Nonlinear design analysis of centrifugal pendulum vibration absorbers: an intrinsic geometry-based framework
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ORIGINAL PAPER
Nonlinear design analysis of centrifugal pendulum vibration absorbers: an intrinsic geometry-based framework Marco Cirelli · Mattia Cera · Ettore Pennestrì · Pier Paolo Valentini
Received: 18 June 2020 / Accepted: 16 October 2020 © Springer Nature B.V. 2020
Abstract The centrifugal pendulum vibration absorber (CPVA) is a device whose purpose is the reduction in torsional vibrations in rotating and reciprocating machinery. Over the last decades, CPVA nonlinear behavior has been thoroughly investigated. In particular, the performance and the local stability of cycloidal, epicycloidal and tautochronic CPVAs have been extensively analyzed. In this paper, on the basis of intrinsic geometry and higher-path curvature theory, a novel and unified modeling approach for the design of a parametric family of CPVAs, herein named λ-CPVA, is proposed. In the first part, the intrinsic geometry framework is applied to derive CPVA equations of motions in terms of higher-order curvature ratios of the damper path. Then, the same approach is extended to describe the curvature kinematics of the rollers of a parallel bifilar pendulum. In the second part, a new family of parametric curves in R3 , denoted as λ-curves, is introduced. This allows a fine adjustment of CPVA nonlinear
dynamics to the design requirements. In the third part, the numerical comparison of the performance and the stability limits between the cycloidal, tautochronic pendula and λ-CPVA are presented. Finally, the λ-CPVA analytical model is more accurately simulated with a multibody dynamics approach. The design analysis framework herein proposed increases the dimension of the solution space and opens new possibilities of tailoring the CPVA performance to the specific application. Keywords Centrifugal pendulum vibration absorber · Nonlinear dynamics · Intrinsic geometry · Higher-path curvature · Perturbation methods · Tautochronic CPVA · Multibody dynamics simulation
List of symbols (r, α)
M. Cera · E. Pennestrì · P. P. Valentini Department of Enterprise Engineering, University of Rome Tor Vergata, 00133 Rome, Italy e-mail: [email protected] E. Pennestrì e-mail: [email protected] P. P. Valentini e-mail: [email protected] M. Cirelli (B) Department of Mechanical Engineering, University Niccolò Cusano, 00166 Rome, Italy e-mail: [email protected]
(X, Y ) (x, y) (xo , yo ) (xΘ , yΘ ) α
Polar coordinates of rotor center O in coordinate system M − tn Cartesian coordinates of a point in the fixed reference system Cartesian coordinates of a point in coordinate system M − tn Cartesian coordinates of O in coordinate system M − tn Cartesian coordinates of a point in the moving reference M − τ ν Angle between axes t and ν (see Fig. 3)
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αR δW ˙ (·) η=
Θ˙ Ω
Angle between the tangent tR and normal νR Virtual work Time derivative
τ Θ σ˜ τ˜
Rotor normalized angular speed
n˜ s˜
T Scaled torque μ0 (I + J ) n 2 Ω 2 c γc = Normalized viscous damping μ0 nΩ ρi ith curvature ratio, (i = 1, 2, . . . , n) λ
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