Passive magnetics can be used to implement a dashpot having a number of advantages. The principle of magnetic damping is shown at right. A conductor such as a copper plate, moves through a magnetic field produced by permanent magnets. By Maxwells laws applied in the reference frame of the conductor, a time varying magnetic field produces an electric field. This causes circulating, or "eddy" currents to flow in the conductor. These currents dissipate energy as they flow through the resistance of the conductor. The resulting drag force on the conductor is proportional to its velocity relative to the field. The device thus functions as a viscous damping element.

The advantages of a magnetic dampers (used in a TMD or otherwise) include: - They are simple and mechanically robust. - They can be constructed entirely of metallic materials, thus avoiding concerns with outgassing or deterioration with age. - They require no fluids or seals - They are noncontacting devices, and thus frictionless and highly linear - They can be designed for very long working strokes - Their temperature dependence is relatively small. At very low temperature, their weight and size efficiency is enhanced. - Given modern high-energy magnets, they can be reasonably compact. - With modern field solvers, their behavior can be predicted accurately at the design stage.

These advantages came to the fore when CSA Engineering was asked to design a very low frequency tuned mass damper for a large solar array that would power a spacecraft in orbit. The development is reported in the 1994 Proceeding of the SPIE Conference on Smart Materials and Structures (Kienholz, Pendleton, Richards, and Morgenthaler, "Demonstration of solar array vibration suppression" from which the following is excerpted.

The frequencies of interest were in the range of 0.12 to 1.0 Hz. At these very low frequencies, stiffness forces in the TMD must be very small and even slight friction can "lock up" the device and prevent it from damping. This, plus the long stroke required by the large vibratory displacements and the fact the device must be usable in space caused magnetics to be selected as the damping method for a TMD.

Three variants of TMD were developed, corresponding to three target modes of the array. All were designed to have natural frequencies and damping ratios that could be varied by remote control. The most important specifications of the devices are shown below.

All three versions of the TMD were similar in construction. A ground demonstration version is shown at right. Because the very low frequency causes elastic (spring) forces to be small compared to weight forces, a special means was required in the ground versions for offloading the weight of the moving mass. Air bearings were used for this purpose and the demonstration device was restricted to operating with its active direction horizontal.

The magnetic dashpot is composed of two opposing horseshoe-shaped magnets placed one on either side of a moving conductor plate. The plate also forms the moving mass of the TMD. Dashpot constant is varied by changing the magnet separation. The spring is composed of two sets of thin steel "leaves" flexing in series. The stiffness of each set is controlled by changing the number of active leaves.

All three devices were bench tested extensively and found to meet the specifications shown in the table above.

A full-scale solar array simulator was built to demonstrate the devices. It accurately simulated the actual array in terms of mode shapes, frequencies, and modal masses. The two plots below show test results. The construction of the TMDs allowed their damping to be turned on and off at will. The moving mass of the TMD could be locked to the frame simply by turning off the supply of compressed air to the air bearings. This allowed the simulator to be tested in three ways: (1) without TMDs, (2) with TMDs attached but not operating, and (3) with TMDs attached and operating.

The plot below shows measured acceleration/force frequency response functions for all three configurations. Resonant response is reduced by about 30 dB (factor of 31.6) by the dampers. The effect of the dampers on free vibration decay is shown in the bottom plot. It is a time history of free vibration with the TMDs turned on at the point indicated.

The importance of magnetic damping in this application is that it is a true passive method that can damp at very low frequencies and be qualified for long-term, high-reliability use in space.

Frequency response functions of solar array simulator with and without
magnetic tuned mass dampers.

Free vibration decay of solar array simulator with and without magnetic tuned mass dampers.