Abstract
In the present work, an innovative design strategy for the optimization of the dynamic performances and the structural loads of heavy loaded vibrating screens is presented. A dynamic model of a vibrating screen for the selection of inert materials in an asphalt plant is proposed, and a numerical optimization procedure is applied to selected design parameters and geometrical features. The algorithm provides a tool to improve the dynamic behavior of vibrating screens of different geometric and inertial properties. The results are analyzed, in order to find the parameters apt to minimize the pitching angle of the examined screen during stationary working conditions, thus providing a better material selection by reducing gravel throwback. A numerical FEM model analysis and an experimental strain-gage campaign have been conducted on a realization of the vibrating screen, testing two optimized and un-optimized configurations, to verify the FEM model results. The complete work gives the machine designer a powerful tool, validated by means of full scale experimental tests, to optimize the dynamic behavior of the screen and to verify its fatigue resistance.
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Abbreviations
- \(x\) (m):
-
Horizontal coordinate of the center of gravity
- \(y\) (m):
-
Vertical coordinate of the center of gravity
- \(\theta \) (\(^\circ \)):
-
Pitching angle of the vibrating screen
- \(A\) (m):
-
Horizontal distance between the center of gravity and the unload side spring support
- \(B\) (m):
-
Horizontal distance between the center of gravity and the load side spring
- \(A'\) (m):
-
Vertical distance between the center of gravity and the unload side spring support—positive in the downward direction
- \(B'\) (m):
-
Vertical distance between the center of gravity and the load side spring—positive in the upward direction
- \(\alpha \) (\(^\circ \)):
-
Inclination of the active force with respect to the vertical
- \(e\) (m):
-
Eccentricity of the direction of application of the active force with respect to the center of gravity
- \(F_{0}\) (N):
-
Active force design amplitude
- \(n\) (rpm):
-
Electric engines rotational speed
- \(\omega \) (rad/s):
-
Electric engines angular frequency
- \(F_{0,x}\) (N):
-
Horizontal component of the active force
- \(F_{0,y}\) (N):
-
Vertical component of the active force
- \(F\) (N):
-
FEM model active force amplitude
- \(F_{x}\) (N):
-
FEM model horizontal component of the active force
- \(F_{y}\) (N):
-
FEM model vertical component of the active force
- \(k\) (N/m):
-
Single spring longitudinal stiffness
- \(k_{t}\) (N/m):
-
Single spring transversal stiffness
- \(E\) (MPa):
-
Longitudinal elastic modulus of the spring
- \(G\) (MPa):
-
Transversal elastic modulus of the spring
- \(d\) (m):
-
Wire diameter of the spring
- \(R\) (m):
-
Radius of the spring helix
- \(c = 2R/d\) :
-
Spring curvature ratio
- \(m\) (kg):
-
Global mass of the system
- \(J\) (kg m\(^{2}\)):
-
Global moment of inertia of the system
- \(k_{1}\) (N/m):
-
Total longitudinal stiffness of the springs related to the unload side supports
- \(k_{t1}\) (N/m):
-
Total transverse stiffness of the springs related to the unload side supports
- \(k_{2}\) (N/m):
-
Total longitudinal stiffness of the springs related to the load side supports
- \(k_{t2}\) (N/m):
-
Total transverse stiffness of the springs related to the load side supports
- \(K\) (N/m):
-
Total longitudinal stiffness of the supports
- \(K_{t}\) (N/m):
-
Total transverse stiffness of the supports
- \(\omega _{nx}\) (rad/s):
-
Natural angular frequency of the system in the \(x\) direction
- \(\omega _{ny}\) (rad/s):
-
Natural angular frequency of the system in the \(y\) direction
- \(c_{1 }\)(Ns/m):
-
Total longitudinal damping coefficient of the springs related to the unload side supports
- \(c_{t1}\) (Ns/m):
-
Total transverse damping coefficient of the springs related to the unload side supports
- \(c_{2}\) (Ns/m):
-
Total longitudinal damping coefficient of the springs related to the load side supports
- \(c_{t2}\) (Ns/m):
-
Total transverse damping coefficient of the springs related to the load side supports
- \(C\) (Ns/m):
-
Total longitudinal damping coefficient of the supports
- \(C_{t}\) (Ns/m):
-
Total transverse damping coefficient of the supports
- \(C_{c}\) (Ns/m):
-
Critical damping coefficient in the longitudinal direction
- \(C_{ct}\) (Ns/m):
-
Critical damping coefficient in the transverse direction
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Acknowledgments
The Authors wish to thank Bernardi Impianti for the support of the research project.
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Baragetti, S., Villa, F. A dynamic optimization theoretical method for heavy loaded vibrating screens. Nonlinear Dyn 78, 609–627 (2014). https://doi.org/10.1007/s11071-014-1464-4
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DOI: https://doi.org/10.1007/s11071-014-1464-4