naa a22 4500 510822630 CHVBK 20180411083541.0 cr unu---uuuuu 180411e20130901xx s 000 0 eng 10.1007/s12541-013-0218-4 doi (NATIONALLICENCE)springer-10.1007/s12541-013-0218-4 Helix beam model of a coil spring including twisting effect to capture lateral deformation [Elektronische Daten] [Hyun-Woo Kim, Jin-Seok Jang, Wan-Suk Yoo, Oleg Dmitrochenko, Aki Mikkola] A coil spring is a widely used mechanical component to store and release energy in mechanical systems. Although the potential energy of a coil spring is related mainly to longitudinal deformation, lateral deformation occurs frequently due to the eccentricity of the applied loads. Most studies focused on numerical modeling of a coil spring just for longitudinal deformation and compared the numerical results with experiments. In this paper, the twisting effect was newly included in the helix beam element to capture lateral deformation. The computational results obtained from the numerical derivation were compared with the experimental results, which were measured using a high speed camera. To calculate the deformation of a coil spring, 36 cases of static deformation were measured by loading 7 additional masses. The modeling of a coil spring was derived by adding a twisting effect term to a helix beam element formulation, and the contribution of the twisting effect was verified. The properties of a coil spring used in the numerical simulation were obtained from the experimental data. Korean Society for Precision Engineering and Springer-Verlag Berlin Heidelberg, 2013 Coil spring nationallicence Lateral deformation nationallicence Twisting effect nationallicence A uk : local rotation matrix of the kth beam element nationallicence $$\dot A_{uk}$$ : time derivative of matrix nationallicence A qk : transformation matrix between the kth local coordinate and global coordinate nationallicence A γ : rotation matrix about the tangent vector through an angle γs nationallicence B uk : Jacobian matrix between local angular velocity of kth beam element and vector $$\dot u_k$$ nationallicence b : bi-normal unit vector nationallicence c : displacement vector of force point nationallicence D uk : Jacobian matrix between the local translational velocity of kth beam element and vector $$\dot u_k$$ nationallicence E : Young's modulus nationallicence f : concentrated point force vector nationallicence G : modulus of rigidity nationallicence I 1, I 2 : principal area moment of inertia nationallicence I t : polar moment of inertia nationallicence I x : area moment of inertia nationallicence l k : length of the kth beam element nationallicence m : point moment vector nationallicence n : normal unit vector nationallicence q k : coordinate of origin of kth beam element nationallicence r 0 : global position vector of origin of first beam element nationallicence r k : global position vector of arbitrary point of the kth beam element nationallicence t : tangent unit vector nationallicence u 0 : global position and orientation vector of the first beam element nationallicence u k : curvature vector of the kth beam element nationallicence $$\dot u_k$$ : time derivative of vector u k nationallicence s : arc coordinate nationallicence t : tangent unit vector nationallicence α : pitch angle nationallicence γ : relative rotational gradient nationallicence κ : curvature nationallicence ρ : radius of curvature nationallicence σ : radius of torsional curvature nationallicence τ : torsional curvature nationallicence φ : rotation angle along the beam centerline nationallicence φ 0 : rotation angle of origin of the kth beam element nationallicence θ0 : rotational angles vector of origin of the first beam element in the global coordinate nationallicence (θ0) x , (θ0) y , (θ0) z : rotational angles about Bryant angles nationallicence ω uk : relative angular velocity of the kth beam element nationallicence Kim Hyun-Woo School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeoun-gu, 609-735, Busan, South Korea aut Jang Jin-Seok School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeoun-gu, 609-735, Busan, South Korea aut Yoo Wan-Suk School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeoun-gu, 609-735, Busan, South Korea aut Dmitrochenko Oleg Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankafu 34, 53851, Lappeenranta, Finland aut Mikkola Aki Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankafu 34, 53851, Lappeenranta, Finland aut International Journal of Precision Engineering and Manufacturing Springer Berlin Heidelberg 14/9(2013-09-01), 1615-1622 2234-7593 14:9<1615 2013 14 12541 https://doi.org/10.1007/s12541-013-0218-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12541-013-0218-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kim Hyun-Woo School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeoun-gu, 609-735, Busan, South Korea aut NATIONALLICENCE 700 1- Jang Jin-Seok School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeoun-gu, 609-735, Busan, South Korea aut NATIONALLICENCE 700 1- Yoo Wan-Suk School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Geumjeoun-gu, 609-735, Busan, South Korea aut NATIONALLICENCE 700 1- Dmitrochenko Oleg Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankafu 34, 53851, Lappeenranta, Finland aut NATIONALLICENCE 700 1- Mikkola Aki Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankafu 34, 53851, Lappeenranta, Finland aut NATIONALLICENCE 773 0- International Journal of Precision Engineering and Manufacturing Springer Berlin Heidelberg 14/9(2013-09-01), 1615-1622 2234-7593 14:9<1615 2013 14 12541 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer