Functional Simulation of Harmonic Drive with S.M.A. Wave Generator VIOREL-IONUT BIZAU, ION VELA, OVIDIU MILOS, ALINA VISAN, ION-CORNEL MITULETU Center of Advanced Research, Design and Technology CARDT Eftimie Murgu University of Resita Piata Traian Vuia 1-4, 320085, Resita ROMANIA v.bizau@uem.ro, i.vela@uem.ro, o.milos@uem.ro, a.visan@uem.ro, i.mituletu@uem.ro. Abstract: - The elements of shape memory alloys replace the conventional components used for the mechanical drive being widely spread in the mechatronics field. Hence, it results the necessity of studying the replacement way of the classic distortion and the compatibleness in the framework of the harmonic drive. In this paper we present the operation of a friction harmonic drive having the wave generator made up of elements of shape memory alloys. Imposing the displacement limit and the way of time variation of the distortion elements displacement validates the operation of the researched drive. Key-Words: - simulation, harmonic drive, wave generator, shape memory alloy, displacement, constraints. 1 Introduction The possibility of achievement in a virtual environment, then the use of simulation programs (with finite element) for solving some technical problem has become a necessity in the field of research, because the costs are smaller, the time allotted is shorter and could determine the possibility of the occurrence of some design problems.[1]. Because in the achievement of some operations a small speed is necessary, the harmonic drives are used as reduction gear; but these ones in their turn, are operated with the help of electric engines, usually, direct current or step by step motor[2]. The electric motor operates the distortion in the framework of the drive which at its turn distorts the flexible wheel and this one by its distortion produces the rotation movement[3]. The replacement of the wave generator which is made up of the electric motor and distortion, with another more simple type of constructive wave generator which should replace the produced distortions and the simulation of its functionality is the subject proposed for research. solidworks2011 because it includes both a proper CAD module and a simulation module. Likewise, this has also included in the internal library some memory shape alloys such as nitinol. 2.1 Harmonic drive design It supposes the achievement of 3D component parts of the harmonic drive and then, the achievement of a set of these parts. 2 Problem Formulation Simulation of harmonic drive with S.M.A. wave generator functionally supposes two distinct phases. The first phase refers to the achievement of the model and the second phase supposes the achievement of a study on the accomplished model. For these two phases, we have chosen the program Fig.1 The set contains the fixed element (1), 8 elements of shape memory alloys (2-9), the flexible wheel (10) and the fixed wheel (11). ISBN: 978-1-61804-014-5 161
2.2 Harmonic drive simulation study The chosen study having in view the achievement of the simulation is a non-linear study because the elements of shape memory alloys have non-linear characteristic. 2.2.1 Material properties The first step in achieving the study supposes the choice of the material for the elements used in the study. The chosen material for the shaft (the fixed element), the flexible wheel and the rigid wheel is Alloy Steel with the characteristics presented in table 1. Table 1 Model Reference Properties Name: Alloy Steel Model type: Linear Elastic Isotropic Default failure criterion: Max von Mises Stress Yield strength: 6.20422e+008 N/m^2 Tensile strength: 7.23826e+008 N/m^2 Elastic modulus: 2.1e+011 N/m^2 Poisson's ratio: 0.28 Mass density: 7700 kg/m^3 Shear modulus: 7.9e+010 N/m^2 Thermal expansion 1.3e-005 /Kelvin coefficient.: The characteristics of the material used for the other components in the studied model are presented in table 2. Table 2 Model Reference Properties Name:nitinol Model type:nitinol Default failure Max von Mises Stress criterion: Initial yield stress 5e+008 N/m^2 (Tensile loading): Final yield stress 5e+008 N/m^2 (Tensile loading): Initial yield stress 3e+008 N/m^2 (Tensile unloading): Final yield stress 3e+008 N/m^2 (Tensile unloading): Initial yield stress 7e+008 N/m^2 (Compressive loading): Final yield stress 7e+008 N/m^2 (Compressive loading): Initial yield stress 4e+008 N/m^2 (Compressive unloading): Final yield stress 4e+008 N/m^2 (Compressive unloading): Ultimate plastic strain0.2 measure (Tension): Elastic modulus:5e+010 N/m^2 Poisson's ratio:0.3 Mass density:1020 kg/m^3 2.2.2 Load and Fixtures In a simulation, the charges and constraints are probably the most important ones, due to the fact that in the simulated model in order to reduce the number of elements subject to the study, some components are replaced only by the effect that these ones produce during the operation. In this sense, the first constraint (fixture) of Fixed type is defined on the two entities of the shaft. Fig.2 It is very important that this constraint should be achieved on the two entities because the number of the degree of freedom of the finite elements resulted after the. Should be automatically reduced and the simulation period should be smaller. The next constraint of Fixed type which is imposed, refers to the contact surfaces of the shaft (fixed element) and the elements in SMA. Fig.3 This is really achieved with the help of a stationary bush on the shaft (the fixed element). This Fixed type constraint which cuts all the degrees of freedom of the surfaces on which it is applied, can be also replaced with other types of constraints. Fig.4 In figure 4, we have presented a constraint on a cylindrical face on which all the possible movements are cancelled. Thenceforth, the other constraints of the harmonic drive are presented. ISBN: 978-1-61804-014-5 162
Fig.5 The constraint used for the 20 entities in figure 5 (10 entities and 10 mirror entities) theoretically limit the displacements of the elements on the two shafts, in plan XOY. However in order to reduce the degrees of freedom of the finite element the followings constraints are required. displacements take place along a shaft. In static conditions, the variation of the elements length can be determined. In the researched case, the maximal radial displacement has the value of 0.6 mm, and a complete cycle is achieved in 12 seconds; the wave generator is a two waves generator. In these conditions, the time variation of the 8 elements has the shape/form presented in figure 8. Fig.8 For the elements 2, 4, 6, 8 in the researched wave generator, the time variation of the displacement is presented in the next figure; Fig.6 In order to simulate the behaviour of the elements in SMA when these ones are educated, the constraint in the following figure is also imposed. Fig. 9 but for the elements 2 and 6, the displacement has the sense of the element compression (Fig.10). Fig.7 Likewise, it is necessary to impose the displacements and their variation way. If the maximal value of the displacements comes out of the geometrical conditions of the harmonic drive, the problem of the determination of the time variation way of these ones appears. Thus, so that the drive is functional, the flexible wheel must be deformed according to the principle w = w 0 cos2φ (1) where: w 0 is the maximum radial displacement, this being determined in the conditions of resistance and the execution precision of the flexible element; φ is the position angle of the section considered in relation to the large shaft of the distortion. [5] So that this displacement takes place, the elements in the construction of the wave generator must, in their turn, achieve well determined displacements tightly connected among them. These Fig.10 Figure 11 presents temporal variation of the displacement for elements 3 and 7. Fig.11 For elements 5 and 9 temporal variation of the displacement is presented in the following figure. ISBN: 978-1-61804-014-5 163
. Fig.12 2.2.3 Contact information This property is not used in the simulation of a single element with no contact area, but it becomes very important when is simulated an assembly of elements which interact and produce displacement. In the figure below are presented the contact areas and the type of contact between investigated elements. Fig.14 3 Problem Solution After the study is completed, the obtained data are interpreted. The figure below shows the resultant displacement of the harmonic transmission components. Fig.13 The type of contact between the SMA elements and the flexible wheel is one without penetration, there is also a contact zone of the same type between the flexible and fixed wheel of the harmonic transmission gear. 2.2.4 Mesh information The phase of meshing of the finite element is the last step before the actual simulation. The meshes used in the simulation of the proposed model are presented in the following table. Table 3 Mesh type Mesher Used: Remesh failed parts with incompatible mesh Solid Mesh Curvature based mesh Off Total Nodes 3048 Total Elements 8222 Maximum Aspect Ratio 19.021 % of elements with Aspect Ratio < 3 83.2 % of elements with Aspect Ratio > 10 0.207 Fig.15 In figure 15 it is noted the fact that the resultant displacement with highest value is achieved by the flexible wheel. Its value in our case is 1.2 mm (2w 0 ) after a complete cycle. 4 Conclusion Making of simulation and validation for a harmonic drive with SMA wave generator is a first step in the field of using the SMA wave generator for harmonic transmissions. It also opens new directions of research for a number of types of mechanic models which could include this type of transmission. In the following figure is presented the harmonic drive system with a discretized SMA generator. ISBN: 978-1-61804-014-5 164
References: [1] Tufoi, M., Vela, I., s.a. Design, Optimization and Realization of Mechanical Parts Using CAD, CAE and CAM, Annals of DAAAM for 2010 & Proceedings of the 21st International DAAAM Symposium, Zadar, Croaţia 2010. [2] Vela, I., Contribuţii privind funcţionarea şi construcţia mecanismelor cu elemente dinţate elastice, Teză de doctorat, Timişoara 1987. [3] Palaghian, L., Reductoare armonice, Editura Tehnică, Bucureşti 1996. [4] Mănescu, St., Nedelcu, D., Analiză structurală prin metoda elementului finit, Editura Orizonturi Universitare, Timişoara 2005. [5] Vela, G.D., Contribuţii la perfecţionarea funcţional constructivă a transmisiilor armonice, Teză doctorat, Timişoara 2010. ISBN: 978-1-61804-014-5 165