Shaft-Elastic Rotor Balancing via Outward Deflection Measurement
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Solution Overview
Problem
Existing methods for balancing elastic rotors are complex and require setting test weights, making it difficult to accurately determine and compensate for unbalance, especially at critical speeds.
Innovation Solution
A method that creates a numerical rotor model to calculate the static compliance and measure outward deflection at speeds below the first critical speed, allowing for the calculation of equivalent modal unbalance without test weights, using a simple and cost-effective approach that ignores rotor-dynamic effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional balancing methods are used for elastic rotors, then unbalance compensation is achieved, but the process becomes complex and requires test weights
Solution Approach 1:
The invention extracts and measures only the relevant deflection component at a specific measurement point using a single displacement sensor, rather than requiring multiple sensors and test weights. By focusing on the deflection at one critical point and using the known mode shape, the method simplifies the measurement system while maintaining accurate unbalance determination
Solution Approach 2:
The invention uses a numerical model (copy) of the rotor that includes its geometric shape and material properties to calculate compliance and determine unbalance. This virtual model replaces the need for physical test weights and multiple measuring runs, allowing unbalance determination through calculation based on measured deflection and pre-computed compliance values
2Measurement precision
If multiple unbalance measuring runs with test weights are performed, then unbalance compensation accuracy improves, but measurement time and effort increase
Solution Approach 1:
The invention performs preliminary calculation of the compliance matrix for the rotor model before the actual measurement. This pre-computed compliance information, based on the known geometric shape and material properties, allows the unbalance to be determined directly from a single deflection measurement without requiring multiple measuring runs with test weights
Solution Approach 2:
The rotor's own geometric shape and material properties, encoded in the numerical model, are used to provide the compliance information needed for unbalance determination. The system uses the rotor's inherent characteristics rather than external test weights to enable the measurement process
3Measurement precision
If rotor-dynamic effects are fully considered, then measurement accuracy at critical speeds improves, but calculation complexity and cost increase
Solution Approach 1:
The invention uses a simplified static compliance calculation rather than a full dynamic analysis. By calculating compliance based on static elastic deformation and using the known mode shape to account for dynamic effects, the method achieves sufficient accuracy for practical balancing without the complexity of complete rotor-dynamic modeling
Solution Approach 2:
The invention changes the approach from dynamic analysis to static compliance calculation. By determining the compliance matrix from static elastic deformation and combining it with measured deflection and mode shape information, the method achieves accurate unbalance determination without requiring complex dynamic simulations
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 unbalance in shaft-elastic rotors, with low inaccuracy and reduced effort, applicable to both simple and complex geometries, and is efficient up to 50% of the rotor's first critical speed.
Implementation Method 1
the centrifugal forces generated by the individual unbalances. In the case of elastic rotors, these forces, which increase with the square of the speed, can lead to impermissibly large deformations
Data Source
AI summary
In a method for determining an equivalent modal unbalance for the first bending characteristic form of a shaft-elastic rotor, which unbalance is to be compensated for, a rotor model is created describing the geometric shape and material properties of the shaft-elastic rotor. The magnitude of compliance of the rotor model is calculated at a measurement point and at the center of gravity of the rotor at an assumed speed. The shaft-elastic rotor is received in a rotatable bearing and accelerated to the assumed speed which is below its first critical speed. Subsequently, the magnitude of outward deflection at the measurement point of the shaft-elastic rotor rotating at the assumed speed can be measured. The equivalent modal unbalance for the first bending characteristic form of the shaft-elastic rotor, which unbalance is to be compensated for, can be calculated from the magnitudes of the calculated compliance and the measured outward deflection.