The ES-18 shaker is a servo-hydraulically controlled system designed to produce 1-D (horizontal) shaking in response to an applied input voltage signal v_in . It has been designed for use with medium-sized (or larger) geotechnical centrifuges, for studies in which application of input motions to the base of a model container is desired. Maximum design shaking force is 18,000 lbf at a supply pressure of 3,000 psi, and when configured with appropriate shims, the maximum stroke (i.e. peak to peak displacement of the slip-table) is 1.25 inches. The nominal operating frequency range is 20-600 Hz.

            Shaking force is developed within the hydraulic actuators and is applied between the actuators, which are fixed to the platform of the centrifuge, and the slip-table, to which the model container is attached. Feedback signals are derived from (1) the position of the slip-table, (2) the internal state of the servovalves, and (3) the force (pressure) developed by each actuator. These signals are compared to the applied input signal within the SC-1 servocontroller to produce an actuating or error signal, e(t). This error signal is amplified (Team model 1528 power amplifiers) and the resulting high current used to drive the voice coils in the pilot stage servovalves (Team model V-20). A second, high flow slave-stage valve (Team model V-750) acts as a hydraulic amplifier, converting the tiny flow produced by the V-20 valve into the large flows needed to supply the actuators.

            Newton’s First Law of Motion guarantees that the same amount of force being used to accelerate the moving masses (i.e. the slip-table /model container/soil system) will also be applied to the “fixed” or reaction masses (ostensibly, the non-moving portions of the shaker, together with portions of the centrifuge rigidly connected to it). For this reason, the mechanical impedance of  the centrifuge as measured at the shaker attachment points will have an influence on the resulting motion of the model and the measured performance of the shaker system. Within this document, all performance specifications are based on an assumed infinitely rigid and massive reaction mass.

The ES-18 consists of four major sub-assemblies:

1 - the slip-table,

2,3 - the left-hand and right-hand hydraulic manifolds with attached actuators, and

4 - the central bearing support assembly.

Assemblies 2, 3, and 4 bolt together using twelve high strength 3/8-  socket head machine screws.

            The displacement of the slip table away from its null (center) position is sensed and converted to a proportional  voltage signal using an LVDT (linear variable differential transformer) and associated signal conditioner. This “displacement voltage”, designated v_xt, is routed to the feedback controller, where it is applied to both the left and right channels in parallel and is used as one of the signals for controlling the motion of the shaker. The slip table LVDT is a model MHR500, manufactured by Lucas Schaevitz Corporation, and the signal conditioner is a model LVM-110, also manufactured by Lucas Schaevitz. Movement of the slip table outward (i.e away from the center of the centrifuge, or upwards if the centrifuge is spinning with the platform rotated up) is considered positive. Because negative feedback is employed exclusively on this shaker, positive displacement of the slip table will produce a negative change in voltage as measured at test points TPL5 and TPR5 on the servocontroller circuit board. (Observe that amplifier U5 is a non-inverting amplifier, so the LVDT voltage applied at P2 is the same polarity as that at TPL5 and TPR5. Also note that amplifiers U6 and U7 are both inverting amplifiers, so positive voltages swings at TPL5 and TPR5 correspond to positive voltages at TPL6 and TPR6, respectively. Amplifiers U2, U3, and U4 are not used in this configuration and the sockets should be left empty.)