A LIGO Double Pendulum Suspension Prototype for Reducing Unwanted Cross-Couplings
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a Michelson Interferometer with 4km long arms used to detect gravitational waves passing through earth. LIGO uses extremely isolated optics in the form of suspensions to measure slight changes in laser path length down the two interfe...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Published: |
Massachusetts Institute of Technology
2023
|
| Online Access: | https://hdl.handle.net/1721.1/152872 https://orcid.org/0009-0004-1910-0391 |
| _version_ | 1826217287271579648 |
|---|---|
| author | Lee, Regina E. |
| author2 | Trumper, David L. |
| author_facet | Trumper, David L. Lee, Regina E. |
| author_sort | Lee, Regina E. |
| collection | MIT |
| description | The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a Michelson Interferometer with 4km long arms used to detect gravitational waves passing through earth. LIGO uses extremely isolated optics in the form of suspensions to measure slight changes in laser path length down the two interferometer arms. Unwanted cross-couplings between degrees of freedom in LIGO suspensions pose a large problem when trying to isolate their optics in the interferometer.
This thesis provides an analysis of the effects of changing the wire geometry of a double pendulum as a case study for LIGO pendulum designs. By changing the wire attachment point to be closer to the center of mass, we are able to see a decrease in longitudinal-to- pitch coupling by about a factor of 3. We observe that the pitch-to-pitch coupling decreases by a factor of approximately 1.5 at DC when comparing the new four wire configuration to the original two wire configuration. However, the first pitch resonance increases slightly. This resonance is most influenced by a combination of the wire attachment point and spring stiffness. The resonance can be moved around by changing these factors.
This project has two main components. The first is a state space model that describes the equations of motion for the double pendulum and is used to predict dynamic responses. The second is the construction of a physical double pendulum prototype which is used to verify results from the model. The experimental results show differences in dynamics compared to the state space model due to forcing off center, and the model was updated to include these dynamics. The physical pendulum is set up outside of vacuum and is not manufactured to the tight tolerance of real LIGO suspensions. Therefore, we do not have the precision necessary to experimentally attach the wires directly at the center of mass and did not measure these transfer functions. In conclusion, our observations lead us to believe that suspending the top mass with four wires is beneficial to reducing the longitudinal-to-pitch coupling. However, it is necessary to align the pivot point of the wires to the actuation point in order to demonstrate this. Future research can be done on placing the wire pivot point directly at the actuation point. |
| first_indexed | 2024-09-23T17:01:01Z |
| format | Thesis |
| id | mit-1721.1/152872 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T17:01:01Z |
| publishDate | 2023 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1528722023-11-03T03:01:55Z A LIGO Double Pendulum Suspension Prototype for Reducing Unwanted Cross-Couplings Lee, Regina E. Trumper, David L. Massachusetts Institute of Technology. Department of Mechanical Engineering The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a Michelson Interferometer with 4km long arms used to detect gravitational waves passing through earth. LIGO uses extremely isolated optics in the form of suspensions to measure slight changes in laser path length down the two interferometer arms. Unwanted cross-couplings between degrees of freedom in LIGO suspensions pose a large problem when trying to isolate their optics in the interferometer. This thesis provides an analysis of the effects of changing the wire geometry of a double pendulum as a case study for LIGO pendulum designs. By changing the wire attachment point to be closer to the center of mass, we are able to see a decrease in longitudinal-to- pitch coupling by about a factor of 3. We observe that the pitch-to-pitch coupling decreases by a factor of approximately 1.5 at DC when comparing the new four wire configuration to the original two wire configuration. However, the first pitch resonance increases slightly. This resonance is most influenced by a combination of the wire attachment point and spring stiffness. The resonance can be moved around by changing these factors. This project has two main components. The first is a state space model that describes the equations of motion for the double pendulum and is used to predict dynamic responses. The second is the construction of a physical double pendulum prototype which is used to verify results from the model. The experimental results show differences in dynamics compared to the state space model due to forcing off center, and the model was updated to include these dynamics. The physical pendulum is set up outside of vacuum and is not manufactured to the tight tolerance of real LIGO suspensions. Therefore, we do not have the precision necessary to experimentally attach the wires directly at the center of mass and did not measure these transfer functions. In conclusion, our observations lead us to believe that suspending the top mass with four wires is beneficial to reducing the longitudinal-to-pitch coupling. However, it is necessary to align the pivot point of the wires to the actuation point in order to demonstrate this. Future research can be done on placing the wire pivot point directly at the actuation point. S.M. 2023-11-02T20:23:49Z 2023-11-02T20:23:49Z 2023-09 2023-09-28T15:50:03.141Z Thesis https://hdl.handle.net/1721.1/152872 https://orcid.org/0009-0004-1910-0391 Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Copyright retained by author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Lee, Regina E. A LIGO Double Pendulum Suspension Prototype for Reducing Unwanted Cross-Couplings |
| title | A LIGO Double Pendulum Suspension Prototype for Reducing Unwanted Cross-Couplings |
| title_full | A LIGO Double Pendulum Suspension Prototype for Reducing Unwanted Cross-Couplings |
| title_fullStr | A LIGO Double Pendulum Suspension Prototype for Reducing Unwanted Cross-Couplings |
| title_full_unstemmed | A LIGO Double Pendulum Suspension Prototype for Reducing Unwanted Cross-Couplings |
| title_short | A LIGO Double Pendulum Suspension Prototype for Reducing Unwanted Cross-Couplings |
| title_sort | ligo double pendulum suspension prototype for reducing unwanted cross couplings |
| url | https://hdl.handle.net/1721.1/152872 https://orcid.org/0009-0004-1910-0391 |
| work_keys_str_mv | AT leereginae aligodoublependulumsuspensionprototypeforreducingunwantedcrosscouplings AT leereginae ligodoublependulumsuspensionprototypeforreducingunwantedcrosscouplings |