Eddy Curent Tuned Mass Damper

Have you seen the video of the Tacoma Narrows Bridge swaying in the wind? That collapse was caused by wind exciting the system at one of its natural frequencies, leading to a resonance catastrophe. To avoid such disasters, engineers use Tuned Mass Dampers (TMDs) to stabilize structures like buildings, bridges, or machine tools when they are subjected to vibrations matching their natural frequencies.

During a course called "Machine Dynamics", my group and I set out to develop a Tuned Mass Damper for a vibration demonstrator. This demonstrator mimics a three-story building and features base excitation to simulate earthquakes. The damper itself is based on the theoretical model of a single-degree-of-freedom (1-DOF) mass-spring system. To generate damping within the system we decided to use permanent magnets and a metallic conducting plate, in order to generate eddy currents.

In this Instructable, we will discuss how we designed and fabricated this Tuned Mass Damper. A full technical report is linked to this introduction; please note that the original documentation is in German.

To ensure the best possible quality for this guide, we have used the AI tool Gemini from Google to refine the English text.

Bill of Materials:

1. 3D-Printer capable of printing PETG and TPU (we used a Bambulab X1C)
2. 1 Spool PETG
3. 2 x Aluminium Rods with 8 mm diameter and a length of 260 mm
4. 4 x Track Roller Bearings (Reference: LFR5201 10 2RS) (Note that you can actually use other bearings, you will just have to design and print adapters to match the axes and Aluminium Rods)
5. 6 x Permanent Magnets (Height: 12 mm, Diameter: 20 mm, 25kg Holding strength)
6. 3 m6 x 15 Dowel Pins (In order to connect the housing halfs together)
7. 2 m6 x 30 Dowel Pins (for stacking mass plates)
8. 10-15 Mass plates made of steel (thickness 1 mm, technical Drawing named: Mass_plate)
9. 2 Springs with a spring stiffness of 200 N/m and an approximate length of 40 mm (Reference: RZ-081JI )
10. Accelerometer to measure natural Frequencies (You can use the mobil App Phyphox)
11. Different length M3 and M4 screws

To build an effective Tuned Mass Damper (TMD), the first step is to identify the specific natural frequency you want to attenuate. This requires measuring the natural frequencies of your primary system.

The Measurement Process:

1. Mount an accelerometer—or a smartphone using an app like phyphox—securely to the structure.
2. Apply a manual displacement (an initial push) and release the system to create a free vibration (a "ring-down" or decay test).
3. Record the acceleration data as the system settles.
4. Perform a Fast Fourier Transform (FFT) on the measured data to convert the time-signal into the frequency domain, where the natural frequencies appear as distinct peaks.

Our Setup:

We used a professional vibration sensor called the RECOVIB Feel, which performs the FFT analysis automatically. In the image below, you can see the vibration demonstrator with the RECOVIB Feel mounted on the first story (highlighted with a red circle).

Experimental Results:

The resulting FFT analysis for our ssystem is shown in the graph below. We identified three distinct natural frequencies:

1. f1 = 1.25 Hz
2. f2 = 3.37 Hz (Our Target)
3. f3 = 4.75 Hz

We chose to design our TMD specifically for the second natural frequency f2 = 3.37 Hz. While f1 is the fundamental frequency, it would require much larger physical oscillations to dampen; f2 provides a strong resonance peak that is easier to manage within a compact 3D-printed design.

In order to desing your TMD, you will also have to determine the modal Mass of your vibrating system for the frequency that you want to attenuate. In our case the modal Mass is roughly around 8 kg.

The parameters of the Tuned Mass Damper can be determined with the Den Hartog Method. In order to keep this instructable simple, we won't be discussing the detailed calculations, which are included in the technical Report, linked to the introduction. We used the following parameters for our TMD:

1. Masse = 0,89 kg
2. Spring Stiffness = 2 x 200 N/m
3. Damping Ration: adjustable from 5 % up to 25 % (These values were determined experimentally after the completion of this project)

With the parameters calculated, it is time to turn theory into hardware. This step involves the construction of the multi-variable Tuned Mass Damper (TMD) housing and carriage.

The Multi-Variable Concept

The goal was to create a compact assembly that allows for independent adjustment of all relevant physical variables:

1. Stiffness (k): Adjusted by swapping or adding parallel extension springs.
2. Mass (m): Adjusted by stacking laser-cut steel plates onto the carriage pins.
3. Damping (D): Adjusted by a manual wedge mechanism that changes the magnetic air gap.

The 3D-Printed Housing

The housing consists of two main PETG halves connected by dowel pins (Pos. 14) and the linear guide rods.

1. Material: PETG (blue) was chosen for its strength and durability.
2. Linear Guidance: Two 8 mm aluminum rods (Pos. 13) serve as the tracks.
3. Magnetic Mounting: Pot magnets are mounted to the bottom of the housing to securely attach the TMD to the demonstrator floors.

The Low-Friction Carriage

To ensure the damping is purely controlled by the magnets and not by unwanted friction, the carriage uses a high-performance roller system¹¹.

1. Rollers: Four track roller bearings (LFR5201) are pressed onto the carriage.
2. Modification: We removed the bearing seals and degreased them using brake cleaner to ensure they spin with near-zero resistance, in order to prevent rosting in the future we oiled them with sewing machine oil.
3. Induction Plate: A slot on the underside holds the copper or aluminum plate (Pos. 9, 10), which is secured with a single M4 screw.

The Wedge Adjustment Mechanism (Damping Control)

This is the most innovative part of the design. A 3D-printed adjustment wedge (Pos. 7) slides within a dovetail groove in the housing.

1. Function: As you slide the wedge, it raises or lowers the magnet plate (Pos. 4, 5, or 6).
2. The Air Gap: This mechanism allows you to precisely set the distance between the magnets and the induction plate from 3 mm to 15 mm.
3. Scale: A laser-engraved wood scale (Pos. 8) is attached to the side so you can repeatably set your damping levels.

The assembly drawing is featured above, this represantation of our TMD doesn't include the springs, which have to mounted in order for the TMD to work.

With the design finalized, we moved into the manufacturing phase. This step combines 3D printing for complex structural components with precision machining for the electromagnetic components.

3D Printing the Housing and Carriage

To maintain the professional aesthetic of the original vibration demonstrator, we carefully chose our filament colors:

1. Stationary Parts: The housing halves, wedge, and magnet plate were printed in blue PETG to match the color of the demonstrator floors.
2. Moving Parts: The carriage was printed in red PLA to follow the existing color scheme, where moving or excited parts are highlighted in red.

Print Settings & Stability: We used Bambu Studio with standard settings, but made two critical modifications for mechanical strength:

1. Infill Density: Increased to 25% to handle the tension from the springs.
2. Infill Pattern: Changed from rectilinear to Gyroid to ensure better multi-directional stability and prevent structural failure during high-frequency oscillations.

Assembly Note: Due to build volume limits, we divided the housing in the center into two separate parts. While our version uses dowel pins to reconnect them, printing the housing as a single solid piece is recommended if your printer allows it, as it improves overall structural rigidity. The STL Files are featured down below.

Machining the Induction Plates

The "heart" of the damping system consists of a conductive plate that interacts with the magnetic field. To investigate how material properties affect performance, we manufactured two identical plates with dimensions of 40 x 80 x 10 mm:

1. Aluminum Plate: Offers a lightweight solution with good conductivity.
2. Copper Plate: Provides superior electrical conductivity, which theoretically leads to higher damping forces via stronger eddy currents.

These plates were machined on a milling machine to ensure a flat surface and a perfect fit into the carriage recess.

The mass plates that were prenseted in the Bill of Materials, were Lasercut, but any other manufacturing process can be used to make them. As long as the dimensions are good.

The final assembled product is shown in the image above, ready for integration into the structural model. Once the Tuned Mass Damper (TMD) was fully assembled, we subjected it to rigorous testing to validate its vibration-damping capabilities.

Experimental Setup

1. The TMD was mounted on the first story of the "high-rise" model, as this location exhibits the largest amplitudes for the second mode.
2. The building was then excited at the base with a frequency of f = f2 = 3.37 Hz, exactly matching the target resonance³³³³.
3. We used eight mass plates (total weight 0.890 kg) and two parallel springs (400 N/m) to achieve the required tuning.

Results

The results can be seen in the featured videos. As you can see, when the TMD is mounted, the vibration has a much lower Amplitude and therefor the TMD is sucessfull.

What we also noticed at this point was, that the TMD we built can also be used to demonstrate a lot of vibration possibilities of a 1 DOF Mass-Spring System