Analytic and numerical results of a disc cam bending with a roller follower
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Analytic and numerical results of a disc cam bending with a roller follower Louay S. Yousuf1 · Dan B. Marghitu1 Received: 26 January 2020 / Accepted: 20 August 2020 © Springer Nature Switzerland AG 2020
Abstract The bending deflection of a disc cam with a roller follower was analyzed by using constant angular velocity of the cam. The objective of this paper was to study the effect of the contact load on the bending deflection of the cam profile. Numerical simulations were carried out using SolidWorks and ANSYS Ver. 19.2 package based on finite element analysis. SolidWorks was used to determine the dynamic response of the follower, while the bending deflection of the cam profile has been investigated using ANSYS package. The modal and harmonic analyses were used to find the natural frequency and the dynamic response of the bending deflection. The theory of circular plate was applied to derive the analytic solution for the bending deflection. The experiment data has been collected with an infrared camera system. The dynamic response of the follower, at the point of contact, was verified analytically and experimentally. The reduction rate for bending deflection is (73.425%) for path no. (1), (85.925%) for path no. (2), and (61.467%) for path no. (3). The harmonic amplitude peak of the point (18) on the nose (2) is bigger than the peak of the point (4) on the nose (1) because of large values for the radius of curvature of the nose (2). Keywords Circular plate theory · Bending deflection · Contact load · ANSYS package Nomenclature P Contact force between cam and follower, N k1 Stiffness of the preload spring, N/mm Δ Spring extension due to the preload external force, mm k, c Spring stiffness and viscous damping coefficient, N/mm, N s/mm ̇ ẍ Linear displacement, velocity, and accelerax, x, tion of the roller follower, mm, mm/s, mm/ s2 w Weight of roller follower, N m Mass of roller follower, kg g Gravitational acceleration, mm/s2 Ω Cam angular velocity, rad/s t Time of contact including the time of the dwell stroke, s Xst Static deflection, mm
xc Analytic dynamic response for the follower, mm L Length of the cam and follower along z-axis, mm Po Maximum contact load per unit length, N/ mm a1 , b1 Major and minor axis of the Hertzian contact ellipse, mm m1 , n1 Functions of the geometry of the contact surfaces R1,R2 Radii of curvatures of contacting cam and follower, mm ′ ′ R1 , R2 Principal radii of relative curvature, mm ν1,ν2 Poisson’s ratio for cam and follower respectively E1,E2 Modulus of elasticity for both cam and follower respectively, N/mm2
* Louay S. Yousuf, [email protected] | 1Department of Mechanical Engineering‑Wiggins Hall, Auburn University, 354 War Eagle Way, Auburn, AL 36849, USA. SN Applied Sciences
(2020) 2:1639
| https://doi.org/10.1007/s42452-020-03383-w
Vol.:(0123456789)
Research Article
SN Applied Sciences
(2020) 2:1639
νxo , νxf Initial and final tangential velocities before and after the contact respectively, mm/s νyo , νyf Initial and final normal veloci
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