A NUMERICAL INVESTIGATION OF COMBINED SHOCK AND VIBRATION ISOLATION THROUGH THE SEMI-ACTIVE CONTROL OF MAGNETORHEOLOGICAL FLUID DAMPER IN PARALLEL WITH AN AIR SPRING

Combining shock and vibration isolation into a single isolation mount is investigated numerically through the use of the Bouc-Wen model of a magnetorheological fluid damper in parallel with an air spring. The stability and dissipative capabilities of the Bouc-Wen model are proven mathematically. The response characteristics of this hybrid isolator to shock and vibration inputs is explored. The advantages of combining shock and vibration isolation into a single package is discussed. I: INTRODUCTION A classic problem in isolation system design is the design of a single isolator that can perform equally well as a shock and a vibration isolator. This problem arises due to the fact that a good vibration isolator tends to be a poor shock isolator and a good vibration isolator tends to be a poor shock isolator. Most attempts to solve the combined isolation problem with a passive device quickly lead to frustration. This is certainly the case in shipboard isolation applications where many inputs are often present simultaneously. The typical approach to solving the shipboard isolation problem involves separate passive isolators for shock and vibration. This inevitably leads to modifying vibration isolators to survive shock inputs and/or modifying shock isolators to perform adequately as vibration isolators. When many different inputs are present, as in shipboard applications, an active, or semi-active, isolation system is justified. Active, or semi-active, isolation systems can be designed to simultaneously isolate for many combined and varying inputs. The advantage to combining shock and vibration isolation into a single package is obvious. A single combined isolation system replaces two separate systems and therefore reduces weight and increases available volume. This is particularly important in submarine applications where space is limited. Also, with varying and diverse inputs, a combined active isolation system can be designed to perform better than separate passive shock and vibration isolation systems operating in parallel. For shipboard applications the ideal isolation system would provide effective vibration isolation in the 10 to 200 Hz range and shock isolation from a variety of inputs such as underwater explosions, wave slap, impact, etc. Thus a "soft" isolator with a natural frequency of approximately 2Hz is desired that can survive varying shock inputs. An ideal vibration isolator that meets this design criteria is an air spring. Air springs have a low natural frequency, but 1 The opinion expressed herein are those of the author and do not necessarily reflect those of Newport News Shipbuilding. tend to behave poorly as shock isolators due to their inherently low damping. An ideal combined isolator would be an air spring that could provide high, variable damping forces on demand during a shock event. Producing high, variable damping forces is an ideal application for a magnetorheological (MR) fluid damper. Therefore, combining an air spring with an MR damper in parallel would provide an ideal combined isolation system provided the optimal damping force can be applied and varied rapidly enough to attenuate the shock input and meet rattle space requirements. To investigate the effectiveness of an air spring/MR damper combination as a combined isolation system requires an accurate model of the highly nonlinear MR damper. One such model that very accurately predicts the response of the MR damper is the so-called Bouc-Wen model. The stability and dissipative capabilities of the Bouc-Wen model can be proven mathematically as will be shown. Since this paper is a numerical study, the MR damper under consideration will be a commercially available model developed by the Lord Corporation (Model RD-1003) which has been adequately characterized in several papers [2-3]. The air spring under consideration is also a commercially available model manufactured by Firestone (Model 20). The air spring was chosen as it's physical dimensions and capacity are a good match for the MR damper. The force-deflection behavior of the air spring was provided by Firestone and incorporated into the model. II: SYSTEM MODEL The system under consideration will be modeled as a single-degree-of-freedom (SDOF) system consisting of a modified Bouc-Wen model with an additional spring and damper to model the air spring. The complete model is shown in Figure (1). Figure 1: SDOF System Model The core of the model is the modified Bouc-Wen model to which several papers have been devoted [2-3]. The next section discusses the stability and dissipative capabilities of the modified Bouc-Wen model. III: STABILITY OF THE MODIFIED BOUC-WEN MODEL The stability of the modified Bouc-Wen model will be addressed by using the SDOF model shown in Figure (1). In the following discussion the air spring stiffness and damping shown in the figure are not included. The dynamics of the system can be described as follows: ( ) ( ) ( ) x r k x y c x y k z x m − + − + − + = 1 0 0 & & & & α (1a) ( ) ( ) ( ) x y c x y k z y r c & & & & − + − + = − 0 0 1 α (1b) ( ) ( ) x y A z x y z z x y z n n & & & & & & & − + − − − − = − β γ 1 (1c) m