25-02-2013, 12:01 PM
RIM-SPOKE COMPOSITE FLYWHEELS - STRESS AND VIBRATION ANALYSIS
RIM-SPOKE COMPOSITE.pdf (Size: 1.12 MB / Downloads: 98)
INTRODUCTION
The use of fiber composite materials in flywheels offers several advantages over
metal flywheels. The major advantages result primarily from the high longitudinal
specific strength (strength/density) and high longitudinal specific stiffness (modulus/
density) of composites compared with metals. Additional advantages offered by composites
are (1) a large number of composites are available with a wide range of mechanical
properties (fig. 1) from which selections can be made to meet diverse design requirements,
(2) various flywheel configuration can be readily fabricated using the extensively
developed filament winding capability that already exists, and (3) less material is required
for containing flywheel bursts (reduced fragment kinetic energy).
APPROACH
The approach pursued in the present investigation is theoretical and consists of the following: derivation of material utilization index criteria, generation of an algorithm for the automatic selection of optimum composite materials, evaluation of radial stresses, use of NASTRAN to analyze a specific example. The details are described in the following sections.
Criteria for Sizing Spokes in Thin-Wall RimSpoke Composite Flywheels
Criteria for sizing spokes in thin-wall rim-spoke composite flywheel configurations may be derived by requiring that the radial deflection of the spoke equal the radial deflection of the rim. When this condition is satisfied, the following are also true: (1)the rim spoke system is statically determinate; (2) the stresses and deflections in the spokes and the rim are easily determined using elementary strength of materials relations; and (3) the spokes, fixed to the rim, do not induce bending in the rim because of differential radial expansion.
NASTRAN APPLICATION
The output of the material selection algorithm is used to generate the required NASTRAN input bulk data deck for all the rims. Each rim is modeled as a series of quadrilateral (CQUAD2) NASTRAN elements with centrifugal radial force loads applied (fig. 5). Rims that radially interfere at operational speed are identified and a set of multiple point constraints are applied at their boundaries. Selected rim materials are referenced and each of the rims are located in free space using NASTRAN single-point constraints instead of supporting spokes. Spokes of appropriate proportions were added later to study spoked flywheel cases (fig. 6).
The two designs selected for further study represent a single-rim design and a multirim design that appear to be of reasonable proportions for construction. Each design was studied in two configurations: (1)Rim flywheel with spokes and (2) rim flywheel without spokes. The four resulting configurations were then studied for stress and displacements in each of the following cases: (1)static analysis, (2) free vibration modal analysis, and (3) free vibration modal analysis with structural stiffening due to centrifugal and gravity loads.
APPLICATION TO TWO SPECIFIC DESIGNS
Design Selection
The results of the computerized selection algorithm are plotted for families of single and multirim designs in figure 7. The single-rim and 25-rim flywheel designs are constrained by a rim thickness to radius ratio of 0.12, the unoptimized materials list, and a total energy storage requirement of 6120 megajoules (1410 kW h (4.5X10 10
in-lb)). Two designs selected for further study represented reasonable operating levels and proportions for construction. The selected designs are shown schematically in
figure 8. In this figure the basic properties and relative sizes of the single and multirim cases are identified.
The single-rim design is much lighter and much larger than the multirim design. The single rim represents a minimum weight condition, while the multirim design represents a maximum energy storage per containment size. Since the first five rims of the multirim design store 75 percent of the total energy, only these rims were included in the detailed NASTRAN analysis of stress and vibration.