Vibration Reduction Engineering Analysis, Simulation and TestingEmperical Testing
Figure 1.1: Longitudinal Impulse Test Data and FFTTesting revealed some very important information regarding the natural freqency of the system which was previously assumed. The natural frequency of the system beleived to be near 3.5 Hz. This was concluded after LORD proprietory software was used to run simulations. However, these simulations do not correlate with the emperical test data that was taken. After exciting the system with an impulse, the system damped to zero at a frequency of 7 Hz which was revealed by the FFT shown above in Figure 1.1.
Systems Level Model
Figure 1.2: Compressor System Model Diagram
Figure 1.2 shows the equations of motion used to model the dynamic motion of the compressor. The forces which were used were proprietary numbers developed by Dresser-Rand. The isolating feet were modeled by the Kelvin-Voigt model, which is a spring and dashpot in parrallel. Figure 1.2 also shows the location of the Y accelerometer, which was used to fit the model parameters.
Figure 1.3: Model Implementation in MATLAB Simulink
Figure 1.3 shows the equations of motion modeled in MATLAB Simulink. This application allows us to continously solve the system using the ODE45 solver in this particular case. A fixed time step of 0.001 seconds was used during the simulations.
Figure 1.4: Model Fit to Emperical Accelerometer Data
Figure 1.4 is a plot of steady state model output overlayed ontop of emperical acceleration data obtained via the National Instuments DAQ. The model was fit to these curves by adjusting the damping coefficients of the rubber isolators. The spring stiffness of the isolators was determined by the natural frequency of the system which we found through empirical testing.
Figure 1.5: Model Parameters and Transmissibility Relation
Figure 1.5 displays all of the final model parameters which were used to analyze the system and potential solutions. It also shows an important relationship between the systems damping ratio, natural frequency, forced frequency and transmissibility.
Figure 1.6: Previous Transmissibility Plot: Nat Freq = 3.5 Hz
Figure 1.6 shows what the initial senior design group, who installed the compressor, thought the transmissibility curve of the system should look like. Unfortunately, the natural frequency of the system was never confirmed until recently.
Figure 1.7: New Transmissibility Plot: Nat Freq = 7 Hz
Clearly, since the natural frequency is not 3.5 Hz our transmissibility curve is going to change. Figure 7 shows the transmissibility plot we generated from our model parameters. It is much more representative of the actual behavior of the system, which accelerates about 3.5 times as fast as it should at a 1:1 force relation. Since the transmissibility curve in figure 7 says the amplification is about 3.77, this leads me to believe our model parameters are much more representative than the previous models which were developed.
Tuned Mass Damper Design and Simulations
Moving forward from the systems design review, we wanted to analyze two countermeasures to our vibration reduction issue. From our Pugh analysis our best option was the tuned mass damper, but there were some risks associated with this, so we wanted to also keep raised MR shocks as a secondary option.
MR Shock Observation Armed with the new information regarding the natural frequency of the system the behavior which was observed when the MR shocks were installed became more understandable.
As the the compressor operates freely with not vibration reduction systems in place, it accelerates at an amplitude of about 4 m/s^2. When the MR shocks are added to the system with no current to stiffen them, the compressor accelerates at an amplitude of about 5 m/s^2. When first recognized, this opposed the intuitive thought of adding damping to a system, but it is explained by the relationship of our natural frequency and our forcing frequency. By adding damping the natural frequency of the system, which was 7 Hz, is lowered. Thereby moving the systems natural frequency closer to the forcing frequency.
Since this is the case, damping the system is a difficult way to reduce vibration. The damping would need to be significantly stiffer, which would result in large amounts of energy being transfered to the floor. For these reasons it is clear, that the best option to reduce vibration is to offset force input.
Figure 1.8: Tuned Mass Damper Operating Principle
Tuned mass dampers are normally used to damp vibrations in structures when they are excited near their natural frequencies. If our compressor operated at multiple frequencies, this type of system would not be an appropriate solution. Fortunately our compressor operates at a very consistent 6.4 Hz. Therefore we can design a spring and mass system with a natural frequency of 6.4 Hz, which will oppose the motion of the compressor.
The displacement of the compressor will force the secondary mass and stretch the spring. As the spring stretches and accelerates the mass back towards the compressor, the compressor will then start accelerating back towards the mass. This cyclic extension and compression of the spring will go through a short transient period and find a steady state equilibrium. The net force accelerating the two mass system will be small thereby transmitting much less force to the floor than the current condition.
Figure 8 shows my Simulink implementation of the system, which will allow the user to change the mass and spring rate being used in the TMD system. The model will also allow you to change the vertical height at which the system acts.
Figure 1.9: Effects of Varying TMD Mass
Figure 1.9 is a chart displaying the various forces, which will result from installing a TMD system on the compressor. From the analysis we can see it is possible, assuming minimal damping in our TMD, that we can cancel 95% of the piston inertial force utilizing a mass of 80 kg.
Figure 1.10 and 1.11: Original TMD Design
Figure 1.10 and 1.11 shows the original TMD design that was developed and proposed at the DDR. The system would have functioned and worked with a 40 kg and 80 kg mass, making it flexible. The system would have also made tuning the system very easy by utilizing stacked discrete plates. However there were great safety risks associated with the design due to stored potential energy in the spring system. Therefore this design was not approved. Figure 1.11 shows some of the FEA, which was conducted.
Figure 1.12: Single Spring TMD Design
Figure 1.12 shows the newly designed TMD attached to the compressor. This TMD is more compact and will only use a single spring to function, which eliminates the need to compress springs and preload the system. Therefore this system is much safer. The spring will act both in tension and compression against a 100 kg mass. The mass is now 100 kg due to the availability of an appropriate spring. The added mass will only make the system more effective. The single spring design allows the chassis of the TMD to be less robust, by loading longidutinally only at the single compression plate. The secondary support which is pictured is to support the end of the hardened guide shaft under the 100 kg load. The mass will glide on the hardened shaft by using a linear guide. The mass will be cut on a waterjet. it would be ideal to be ble to buy prefabricated weights, but the design envelope requires a proprietary mass design to 100 kg.
'''Figure 1.13: Single Spring TMD Exploded View
Figure 1.13 shows a more detailed image of the design. To restrain the spring, high strength U-bolts will be utilized. Since this design is a new development, there is still a lot of stress analysis to be don in the coming weeks, but the analysis on the purchased compenents has been completed so purchases should move forward shortly.
Bill of Material (BOM)
The user must be able to continuously monitor rider ring health. The wear part is a teflon consumable component. They can go without warning and cause catastrophic failure. Our health monitoring system will prevent metal on metal contact in the cylinder. The wear cannot be measured within the compression chamber where the wear is occurring. The wear is measured on the rod to the piston and the wear is determined.
Previous Proposed Solution
Previously proposed was the Keyence laser system. In our Pugh Matrix the parameters changed due to new incite and changes in cost due to the donation from Bentley Nevada.
Updated Pugh Matrix
Figure 2.1: Keyence Laser vs. Bentley Nevada Proximity Probe
Updated Proposed Solution
-3300XL NSv Proximity Transducer System
Met with Bentley Nevada and they identified the same piece of equipment as we had selected.
It is specifically designed for small shaft sizes down to a diameter of 1.2 inches.
Bentley Nevada has agreed to donate the 3300XL NSv Proximity Transducer System.
Includes the entire proximity transducer system for dual axis measurements.
Moved to dual axis monitoring. Ring may wear in any direction not just descend vertically.
Power Source: -17.5Vdc to -26Vdc
Linear Range: 1.5mm (60 mils)
Gap: 1.0mm (40 mils)
Minimum Shaft Diameter: 30mm (1.2in)
Average Scale Factor: 7.87V/mm (200mV/mil)
Temp Range: 0 to +45 degrees celsius (+32:+113 degrees F)
Figure 2.2: Detailed Drawing of 3-D Proximity Probe Mount
Figure 2.3: Finite Element Analysis with a 50lbf on the Proximity Probe Mount
-Proximity Probes Delivery: 03/11/2013
-Mounting Bracket Machining: 03/08/2013
-Instillation Details: Time to be determined.
-Our lab has an instructional manual on the process in both hard copy and e copy.-3 Day implementation timeline: -Day 1: Disassembly -Day 2: Machine
-Day 3: Reassemble
A bench experiment will consist of a 1.2 inch diameter steel pipe which will be moved in the x and y axis to verify a proper output a signal on the DAQ system.
Thermosyphoning and Flowmeter Engineering Analysis and Testing
Understanding the flowmeter problem: Group 12452 installed an OMEGA FTB 325 flow meter in line with the thermosyphoning piping. It is hardwired directly into the DAQ system with an analog output in LabView. 12452 believed that they could not get a value to read in the DAQ system because the flow meter was not sensitive enough. They estimated that the flow throughout the thermosyphoning system was approximately 1,135.62 ml/min, while the flow meter is capable of reading from 500-5000 ml/min.
As a result, we will first determine the volumetric flow rate of a bilge pump that was borrowed from Dr. K to use as a datum for the flow meter measurement. As a result, we will use the bilge pump at the same voltage and amperage as the volumetric flow test to flow water through our flow meter.
Drawings, Schematics, Flow Charts, Simulations
The flow chart, shown in Figure 3.1, represent the process in which the flowmeter was tested and analyzed.
The problem solving wheel, shown in Figure 3.2, represents the structure in which the flowmeter was broken down and analyzed to ensure that no steps were missing along the way.
Setup for the flowmeter test consisted of a power supply (Figure 3.3) to drive the bilge pump under 5 gallons of water (Figure 3.4).
-Measure flow through bilge pump at exceeding flow rate and compare to analog output (shown in Figure 3.5)
-Measure flow through bilge pump at nominal flow rate and compare to analog output (shown in Figure 3.6)
-Measure flow through bilge pump below nominal flow rate and compare to analog output (shown in Figure 3.7)
-Run dirty liquid through the flowmeter and see if continues to output an analog signal (shown in Figure 3.8). The liquid used for the test was black coffee.
-Replace inline with thermosyphoning system and make sure the flowmeter is hardwired correctly. Allow thermosyphon reservoir to gravity feed into the pumps reservoir, which would ensure that the water is going through the flowmeter and reading appropriately. Then run thermosyphoning system for two hours and see if flow is measured (shown in Figure 3.9).
From running each experiment, we can conclude that the pre-existing system is not flowing, ultimately not cooling the cylinder. As a result, a bench experiment will be designed with the radiators and piping used on the compressor to test the theory of thermosyphoning but under our conditions including headloss, piping dimensions and material, and current condition temperatures.
The following figures represent the 2-D schematics of the test rig that will be built for the thermosyphoning bench experiment. This system will be built on a rolling cart so that it has simple capabilities to move to an area with a pre-existing DAQ system. Heating wrap will have varying locations to assure that the experiment is mimicking the compressor location properly along with potential other heat source locations.
BOM for Upcoming Bench Experiment
Steady State Heat and Flow Model
4.1 User Interface
From the original proposed design, modeled after our predecessors, the user interface has been expanded into a fully functional excel model with inputs, intermediate outputs, and ultimate outputs. This new design is illustrated below, in Figure 4-1. The interface is divided into two interlinked segments and a separate segment for a comparison to empirical data.
Figure 4-1: User Interface Design
4.2 Engineering Model
In order to develop the most accurate mathematical model possible, it is important to explicitly state all relevant assumptions made and illustrate analyzed flow paths through schematic diagrams.
4.2.1 Relevant Assumptions
- Steady state, steady flow situation
- One dimensional analysis for heat and flow
- Fully developed, laminar flow
- Incompressible fluid (for steady state case only)
- Constant Thermal and Fluid Properties (h and k, mu and rho)
- Neglect the effects of external radiation
- Uniform convection coefficient over outer surface
- Constant ambient temperature (Tinf)
- Neglect the effects of head loss for flanged section heat transfer analysis
4.2.2 Heat Flow Diagram
The thermal resistance diagram, depicted in Figure 4-2, displays the flow of heat from the working compressor fluidâ€”waterâ€”to the ambient atmosphere, through the fins and tubing walls.
Figure 4-2: Thermal Resistance Diagram
4.2.3 Fluid Flow Diagrams
Figure 4-3 shows the flow of the working fluid through the finned tubing cross section, while identifying all relevant variables. An external view is displayed in Figure 4-4.
Figure 4-3: Finned Tubing Cross-section
Figure 4-4: External Flow Diagram
4.3 Heat Model
System inputs for the heat model are: Number of fins, geometry of the fins, radii of tube and fin tip from tube center, ambient temperature, mean temperature of incoming fluid, conductivity coefficients, and convective coefficients.
The governing equation for heat transfer through the finned tubing is displayed in Figure 4-5.
Figure 4-5: Heat Governing Equation
Where A_f is area of a fin, A_t is the total area exposed, Theta_b is the difference between surface temperature and ambient temperature, and Eta_f is the fin efficiency.
4.4 Flow Model
System inputs for the flow model are: Geometry of the pipe, fluid properties, and inlet and outlet temperature.
Using conservation of energy for an incompressible, steady state case with uniform pressures across boundaries, fully developed laminar flow through a pipe of constant diameter, and no shaft or boundary work the energy equation is simplified and analyzed to fit our particular situation.
The governing equation for flow through the finned tubing is displayed in Figure 4-6, once the mass flow rate has been dissolved into terms of velocity, Figures 4-7 through 4-8 describe the analysis technique for the model.
Figure 4-6: Flow Governing Equation
Figure 4-7: Flow Governing Equation in Terms of Velocity
Figure 4-8: Used to find mass- and volumetric-flow rate from velocity
Where V is average velocity, k is the minor head-loss coefficient, rho is the fluid density, A is the cross-sectional area of the pipe, C_v is the specific heat of the working fluid, delta_T is the difference in temperature from pipe inlet to exit, L is the length of pipe, mu is the fluid viscosity, and D is the pipe diameter.