Viscoelastic materials (VEMs) are those which dissipate mechanical energy into heat when they undergo cyclic stress. They can be applied to TMDs to obtain a simple, inexpensive, lightweight damping mechanism applicable to a wide range of structures. The main limitation of VEMs for TMD applications is that the VEM properties affect not only the TMD damping but also its natural frequency. The two cannot be controlled independently. Also, VEMs with high damping usually have high temperature sensitivity. VEM-based TMDs are therefore most effective in situations where the ambient temperature is well known and remains within a narrow range.

A manufacturer of a robotic manipulator for semiconductor manufacturing had a vibration problem. The primary structural element of his robotic "arm" was a cantilevered stainless steel tube, about 50 inches in length, 2 inches OD, and 1.25 inches ID. The effector at the free end of the arm was required to move vertically over a range of several inches and then settle to its final resting position with microinch stability. The throughput of the system obviously depended on minimizing the step-and-settle time. However increasing the step speed simply increased the excitation of the first bending mode of the cantilever and increased the settling time. Without damping, the settling time dominated the cycle time. The structure was already well-designed for high stiffness with low weight so increasing the natural frequency was not a viable option. Added damping was clearly the answer.

Constrained VEM layers could not be used on the outside of the tube because of requirements on circularity and surface finish. Constrained layers on the inside would have been expensive to apply and would not have given adequate damping. Fortunately, the operating temperature was essentially constant and the volume inside the tube was available. It was decided to design a TMD to fit in the long, slender volume inside a tube.

The first step was characterizing the base structure. While the tubular arm and end-effector would have been straightforward to model with finite elements, the traversing mechanism supporting the cantilever at its root would have impractical. Extensive experimental confirmation and tuning would have been required before any such FE model could be used with confidence. Fortunately, the first prototype arm was available for testing. A straightforward test requiring only a few hours was devised that gave the properties of the target mode needed for TMD design. This test produced data that was used to establish the natural frequency, moving mass, and damping level required of the TMD.

Assembled views of TMD using viscoelastic material.

The next step was conceptual design. The figure above shows one of the concepts. The red cylinder is the moving mass of the TMD. The spring is the purple shaft down the center, which acts as a cantilever beam extending back down the inside of the robot arm tube from its free end. The assembly in shades of blue at the upper left is an expanding clamp that fixes the root of the TMD flexure beam to the inside diameter of the robot arm tube at its free end with no modifications to the arm itself. Damping is introduced into the TMD by a constrained VEM layer. The green material is VEM and the dark purple over the VEM is the constraining layer.

A key element of the design process was finite element modeling of the TMD alone to identify a suitable geometry and VEM for the constrained layer damper, as well as an analytical design of the damped flexure spring and end mass to obtain the desired natural frequency. After a number of FE design iterations, a prototype was built and tested. Several small but crucial modifications were identified and implemented to make the actual hardware fit the modeling assumptions, and thus to give comparable performance

A dynamic simulator of the robot arm was designed and built. Shown below, it replicated the important features of the actual robot arm including its natural frequency and modal mass.

Test results are shown below in terms of the impulse response at the end weight of the simulator. The TMD produces 6-8% of critical damping and reduces the settling time by about 95%, relative to an undamped design. It even produces a significant reduction in tip vibration caused by the seismic background in the test lab. This is evidenced by the reduced steady-state vibration between t = 0 and t = 3 seconds, before the force impulse is applied.

Various enhancements were subsequently made to the TMD design to improve manufacturability and to allow tuning of the TMD natural frequency in the field. The design is currently in production and in use on the robot arms.

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