Disk Stiffness Research Articles

Mechanical Basis of Lumbar Intervertebral Disk Degeneration

Abstract The etiology of degenerative disk disease (DDD) is multifactorial. Among the various factors, mechanical processes contributing to endplate or discal injuries have been discussed as the initiating events in the degenerative cascade. DDD encompasses the multitudinous changes undergone by the different structures of the spinal segment, namely intervertebral disk (IVD), facet joints, vertebral end plate (VEP), adjoining marrow (Modic changes), and vertebral body. It has been etiologically linked to a complex interplay of diverse mechanisms. Mechanically, two different mechanisms have been proposed for intervertebral disk degeneration (IVDD): endplate-driven, especially in upper lumbar levels, and annulus-driven degeneration. VEP is the weakest link of the lumbar spine, and fatigue damage can be inflicted upon them under physiological loads, leading to the initiation of DDD. Disk calcification has been put forth as another initiator of inflammation, stiffening, and abnormal stresses across the IVD. The initial mechanical disruption leads to secondary IVDD through unfavorable loading of the nucleus pulposus and annulus fibrosis. The final degenerative cascade is then propagated through a combination of biological, inflammatory, autoimmune, or metabolic pathways (impaired transport of metabolites or nutrients). Abnormal spinopelvic alignment, especially pelvic incidence, also significantly impacts the degenerative process. Hence, the etiology of DDD is multifactorial. Mechanical pathways, including VEP injuries, increased disk stiffness, and abnormal spinopelvic alignment, play a significant role in the initiation of IVDD.

The usefulness of quantitatively assessing temporomandibular joint disk stiffness with shear wave elastography in adolescents with bruxism

The objectives of this study were to quantitatively measure temporomandibular joint (TMJ) disk stiffness in adolescents with bruxism using shear wave elastography (SWE) and to examine the relationship between elastography values, patient age, and duration of bruxism. This prospective study evaluated 120 TMJ disks of 60 adolescents (30 patients with bruxism and 30 controls). The stiffness of the anterior, intermediate, and posterior parts of the disk was measured. The patient and control groups' respective quantitative SWE values of elasticity (kilopascals [kPa]) and velocity (meters/second [m/s]) were compared. The elasticity and velocity values of the anterior and intermediate parts were significantly higher in the patients than in the controls (P ≤ .013), with no significant difference in the size of the joint space (P=.886). A receiver operating characteristic analysis resulted in sensitivity for the anterior part of 0.80 for kPa and 0.83 for m/s, with specificity of 0.57 (kPa) and 0.60 (m/s). For the intermediate part, the sensitivity was 0.80 for kPa and 0.86 for m/s, with specificity of 0.64 (kPa) and 0.57 (m/s). No correlations were found between the SWE values and patient age (P ≥ .098) or duration of bruxism (P ≥ .134). SWE may be useful in the evaluation of TMJ disk stiffness in patients with bruxism.

Stiffness degradation effects on disk-shaft connection behavior of a three-dimensionally carbon-fiber-reinforced composite rotating disk

High-speed rotation tests of a three-dimensionally reinforced annular disk were conducted with specimens, but were suspended at a speed below that predicted for disk fracture by high-amplitude vibrations. As described herein, the vibration source was assumed to be disk stiffness degradation. This study examined the validity of this mechanism. First, laser devices were used to measure elastic displacement at the disk periphery and to estimate global disk stiffness. Second, static ring burst tests using circular ring specimens machined from composite disks were conducted to evaluate the circumferential stiffness. Compression tests were done using rectangular parallelepiped specimens for the radial stiffness. Results show that the circumferential stiffness was 67% of the prediction by the rule of mixture. The radial stiffness was 85% of that. Locally wavy carbon fiber bundles were responsible for stiffness degradation. Stiffness degradation effects on the shaft–disk connection were specifically examined based on those results.

Modal analysis of the coupled vibration in an aero-turbine compressor blisk considering both aerodynamic and centrifugal load

To lighten the aircraft engine and improve its propulsion efficiency, many aero engines adopt the blisk structure comprising both the rotor disk and blades. Since the disk becomes thinner, the stiffness of the structure decreased apparently, which causes the occurrence of large amplitude vibration in the blisk. This passage utilizes the finite element analysis (FEA) and computational fluid dynamics (CFD) simulation software to investigate the coupled vibration characteristics between the blades and the disk of the blisk with realistic geometric data, in which the aerodynamic load and centrifugal load are considered. At first, the CFD and finite element models of an aero-turbine compressor blisk are built. Then the pressure load data under some critical rotating speeds from CFD simulation are communicated to FEA software by data interpolating method, and the simulation of modal characteristics of the blisk is conducted in FEA. At last, the natural modal characteristics of the blisk structure are obtained, including the resonance speed Campbell diagram, the natural frequencies and corresponding mode shapes. According to the Campbell diagram, it indicates that the most critical mode is the fourth order mode. It is found that the mode shape of the fourth order in the blisk is the coupling of the disk torsional and blades first bending vibration. It is easy to lead to vibration failure when large amplitude vibration of the fourth mode occurs in the blisk. Also, it could also conclude that the modal characteristics of the coupled vibration in the rotating blisk are very sensitive to the disk stiffness. These results provide basic data for the further research in nonlinear vibration and structure optimization of the blisk, and also a simulating method to investigate coupled vibration between the blades and the disk of the blisk considering both aerodynamic and centrifugal load.

Forced Response Analysis of a Mistuned Compressor Blisk

The forced response of an E3E-type high pressure compressor (HPC) blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades, namely stiffness and damping, are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order, and aerodynamic influences, it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade-alone frequencies as design variables are applied. The validity of the Whitehead limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk's stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.

The Effect of Arthrodesis, Implant Stiffness, and Time on the Canine Lumbar Spine

Canine posterior lumbar instrumentation and fusion. To study effects of implant rod size and time on the stiffness of related spine construct elements. The ideal stiffness of posterior spinal implants to successfully treat clinical instability or deformity with minimal side effects is unknown. Twenty-six canines were divided into 7 groups: control, and 6 or 12-month survival after sham or lumbar L3-5 arthrodesis (facet, posterior, and posterolateral) with either 4.76 or 6.35 mm diameter rod-pedicle screw instrumentation. Axial flexion-compression stiffness of the L3-5 segment components and axial compression stiffness of the bypassed and adjacent anterior column elements were measured. Posterior instrumentation initially increased flexion-compression stiffness of the L3-5 segment more than the intrinsic stiffness of the implant due to control of spinal column flexion buckling. Sham operation did likewise, apparently by posterior scar tissue tethering. The percent contribution of the implant construct to instrumented segment stiffness was significantly less at 6 months without further change from 6 to 12 months; 14% and 22% for 4.76 and 6.35 mm rod constructs, respectively. Spinal column as well as posterior column stiffness after fusion was independent of rod size at 6 months and increased at 12 months in only the 4.76 mm rod group. Bypassed L4 vertebral body stiffness decreased significantly at 6 months, was not rod size dependent and changed little between 6 and 12 months. Bypassed disk stiffness responded in a biphasic manner, apparently increasing at 6 months with significant decrease from 6 to 12 months. Adjacent disk compression stiffness progressively decreased over time independent of rod size, also decreasing after sham operation. Both rod sizes were associated with 100% fusion and produced similar changes in bypassed bone and disks, and adjacent disks. There was delayed fusion stress shielding by 6.35 mm rod constructs.

FREE VIBRATION OF FLEXIBLE ROTATING DISKS

Perturbation techniques are employed to estimate the free vibration characteristics, i.e., the natural frequencies and mode shapes, of a flexible rotating disk. The normalized disk stiffness ϵ = 8 D/[ hb 4(3 + v) mO 2] is introduced and treated as a small parameter. Then, singular perturbation solutions to the governing eigenvalue problem are derived that are valid up to and including order ϵ for any given non-zero hub radius. The special case of a zero hub radius is then considered and the corresponding solutions are presented. Next, a regular perturbation formulation valid for the limiting case of a very narrow rotating annulus is developed.The natural frequency/mode shape predictions from the various perturbation formulations are compared with “exact” values obtained from power series solutions of the eigenvalue problem. It is found that the singular perturbation solutions match well with the “exact” values for small stiffnesses, hub radii and nodal circles,while the regular perturbation solution provides excellent accuracy for large hub radii.

Experimental Investigation of the Bernoulli Head/Disk Interface

The Bernoulli head/disk interface is investigated using interferometry as well as the measurement of acoustic emission, normal force, and disk deflection. The dependence of head-to-disk spacing on radial head position and velocity for upper and lower heads is measured by monochromatic light interferometry. Acoustic emission measurements are used to study intermittent contacts between head and flexible disk. The normal force between the head and the disk h measured and is found to correlate with the acoustic emission signal. The disk deflection characteristics show that the normal force at the head/disk interface is related to the vertical displacement of the head. The normal force at the head/disk interface is determined from the relative disk deflection using the disk stiffness in the normal direction and compared with the measured force.

Effect of Displacement-Dependent Membrane Stresses on the Axisymmetric Configuration of a Spinning Flexible Disk

A flexible elastic disk is rotating at constant angular velocity in close proximity to a stationary baseplate. Such a configuration can be used to stabilize the flexible medium in magnetic and/or optical recording applications. The influence of coupling between in-plane displacements and transverse deflections is investigated. The effects of bending stiffness and of the air flow between the disk and the backplate are also included. Solutions of the nonlinear differential equations are obtained using finite difference approximations and an iterative approach. The results for this reference configuration are the transverse deflections, the air film pressure, and the displacement-induced membrane state. The significance of coupling is assessed. The governing equations of the disk and of the air film are then linearized about the reference configuration and a measure of the disk stiffness is determined. Comparisons are made with another model which uses an elastic foundation parameter in order to represent th...

The Effect of Limiting Aerodynamic and Structural Coupling in Models of Mistuned Bladed Disk Vibration

A model has been developed for studying the effect of mistuning on bladed disk vibration. Its unique feature is the extent of aerodynamic and structural interaction which it simulates can be readily varied from full coupling of all blades on the disk to coupling of each blade with only its nearest neighbors. Simulations utilizing the resulting algorithm shows that limited coupling models may be used to predict the statistical distribution of blade amplitudes that characterizes the mistuning effect, which in turn determines stage durability. This approach is used to study the effect of changing various system parameters on amplitude scatter. Gas density, the number of blades on the disk, disk stiffness, and the engine order of the excitation are considered. The results are used to draw some conclusions about how to improve laboratory tests and component design.

Observations on the Steady-State Solution of an Extremely Flexible Spinning Disk With a Transverse Load

The steady deflection of a transversely loaded, extremely flexible, spinning disk is studied. Membrane theory is used to predict the shapes and locations of waves that dominate the response. It is found that waves in disconnected regions are possible. Some results are presented to show how disk stiffness moderates the membrane waves, the most important result being an upper bound on the highest ordered wave of significant amplitude. A hybrid system of differential equations and boundary conditions is developed to replace the pure membrane formulation that is singular, and the full fourth-order plate formulation that is numerically sensitive. The hybrid formulation retains the salient features of the flexible disk response and facilitates calculations for very small disk stiffnesses.

Significance of Disk Flexing in Viscous-Damped Jet Engine Dynamics

A new method of analyzing multishaft jet engine critical speeds and unbalance response is derived to account for flexible bladed disks, asymmetric mounting, and squeeze film bearing damping. The resulting elliptical shaft whirling drives traveling waves in disks at speeds equal to the sum and the difference of the rotating speed and the whirling speed. To illustrate a possible problem that cannot be predicted by current methods, a sample calculation shows a simplified model representing possible engine parameters tuned so that a critical speed associated with backward whirling is lowered into the operating range by reduction in disk stiffness. In contradiction to the current literature, the rotor is shown highly responsive to unbalance at this critical speed.