Research On Vibration Isolation System Impedance Characteristics And Active Control

Non-rigid foundation, distributed parameter characteristics of isolator and elastic properties of machine performance at high frequency caused the difference between the traditional theory of vibration isolation and actual situation. Flexible isolation theory replaced the subsystem by appropriate elastic model and analyzed its impedance characteristics at high frequency. The defects of traditional theory are as follows:Firstly, non-rigid foundation is the main factor leading to the difference between traditional theory and actual situation. Secondly, the isolator is a distributed parameter system with mass. If the excitation frequency reach to integral multiple of half wavelength of the isolator, it may cause standing wave, which is another factor leading to isolation effect decline at high frequency. Thirdly, some subsystems may be relatively weak or have a large longitudinal span ratio, whose elastic modes will be excited for poor stiffness at high frequency. For instance, vibration isolation equipment can be considered as rigid body, but the supporting feet or frame of the equipment may be due to lack of rigidity and exhibit elastic properties at high frequency; In two-stage isolation system or floating raft isolation system, the elastic modes of intermediate mass may be excited at high frequency and its finite impedance characteristics can not be ignored at this frequency area. Ignoring the above components’impedance characteristics may also cause the theoretical prediction error. This thesis emphatically discusses the impedance characteristics of the system and use power flow as the evaluation index to study the elastic properties of the subsystems, in order to provide theoretical guidance for the practical engineering.In order to investigate the effect of subsystem elastic properties in flexible isolation system, the bending vibration differential equation and modes function under different boundary conditions of Euler-Bernoulli beam theory, Timoshenko beam theory, thin plate theory and thick plate theory are established. Orthogonality condition and mobility functions of different models are derived based on Duhamel’s principle and the mobility functions are compared though an example.A single isolation system is established which is using Euler-Bernoulli beam, Timoshenko beam, thin plate and thick plate as foundation respectively. Two kinds of theory model of beam and plate are compared through power flow method. It is shows that there are no obviously differences at low frequency between Euler-Bernoulli model and Timoshenko model, thin plate model and thick plate model. But with the increase of vibration frequency and plate thickness or decrease of slendemess ratio of beam, the differences will appear and increase gradually; The installation position of the isolators on the foundation will effect its modes. For example, the unsymmetrical arrangement of the isolators on fix-fix beam will excite all the modes of the beam whereas symmetrical arrangement only excite odd order modes; The unsymmetrical arrangement of the isolators on simply supported plate to x and y axis will excite all the modes of the plate and only to x(or y) axis will excite the modes whose subscript n(or m) are odd numbers. If the isolators is symmetrical arrangement to both x and y axis on the plate, then only a quarter modes are excited whose subscript m and n are all odd numbers. In order to investigate the effects of finite impedance characteristics of the equipment, a single isolation system is established which divided the equipment into two parts, containing rigid machine and elastic equipment support. Using Euler-Bernoulli beam or plate with free edge to model the equipment support. The rigid machine is regard as source and output a constant force acting on the equipment support. The properties of flexible equipment support and the effects of source and isolator position is studied utilizing power flow method. The study found that source and isolators should be symmetrical arrangement in order to avoid the pitching modes of the system and the flexural oscillation modes of support and foundation being excited. The flexural oscillation of the flexible equipment support may cause downward speak modes, and the frequency of these modes only depending on its physical parameters and force position.A three-dimensional coupled active\passive two-stage vibration isolation system is developed based on Euler-Bernoulli beam model, in which the rigid body modes of the system, standing wave of the isolator and the elastic properties of the foundation and intermediate mass are taken into consideration. The minimization of total power transmission, which is the optimal strategy, is studied in the thesis. Research shows that if the isolators are symmetrical arrangement, then a couple of axial modes of the system, longitudinal standing wave of the isolators and flexural oscillation modes with odd order of the foundation will be excited by axial oscillation; A couple of pitching modes and a couple of coupling transverse modes, flexural standing wave of the isolators and flexural oscillation modes with even order of the foundation will be excited by pitch oscillation; A couple of transverse modes and a couple of coupling pitching modes, flexural standing wave of the isolators, even order flexural oscillation modes and longitudinal oscillation modes of the foundation will be excited by transverse oscillation. The elastic modes of the intermediate mass will be excited after its fundamental frequency and may cause "anti-resonance" peak, so the rigid body model of the intermediate mass is no longer applicable after its fundamental frequency. The minimization of total power transmission control strategy makes axial and pitching modes of the system, longitudinal standing wave of the isolators and flexural oscillation modes of the foundation disappear, but the secondary control forces are extremely high compared with primary force. Although the effect of vibration isolation will decline if limit the output forces of the actuators, the secondary control forces are more less than unlimited situation and more suitable for engineering practice.