Constant-Stress Flywheel Rotor Structure for Flat Stress Distribution
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional solid disk rotors for flywheel energy storage systems have indeterminate structures, making it difficult to predict stress distribution and limit energy density, and thus, obtaining an optimum structure is challenging.
Innovation Solution
A constant stress solid disk rotor design with specific shape parameters and equations that determine the thickness distribution and rotation angular velocity, ensuring a plane-symmetric shape and invariant in-plane stress, allowing for the calculation of limit energy density and mass.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a conventional solid disk rotor design is used, then the structure is simple to manufacture, but the stress distribution is indeterminate and limit energy density cannot be optimized
Solution Approach 1:
The patent applies parameter changes by modifying the thickness distribution parameter t(r) from a conventional uniform or simple tapered design to a specific functional form t(r)=t0exp(—Cr2) where C=ρω2/2S0. This parameter transformation enables the stress distribution to become deterministic and optimizable, allowing the maximum stress to be controlled and the limit energy density to be enhanced while maintaining manufacturing feasibility.
Solution Approach 2:
The patent introduces dynamics by making the thickness distribution function dependent on rotational parameters (ω, ρ, S0) rather than being a static geometric parameter. The coefficient C=ρω2/2S0 dynamically adjusts the thickness profile based on operating conditions, enabling the rotor to achieve optimal stress distribution at the design rotation speed while maintaining a determinate structural form.
2Strength
If the thickness of a solid flat disk rotor is reduced toward the outer circumference, then the maximum rotation stress is diminished and fracture angular velocity increases, but the structure becomes complex with indeterminate relationships between outer radius R and connection radius RC
Solution Approach 1:
The patent transforms the thickness profile from a conventional linear or piecewise function to an exponential function t(r)=t0exp(—Cr2) with C=ρω2/2S0. This parameter transformation creates a determinate relationship between the outer radius R and connection radius RC, eliminating the indeterminate relationship problem while achieving the desired stress distribution that increases fracture angular velocity.
Solution Approach 2:
The patent replaces the conventional mechanical design approach (trial-and-error or empirical methods for determining radius relationships) with an analytical mechanics-based solution. By deriving the thickness distribution from first principles of stress analysis and substituting the exponential function form, the patent creates a determinate analytical relationship between geometric parameters that can be directly calculated rather than empirically determined.
3Measurement precision
If a conventional solid disk rotor with indeterminate structure is used, then manufacturing is simpler, but it is difficult to analytically predict stress distribution and limit energy density
Solution Approach 1:
The patent changes the structural parameter formulation from indeterminate geometric relationships to a determinate exponential function t(r)=t0exp(—Cr2) where C=ρω2/2S0. This parameter transformation enables analytical prediction of stress distribution and limit energy density by providing a closed-form mathematical relationship between the geometric parameters and material properties, eliminating the need for complex numerical methods or empirical correlations.
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
The design achieves a flat rotation stress distribution, reduces peak stress, and optimizes structural parameters to maximize energy density, enabling the determination of an optimum rotor structure.
Implementation Method 1
A flywheel energy storage system is a system having functions of storing external electric power in a flywheel and conversely, feeding electric power of the flywheel to the outside via means for alternately converting electric power and a rotational kinetic energy
Implementation Method 2
When rotors having the same outer radius are rotated at the same angular velocity, a solid disk rotor has an excellent characteristic that a rotation stress (maximum value) is about the half of the rotation stress in a hollow disk rotor
Data Source
AI summary
A constant stress solid disk rotor of a flywheel has an outer shape having a plane-symmetric upper surface and lower surface, an outer circumferential radius b, and a rotation center thickness h0, and includes a thickness decreasing region which decreases monotonously in thickness from a rotation center to a connection radius a and a constant thickness region located on an outer edge of the thickness decreasing region and having a constant thickness ha from the connection radius a to the outer circumferential radius b. Shape parameters including the outer circumferential radius b, the rotation center thickness h0, the connection radius a, and the outer edge thickness ha satisfy an equation below. Here, ν is a Poisson's ratio of a rotor material.ab=12(-21-v(1+v-2ln(hah0))+(21-v(1+v-2ln(hah0)))2+4(3+v)1-v)