Group 4, Lab 10

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California State University, Northridge *

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317

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Mechanical Engineering

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Feb 20, 2024

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Fall 2023 California State University, Northridge Experiment 10 Dynamic Imbalance Mechanics Lab AM 317 Written By:

Abstract: In engineering, dynamic imbalance delves into the realm of analyzing machinery with rotation parts. Dynamic imbalance is when the mass of a rotating member in a machine is not equally distributed about the axis of rotation. This imbalance is certainly an issue to be wary of, especially with machinery that operates at high speeds. Some common devices that experience dynamic imbalance are engines, turbines, shafts, and fans. It is important to try to minimize dynamic imbalance wherever possible as it can lead to many different issues in the future if left alone. Some things to consider when analyzing systems to find dynamic imbalances are its causes, its effects, its remedies, and its applications. There are various causes for dynamic imbalances. It could be caused by uneven material distribution when the part was manufactured or even normal wear and tear. The effects of dynamic imbalance are also numerous. Dynamic imbalances can lead to vibrations in the system which create noise, reduces the overall efficiency, and lead to increased stress on the rotating machinery. When left untreated, excessive vibration can lead to compromised safety of the system. When treating dynamic imbalance, there are two ways to approach it. One method is static balancing, where the components are stationary and seeing where the center of mass lines up in the vertical plane. Another method is dynamic balancing where the same types of balancing techniques as static balancing are applied but, in all planes, not just the vertical plane. We expect to see an exponential growth graph for both the experimental and theoretical values, and for the most part that is what we saw, with a small degree of error, but a consistent error, letting us know that our values were precise.

Introduction: Dynamic imbalance is when the mass of a rotating member in a machine is not equally distributed about the axis of rotation. This imbalance is certainly an issue to be wary of, especially with machinery that operates at high speeds. Some common devices that experience dynamic imbalance are engines, turbines, shafts, and fans. Some things to consider when analyzing systems to find dynamic imbalances are its causes, its effects, its remedies, and its applications. There are various causes for dynamic imbalances. It could be caused by uneven material distribution when the part was manufactured or even normal wear and tear. The effects of dynamic imbalance are also numerous. Dynamic imbalances can lead to vibrations in the system which create noise, reduces the overall efficiency, and lead to increased stress on the rotating machinery. When left untreated, excessive vibration can lead to compromised safety of the system. When treating dynamic imbalance, there are two ways to approach it. One method is static balancing, where the components are stationary and seeing where the center of mass lines up in the vertical plane. Another method is dynamic balancing where the same types of balancing techniques as static balancing are applied but, in all planes, not just the vertical plane. In this lab, using the rotor mounted in bearings, the 12” steel scale, charge amplifier, multi-meter (voltmeter), and wheel balance. Using this equipment, we hope to be able to find an exponential growth graph between the reaction force and the angular frequency.

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Theory: There are a few things to know when analyzing dynamic unbalance in systems. One of which is the force that the eccentric mass gives off. This is used in order to find the maximum reaction force at the different locations on the balance wheel. Once we know that, we can do a more detailed study on systems that experience dynamic unbalance. The formula for finding the force of the eccentric mass is m, the mass of the weight, times r, the distance of the weight to the center of the shaft, times the angular velocity, also referred as angular frequency of the motor, squared, is equal to the force of the eccentric mass. The next equation that we need is the force in the y direction. These forces are the forces that act in the y plane that occur when the balance wheel is spinning. The force in the y direction is a result of the forces that the motor puts on the wheel. The equation is as follows, m, the mass of the weight, times r, the distance of the weight to the center of the shaft, times b, the distance from the bearing to the unbalanced disk, over L, the length of the shaft between the bearings, all times the angular velocity, also referred as angular frequency of the motor, squared, is equal to the peak force at the location of the force transducer. We also need to calculate the percent error between two values in order to compare the difference between the calculated value and the experimental value.

Procedures: To begin the lab, we had to measure various dimensions of the shaft and balanced wheels. Once those dimensions were recorded, we went on and found the balance, which consisted of a bolt, a nut, and a washer. We weighed those in ounces and recorded those values into its subsequent table. We then made sure that all the equipment was plugged into the outlet, plugged into each other, and turned on. Once we made sure of that, we were then ready to perform the actual testing for the lab. For the first part of the lab, we placed the weight in one of the holes on the balance wheel and set the machine to run at 700 rpm. Once we got a steady reading of force, we recorded the value into our table. There were 8 different holes throughout the balance wheel, and we repeated the steps of installing and reading the force for each hole. During this whole first process, we did not change the motor speed in order to get a consistent reading across all the holes. When looking at our table, we found one hole whose value had the highest reaction force. We took note of the hole that experienced the highest reaction force, as we will need it for the second stage of the experiment. For the second part of the lab, we first took out the weight from the balance wheel. We started the motor at 300 rpm’s. From there, we increased the speed by 100 rpms until we reached 700 rpms. Then, we inserted the weight back into the hole that we found the highest reaction force into and started the testing over back at 300 rpm. We found that we were getting much higher loads with the weight in compared to without the weight. Once we completed the lab, we turned off all the equipment and cleaned everything up.

Results: Table 1: System Specifications. Measured Data L (in.) 11.50 b (in.) 10.00 r (in.) 4.50 m (lb-s2/in.) 0.000161825 Table 2: Reaction Force for Different Mass Locations at 700 RPM. Hole Number 1 2 3 4 5 6 7 8 Force (lb) 2.75 3.25 3.55 3.47 3.08 2.48 2.21 2.40 Table 3: Experimental Data FREQUENC Y (rpm) FREQUENCY ω (rad/sec) FORCE READINGS w/o mass w/ mass* FORCE (lb) Exp. Theory % Error 300 31.4159265 0.6 1.09 0.5 0.62496996 13.5958477 400 41.8879021 0.6 1.6 1 1.11105771 13.5958477 500 52.3598776 0.6 2.13 1.5 1.73602768 14.1718754 600 62.8318531 0.7 2.8 2.2 2.49987986 13.9958669 700 73.3038286 0.7 3.74 3.1 3.40261425 9.18747254 800 83.7758041 0 4.44423086 100 900 94.2477796 0 5.62472968 100 1000 104.719755 0 6.94411071 100 1100 115.191731 0 8.40237396 100 1200 125.663706 0 9.99951943 100 1300 136.135682 0 11.7355471 100 1400 146.607657 0 13.610457 100

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Graph 1: Experimental Reaction Force vs. Angular Frequency 250 300 350 400 450 500 550 600 650 700 750 0 0.5 1 1.5 2 2.5 3 3.5 f(x) = 0.01 x − 1.5 R² = 0.98 Experimental Reaction Force vs. Angular Frequency Angular Frequency (rpm) Reaction Force (lb) Graph 2: Theoretical Reaction Force vs. Angular Frequency 200 400 600 800 1000 1200 1400 1600 0 2 4 6 8 10 12 14 16 f(x) = 0.01 x − 4.19 R² = 0.97 Theoretical Reaction Force vs. Angular Frequency Angular Frequency (rpm) Reaction Force (lb)

Discussions and Conclusions: There were a lot of different values that go into play when analyzing dynamic imbalance. The first things that we had to get were the system specifications, or the measurements of the system. We recorded the total length of the system, the length of the balance to the motor, the radius of the balance wheel, and the mass of the washer, bolt, and nut. These values were used to find other values later in the experiment. In Table 2, we recorded our reaction forces for different mass locations at 700 rpm instead of the recommended 900 rpm. There, we started the seeing values starting at 2.75 lb for the first hole and ended with 2.4 lb on the eighth hole. The values rose and fell, with the highest value being on the third hole that we tested. The third hole was determined to be the one that the highest reaction force occurs at. In Table 3, we recorded our calculated values and our recorded values. Using the values that we obtained in Table 1; we were able to get our values. We only performed tests from 300 rpm to 700 rpm but calculated our values from 300 rpm to 1400 rpm. We found that our forces in theory were always slightly higher than the force that we got from experimentation, but not by a large amount, the error between the two ranged from 9.19% to 14.17%. In Graph 1, you can see that the experimental values seem to form an exponential growth graph, had the experimentation been continued we would have seen results that would reflect a more noticeable exponential growth. In Graph 2, because we were able to calculate more values the exponential growth graph was more obvious to see. Overall, we saw the values that we expected to see from the experiment.

Appendix:

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