Optimal design of support parameters for minimum force transmissibility of a flexible rotor based on H_∞ and H₂ optimization methods

ABSTRACT

Rotating machinery support design with the aim of reducing the force transmitted to the foundation has significant importance regarding the various applications of this machinery. This article presents H_∞ and H₂ methods for calculating the optimum support flexibility and damping of flexible rotors to minimize force transmissibility in the vicinity of the rotor’s first critical speed. First, the governing equations for the Jeffcott rotor model mounted on flexible supports are derived and the optimal parameters for the supports are analytically achieved by H_∞ and H₂ optimization procedures. The proposed approach of the tuned damper support system is similar to that designed for dynamic vibration absorber optimization. The main objective of the H_∞ optimization is to minimize the force transmitted based on fixed-point theory and the mean square transmissibility of flexible rotor is minimized in the H₂ optimization design as analytical formulae. It is proven by numerical solution that the system optimization design can effectively minimize the force transmitted to the foundation. Comparison of two optimization than with H_∞.

KEYWORDS:

• Force transmissibility
• support
• Jeffcott rotor
• rotor designs
• optimal damping

Disclosure statement

No potential conflict of interest was reported by the authors.

Nomenclature

	=	support mass
	=	disc mass
	=	damping coefficient for the rotor shaft
	=	stiffness coefficient for the rotor shaft
	=	damping coefficient for bearings
	=	stiffness coefficient for bearings
	=	rotor amplitude
	=	optimum support damping ratio
	=	damping coefficient for supports
	=	stiffness coefficient for supports
	=	rotating speed
	=	disc eccentricity
	=	support amplitude
	=	bearing amplitude
	=	optimum support flexibility ratio
	=	support dynamic transmissibility factor

ORCID

Hamidreza Heidari http://orcid.org/0000-0001-7405-3218