Method for determining minimum-order mass and stiffness matrices from modal test data

Active hard mount vibration isolation for precision equipment

“…The sensors and actuators require conditioning and power electronics respectively, which contain active electrical components, hence the name active isolation. Active vibration isolation is discussed in the next sections, the mechanical design parameters for passive vibration isolation, in particular k 1 The transmissibility and compliance can be calculated with Eq. (2.4) as ) it is observed that the vibration isolator can be interpreted as a mechanical low-pass filter for floor vibrations with corner frequency f r = 2πω r = 2π √ k 1 /m which is the resonance frequency of the vibration isolator.…”

“…Parameters k 1 and d 1 [59]. The effects of parameters m 1 , m 2 , k 2 , and d 2 on the four transfer functions are not discussed in this thesis since these parameters have to do with the design of the equipment rather than with the design of the vibration isolator.…”

“…(2.4) as ) it is observed that the vibration isolator can be interpreted as a mechanical low-pass filter for floor vibrations with corner frequency f r = 2πω r = 2π √ k 1 /m which is the resonance frequency of the vibration isolator. Given a certain mass m for the equipment, resonance frequency f r , also referred to as the suspension frequency, is determined by suspension stiffness k 1 . Vibration isolators with a low suspension frequency are also referred to as soft mounts.…”

“…The flexible payload body consists of two bodies with mass m 1 and m 2 (where m 1 + m 2 = m) that are interconnected by spring k 2 and damper d 2 , allowing an internal deformation. The suspension or mount that connects the equipment to the floor is modeled as a parallel connection of spring k 1 and damper d 1 . In both models, it is assumed that the floor motion x 0 is an independent input disturbance.…”

“…• (s) Diagonal controller transfer function I n n × n identity matrix j = √ −1 Imaginary unit J Jacobian matrix of the least squares problem k Axial stiffness of a leg (N/m) k 1 Suspension stiffness (N/m) k 2 Internal stiffness (N/m) k a , K a Proportional gain (matrix) (kg) …”