Shaft-Elastic Rotor Balancing from Measured Outward Deflection
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Solution Overview
Problem
Existing methods for balancing wave-elastic rotors are complex and require test weights, making it difficult to accurately determine and compensate for modal imbalances, especially at low speeds.
Innovation Solution
A method that creates a simple numerical rotor model to calculate the equivalent modal imbalance for the first natural bending mode by measuring deflection at a specific speed below the critical speed, using static compliance and material properties, without considering rotordynamic effects, allowing for compensation without test weights.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional balancing methods are used for shaft-elastic rotors, then balancing can be achieved, but the process becomes complex and requires test weights
Solution Approach 1:
The invention extracts and separates the elastic deflection component from the total measured vibration. By calculating the static compliance of the rotor and using it to determine the elastic deflection at the measurement point, the method isolates the modal imbalance component that needs to be compensated, eliminating the need for complex test weight procedures
Solution Approach 2:
The invention replaces the mechanical test weight balancing procedure with a calculation-based approach. By measuring total deflection, calculating elastic deflection using static compliance, and deriving modal imbalance from their difference, the method substitutes physical test weights with computational analysis
2Measurement precision
If balancing is performed at operating speed, then accurate modal imbalance determination is possible, but the method becomes complex requiring multiple measurement runs
Solution Approach 1:
The invention performs preliminary calculation of the rotor's static compliance before the actual balancing measurement. This pre-calculated compliance value is then used to determine elastic deflection from a single measurement at any speed below the first critical speed, eliminating the need for multiple measurement runs at different speeds
3Measurement precision
If the rotor speed approaches the first critical speed, then the deflection pattern becomes more pronounced for measurement, but rotor-dynamic effects increase measurement inaccuracy
Solution Approach 1:
The invention changes the measurement parameter from total vibration amplitude to the difference between total deflection and calculated elastic deflection. By measuring at speeds up to 50% of the first critical speed and using the known static compliance to calculate and subtract the elastic component, the method maintains measurement sensitivity while avoiding the inaccuracies of rotor-dynamic effects
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 method provides a straightforward and accurate way to determine and compensate for imbalances in wave-elastic rotors, reducing complexity and effort, with low inaccuracy even at speeds up to 50% of the critical speed.
Implementation Method 1
calculating the magnitude of the static compliance of the rotor model at at least one measuring point and at the rotor's center of gravity
Implementation Method 2
internal bending moments remain due to the centrifugal forces generated by the individual imbalances
Implementation Method 3
A simple cylindrical rotor will therefore deflect in a V-shape near the first critical speed, in an S-shape near the second, and in a W-shape near the third
Data Source
Figure 1~2
AI summary
In a method for determining the equivalent modal imbalance to be compensated for the first bending mode of a wave-elastic rotor (1), a rotor model is created that describes the geometric shape and material properties of the wave-elastic rotor (1). The compliance of the model of the rotor (1) is calculated at a measuring point and at the rotor's center of gravity at an assumed rotational speed. The wave-elastic rotor (1) is mounted in a rotatable bearing (2) and accelerated to the assumed rotational speed, which is below its first critical speed. Subsequently, the deflection at the measuring point of the wave-elastic rotor (1) rotating at the assumed rotational speed can be measured, and the equivalent modal imbalance to be compensated for the first bending mode of the wave-elastic rotor (1) can be calculated from the calculated compliance and the measured deflection.