Using average order spectra to determine point ordering

doi:10.21203/rs.3.rs-3665086/v1

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Using average order spectra to determine point ordering

https://doi.org/10.21203/rs.3.rs-3665086/v1

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This application used order analysis to identify the main and tail rotors of a helicopter as potential sources of high-amplitude vibration in the cabin. First, rpmfreqmap and rpmordermap were used to visualize orders. The RPM-order map provided order separation throughout the RPM range without the smearing artifacts present in the RPM-frequency map. rpmordermap was the best choice to visualize vibration components at lower RPM during the engine run-up and coast-down.

Vibration analysis is a technique used to study the dynamic behavior of structures or systems by analyzing their vibration characteristics. It involves measuring and analyzing vibrations to understand the causes, effects, and potential issues related to the vibrational behavior of a system [1–22].

Vibration measurements are typically performed using sensors such as accelerometers or displacement transducers. These sensors record the vibrational response of a system in terms of displacement, velocity, or acceleration [23–45].

Time domain analysis involves studying the vibrational data directly in the time domain. This analysis helps identify specific events, transients, or irregularities in the vibration signal. Parameters such as amplitude, frequency, and phase can be analyzed to assess the vibrational behavior. Time domain analysis techniques include time waveform analysis, root mean square (RMS) analysis, and crest factor analysis [46–58].

Frequency domain analysis involves analyzing the vibrational data in the frequency domain. This analysis helps identify the frequency components and dominant frequencies present in the vibration signal. Techniques such as Fourier Transform, Power Spectral Density (PSD) analysis, and Fast Fourier Transform (FFT) are used to transform the signal from the time domain to the frequency domain. Frequency domain analysis helps identify resonances, natural frequencies, and harmonic components [59–70].

Modal analysis is a technique used to determine the natural frequencies, mode shapes, and damping properties of a system. It involves exciting a structure or system and measuring the corresponding response to identify the dynamic characteristics. Modal analysis helps understand the dynamic behavior of a system and is useful in structural design, optimization, and diagnosing potential issues[71–78].

Vibration analysis is commonly used for fault diagnosis in machinery and rotating equipment. Changes in vibration patterns can indicate issues such as unbalance, misalignment, bearing faults, or gear problems. By analyzing vibration signatures or trends over time, potential faults can be detected early, allowing for preventive or corrective maintenance actions [79–85].

Vibration analysis is often used as part of a condition monitoring program. Continuous monitoring of vibration parameters allows for the early detection of deteriorating conditions in machinery, reducing the risk of unexpected failures and optimizing maintenance strategies.

Vibration analysis is typically performed using specialized software tools that provide various analysis techniques and visualizations to interpret and analyze vibration data. These tools may include features for time domain analysis, frequency domain analysis, modal analysis, and fault diagnostics [86–89].

Overall, vibration analysis is a powerful tool for understanding and diagnosing the behavior of structures and systems, enabling efficient maintenance, improved performance, and increased safety.

To determine the locations of the peaks in the order map and identify the orders of high-amplitude vibration in the helicopter cabin, you can use the "rpmordermap" function. Taking the vibration data and corresponding order and RPM values as inputs, this function calculates and returns the order map. Here's an outline of the steps involved:

1. Preprocess the Data: Ensure the vibration data is properly preprocessed, removing any noise or extraneous frequencies that could interfere with the analysis. This step helps ensure accurate results.

2. Use the "rpmordermap" Function: Call the "rpmordermap" function, providing the vibration data, order, and RPM values as input arguments. This function calculates the order map, which represents the distribution of vibration energy in the frequency vs. order domain.

3. Analyze the Order Map: Analyze the generated order map to determine the locations of the peaks. Look for orders that are integer multiples of the order of the main and tail rotors. Vibration generated by these rotors typically occurs at specific orders.

4. Identify High-Amplitude Vibration Orders: Identify the orders in the order map that exhibit high-amplitude vibration. These orders represent the frequencies that contribute significantly to the vibration levels in the helicopter cabin.

5. Return the Order Map: Return the computed order map as the output. This map provides a visual representation of the vibration energy distribution across different orders and frequencies.

By following these steps and utilizing the "rpmordermap" function, you can compute the order map and identify the orders of high-amplitude vibration in the helicopter cabin. The order map will help you analyze the distribution and magnitude of vibration energy across different orders, aiding in the identification of critical vibration sources.

The specific implementation may depend on the software or programming language you are using. Consult the documentation or resources specific to your tool to understand the precise usage and relevant parameters of the "rpmordermap" function (see Figure 1).

The steps mentioned above may vary depending on the software or programming language you are using. Using the appropriate syntax and parameters specific to the "orderspectrum" function in your selected tool, you should be able to generate the average spectrum of the order map.

To analyze peak orders over time, follow these steps:

- Collect the necessary data on peak orders, including the date and time of each order. This data may be available through your sales platform or order tracking system.

- Determine the time intervals you consider as peak periods. For example, you might define peak periods as weekdays from 12 pm to 2 pm and 6 pm to 8 pm, or weekends from 10 am to 1 pm.

- Group the orders based on your defined peak periods. Assign each order to the corresponding time interval.

- Count the number of orders within each peak period to determine the order count during each time interval. This will provide you with insights into the order volume during different peak periods.

- Create a visual representation of the order counts over time using a line chart, bar chart, or any other suitable graph. This will help you identify trends or patterns in peak order volumes.

- Analyze your visual representation by looking for trends, spikes, or changes in order counts during different peak periods. This analysis can assist you in understanding peak demand periods, optimizing staffing levels, or adjusting your business operations to meet customer needs more efficiently.

The frequency of data collection and the duration over which you analyze peak orders will depend on your business needs. Regularly reviewing and updating this analysis will help you make informed decisions to optimize your operations (see Figure 2) .

That's interesting to note that the amplitude of both orders increases as the rotational speed of the motor increases. It suggests a correlation between the motor speed and the order amplitudes.

Regarding the capability of "ordertrack" to separate crossing orders when multiple RPM signals are present, it highlights the usefulness of this function for analyzing complex signals.

By utilizing "ordertrack," you can process and analyze RPM signals, allowing you to separate and identify individual orders even in cases where there are multiple overlapping signals. This can be valuable for understanding the characteristics and behavior of the motor and its components.

To extract time-domain order waveforms for each peak order using the "orderwaveform" function and compare them to the original vibration signal, you can follow these steps:

1. Preprocess the Vibration Signal: If necessary, preprocess the original vibration signal by removing any noise or irrelevant frequencies. This step helps ensure accurate order waveform extraction.

2. Specify Peak Orders: Determine the two peak orders for which you want to extract order waveforms.

3. Use the "orderwaveform" Function: Utilize the "orderwaveform" function, passing in the original vibration signal, the specified peak orders, and any other necessary parameters. This function applies the Vold-Kalman filter to extract the order waveforms for the specified orders.

4. Compare Waveforms: Once you've extracted the order waveforms, you can compare them to the original signal. Plotting the waveforms separately or overlaying them on the original signal can help visualize any differences or similarities.

5. Playback as Audio: If desired, you can convert the extracted order waveforms into audio files and play them back to audibly experience the individual peak orders.

The specific implementation of "orderwaveform" may vary depending on the program or library you are using. Consult the documentation or resources specific to your chosen tool for more detailed instructions and examples (see figure 3).

To identify the sources of cabin vibration and determine if they align with the orders of the helicopter's rotors, it can follow these steps:

- Collect vibration data from the cabin area where the vibration is occurring. This data can be collected through sensors or accelerometers placed in the cabin.

- Analyze the vibration data to identify the peak orders corresponding to the highest vibration amplitudes. These peak orders represent the dominant frequencies contributing to the cabin vibration.

-Calculate the order values for each rotor in the helicopter. The order of each rotor is defined as the fixed ratio of the rotor speed to the engine speed. This ratio can be determined based on the rotor speed and engine speed specifications.

- Compare the identified peak orders from the cabin vibration with the orders of each rotor. Check if the peak orders align with the expected orders of the rotors. If the peak orders correspond closely to the rotor orders, it suggests that the rotor system may be a significant source of the cabin vibration.

- While comparing the peak orders with rotor orders is a useful approach, it's important to consider other factors that may contribute to cabin vibration as well. Factors such as engine vibrations, gearbox or transmission vibrations, balance issues, and structural resonances can also influence cabin vibration.

- If the comparisons indicate a close alignment between the peak orders and rotor orders, it may be necessary to further investigate the rotor system. This can involve inspections, maintenance checks, and checks for any anomalies or issues with the rotor components.

By comparing the peak orders of the cabin vibration with the orders of the helicopter's rotors, you can gain insights into potential sources of the vibration. This information can help in identifying and addressing the underlying causes of cabin vibration, leading to appropriate measures for its reduction (see figure 4).

Comparing the order spectra before and after the track and balance adjustments provides valuable insights into the impact of these adjustments on cabin vibration levels. It helps assess the effectiveness of the adjustments in reducing vibrations associated with the main and tail rotors, leading to a more comfortable and stable cabin environment.

The specific implementation details may depend on the software or programming language you are using for order spectrum analysis. Ensure you adapt the steps and processes according to your selected tool and data format.

This paper used order analysis to identify the main and tail rotors of a helicopter as potential sources of high-amplitude vibration in the cabin. First, rpmfreqmap and rpmordermap were used to visualize orders. The RPM-order map provided order separation throughout the RPM range without the smearing artifacts present in the RPM-frequency map. rpmordermap was the best choice to visualize vibration components at lower RPM during the engine run-up and coast-down.

Author Contribution

Saci felahi wrote the main manuscript text . All authors reviewed the manuscript."

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No competing interests reported.

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Using average order spectra to determine point ordering

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Abstract

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1- Introduction

2- Determining Peak Orders Using an Average Order Spectrum

3- Analyzing Peak Orders Over Time

4- Reducing Cabin Vibration

5- Conclusion

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Author Contribution

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