Final Design

Universal Shaker Stand for Aircraft Modal Testing

Figure 1: Collapsed and extended version of shaker stand

Figure 2: CAD model of the shaker stand

Description of Final Design

    The final design was divided into four major components: telescoping legs with delrin bushings, truss elements attached with fittings, a hinged top plate, and adjustable swivel feet.

Telescoping Legs

    Two of the major requirements of the shaker stand are that it must be adjustable between 1.22 m (4’) to 4.27 m (14’) and have a stiffness such that the first mode in one axis be above 9 Hz and 15 Hz in another axis. Stainless Steel telescoping legs with five segments were used in order to achieve this range of adjustability. The telescoping legs were laid out in an A-frame truss structure as shown in Figure 2.

    The functional requirement in this area was to be able to hold a 890 N axial load without slip. Given that the shaker weighs approximately 25 kg, that would equate to a factor of safety of 7.26 when the load is distributed across four legs. A high factor of safety is important due to the high cost of the shaker as well as the safety concern with this large mass raised more than 4 meters high, which creates an overhead hazard. Using off-the-shelf shaft collar clamps provided effective clamping force at a low cost and the clamp was tested to the required 890 N of force without slip. Lever lock clamps were expensive and difficult to find in the correct sizes.  Hand tightening to the correct tightness was also difficult. Sanitation clamps were hinged for versatility but this presented problems with securing them to the tubes.  They also did not tighten sufficiently enough to prevent slip while under 890 N of force.

Figure 3: Telescoping legs with delrin bushings and shaft collar clamp

Delrin Bushings

    The delrin bushings were designed to prevent galling between the stainless steel tubing while also decreasing the amount of friction in the telescoping mechanism.  To accomplish this, two kinds of bushings were implemented:

• Outer Bushing - machined to be press fitted on the inside of the four larger OD tube segments.  Once the bushings were secured on the inside of the tube, each smaller segment was able to slide through the bushing smoothly.

• Inner Bushing - machined to be press fitted over the ends of the four smaller OD tube segments.  Once press fitted, each segment was able to slip into the next size tube smoothly.

    The conjunction of outer and inner delrin bushings provided superior stability and adjustability in comparison to only one single bushing. Not only did it allow the user to clamp the telescoping legs at any desired height, but it also prevented undesired movement between the leg sections.

Figure 7(Left): Outer bushing fitted on the inside of the outer pipe (left) & inner bushing fitted on the outside of the inner pipe (Right).

Truss Elements with Fittings

In order to reach the necessary stiffness, truss elements were added to the structure and connected with slip on pipe fittings. Since a design feature of the structure was that it be adjustable across a wide range of sizes, the truss elements must be adjustable and removable. A solution was found using telescoping truss members designed and fabricated in the same way as the telescoping legs of the main frame. The truss members were fabricated using the 2.54 cm (1”) tubing and are detachable from the structure by removing a nut and bolt from the pipe fitting. Telescoping the element and adjusting the angle on the swivel allows for bracing of any angle configuration of the legs.

The truss elements were determined to be necessary through finite element analysis of the A-frame structure using FEMAP. Without the truss elements, the structure had a first mode on the order of 10-3 Hz. Once a sufficient number of elements were added, the modes were determined to be 17.61 Hz in the first lateral axis and 9.64 Hz in the second lateral axis. While under the sponsor’s original specifications of 9 Hz and 15 Hz, they adjusted their functional requirements and these frequencies were deemed sufficient. The telescoping truss elements bring flexibility and adaptability to the structure as it is able to be stiffened over a wide range of configurations.

Figure 4: Truss elements and fittings

Hinged Top Plate

The top plate is made of 0.952 cm (3/8”) aluminum to reduce weight. The main shaker’s hole pattern was drilled into the top plate to provide a secure mounting base for the shaker. Additionally, slots were cut into the plate using the CNC mill to accommodate a wider range of shakers in different orientations.

Figure 5: Top hinged plate

Adjustable Swivel Feet

With the A-frame design of four telescoping legs, instability from uneven ground or legs is a concern. This was addressed using adjustable swivel feet at the bottom of each of the four legs.  This adjustability prevents any undesired instability when the structure is placed on uneven ground.  With an adjustability of fifteen degrees, the foot is able to keep the shaker stand level. An aluminum tube end with threads was machined to be fit inside of the bottom leg as an attachment point for the swivel feet

Figure 6 (Right): Threaded tube ends for swivel feet

    A slit is included in the bottom of the leg so that a ratchet strap could be run through the entire perimeter of the structure.  This provides a layer of redundancy to the lever lock hinges at the top plate. The functionality of the ratchet strap is not to be a stiffening component but to prevent the legs from slipping outward.

Figure 7 & 8: Model of swivel feet and slit for ratchet strap

Performance Results

        Each stainless steel telescoping leg of the shaker stand can support 890 N of force axial along the length of the tubing with less than 1 mm of slip. The first mode of the shaker stand in the lateral axis and second lateral axis was calculated by placing the shaker on the shaker stand and exciting the structure with the shaker. The modes were measured using accelerometers attached to the structure. The first mode in the lateral axis (preferential axis) was found to be 17.61 Hz and the first mode in the second lateral axis was found to be 9.64 Hz. The setup time of the shaker stand was tested by having the stand completely collapsed and allowing two people to set it up at a reasonable speed. The stand was set up in 30 minutes to its maximum height.

Figure 9 (left): FEMAP model of lateral axis - 17.61Hz

Figure 10 (Right) - FEMAP model of second lateral axis - 9.64Hz

         The top plate is made of  0.952 cm (3/8”)  aluminum in order to reduce weight. The main shaker’s hole pattern is drilled into the top plate to provide a secure mounting base for the shaker. Additionally, slots are cut into the plate using the CNC mill in order to accommodate a wider range of shakers in different orientations.

        Analysis was done using Solidworks simulation tools to verify the integrity of the 0.635 cm aluminum top plate. The contour graph of the displacement is shown in Figure 11 and the stress analysis is shown in Figure 12.

Figure 11: Contour graph showing displacement in top plate when subject to a 1000N load.

Figure 12: Contour graph showing stress in top plate when subject to a 1000N load.

        A test of the structure’s stiffness was conducted at ATA Engineering, Inc. Their test engineers mounted the shaker on top of the fully erected structure and excited the structure with an impulse hammer. An image of the test setup is shown in Figure 13. An accelerometer was attached at the top of the shaker stand to collect vibration data for the test. 

Figure 13: Stiffness test of shaker stand using an impulse hammer and accelerometer..

        The point of excitation of the shaker stand was at the top where the shaker is mounted, due to it being the largest mass. The test engineer excited the structure in the X, Y, and Z directions in order to determine the modes in the three axes. A frequency response function was generated with the data collected from the accelerometer. This is shown in Figure 14. From the FRF plot, it is evident that the first mode along the lateral axis is 5.5 Hz, the second mode along the other lateral axis is 12.9 Hz, and the mode in the vertical axis was 20.2 Hz. While these results fall below our original design goals, it was determined that these actual frequencies would be sufficient to provide a stable excitation platform for the shaker stand. Additionally, though no testing was done for it, it can be expected that the modes would increase if the shaker stand was collapsed to a lower height, adding further stiffness to the overall structure.

Figure 14: Frequency response function for modal testing of shaker stand.