting in contact with the plates, andalso sensors from being subjected to a light torsion, inpresence of a rolling moment transmitted by the skierfoot. As far as strain gauges connections are concerned,it can be said that four half and four full Wheatstonebridges are employed, which assures an improvedresolution and natural compensation of thermal effects.Also in this case an experimental calibration has beencarried out in the DIEM laboratory, charging eachsensor with note loads, and reading the correspondingstrength signals. After the analysis of the dates it hasbeen possible to emphasize a good linearity andrepeatability of measures. These results have been

elaborated in order to calculatethe compliance matrixes and toevaluate sensors gooddecoupling. Compliancematrixes have been inverted, toexpress calibration ones,which have been composed inorder to find the 6×8 matrixexpressing the relationshipbetween the six degree offreedom and the eightstrengths signals. In nextfuture, thank to thecollaboration of the Nordicapersonnel, we plan to executetests on the field, with the useof this new transducer.

� 2 2DI9G 4 @ 8;E�0 @ 0 E @ C M 698������L=[1] Sciare – guida tecnica all’acquisto, DMK, Milano(1999)[2] DR. ING. PETER JUNG, ������ ������� �������� ����� � � ��� – Messtechnische Briefe, Stuttgart (1975)[3] Alpine ski-bindings --- Safety requirements and testmethods. !���� ����������" ����# � ��� ��$���$�% ! �'&�(�)+*-, %[4] Lu-Ping Chao, Ching-Yan Yin. The six-componentforce sensor for measuring the loading of the feet inlocomotion. �.��� ������# �/���$102 ���� 3�� 20 (1999) 237 –244.