Machine Speed Determination via Spectral Probability Density
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Solution Overview
Problem
Existing methods for determining machine speeds based on vibration measurements are not sufficiently reliable, as they rely on frequency-discrete spectra which can introduce artifacts and fail to accurately account for higher harmonics and other speed-dependent components.
Innovation Solution
The method involves determining a frequency-continuous spectrum through oversampling or frequency shifting, calculating a spectral probability density within a permissible frequency range, and iteratively refining the main speed determination by removing components related to the last determined speed, with a trust probability assessment to ensure accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If frequency-discrete spectra using FFT or DFT are used for speed determination, then the measurement process is simple and fast, but the determination reliability is insufficient and artifacts are introduced
Solution Approach 1:
The patent applies preliminary action by performing zero-padding in the time domain before Fourier transformation. This preliminary step increases the frequency resolution of the spectrum without requiring longer measurement times or more complex hardware. By appending zeros to the time signal, the frequency spectrum becomes more densely sampled, allowing for more accurate identification of speed-related frequency components and their harmonics, thus improving determination reliability while maintaining computational efficiency
Solution Approach 2:
The patent uses spectral probability density as an intermediary between the raw frequency spectrum and the final speed determination. Instead of directly interpreting discrete spectral peaks, the method computes a probability density function that incorporates prior knowledge about expected speed ranges and harmonic relationships. This intermediary representation smooths out artifacts and noise in the discrete spectrum, providing a more reliable basis for identifying the fundamental speed and its harmonics
2Measurement precision
If frequency-discrete spectra are used, then computational effort is low, but higher harmonics and speed-dependent components are not accurately accounted for
Solution Approach 1:
The patent applies preliminary action by performing zero-padding in the time domain before Fourier transformation. This preliminary step increases the frequency resolution of the spectrum without requiring longer measurement times or more complex hardware. By appending zeros to the time signal, the frequency spectrum becomes more densely sampled, allowing for more accurate identification of speed-related frequency components and their harmonics, thus improving determination reliability while maintaining computational efficiency
Solution Approach 2:
The patent changes the parameter of frequency resolution by using zero-padding to increase the number of frequency samples. This parameter change allows the spectrum to more accurately represent the continuous frequency distribution, making it possible to distinguish between closely spaced harmonics and speed-dependent components. The increased frequency sample density improves measurement precision for harmonic analysis while the computational overhead remains manageable due to the efficient FFT algorithm
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly enhances the reliability of machine speed determination by accurately accounting for higher harmonics and other speed-dependent components, providing a high trust value for the determined main speed, thus improving the precision and confidence in the measurement.
Implementation Method 1
record at least one vibration quantity, such as deflection, speed or acceleration, using a sensor on the machine
Implementation Method 2
determine this quantity by means of a suitable spectral transformation, in which case the spectrum consisting of Real and imaginary part
Implementation Method 3
the underlying frequency-continuous spectrum can be determined by frequency interpolation, e.g. by oversampling
Data Source
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AI summary
The invention relates to a method for determining at least one rotational speed of a machine (10), wherein the complex spectrum of a vibration quantity on the machine is determined from the measurement of this quantity over time, and frequency interpolation is performed; boundary conditions for the evaluation of the spectrum are defined, which include the permissible frequency range of an expected main rotational speed, a set of relative frequencies related to the main rotational speed in the form of frequency multipliers, and a weighting factor for the respective relative frequency; a spectral probability density is calculated taking into account the boundary conditions, which for each frequency of the permissible frequency range results as the sum of the amplitude of the spectrum weighted by the respective weighting factor at the frequency multiplied by the respective frequency multiplier;and the main rotational speed is determined from the frequency with the maximum probability density.