Torsional Dynamics Response of Shafts with Longitudinal and Circumferential Cracks

2018 ◽  
Author(s):  
Mohsen Nabian ◽  
Mohammad Ali Nabian ◽  
Hamid Nayeb Hashemi
Keyword(s):  
Crack Surface ◽  
Torsional Rigidity ◽  
Crack Depth ◽  
Longitudinal Crack ◽  
Extrusion Process ◽  
Circumferential Crack ◽  
Torsional Spring ◽  
Resonance Frequencies ◽  
Dynamics Response ◽  
Longitudinal Cracks

Turbo generators shafts are manufactured through the extrusion process. This results in formation of weak planes along the extrusion process. It has been observed that large longitudinal cracks often form in these shafts before any circumferential cracks when these shafts are subjected to cyclic torsion due to electrical line faults. The presence of these cracks could severely compromise the shaft resonance frequencies. Dynamic response of shafts with longitudinal and circumferential cracks is investigated. The longitudinal cracked section of the shaft section is modeled as a shaft with reduced torsional rigidity. The torsional rigidity is obtained as a function of the crack depth. It was found for various shaft diameters, torsional rigidity could be represented as a function of crack depth/ shaft radius only. The circumferential cracked section is modeled as a torsional spring. The torsional spring constant has been obtained using fracture mechanics. It was found the resonance frequency of the shaft may be little affected by the presence of longitudinal crack. The resonance frequencies of the shaft with the circumferential crack depend on the crack length and location. The effects of crack surface interactions for both longitudinal and circumferential cracks were also investigated.

Torsional Dynamic Response of a Shaft With Longitudinal and Circumferential Cracks

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
H. Abdi ◽  
H. Nayeb-Hashemi ◽  
A. M. S. Hamouda ◽  
A. Vaziri
Keyword(s):  
Dynamic Response ◽  
Resonance Frequency ◽  
Torsional Rigidity ◽  
Crack Depth ◽  
Longitudinal Crack ◽  
Element Analysis ◽  
Crack Location ◽  
Circumferential Crack ◽  
Turbo Generator ◽  
Resonance Frequencies

Turbo generator shafts are often subjected to cyclic torsion resulting in formation of large longitudinal cracks as well as circumferential cracks. The presence of these cracks could greatly impact the shaft resonance frequencies. In this paper, dynamic response of a shaft with longitudinal and circumferential cracks is investigated through a comprehensive analytical study. The longitudinally cracked section of the shaft was modeled as an uncracked shaft with reduced torsional rigidity. Torsional rigidity correction factor (i.e., the ratio of torsional rigidity of the cracked shaft to that of the uncracked shaft) was obtained from finite element analysis and was shown to be only a function of crack depth to the shaft radius. The resonance frequency and frictional energy loss of a shaft with a longitudinal crack were found little affected by the presence of the crack as long as the crack depth was less than 20% of the shaft radius even if the entire shaft is cracked longitudinally. Moreover, we showed that the longitudinal crack location could be more conveniently identified by monitoring the slope of the torsional response along the shaft. The circumferential crack was modeled as a torsional spring with a torsional damping. The torsion spring and damping constants were obtained using fracture mechanics. For a shaft with both a longitudinal crack and a circumferential crack, the resonance frequency was governed by the longitudinal crack when the circumferential crack depth was less than 30% of the shaft radius.

scholarly journals The Effects of Longitudinal and Circumferential Cracks on the Torsional Dynamic Response of Shafts

2013 ◽  
Author(s):  
M. Nabian ◽  
A. Vaziri ◽  
M. Olia ◽  
H. Nayeb-Hashemi
Keyword(s):  
Dynamic Response ◽  
Resonance Frequency ◽  
Crack Surface ◽  
Torsional Rigidity ◽  
Peak Response ◽  
Torsional Spring ◽  
Turbo Generator ◽  
Resonance Frequencies ◽  
Cracked Shafts ◽  
Cracked Shaft

Turbo generator shafts are manufactured through the extrusion process. This results in formation of weak planes along the extrusion direction. Under service loading (e.g. cyclic torsion due to electrical line faults), large longitudinal cracks often form in these shafts before the appearance of any circumferential cracks. The presence of these cracks could severely compromise the shaft resonance frequencies. Here, we investigated the dynamic response of solid turbo generator shafts with longitudinal and circumferential cracks. The longitudinal cracked section of the shaft section was modeled as a shaft with reduced effective torsional rigidity. The effective torsional rigidity was found to be a function of ratio of crack depth to the shaft radius only. The circumferential cracked section was modeled as a torsional spring, with the torsional spring constant determined using fracture mechanics principles. It was found that the resonance frequency of the shaft may be little affected by the presence of a longitudinal crack. The resonance frequencies of the shaft with the circumferential crack depend on the crack length and its location. The effects of crack surface interactions for both longitudinal and circumferential cracks were also investigated. For circumferential cracked shafts, the sever crack surface interaction results in the peak response frequency approaches to that of un-cracked shafts. However the frequency where the peak response occurs for a longitudinally-cracked shaft generally exceeds that of un-cracked shaft first resonance frequency.

Survey and Analysis of the Regularity of the Surface Crack in the Loess Tunnel of the Special Passenger Line

2011 ◽  
Vol 90-93 ◽  
pp. 2258-2264 ◽  
Author(s):  
Xin Qiang Gao ◽  
Yong Quan Zhu ◽  
Chao Liang Ye
Keyword(s):  
Surface Crack ◽  
Seismic Reflection ◽  
Field Survey ◽  
Crack Depth ◽  
Longitudinal Crack ◽  
Electrical Method ◽  
Geophysical Exploration ◽  
Circumferential Crack ◽  
Shallow Area ◽  
Tunnel Entrance

We have done a survey about the surface crack of the loess tunnel of Zheng-xi passenger railway by field survey, geophysical exploration test and pit detection and also have researched the produced regularity of the surface crack of the loess tunnel, especially about in the depth. The result of the survey and the detection indicates that: (1)The surface crack is mostly visible in the shallow area of the loess tunnel entrance. The visible width of the surface is extensive (0.2~200mm) and it is mostly visible in the tunnel, the depth of which is below 60m. The visible or wide cracks mostly appear in the area whose surface settlement is above 80mm. The width of the surface crack of the tunnel, which has a more shallow depth and a larger settlement, is much wider. (2)The effect of the High-density electrical method reflecting the development of the surface crack is obvious. The method of seismic reflection wave and seismic imaging is more accurate than Rayleigh wave in interpreting depth development of the crack. (3)There are two kinds of performance of the surface crack: longitudinal crack that inclines to the inside on both side of the tunnel and circumferential crack perpendicular to the axis of the tunnel. (4)The visible crack depth of the surface crack is limited, which is about 3.0~10m and it always doesn't reach the top of the tunnel. The depth by the geophysical exploration test is much more depth, which is about 10~15m.

Influence of Longitudinal Cracks in Bottom Flange of Concrete Continuous Box Girder

2015 ◽  
Vol 744-746 ◽  
pp. 773-778 ◽  
Author(s):  
Ling Chen ◽  
Guo Bin Tang
Keyword(s):  
Crack Length ◽  
Crack Depth ◽  
Longitudinal Crack ◽  
Parameter Analysis ◽  
Crack Model ◽  
Bottom Flange ◽  
Negative Effects ◽  
Box Girder ◽  
Concrete Box Girder Bridges ◽  
Longitudinal Cracks

Longitudinal crack in bottom flange is one of the most common defects in concrete box girder bridges. This paper focuses on the influence of the longitudinal cracks on the mechanical properties of box girder using numerical method. Smear crack model and strain softening model was employed to simulate cracking process. Parameter analysis was also carried out to study the effect of length, crack depth and amounts of cracks in bottom flange. The results indicate longitudinal cracks in one span have a significant effect on the transverse stress and deflection, but have little effect on the other spans. The negative effects of longitudinal cracks increase with the crack length and depth. When the crack length is up to 10% of the girder span, the deflection of the span amplifies to 13%. Compared with the length and depth, the amounts of cracks don’t have much influence on the deformation of girder but affect stress.

Vibration Response of Functionally Graded Rotating Disk With a Circumferential Crack

2010 ◽  
Author(s):  
Rui Liu ◽  
Hamid Nayeb-Hashemi
Keyword(s):  
Critical Speed ◽  
Crack Depth ◽  
Rotating Disk ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Campbell Diagram ◽  
Circumferential Crack ◽  
Inner Radius ◽  
The Galerkin Method

In this study, the vibration characteristics of a functionally graded rotating hollow disk with the circumferential surface crack are investigated. In order to simplify the problem, the circumferential crack of the rotating hollow disk is modeled as circumferential step indentation. The Galerkin Method is used to obtain the radial and hoop stresses for disks with clamped edge at the inner radius. Finite Difference scheme is adopted to solve the partial differential equation of motion of the rotating hollow disk to obtain the mode shapes and the Campbell Diagram. The first critical speed, which is one of the important parameters limiting the performance of the rotating disk, was obtained from the Campbell Diagram. The results show that the crack will reduce the stiffness and the critical speed of the rotating disk. Critical speed increases with decreasing the distance from inner radius to the crack and decreases with increasing crack depth. Furthermore, considering the functionally graded disk, the distribution of elastic modulus does not change significantly the effects of circumferential cracks on the vibration characteristics of the rotating.

Fatigue Life Assessment for NPS30 Steel Pipe

2012 ◽  
Author(s):  
Jorge Silva ◽  
Hossein Ghaednia ◽  
Sreekanta Das
Keyword(s):  
Fatigue Life ◽  
Test Data ◽  
Crack Depth ◽  
Research Work ◽  
Longitudinal Crack ◽  
Assessment Model ◽  
Life Assessment ◽  
Fatigue Life Assessment ◽  
Remaining Fatigue Life ◽  
Crack Defect

Pipeline is the common mode for transporting oil, gas, and various petroleum products. Aging and corrosive environment may lead to formation of various defects such as crack, dent, gouge, and corrosion. The performance evaluation of field pipelines with crack defect is important. Accurate assessment of crack depth and remaining fatigue life of pipelines with crack defect is vital for pipeline’s structural integrity, inspection interval, management, and maintenance. An experimental based research work was completed at the University of Windsor for developing a semi-empirical model for estimating the remaining fatigue life of oil and gas pipes when a longitudinal crack defect has formed. A statistical approach in conjunction with fracture mechanics was used to develop this model. Statistical analysis was undertaken on CT specimen data to develop this fatigue life assessment model. Finite element method was used for determining the stress intensity factor. The fatigue life assessment model was then validated using full-scale fatigue test data obtained from 762 mm (30 inch) diameter X65 pipe. This paper discusses the test specimens and test data obtained from this study. Development and validation of the fatigue life assessment model is also presented in this paper.

Effect of Crosslink Density on Cut Growth in Black-Filled Natural Rubber Vulcanizates

2002 ◽  
Vol 75 (5) ◽  
pp. 935-942 ◽  
Author(s):  
G. R. Hamed ◽  
N. Rattanasom
Keyword(s):  
Carbon Black ◽  
Natural Rubber ◽  
Crack Growth ◽  
Crosslink Density ◽  
Longitudinal Crack ◽  
Test Pieces ◽  
Filled Rubber ◽  
Longitudinal Cracks ◽  
Natural Rubber Vulcanizates ◽  
High Crosslink Density

Abstract Tensile strengths, σb, of gum and N115-filled natural rubber test pieces, with and without edge pre-cuts, have been determined. At low crosslink density, the regular (uncut) σb of filled and gum vulcanizates is similar. However, at high crosslink density, the gum NR becomes brittle, while the corresponding filled rubber remains strong and resistant to cut growth. It is proposed that the tightly linked gum does not strain-crystallize appreciably during stretching, but that its filled counterpart does. Carbon black appears capable of inducing crystallization in a network that alone remains amorphous during extension. Filled vulcanizates of various crosslink densities have similar normal tensile strengths ( ≈ 30 MPa), but strengths differ, sometimes more than twofold, if a pre-cut is present. Lightly crosslinked specimens containing a small cut have strengths that depend very weakly on cut size, c. Furthermore, these develop long longitudinal cracks from which catastrophic rupture initiates. With larger cuts, strength decreases more rapidly with increasing c, there is less longitudinal crack growth, and rupture initiates near the original cut tip. In contrast, the strength of a highly crosslinked vulcanizate is sensitive to small cuts and test pieces exhibit minimal longitudinal cracking before failure.

Investigation on the Post-Ultimate Strength Behaviour of Damaged Stiffened Plate of Ship Structure

2016 ◽  
Author(s):  
Weijun Xu ◽  
Minjie Yuan ◽  
Xiaotian Wang
Keyword(s):  
Ultimate Strength ◽  
Carrying Capacity ◽  
Crack Depth ◽  
Plate Thickness ◽  
Longitudinal Crack ◽  
Load Carrying Capacity ◽  
Stiffened Plate ◽  
Ship Structure ◽  
Plate Length ◽  
Load Carrying

Post-ultimate strength behaviour of ship structure can directly reflect its changing tendency of load carrying capacity. When the external load exerted on the ship structure exceeds the ultimate strength, sharply reduction of load carrying capacity will occur, especially for the damaged ship structure induced from grounding or collision. This paper focuses on the investigation on the post-ultimate strength behaviour of damaged stiffened plate of ship structure by using FEM, a series of stiffened plate modeling with different kinds of cracks are constructed. The parameters of crack includes length, width, depth, plate thickness and distribution direction. The post-ultimate strength behaviour of stiffened plate with cracks and intact ones are compared. Conclusion can be drawn as follows: (1) crack can induce the reduction of ultimate strength of stiffened plate, meanwhile, the stiffness and its load carrying capacity decrease accordingly. (2) in terms of stiffened thin plate, length of crack has a significant influence on the post-ultimate strength behaviour, the width of the crack has a huge influence on ultimate strength while the depth of crack has little influence; in terms of stiffened thick plate, the influence of crack depth on the post-ultimate strength behaviour becomes obvious. The width of the crack influence the post-ultimate strength behaviour a lot. (3) compare to the transverse crack, the influence of longitudinal crack on the post-ultimate strength behaviour is not obvious.

scholarly journals Design optimization analysis of an anti-backlash geared servo system using a mechanical resonance simulation and experiment

2021 ◽  
Vol 12 (1) ◽  
pp. 305-319
Author(s):  
Lianchao Zhang ◽  
Hongbo Liao ◽  
Dapeng Fan ◽  
Shixun Fan ◽  
Jigui Zheng
Keyword(s):  
Design Optimization ◽  
Servo System ◽  
Optimization Methods ◽  
Gear Transmission ◽  
Spring Stiffness ◽  
Mechatronic Systems ◽  
Torsional Spring ◽  
Resonance Frequencies ◽  
Simulation And Experiment ◽  
Gear Systems

Abstract. In many mechatronic systems, gear transmission chains are often used to transmit motion and power between motors and loads, especially for light, small but large torque output systems. Gear transmission chains will inevitably bring backlash as well as elasticity of shafts and meshing teeth. All of these nonlinear factors will affect the performance of mechatronic systems. Anti-backlash gear systems can reduce the transmission error, but elasticity has to be considered too. The aim of this paper is to find the key parameters affecting the resonance and anti-resonance frequencies of anti-backlash gear systems and then to give the design optimization methods of improving performance, both from element parameters and mechanical designing. The anti-backlash geared servo system is modeled using a two-inertia approximate model; a method of computing the equivalent stiffness of anti-backlash gear train is proposed, which comprehensively considers the total backlash of transmission chain, gear mesh stiffness, gear shaft stiffness and torsional spring stiffness. With the s-domain block diagram model of the anti-backlash geared servo system, the influences of four main factors on the resonance and anti-resonance frequencies of system are analyzed by simulation according to the frequency response, and the simulation analysis results dependent on torsional spring stiffness of anti-backlash gear pair and load moment of inertia variation are verified by the experiment. The errors between simulation and experimental results are less than 10 Hz. With these simulation and experiment results, the design optimization methods of improving the resonance and anti-resonance frequencies such as designing the center distance adjusting mechanism to reduce the initial total backlash, increasing the stiffness of torsional spring and lightweight design of load are proposed in engineering applications.

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