Mesh stiffness of micro-spur gears by finite element formulations based on modified couple stress theory
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TECHNICAL PAPER
Mesh stiffness of micro-spur gears by finite element formulations based on modified couple stress theory Yucel Pehlivanoglu1
•
M. Ozgur Aydogan1,2 • Baris Sabuncuoglu3
Received: 3 March 2020 / Accepted: 6 May 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Finite element formulations developed for micro-sized structures are utilized for the determination of mesh stiffness of micro-spur gear pairs. The equations are based on Modified Couple Stress Theory developed for micro-beams. Timoshenko and Euler–Bernoulli type formulations are used separately to observe the difference. Calculations are performed for microgear pairs having two different module types and the stiffness of both double and single mesh regions are obtained. The results reveal the size effect on the mesh stiffness of micro-gears, and can be used in the future for more advanced gear configurations. The comparison study shows that performing calculations with classical continuum theories as well as Euler–Bernoulli type beam formulations can cause significant errors in the mesh stiffness depending on the size of microgears. List of wv wh M a E I L u f K l A l fi ui ki nc kipinion kjgear
symbols Vertical force component Horizontal force component Moment Angle Young’s modulus Moment of inertia Length of a beam element Displacement vector Nodal force vector Stiffness matrix Shear modulus Area of cross-section Length scale parameter Applied load at a point Deflection of a point Stiffness value of a point Total number of contact points Stiffness of a point on pinion Stiffness of a point on gear
& Yucel Pehlivanoglu [email protected] 1
Turkish Aerospace Industries, Ankara, Turkey
2
Mechanical Engineering Department, Middle East Technical University, Ankara, Turkey
3
Mechanical Engineering Department, Hacettepe University, Ankara, Turkey
kijmesh
Mesh stiffness of a contact point
1 Introduction Since the last few decades, the miniaturization of components and structures has gained attention due to ‘‘high performance in low volume’’ demands. These so called micro parts are components with outer dimensions in the range of a few millimeters, which mostly have details in the sub-millimeter range (Loh et al. 2008). Mainly used in micro-mechanical systems (MEMS), such components find a wide variety of applications in micro-fluidic devices (Denoual et al. 2003) and medical technology (Meng et al. 2011; Tay et al. 2009). Among these, micro-gears are important components, widely used as driving systems in such micro-scale systems (Loh et al. 2008; Burisch and Raatz 2011; Dong et al. 2015). The development of novel production methods is the main research area in the field of micro-gears. Many techniques such as UV-LIGA process (Dong et al. 2015; Malek and Saile 2004), ultra-violet assisted anisotropic etching (Sadeghi-Makki et al. 2004), micro powder injection (Zauner 2006), and vacuum casting (Tang et al. 2007) have been continuously developed in the last
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