This paper investigates the non-linear behavior of bolted disk-drum joint in a rotor subjected to
bending loads during operation, using Finite element analysis (ANSYS- Workbench). The variation in contact
area due to these bending loads results in non-linear deformation.The non-linear behavior of bending stiffness
is studied from bending moment versus deflection plot obtained under static condition for different bolt preloads
using ANSYS Workbench. The results predicted by finite element simulation are validated analytically using
MATLAB. Considering the non-linear behavior of bending stiffness, rotor dynamic analysis of bolted and
without bolted (continuous) disk-drum rotor is performed. For any given operational speed range, by varying
the number of bolts under the condition of with and without bolted joints, the modal analysis is carried out to
study the effect of bolted joints on modal frequencies of the disk-drum rotor bearing system. These responses are
validated analytically using MATLAB. Also to study the effect of bolted joints on critical speeds, the Campbell
diagram is obtained under the condition of with and without bolted joints for different number of bolts. Finally
Harmonic analysis is carried out to determine the rotor whirl amplitude at critical speeds obtained for with and
without bolted joint.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Vibration analysis of lathe structrure due to gear defect using fem 02THANMAY JS
The document discusses vibration analysis of lathe structures due to gear defects using finite element modeling. It aims to analyze the effects of unbalanced forces generated by machine elements like spindles and gears on the lathe structure. Both frequency domain and time domain analyses will be conducted using FEM. Experiments will also be conducted to measure vibration velocities on critical points of a lathe for different spindle speeds using a vibration tester. The results of experimental and theoretical analyses will be discussed to monitor machine elements and understand the effects of vibration on the lathe structure.
Design and Analysis of Auger in KAMCO Power Tillerinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Design against fluctuating loads, stress concentration, Goodman and Modified Goodman Diagrams, Factors affecting stress concentration, Use of charts for finding stress concentration facotrs
Analysis of Crack Severity on Power Density Increment of GearsIDES Editor
Helical gears are commonly used in industry as
they have advantages of higher power density, quieter
operation etc., compared to spur gears. Conventional gear
design is based on various design criteria, including durability
and bending strength load rating. In recent times, fracture
failure modes are gaining importance in addition to
conventional failure modes. Stresses due to operating fatigue
loads and internal residual stresses can cause fatigue fracture
failure on the surface, sub-surface of gear flanks or at tooth
root of gears. During gear design, various parameters are
optimized, and one such parameter is the helix angle that is
optimized for power density and gear noise. However, effect of
possible defects (voids and inclusions) in the gear tooth is not
usually considered in these calculations. This paper is a study
on severity of defects in a gear blank relative to power density
increment. Three different gear geometries (spur and helical
gears with two different helix angles) each with similar defects
are considered. Finite Element Analysis (FEA) is used to
analyze Tooth Interior Fracture (TIF), and study variation of
Stress Intensity Factor (SIF) with crack size and helix angle.
It is seen that power density increment of a common gear
blank through helix angle increment poses a higher risk of
crack severity, as the same gear blank is exposed to higher
operating loads.
This document discusses stress, strain, and deformation of solids. It provides definitions for key terms like rigid bodies, deformable bodies, stress, strain, stiffness, stability, and ductility. It also describes different models used to simulate rigid and deformable body motion, including mass-spring models and finite element method (FEM) models. Additionally, it covers mechanical properties of materials like strength, stiffness, stability, and ductility. It discusses stress-strain diagrams and properties like elasticity, yield strength, plasticity, necking, and breaking strength for ductile and brittle materials. It also defines true stress and true strain which are important for large deformations, and describes different types of stresses like normal stresses (
The document discusses stress analysis in restorative dentistry using finite element analysis. It provides an overview of finite element analysis, including its history, basic concepts, advantages, and limitations. It also discusses mechanical properties of dental materials and various studies that have used finite element analysis to analyze stresses in dental structures and restorations. The document aims to present finite element analysis as a useful tool for stress analysis in restorative dentistry.
This document discusses estimating the stress intensity factor (SIF) on cracked components using finite element analysis. It begins with an introduction to fracture mechanics and SIF. Then it describes using FEA to model edge cracks and center cracks in plates to calculate SIF and compare results to theoretical solutions. Finally, it explains how the same FEA process was used to model cracks in a connecting rod component to determine SIF at various crack lengths. The document concludes the SIF values increase with crack length and FEA results closely match theoretical solutions.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Vibration analysis of lathe structrure due to gear defect using fem 02THANMAY JS
The document discusses vibration analysis of lathe structures due to gear defects using finite element modeling. It aims to analyze the effects of unbalanced forces generated by machine elements like spindles and gears on the lathe structure. Both frequency domain and time domain analyses will be conducted using FEM. Experiments will also be conducted to measure vibration velocities on critical points of a lathe for different spindle speeds using a vibration tester. The results of experimental and theoretical analyses will be discussed to monitor machine elements and understand the effects of vibration on the lathe structure.
Design and Analysis of Auger in KAMCO Power Tillerinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Design against fluctuating loads, stress concentration, Goodman and Modified Goodman Diagrams, Factors affecting stress concentration, Use of charts for finding stress concentration facotrs
Analysis of Crack Severity on Power Density Increment of GearsIDES Editor
Helical gears are commonly used in industry as
they have advantages of higher power density, quieter
operation etc., compared to spur gears. Conventional gear
design is based on various design criteria, including durability
and bending strength load rating. In recent times, fracture
failure modes are gaining importance in addition to
conventional failure modes. Stresses due to operating fatigue
loads and internal residual stresses can cause fatigue fracture
failure on the surface, sub-surface of gear flanks or at tooth
root of gears. During gear design, various parameters are
optimized, and one such parameter is the helix angle that is
optimized for power density and gear noise. However, effect of
possible defects (voids and inclusions) in the gear tooth is not
usually considered in these calculations. This paper is a study
on severity of defects in a gear blank relative to power density
increment. Three different gear geometries (spur and helical
gears with two different helix angles) each with similar defects
are considered. Finite Element Analysis (FEA) is used to
analyze Tooth Interior Fracture (TIF), and study variation of
Stress Intensity Factor (SIF) with crack size and helix angle.
It is seen that power density increment of a common gear
blank through helix angle increment poses a higher risk of
crack severity, as the same gear blank is exposed to higher
operating loads.
This document discusses stress, strain, and deformation of solids. It provides definitions for key terms like rigid bodies, deformable bodies, stress, strain, stiffness, stability, and ductility. It also describes different models used to simulate rigid and deformable body motion, including mass-spring models and finite element method (FEM) models. Additionally, it covers mechanical properties of materials like strength, stiffness, stability, and ductility. It discusses stress-strain diagrams and properties like elasticity, yield strength, plasticity, necking, and breaking strength for ductile and brittle materials. It also defines true stress and true strain which are important for large deformations, and describes different types of stresses like normal stresses (
The document discusses stress analysis in restorative dentistry using finite element analysis. It provides an overview of finite element analysis, including its history, basic concepts, advantages, and limitations. It also discusses mechanical properties of dental materials and various studies that have used finite element analysis to analyze stresses in dental structures and restorations. The document aims to present finite element analysis as a useful tool for stress analysis in restorative dentistry.
This document discusses estimating the stress intensity factor (SIF) on cracked components using finite element analysis. It begins with an introduction to fracture mechanics and SIF. Then it describes using FEA to model edge cracks and center cracks in plates to calculate SIF and compare results to theoretical solutions. Finally, it explains how the same FEA process was used to model cracks in a connecting rod component to determine SIF at various crack lengths. The document concludes the SIF values increase with crack length and FEA results closely match theoretical solutions.
IRJET- Design & Development of Bending Fatigue Testing Machine for Composite ...IRJET Journal
1. The document describes the design of a bending fatigue testing machine for composite materials. It aims to provide a low-cost option for generating fatigue data of composites.
2. The machine was designed with a simple operating mechanism using a crank-linkage driven by a V-belt that applies alternating displacement on composite specimens clamped in bending. Strain gauges measure the force and compensate for temperature effects.
3. The machine will help engineers study the behavior of composite components subjected to bending loads, like airplane bodies, at a lower cost than existing commercial machines. This could generate fatigue data to evaluate composite designs.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IRJET- Finite Element Analysis of a Laminated Conoid Shell under Uniform Pres...IRJET Journal
This document analyzes a four-layered rectangular laminated conoid shell with equal thickness layers in an anti-symmetrical stacking sequence. The shell is subjected to uniform pressure and analyzed using finite element analysis software ANSYS 15.0. The effects of varying the rise-to-span ratio from 0.05 to 0.5 on maximum principal stresses and deflection are studied. The results show that stresses increase with increasing rise-to-span ratio, with cross-ply laminates performing better than angle-ply. A rise-to-span ratio between 0.25-0.35 is found to provide better performance.
Performance Optimization of Tie rod using FEAIJERD Editor
Structural performance of any mechanical component is measured basically in terms of its natural frequency, deformation, stiffness, maximum stress level, fatigue life etc. In case of vehicle suspension system; however tie rod is mainly under compressive and fluctuating forces encounter from steering and bumping of vehicle. When steering acts to turn the vehicle, tie rod comes under compressive load. And when vehicle running on rough road condition, fluctuating forces.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
1. The document analyzes damage tolerance of a fuselage stiffened panel using finite element analysis. It calculates stress intensity factors for longitudinal cracks initiated at rivet holes under internal pressurization loads.
2. The stress intensity factor is calculated using the modified virtual crack closure integral method for crack lengths from 50mm to 1000mm. The stress intensity factor increases with crack length but decreases when the crack reaches frames.
3. For a crack length of 900mm, the calculated stress intensity factor is below the material's fracture toughness, indicating the design is safe for the analyzed internal pressurization loads.
Comparative Study of End Moments Regarding Application of Rotation Contributi...IOSR Journals
Abstract: Analysis of portal frames involves lot of complications and tedious calculations by conventional
methods. To carry out such analysis is a time consuming task. The rotation contribution method i.e. Kani’s
Method & Moment Distribution Method for analysis of portal frames can be handy in approximate and quick
analysis so as to get the detailed estimates ready. In this work, these two methods have been applied only for
vertical loading conditions. This paper presents the analysis of portal frame, considering mainly the case of
single bay portal frame, which is the most common in practice. The Kani’s method is self correcting, that is, the
error, if any, in a cycle is corrected automatically in the subsequent cycles. The checking is easier as only the
last cycle is required to be checked. The convergence is generally fast. It leads to the solutions in just a few
cycles of iterations.
In today’s lecture we present techniques for analyzing situations in which there can be large scale yielding, and determine expressions for the stress components inside the plastic zone. We will begin with a discussion of the J integral.
SMA
This document discusses various fundamental mechanical properties of materials including tensile strength, hardness, and impact strength. It provides definitions and testing methods for each property. Tensile strength is the maximum stress a material can withstand before breaking, and is measured through tension tests. Hardness tests measure a material's resistance to plastic deformation, and there are several methods like Rockwell, Brinell, and Vickers. Impact strength refers to a material's ability to absorb energy during dynamic loading like impacts without fracturing.
1) This document outlines the course objectives and syllabus for the Strength of Materials course taught by Dr. B. Janarthanan.
2) The course will cover concepts of stress, strain, deformation of solids, bending of beams, torsion of shafts, and stresses in thin shells.
3) The objectives are for students to understand stress and strain concepts, load transfer mechanisms, torsion and bending analyses, and thin shell design.
Stress concentration occurs where there is a discontinuity or abrupt change in geometry, such as a hole, notch, or crack. The theoretical stress concentration factor (Kt) is used to quantify the maximum stress at these locations compared to the nominal stress. Experimental methods like photoelasticity, brittle coatings, and strain gauges can be used to determine the actual stress concentration factor. The finite element method also allows modeling stress concentration by subdividing a component into small elements.
1. The document is notes on solid mechanics written by Saqib Imran, a civil engineering student, for other students and engineers.
2. It covers topics in solid mechanics including stress, strain, tensile strength, yield strength, ductile and brittle materials, Young's modulus, elastic and plastic regions, shear force, and bending moment.
3. Saqib provides contact information and invites readers to contact him if they have any questions about the notes.
In this study Dynamic property of a structural element which is frequency, damping and mode shapes are described by a process called modal analysis. Structural condition can be monitored by analyzing the changes in frequencies and mode shapes. All materials posses certain amount of internal damping. Similarly steel fibers also produce some internal damping. A system is a combination of elements, for example a structure is a system whose elements are beams, columns, slabs, footings .etc. In all those elements I have selected beam elements. Many research works are conducted on different type of materials under dynamic loading.
This document discusses various modes of failure for components in industrial power transmission gear drives, including gears, shafts, bearings, and seals. It describes different types of gear failures such as surface fatigue (pitting), wear, plastic flow, and breakage. Pitting is subdivided into initial, destructive, and normal pitting. The document explains the causes and appearances of each failure mode with diagrams and photos. It aims to help identify the causes of problems in gear drives and indicate potential remedies.
A novel method for evaluating the dynamic load factor of an involute gear to...Alexander Decker
This document presents a new mathematical model for evaluating the dynamic load factor of an involute gear tooth with asymmetric profiles. It develops typical dynamic load factor equations for symmetric and asymmetric tooth gear in single and double tooth contact. A nonlinear time-varying mesh stiffness model is presented based on bending, shear, Hertzian, and foundation deflections. The effect of pressure angle asymmetry and static transmitted load on transmission error and dynamic load factor are studied. The results indicate that asymmetric tooth profiles can enhance transmission error and dynamic load factor compared to symmetric profiles.
A review and buckling analysis of stiffened plateeSAT Journals
Abstract It happens many times that the structure is safe in normal stress and deflection but fails in buckling. Buckling analysis is one of the method to go for such type of analysis.It predicts various modes of buckling. Plates are used in many applications such as structures, aerospace, automobile etc. Such structures are subjected to heavy uniformly distributed load and concentrated load many times over it’s life span. Strength of these structures are increased by adding stiffeners to its plate. This paper deals with the analysis of rectangular stiffened plates which forms the basis of structures. A comparison of stiffened plate and unstiffened plate is done for the same dimensions. In order to continue this analysis various research papers were studied to understand the previous tasks done for stiffened plate. Hyper mesh and Nastran is used in this research work.Buckling analysis is performed for the component with aspect ratio of 2.Rectangular flat bar is used as stiffener Keywords: Stiffened Plate; Dynamic load; Buckling; Aspect ratio;Buckling Analysis.
A fracture mechanics based method for prediction ofSAJITH GEORGE
The document presents a fracture mechanics-based method for predicting cracking in circular and elliptical concrete rings undergoing restrained shrinkage. It describes an experimental program using different ring geometries and material tests to determine properties. A numerical model is developed using ANSYS to model the restrained shrinkage process and calculate stress intensity factors. The model uses a fictitious temperature field to simulate shrinkage and determines cracking age by comparing driving and resistance curves. It finds cracking occurs earlier in elliptical rings and the method accurately predicts experimental cracking ages.
International Refereed Journal of Engineering and Science (IRJES) is a peer reviewed online journal for professionals and researchers in the field of computer science. The main aim is to resolve emerging and outstanding problems revealed by recent social and technological change. IJRES provides the platform for the researchers to present and evaluate their work from both theoretical and technical aspects and to share their views.
The document provides an overview of rotor system dynamics and modeling. It defines key concepts like critical speeds, lateral and torsional vibration, stability analysis, and the Campbell diagram. The document also describes modeling approaches like the Jeffcott rotor and analyzing rotor response through modal, harmonic, and transient analysis. Key causes of rotor vibration like unbalance and methods to monitor rotor health are discussed.
COMPARISON OF RESPONSE TO UNBALANCE OF OVERHUNG ROTOR SYSTEM FOR DIFFERENT SU...IAEME Publication
Rotor unbalance is most common fault found in the rotating machines. Methods
are adopted to analyze the position of unbalance and to bring its effect into acceptablelimit. Vibration analysis is the most common technique used to analyze the rotor
system. Research have been performed on rotor supported atboth ends, however lessstudy has been done for overhung rotor. In this paper the response of overhung rotoron isotropic support and anisotropic support subject tounbalance has been presented.and equations aresolved using MATLAB programming. The effect of unbalancehas been studied on thebode plot. Forward and Reverse whirl are observed through Campbell diagram andmode shapes are plotted.
IRJET- Design & Development of Bending Fatigue Testing Machine for Composite ...IRJET Journal
1. The document describes the design of a bending fatigue testing machine for composite materials. It aims to provide a low-cost option for generating fatigue data of composites.
2. The machine was designed with a simple operating mechanism using a crank-linkage driven by a V-belt that applies alternating displacement on composite specimens clamped in bending. Strain gauges measure the force and compensate for temperature effects.
3. The machine will help engineers study the behavior of composite components subjected to bending loads, like airplane bodies, at a lower cost than existing commercial machines. This could generate fatigue data to evaluate composite designs.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IRJET- Finite Element Analysis of a Laminated Conoid Shell under Uniform Pres...IRJET Journal
This document analyzes a four-layered rectangular laminated conoid shell with equal thickness layers in an anti-symmetrical stacking sequence. The shell is subjected to uniform pressure and analyzed using finite element analysis software ANSYS 15.0. The effects of varying the rise-to-span ratio from 0.05 to 0.5 on maximum principal stresses and deflection are studied. The results show that stresses increase with increasing rise-to-span ratio, with cross-ply laminates performing better than angle-ply. A rise-to-span ratio between 0.25-0.35 is found to provide better performance.
Performance Optimization of Tie rod using FEAIJERD Editor
Structural performance of any mechanical component is measured basically in terms of its natural frequency, deformation, stiffness, maximum stress level, fatigue life etc. In case of vehicle suspension system; however tie rod is mainly under compressive and fluctuating forces encounter from steering and bumping of vehicle. When steering acts to turn the vehicle, tie rod comes under compressive load. And when vehicle running on rough road condition, fluctuating forces.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
1. The document analyzes damage tolerance of a fuselage stiffened panel using finite element analysis. It calculates stress intensity factors for longitudinal cracks initiated at rivet holes under internal pressurization loads.
2. The stress intensity factor is calculated using the modified virtual crack closure integral method for crack lengths from 50mm to 1000mm. The stress intensity factor increases with crack length but decreases when the crack reaches frames.
3. For a crack length of 900mm, the calculated stress intensity factor is below the material's fracture toughness, indicating the design is safe for the analyzed internal pressurization loads.
Comparative Study of End Moments Regarding Application of Rotation Contributi...IOSR Journals
Abstract: Analysis of portal frames involves lot of complications and tedious calculations by conventional
methods. To carry out such analysis is a time consuming task. The rotation contribution method i.e. Kani’s
Method & Moment Distribution Method for analysis of portal frames can be handy in approximate and quick
analysis so as to get the detailed estimates ready. In this work, these two methods have been applied only for
vertical loading conditions. This paper presents the analysis of portal frame, considering mainly the case of
single bay portal frame, which is the most common in practice. The Kani’s method is self correcting, that is, the
error, if any, in a cycle is corrected automatically in the subsequent cycles. The checking is easier as only the
last cycle is required to be checked. The convergence is generally fast. It leads to the solutions in just a few
cycles of iterations.
In today’s lecture we present techniques for analyzing situations in which there can be large scale yielding, and determine expressions for the stress components inside the plastic zone. We will begin with a discussion of the J integral.
SMA
This document discusses various fundamental mechanical properties of materials including tensile strength, hardness, and impact strength. It provides definitions and testing methods for each property. Tensile strength is the maximum stress a material can withstand before breaking, and is measured through tension tests. Hardness tests measure a material's resistance to plastic deformation, and there are several methods like Rockwell, Brinell, and Vickers. Impact strength refers to a material's ability to absorb energy during dynamic loading like impacts without fracturing.
1) This document outlines the course objectives and syllabus for the Strength of Materials course taught by Dr. B. Janarthanan.
2) The course will cover concepts of stress, strain, deformation of solids, bending of beams, torsion of shafts, and stresses in thin shells.
3) The objectives are for students to understand stress and strain concepts, load transfer mechanisms, torsion and bending analyses, and thin shell design.
Stress concentration occurs where there is a discontinuity or abrupt change in geometry, such as a hole, notch, or crack. The theoretical stress concentration factor (Kt) is used to quantify the maximum stress at these locations compared to the nominal stress. Experimental methods like photoelasticity, brittle coatings, and strain gauges can be used to determine the actual stress concentration factor. The finite element method also allows modeling stress concentration by subdividing a component into small elements.
1. The document is notes on solid mechanics written by Saqib Imran, a civil engineering student, for other students and engineers.
2. It covers topics in solid mechanics including stress, strain, tensile strength, yield strength, ductile and brittle materials, Young's modulus, elastic and plastic regions, shear force, and bending moment.
3. Saqib provides contact information and invites readers to contact him if they have any questions about the notes.
In this study Dynamic property of a structural element which is frequency, damping and mode shapes are described by a process called modal analysis. Structural condition can be monitored by analyzing the changes in frequencies and mode shapes. All materials posses certain amount of internal damping. Similarly steel fibers also produce some internal damping. A system is a combination of elements, for example a structure is a system whose elements are beams, columns, slabs, footings .etc. In all those elements I have selected beam elements. Many research works are conducted on different type of materials under dynamic loading.
This document discusses various modes of failure for components in industrial power transmission gear drives, including gears, shafts, bearings, and seals. It describes different types of gear failures such as surface fatigue (pitting), wear, plastic flow, and breakage. Pitting is subdivided into initial, destructive, and normal pitting. The document explains the causes and appearances of each failure mode with diagrams and photos. It aims to help identify the causes of problems in gear drives and indicate potential remedies.
A novel method for evaluating the dynamic load factor of an involute gear to...Alexander Decker
This document presents a new mathematical model for evaluating the dynamic load factor of an involute gear tooth with asymmetric profiles. It develops typical dynamic load factor equations for symmetric and asymmetric tooth gear in single and double tooth contact. A nonlinear time-varying mesh stiffness model is presented based on bending, shear, Hertzian, and foundation deflections. The effect of pressure angle asymmetry and static transmitted load on transmission error and dynamic load factor are studied. The results indicate that asymmetric tooth profiles can enhance transmission error and dynamic load factor compared to symmetric profiles.
A review and buckling analysis of stiffened plateeSAT Journals
Abstract It happens many times that the structure is safe in normal stress and deflection but fails in buckling. Buckling analysis is one of the method to go for such type of analysis.It predicts various modes of buckling. Plates are used in many applications such as structures, aerospace, automobile etc. Such structures are subjected to heavy uniformly distributed load and concentrated load many times over it’s life span. Strength of these structures are increased by adding stiffeners to its plate. This paper deals with the analysis of rectangular stiffened plates which forms the basis of structures. A comparison of stiffened plate and unstiffened plate is done for the same dimensions. In order to continue this analysis various research papers were studied to understand the previous tasks done for stiffened plate. Hyper mesh and Nastran is used in this research work.Buckling analysis is performed for the component with aspect ratio of 2.Rectangular flat bar is used as stiffener Keywords: Stiffened Plate; Dynamic load; Buckling; Aspect ratio;Buckling Analysis.
A fracture mechanics based method for prediction ofSAJITH GEORGE
The document presents a fracture mechanics-based method for predicting cracking in circular and elliptical concrete rings undergoing restrained shrinkage. It describes an experimental program using different ring geometries and material tests to determine properties. A numerical model is developed using ANSYS to model the restrained shrinkage process and calculate stress intensity factors. The model uses a fictitious temperature field to simulate shrinkage and determines cracking age by comparing driving and resistance curves. It finds cracking occurs earlier in elliptical rings and the method accurately predicts experimental cracking ages.
International Refereed Journal of Engineering and Science (IRJES) is a peer reviewed online journal for professionals and researchers in the field of computer science. The main aim is to resolve emerging and outstanding problems revealed by recent social and technological change. IJRES provides the platform for the researchers to present and evaluate their work from both theoretical and technical aspects and to share their views.
The document provides an overview of rotor system dynamics and modeling. It defines key concepts like critical speeds, lateral and torsional vibration, stability analysis, and the Campbell diagram. The document also describes modeling approaches like the Jeffcott rotor and analyzing rotor response through modal, harmonic, and transient analysis. Key causes of rotor vibration like unbalance and methods to monitor rotor health are discussed.
COMPARISON OF RESPONSE TO UNBALANCE OF OVERHUNG ROTOR SYSTEM FOR DIFFERENT SU...IAEME Publication
Rotor unbalance is most common fault found in the rotating machines. Methods
are adopted to analyze the position of unbalance and to bring its effect into acceptablelimit. Vibration analysis is the most common technique used to analyze the rotor
system. Research have been performed on rotor supported atboth ends, however lessstudy has been done for overhung rotor. In this paper the response of overhung rotoron isotropic support and anisotropic support subject tounbalance has been presented.and equations aresolved using MATLAB programming. The effect of unbalancehas been studied on thebode plot. Forward and Reverse whirl are observed through Campbell diagram andmode shapes are plotted.
A Review on Dynamic Analysis of Machine StructureIRJET Journal
This document provides a review of dynamic analysis techniques for machine structures. It discusses how dynamic analysis is used to determine vibration characteristics and model the behavior of structures under forced vibrations. The review covers several papers that analyze machine components like crankshafts, connecting rods, and foundations using finite element modeling and modal analysis. The goal of dynamic analysis is to understand vibration response, optimize designs, and prevent structural failures from resonance.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Effect of gear design variables on the dynamic stress of multistage gearsAlexander Decker
The document describes a numerical model developed to simulate and optimize the dynamic stress of multistage spur gears. The model considers three design variables: module, pressure angle, and contact ratio. Simulation results showed that increasing module and decreasing pressure angle and contact ratio can increase dynamic stress levels. A module of 2.5 and contact ratio of 2.0 were found to yield the lowest dynamic stresses for the given multistage gear train design. The model can be used as a tool to determine optimal gear design parameters for minimizing dynamic stresses.
11.effect of gear design variables on the dynamic stress of multistage gearsAlexander Decker
This document presents a numerical model to simulate and optimize the dynamic stress of multistage spur gears. The model considers time-varying mesh stiffness and frictional torque. It was used to study the effects of three gear design variables - module, pressure angle, and contact ratio - on dynamic stress. Increasing the module increased stress levels, while a pressure angle of 25 degrees and contact ratio of 2.0 reduced stresses the most for the gear train studied. The model can be used as a tool to obtain optimal design parameters for a given multistage gear train.
Identification of dynamic rigidity for high speed spindles supported on ball ...eSAT Journals
Abstract The widespread use of high-speed machining in recent decades has led to a significant area of research on issues that limit its productivity. Regenerative chatter is a well‐known machining problem that results in unstable cutting process, leads to the poor surface quality, reduced material removal rate and damage on the machine tool itself. The main requirement for the stability of system dynamics is the information of tool tip frequency response functions (FRF’s).The present work considered a coupled model of spindle-bearing system by using the angular contact ball bearing forces on stability of machining. Using Timoshenko beam element formulation, the spindle unit is analyzed by including the gyroscopic and centrifugal terms and the bearing contact forces are arrived from Hertzian contact theory. Then, the model is used for studying the effects of viscous damping to obtain the tool point FRF for the dynamic spindle. Index Terms: Spindle dynamics, Stability, High speed effects, Bearing contact forces, Hertzian contact theory, Finite element modeling.
Misalignment of shaft in rotating systems is one of the most common faults. Improper aligning of shafts through couplings often leads to severe vibration problems in many rotating machines. Vibration monitoring is a useful technique which provides valuable information regarding symptoms of machinery failures, and in turn may avoid costly breakdowns. In the present paper experiment investigation of parallel misalignment in rotating machinery is presented. by Mr. Bhawthankar A. A, Mr. Mane M. B, Mr. Phopale Y. A and Mr. Korshetti V. V 2018. EFFECT OF PARALLEL MISALIGNMENT IN ROTATING MACHINERY. International Journal on Integrated Education. 1, 1 (Dec. 2018), 82-84 https://journals.researchparks.org/index.php/IJIE/article/view/789/758 https://journals.researchparks.org/index.php/IJIE/article/view/789
ANALYSIS OF DYNAMIC CHARACTERISTICS OF SHORT JOURNAL BEARINGS - A REVIEWijiert bestjournal
The stability of bearing - rotor system is a very important problem for design,manufacturing,and operation of rotating machinery. The instability of rotor system will result in the strong vibration and even disastrous accident of machinery. The researches for decades indicate that the strong - nonlinear exciting sources such a s oil - film forces,sealing forces and non uniform steam forces etc. all are main reasons which can make unstable accidents in rotating machineries. The oil - film forces are the leading nonlinear exciting source which makes the bearing rotor system to be a s elf - exciting vibration system and results in fatal accidents. So solution of nonlinear oil - film forces in sliding bearings is always very important for dynamic analysis of rotor - bearing system. The computational methods of bearing nonlinear fluid - film forc es must be studied to carry out the nonlinear dynamic analysis of rotor systems and widely reveal the operation laws of large - scale rotating machineries. It has very important theoretical significance for advancing the stability,safety and reliability of rotating machineries.
This document summarizes a research paper that evaluates the critical speed of a generator rotor while considering external loads. It introduces the importance of evaluating critical speed while accounting for external loads. It describes the methodology used, which automates the critical speed analysis in ANSYS using a script. The script allows inputs like rotor dimensions and loads to be variables. Results from the script are compared to analytical calculations and show good agreement. The research demonstrates a method to automatically evaluate critical speeds for any rotor configuration while considering important external loads.
IRJET- Dynamic Stability Analysis of Functionally Graded MaterialsIRJET Journal
The document summarizes a study on the dynamic stability analysis of functionally graded materials (FGM) plates subjected to in-plane periodic loading. It discusses how FGMs have graded material properties that vary continuously from one surface to another, making them advantageous over conventional composite materials. A finite element model is developed using higher-order shear deformation theory to analyze the dynamic stability of FGM plates under different loading and boundary conditions. Parameters like volume fraction index, temperature rise, loading amplitude are varied to understand their influence on the stability boundaries of the FGM plates.
This document provides an overview of bearing vibration analysis. It discusses the various sources of bearing vibration, including variable compliance, geometrical imperfections like surface roughness and waviness, and discrete defects. It describes how these factors can generate complex vibration signatures. The document also outlines characteristic bearing frequencies that may be present in vibration spectra and how they are calculated based on bearing geometry. It provides an example of how vibration analysis can detect deterioration by identifying anomalies in the bearing speed ratio. In summary, the document examines the causes of bearing vibration and how vibration analysis is used to monitor bearing health and detect issues.
The document discusses the thermo-mechanical analysis of a crankcase for a six cylinder truck diesel engine. It outlines the process of identifying loads from combustion, inertia, thermal effects and assembly and applying them in a finite element analysis of the crankcase. The analysis seeks to determine the durability and fatigue life of the crankcase under the varying operating loads of the engine.
IRJET- Modification of Root Fillet Profile for Optimum Gear LifeIRJET Journal
1. The document discusses the modification of root fillet profiles in spur gears to optimize gear life and reduce failure from pitting.
2. Finite element analysis is conducted in ANSYS on spur gear models with varying root fillet radii. Maximum contact stresses and deformations are compared for different fillet profiles.
3. Experimental analysis is also carried out using the photoelastic method to validate the finite element results. Optimizing the root fillet profile can help improve the strength of gears and increase gear life.
Estimating damping in structure made of different m aterials (steel,brass,aluminum) and processes sti ll remains as one of the biggest challengers. All mate rials posses certain amount of internal damping,wh ich manifested as dissipation of energy from the system . This energy in a vibratory system is either dissipated into heat or radiated away from the syst em. Material damping or internal damping contribute s to about 10-15% of total system damping. Cantilever beams of required size & shape are prepared for experimental purpose & damping ratio is investigate d. Damping ratio is determined by half-power bandwidth method. It is observed that damping ratio is higher for steel than brass than aluminum.
IRJET - Vibration Analysis of Disc Brake by using FEA and FFT AnalyzerIRJET Journal
This document summarizes a research paper that analyzed vibration in disc brakes through finite element analysis (FEA) and experimental testing. The researchers created 3D models of a disc brake in different designs and performed modal analysis to evaluate the natural frequencies and mode shapes. They then conducted experimental vibration testing on the physical disc brakes using an FFT analyzer to measure the natural frequencies and compared the results to the FEA analysis. The goal was to optimize the disc brake design by changing the hole shapes to reduce vibrations while maintaining the original natural frequencies through both analytical modeling and experimental validation.
IRJET- Nonlinear Transient Vibration Analysis of Mounting Superstructure for ...IRJET Journal
1) The document describes a nonlinear transient vibration analysis of a mounting superstructure designed to isolate vibration sensitive cargo during road transportation.
2) Wire rope isolators are selected to connect the mounting frame to the vehicle base frame in order to dissipate vibration energy from road shocks and impacts.
3) A nonlinear transient analysis is conducted to investigate the shock response of the designed mounting superstructure when subjected to road generated shock pulses, as the isolators exhibit nonlinear stiffness.
Active magnetic bearings used as exciters for rolling element bearing outer r...ISA Interchange
The active health monitoring of rotordynamic systems in the presence of bearing outer race defect is considered in this paper. The shaft is assumed to be supported by conventional mechanical bearings and an active magnetic bearing (AMB) is used in the mid of the shaft location as an exciter to apply electromagnetic force to the system. We investigate a nonlinear bearing-pedestal system model with the outer race defect under the electromagnetic force. The nonlinear differential equations are integrated using the fourth-order Runge–Kutta algorithm. The simulation and experimental results show that the characteristic signal of outer race incipient defect is significantly amplified under the electromagnetic force through the AMBs, which is helpful to improve the diagnosis accuracy of rolling element bearing's incipient outer race defect.
IRJET- Explicit Dynamic Analysis of Gear Tooth of a Synchromesh Manual Transm...IRJET Journal
This document presents an explicit dynamic analysis of the gear tooth of a manual transmission gearbox. The analysis used finite element modeling and simulation software. Key steps included:
1. Creating a 3D CAD model of the gearbox components in SolidEdge.
2. Importing the model into ABAQUS for meshing and simulation. A dynamic analysis was performed under different loading conditions to determine stress levels.
3. The results showed the displacement of the gears increased over time up to 6mm as the load increased. Stages of the displacement and developing stress were visualized at different time intervals. The maximum contact stress between gear surfaces was also determined.
Design optimization and new product development of hub idler gearIRJET Journal
This document discusses the design optimization and new product development of a hub idler gear. It begins with an introduction to new product development and its importance. It then reviews the manufacturing processes used to create the hub idler gear, including turning, milling, grinding and marking. The document compares the original design of the hub idler gear to the new optimized design using finite element analysis to evaluate stress, displacement, and strain. The analysis found an 8.76% reduction in stress, 14% reduction in displacement, and 4% reduction in strain in the new design compared to the original. The document concludes the optimized design of the hub idler gear could potentially replace the original design.
Similar to Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity (20)
Efforts made in many countries to stop the COVID-19 pandemic include vaccinations. However,
public skepticism about vaccines is a pressing issue for health authorities. With the COVID-19 vaccine
available,
SARS-CoV-2, as the causative agent of COVID-19, has spread throughout the world after becoming
a pandemic in March 2020. In the midst of the ongoing COVID-19 pandemic, we are also faced with another
serious health problem
This paper discusses the construction and implementation of a system for the measurement of
electrical power parameters; amperage and voltage of the hybrid system photovoltaic solar-wind, to evaluate
the system parameters and performance. The basis of the development of the measuring apparatus is the use of
an Arduino Mega 2560 to provide the interface between the electrical circuits of the sensors and the dynamics
of the voltage-amperage as well as collect data in an analog format as well as development of functional
dependence relationships. The collected data is converted into digital format and stored it in an Excel format
through the "PLX-DAQ Spreadsheet" that connects the Arduino and the PC for display and analysis of the
system parameters. The proposed technique for power measurements of AC and DC proved to be reliable and
can predict the power amperage and voltage within relative error of 1.63 % for AC and 4.16% for DC,
respectively.
The optimum speed required for mass-size reduction of shells to produce most sizes that are small
comparable with kernel sizes; coupled with retention of kernel wholeness in cracked palm nut mixture under
repeated impact was investigated. This is to enhance whole kernel separation by dry method, reduce maintenance
and production cost of palm kernel oil (PK0); and lower the risk of oil rancidity associated with split kernel
production and wet method of separation. A static nut cracker and centrifugal nut cracker were used in this study as
Test Rigs while sieves were used to grade cracked shells and whole kernels. The data generated were evaluated. A
model was developed for energy via speed required to retain kernels wholeness following repeated impact in the
crackers. Technical analysis revealed that the maximum allowable speed to retain kernel wholeness is 27.93 m/s;
the minimum allowable average speed to fragment cracked shells is 24.95 m/s. Further analysis showed that the
optimum speed and energy required for cracked nut mixture under repeated impact to have kernel wholeness
retention and production of small sizes of cracked shells relative to kernel sizes are 25.71 m/s and 0.4 J,
respectively.
This review was written to provide a comprehensive summary of the suggested etiologies of Chronic Kidney
Disease of Unknown Etiology (CKDu) in Sri Lanka. In this review, Chronic Kidney Disease (CKD) is explained
in detail and its known etiologies are discussed. CKDu is defined and its epidemiology is discussed, with the
compilation of statistic from over 15 research papers through the years 2000 to present.
This work contributes to the monitoring of water pollution of some selected Dams in Katsina
State, North western Nigeria by assessing the degree of heavy metal pollution in the Dams sediment samples.
The study was conducted in the year 2017 within some selected Dams in the State (Ajiwa, Zobe,
Sabke/Dannakola) that are beehives of fishing and Agricultural activities in Katsina State. Analysis for the
concentration of these heavy metals; Cr, Cd, Fe, Ni, Mn, Pb and Zn was conducted by the use of AAS (by
Atomic Absorption Spectrophotometry) method. Several indices were used to assess the metal contamination
levels in the sediment samples, namely; Geo-accumulation Index (Igeo), Enrichment Factor (EF),
Contamination Factor (CF), Degree of Contamination (Cd), Pollution Load Index (PLI) and Potential
Ecological Risk Index (PERI). The result of this study has shown that generally among the heavy metals
evaluated, the highest concentration was observed for Fe (range: 2.6718-4.2830 ppm), followed by Zn (range:
0.4265-0.7376 ppm), Cr (range: 0.1106-0.1836 ppm), Cd (range: 0.1333-0.1273 ppm) and Mn (range: 0.1136-
0.1271 ppm). While Pb has the lowest concentration (range: 0.0472-0.0598 ppm). For all the site sampled the
heavy metal Ni was below detection level (BDL). From the results of heavy metals I-geo values, according to
Muller’s classification, all the sediment samples from the selected dams were unpolluted (class 0). The result for
the enrichment factor has shown that for all the selected dam sediment samples the heavy metals show
deficiency to minimal enrichment. Also based on the contamination factors for all sediment samples the heavy
metal Cd has a CF values range of 0.5430-0.6665 (~1), indicating that the sediment samples are moderately
contaminated with Cd. In contrast, the rest of the heavy metals exhibit low contamination in general. The value
of PLI ranges from 0.2408 to 0.4935, indicating unpolluted to moderate pollution. The Eri values for all
samples are all < 40, presenting low ecological risk. The results suggest that the sediment samples from the
selected dams in Katsina state has low contamination by the heavy metals evaluated.
Using QR Decomposition to calculate the sum of squares of a model has a limitation that the number of rows,
which is also the number of observations or responses, has to be greater than the total number of parameters used in the
model. The main goal in the experimental design model, as a part of the Linear Model, is to analyze the estimable function
of the parameters used in the model. In order not to deal with generalized invers, partitioned design matrix may be used
instead. This partitioned design matrix method may be used to calculate the sum of squares of the models whenever the total
number of parameters is greater than the number of observations. It can also be used to find the degrees of freedom of each
source of variation components. This method is discussed in a Balanced Nested-Factorial Experimental Design.
Introduction:It has been proven twice that the Hambantota District has the highest life expectancy in male
population. This study focused to find and identify reasons for Hambantota District people to have high life
expectancy at birth.
Methodology: Research was carried out in both qualitative and quantitative phases in five MOH (Medical
Health Officer) divisions in HambantotaDistrict. Study focused on 3 age categories, 55-65 Years, 66-75 Years,
and above 76 Years. Main objectives and key information areas are Life Style and Social Behaviors, Food
Consumption and Diet, Familial Trait and Physical and Mental Health.
Findings: Majority of the male population have educated up to grade 5and most are engaged in the agriculture
while others engaged in fishery and self-employment etc. Almost everyone reachestheir workplaces by foot or by
bicycle. Many of them work less than six hours. They spend their free time with their family members and watch
TV. Most of them do not consume alcohol and smoke. Almost everyone take part in social activities. Majority eat
red rice for all three meals. Almost everyone eats fish every day. They have a high salt intake. Their parents and
ancestors have also have had a high life expectancy. Only a minority suffer from chronic illnesses. They all have
a good physical and mental health condition. They spend happy and relaxed lifestyle.
Conclusion: Healthy diet, low alcohols consumption and smoking, high iodine intake, physical activeness and
their social wellbeing effect for high life expectancy within the male population of selected five MOH divisions
in Hambantota District. They have a free and happy life. Genetics of these people also may contribute for high
life expectancy. Abundance of neem trees in this area also may effect on their high life expectancy.
A clay deposit in Chavakali of western Kenya was evaluated for its potential as refractory raw
material. The collected clay sample was crushed, sieved and the chemical composition determined in
percentage weight (wt %) of (SiO2, Al2O3, Fe2O3, etc) using Atomic Absorption Spectrophotometer (AAS). The
samples were moulded into rectangular shaped bricks of 40mm height, 40mm width and 80mm length, allowed
to dry and later fired up to a temperature of 10000C. Refractory properties like Compressive strength,
Hardness, Linear shrinkage on firing, Apparent porosity and Density were determined using standard
techniques. The result of chemical analysis indicated that the clay was composed of Silica (SiO2), 67.3%;
Alumina (Al2O3), 16.67%; Iron Oxide (Fe2O3), 3.87%; Calcium Oxide (CaO), 0.37%; Potassium Oxide (K2O),
2.30%; Sodium Oxide (Na2O), 1.39%; and other traces. The physical and mechanical tests show that the clay
has Cold Crushing Strength of 10.36MPa, Hardness of 40.080 GPa, Linear shrinkage of 6.17%, Apparent
Porosity of 32.71% and Bulk Density of 2.77g/cm3
. Chavakali clay can make better local refractory
Nihon University challenged world record of the human-powered aircraft flight based on the
regulation of Fédération Aérionautique Internationale in Kasumigaura Lake, Japan, 2014. The wing fell off in
midair immediately after take-off, the pilot landed to the lake for safety. So, the challenge failed. It guessed the
operational errors were correlated with the wing falling in midair, which had not happened in our experience.
The flight recording camera and the salvaged airplane were investigated. The fault tree analysis was conducted
for cause investigation. The wing falling was the result as the chain destruction starting from the coupling parts
being damaged in take-off. The defective take-off was caused by composite factors on only operational errors.
The risk that the ultralight airplane might disintegrate in midair by only operational error became apparent.
Due to the large-scale exploitation of mineral resources and the unreasonable human activities, the
geological disasters in Jiaozuo City have become increasingly prominent and the degree of harm increased. This
leds to a tremendous threat to human life and property safety. Jiaozuo City, the main types of geological
disasters, landslides, ground subsidence, debris flow and ground fissures. It has great significance to the
development of the city and the protection of people's life and property to explore the hidden dangers of
geological disasters and actively take preventive and control measures. The establishment of geological
hazard group measurement system of prevention and control to achieve the timely detection of geological
disasters, rapid early warning and effective avoidance.
Dangerous gas explosion accidents result in considerable amount of casualties and property damage.
Hence, an investigation on the generation of poisonous gases in gas explosions exerts important implications
for accident prevention and control and in the decision-making processes of fire rescue. Therefore, a gas
explosion piping test system is established in this paper. Experimental research on gas explosion is conducted by
selecting methane/air premixed gases with concentrations of 7%, 9%, 11%, 13%, and 15% in the gas explosive
range. This research aims to reveal the regularity of CO generation after gas explosion in pipelines.
Experimental results showed that when the gas concentration is small (< 9%), 1500–3000 ppm CO will be
produced. When the gas concentration is large (> 9%), the CO amount will reach 3000–40000 ppm. The
variation trend in CO concentration and the quantity of explosive gas are also obtained.
1) The document examines the influence of entry speed on water entry phenomena through experimental visualization of the flow field above the water surface. Entry speeds ranged from 0.2 to 1.5 km/s.
2) It was found that above a critical entry speed, the vertical velocity of the water splash tip was linearly proportional to its vertical location, and the ratio of initial splash velocity to entry speed was constant.
3) A shock wave was driven above the water surface even for subsonic entry speeds, and its propagation followed a scaling law for explosive shock waves where projectile kinetic energy replaced explosive energy.
Pingdingshan Coal Mine district is one of the six mining areas of Henan Province, which is a
large coal base in China. After 60 years of exploitation, it has brought great benefits, at the same time,
serious geological disasters have been occurred. It has seriously damaged the normal production of the
masses, life, restricting the development of Pingdingshan coal mine economy. In this paper, the
geological disasters such as ground collapse, ground fissures and ground subsidence in Pingdingshan coal
mine are analyzed, and the degree of geological disasters in the mining area is analyzed in combination
with the severely affected mining area. Finally, reasonable and feasible countermeasures have been put
forward.
Kelud volcano is located in East Java Province, Indonesia. According to Geochemical study of
Kelud Volcano, it could be divided into 3 periods which are Kelud I (older than 100 ky BP), Kelud II (40 – 100
ky BP), and Kelud III (younger than 40 ky BP). A specific petrogenesis of Kelud are dominatad by magma
mixing and fractional crystalization. New petrological data from Kelud volcano was taken through products of
the eruption in 1990 (Vulkanian type), 2007 (Lava plug forming) and 2014 (Plinian type). Petrographic study
on these rocks showed that reverse and oscilatory zoning on plagioclases, Shieve-like and corroded textures on
plagioclases and pyroxenes are common. However, normal zoning textures were also found on plagioclases and
pyroxenes. Whole rock study on these rocks showed all rocks were classified into Basalt to Andesite in
composition with calc-alkaline group. The study indicated that their magma origin derrived from slab with
fractional crystallization during in the magma reservoir, and magma mixing processes are dominant expecially
in magma pockets. Concequently, the magma origin and petrogenesis of Kelud magma after the 1966 eruption
are still the same as those of old magma of Kelud.
Black cotton soils are among a group of soils termed as problematic soils. These soils have
undesirable characteristics in relation to construction works and therefore need some form of improvement
when encountered in construction projects. Techniques for improvement of black cotton soils include
replacement, moisture control or adding a stabilizer. Cement and/or lime has been commonly used in soil
stabilization for ages. However, due to the associated cost, required quality control and the need to utilize waste
materials in construction, new stabilizing materials are emerging. This paper presents a study on application of
quarry dust for improving properties of black cotton soil in Mbeya region, Tanzania. The targeted improvement
was to achieve minimum acceptable characteristics for road subgrade as per Tanzania standards. It was
determined that 40% by weight of quarry dust added to the black cotton soil was able to improve the
characteristics by increasing CBR value from 3.8 to 15.7 and reducing PI from 32% to 15%. It will be worthy
studying the cost implication of the suggested improvement in relation to other techniques before application of
the study findings.
High intensity rain and morphometri in Padang city cause at Arau. Morphometri
geomorphologi that is related to wide of, river network, stream pattern and gradien of river. The form wide
of DAS will be by stream pattern and level.This will influence to the number of rain. Make an index to
closeness of stream depict closeness of river stream at one particular DAS. Speed of river stream influenced
by storey, level steepness of river. Steepness storey, level is comparison of difference height of river
downstream and upstream. Ever greater of steepness of river stream, excelsior speed of river stream that
way on the contrary. High to lower speed of river stream influence occurence of floods, more than anything
else if when influenced by debit big. By using rainfall from year 2005 to year 2015, and use Thiessen method
got a rainfall. Use the DEM IFSAR, analysed sofware ARGIS, and with from earth map, the result got DAS
in at condition of floods gristle and sedimentation. There are band evakuasi for resident which data in
floods area.
The chemical (extractives and lignin) content and histological property (microscopic structure)
of tissues of Ricinodendron heudelotii (Baill, Pierre ex Pax), an angiosperm, were investigated for its potential
as a fibrous raw material for pulp and paper production. Bolts of about 70 cm were cut from the felled trees at
three different merchantable height levels of 10%, 50%, and 90% to obtain: corewood, middlewood and
outerwood samples. The fiber characteristics of the selected trees viz: the fiber length, fibre diameter and lumen
diameter were measured while the cell wall thickness was derived from the measured fibre dimensions. The
average fiber length, cell wall thickness, and lumen width, were 1.40 mm, 4.6 µm, and 32.3 µm, respectively.
The extractive and lignin contents were determined. Klason lignin content was about 30%. Extractive content of
R. heudelotii ranged from 0.41 to 0.5%. Based on these findings R. heudelotii is suitable for pulp and paper
production.
The prolific Niger Delta Basin is a mature petroleum province. Therefore, further prospectivity in
the basin lies within deeper plays which are high pressure and high temperature (HPHT) targets. One of the
main characteristics of the Niger Delta is its unique diachronous tripartite stratigraphy. Its gross onshore and
shallow offshore lithostratigraphy consists of the deep-seated Akata Formation and is virtually exclusively
shale, the petroliferous paralic Agbada Formation in which sand/shale proportion systematically increases
upward, and at the top the Benin Formation composed almost exclusively of sand. This stratigraphic pattern is
not exactly replicated in the deep offshore part of the delta.
A low-carbon steel wire of AISI 1022 is used to easily fabricate into self-drilling tapping screws,
which are widely used for construction works. The majority of carbonitriding activity is performed to improve
the wear resistance without affecting the soft, tough interior of the screws in self-drilling operation. In this
study, Taguchi technique is used to obtain optimum carbonitriding conditions to improve the mechanical
properties of AISI 1022 self-drilling tapping screws. The carbonitriding qualities of self-drilling tapping screws
are affected by various factors, such as quenching temperature, carbonitriding time, atmosphere composition
(carbon potential and ammonia level), tempering temperature and tempering time. The quality characteristics of
carbonitrided tapping screws, such as case hardness and core hardness, are investigated, and so are their
process capabilities. It is experimentally revealed that the factors of carbonitriding time and tempering
temperature are significant for case hardness. The optimum mean case hardness is 649.2HV. For the case
hardness, the optimum process-capability ratio increases by about 200% compared to the original result. The
new carbonitriding parameter settings evidently improve the performance measures over their values at the
original settings. The strength of the carbonitrided AISI 1022 self-drilling tapping screws is effectively improved.
More from International journal of scientific and technical research in engineering (IJSTRE) (20)
UNLOCKING HEALTHCARE 4.0: NAVIGATING CRITICAL SUCCESS FACTORS FOR EFFECTIVE I...amsjournal
The Fourth Industrial Revolution is transforming industries, including healthcare, by integrating digital,
physical, and biological technologies. This study examines the integration of 4.0 technologies into
healthcare, identifying success factors and challenges through interviews with 70 stakeholders from 33
countries. Healthcare is evolving significantly, with varied objectives across nations aiming to improve
population health. The study explores stakeholders' perceptions on critical success factors, identifying
challenges such as insufficiently trained personnel, organizational silos, and structural barriers to data
exchange. Facilitators for integration include cost reduction initiatives and interoperability policies.
Technologies like IoT, Big Data, AI, Machine Learning, and robotics enhance diagnostics, treatment
precision, and real-time monitoring, reducing errors and optimizing resource utilization. Automation
improves employee satisfaction and patient care, while Blockchain and telemedicine drive cost reductions.
Successful integration requires skilled professionals and supportive policies, promising efficient resource
use, lower error rates, and accelerated processes, leading to optimized global healthcare outcomes.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
john krisinger-the science and history of the alcoholic beverage.pptx
Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
1. International journal of scientific and technical research in engineering (IJSTRE)
www.ijstre.com Volume 1 Issue 3 ǁ June 2016.
Manuscript id. 45432600 www.ijstre.com Page 1
Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact
Nonlinearity
Nagaraj B.D1#
, Lokesh Patil2*
,Pravin Kumar Kamanat3
,Dr. Krishnarao Dhuri4
,
Dr. Mohd. S.Azam5
1
(P G Scholar, Department of Mechanical engineering, CMRIT, Bengaluru, India)
2
(P G Scholar, Department of Mechanical engineering, ISM Dhanbad, India)
3
(Group Director, Rotor Support Structure, GTRE, Bengaluru, India)
4
(Associate Professor, Department of Mechanical engineering, CMRIT, Bengaluru, India)
5
(Assistant Professor, Department of Mechanical engineering, ISM Dhanbad, India)
#nagarajbd@gmail.com
*lokeshpatil55@gmail.com
ABSTRACT:This paper investigates the non-linear behavior of bolted disk-drum joint in a rotor subjected to
bending loads during operation, using Finite element analysis (ANSYS- Workbench). The variation in contact
area due to these bending loads results in non-linear deformation.The non-linear behavior of bending stiffness
is studied from bending moment versus deflection plot obtained under static condition for different bolt preloads
using ANSYS Workbench. The results predicted by finite element simulation are validated analytically using
MATLAB. Considering the non-linear behavior of bending stiffness, rotor dynamic analysis of bolted and
without bolted (continuous) disk-drum rotor is performed. For any given operational speed range, by varying
the number of bolts under the condition of with and without bolted joints, the modal analysis is carried out to
study the effect of bolted joints on modal frequencies of the disk-drum rotor bearing system. These responses are
validated analytically using MATLAB. Also to study the effect of bolted joints on critical speeds, the Campbell
diagram is obtained under the condition of with and without bolted joints for different number of bolts. Finally
Harmonic analysis is carried out to determine the rotor whirl amplitude at critical speeds obtained for with and
without bolted joint.
KEYWORDS -Bolted joint, Campbell diagram, Harmonic excitation, Nonlinear, Rotordynamic analysis,
Unbalance response.
I. INTRODUCTION
The introduction of the paper should explain the nature of the problem, A Gas Turbine (GT) engine
consists of various components and these are grouped accordingly based on their functionality. The rotating
shafts, also known as rotors, are used to transmit the energy from the exhaust gases in downstream of turbine
region to the upstream compressor region of the engine. The rotors also transmit power to other auxiliary
components needed for functioning of the engine. These rotors are held intact by bearings at specified locations
to isolate with the static parts and maintain stability under extreme operating conditions.
Bolted joints are frequently used in gas turbine engines and its structures to remove the complexity in
the architecture of the engine. The most common application is to connect different rotor disc to the drum by
means of bolted joints.The frictional contact at the joint interface induces nonlinear behavior of the bending
stiffness in a bolted disk-drum joint configuration, which force these drums to flex in and flex out under the
operating condition. The friction at contact interface in the joint inducing nonlinearity is more of a practical
phenomenon and is very significant in rotor dynamic analysis during the design of rotor system. Generally effect
of nonlinearity is neglected during such an analysis to keep things simpler. A simplified analysis disregarding
the nonlinearity will yield erroneous results which predict an oversimplified behavior. Also the change in
mating contact area and rigidity would vary with the operating cycle and excessive movement due to loading
and offloading conditions of the joint structure could also cause severe wear and catastrophic failures.
Determining the joint stiffness and studying the dynamic behavior under such conditions is of biggest
concern in accurate design of rotor system. To find a solution for the above quoted problem statement; an
attempt is to be made for studying the nonlinear behavior of the bending stiffness. With the need for cost
effectiveness and life expectancy, dynamic analysis should be performed to study the effect of such a bolted
2. Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
Manuscript id. 45432600 www.ijstre.com Page 2
joint on dynamic behavior of rotor-bearing system and compare the findings with the results obtained from the
same rotor-bearing system without a bolted joint.
This present study is put forward to predict the dynamic characteristics of the rotor system such as
determining the critical speeds, harmonic responses for a given operating conditions. These responses are
obtained for with bolted and without bolted conditions and are correlated to understand the dynamic behavior.
1.1 Rotordynamics
Rotordynamics deals with study of mechanical devices consisting of rotating parts, also known as
rotors, rotating with significant angular momentum about a fixed axis. In rotordynamics, resonant condition is
said to be attained as the system frequency equals the rotational frequency of the rotor caused by unbalance
excitation. This particular rotational speed is called critical speed. The amplitude of the rotor vibration exhibits a
peak in the vicinity of the critical speed. Thus the critical speed assists in determining the rotor rigidity and
flexibility conditions. Hence the rotordynamic study intensifies the understanding of rotor vibration phenomena
and assists in eliminating the undesirable vibrations and improve the efficiency of the rotating machinery.
Rotordynamic analysis is not merely carried out during design stage, but also essentially used in testing
and during actual operation of the machine to obtain the behavior of the machinery for preventive maintenance
to identify the problematic mechanical signature, i.e., the vibration spectrum.
1.2 Nonlinearity in bolted joints
The rigidity of any joint structures and its contact state influence the rotor dynamic behaviour and also
the responses due to mass unbalance. The joint stiffness is not constant at lower values of external loads and
behaves nonlinearly up to the critical transition loads. When the external load exceeds these transition load, the
stiffness value will increase and slightly attains a constant value, linearly [1]. The rigidity will vary as the
external loads changes and affect dynamics of the joint structure.This behaviour is influenced from the contact
state at the joint interface and bolt preloads. The contact state varies with the geometry and the loading
condition.
In dynamic conditions, where the parts are in motion, the forces and the motion are transferred by
means of contact. Hence it is important to consider the force distribution, related deformation and friction at
contact before carrying out any analysis. This contact also behaves like a geometrical constraint restricting the
displacement of the body. In general, the contact surface is a variable function of the load applied and the
contact surface remains constant only in the case of stationary contact. Considering the theoretical aspect of
contact condition, the correlations between the normal components and the tangential components are different.
Nonlinearity due to contact arises whenever contact or mating is present, because, in most of the cases, the
geometry of the contact zone is unknown. The nonlinear behavior depends on the contact status. The status
might change directly with the load or might be determined by several external causes. When the frictional
forces are considered, the contact problem becomes specially complicated due to dissipation of energy.The
presence of frictional slippage at the interface dissipates the energy relative to the contact state in the joint
interface.
The concept of nonlinearity is more of a practical concern because the displacements behave as a
nonlinear function of the applied loads. In a theoretical way of solving such a problem many assumptions are
made to disregard the nonlinearity and simplify the solution process. The analysis of tangential components
increases the complications and requires exhaustive inspection. Eventually, FE methods involving
comprehensive numerical techniques are required to solve the contact problems.
II. RELATED WORK
The presence of bolted joints in any structure will certainly influence the overall stiffness of the system.
The frictional contact that exists between the joined components will be continuously varying along with the
mating contact area during the operating cycle. Hence determining the joint stiffness and implementing the same
during the dynamic analysis of the rotor system will be a more realistic approach of solving the problems
pertaining to vibration in rotor systems [1].
3. Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
Manuscript id. 45432600 www.ijstre.com Page 3
The stiffness of the joined structure will be a function of number of bolts as well as the pre-tension
effect unveiled by each bolt. Such a study on various parameters influencing the joint stiffness along with its
nonlinear behavioral study using FE method and experimental approach yields feasible results. Also sensitivity
analysis of mode shapes and critical speeds using Finite Difference Methods reveals the variation of joint
stiffness proportional to externally applied loads and the geometrical configuration affecting the dynamic
behavior [2].
The integrity of any gas turbine can be appropriately assessed by evaluating its dynamic behavior. This
is a highly complex scenario that prompts the use of FE methods. ANSYS program developed on FE platform
reduces the complexity in determining the dynamic behavior. The natural frequencies and associated critical
speeds are determined by developing the Campbell diagram. ANSYS provides different environment such as
APDL, ANSYS Workbench etc. through which similar results can be obtained [3].
Rotordynamic study involves both qualitative and quantitative study of the rotor-bearing system. When
a rotor body rotates with significant angular momentum, resonance conditions are achieved at particular speeds
called critical speeds. These critical speeds are found out by a plot of Natural frequency vs. Rotational speed.
This becomes a complex phenomenon for complex shaped rotors. Hence simplified rotors are such as Jeffcott
rotors can be widely used to understand the dynamics of rotating structures. Eventually Jeffcott rotors fail to
provide a precise behavior quantitatively, but explain the qualitative behavior in an effective manner for an
oversimplified rotor model than for a realistic rotor [4].
In the Finite element method to determine the dynamic behavior analytically, involves formulating the
problem based on Euler-Bernoulli theory of beams considering 2-D beam element. The rotor is discretized into
these beam elements. The rotation of the beam induces the gyroscopic effect which is a major concern in rotor
dynamics. Determining the global Stiffness matrix, gyroscopic matrix & Mass matrix and solving the governing
dynamic equation considering the unbalance mass as the excitation force will provide the harmonic behavior the
discretized rotor system [5].
Nonlinearity is more of a practical and complex scenario. Hence for simplifying the analysis process
the effects of nonlinearity is generally neglected. The nonlinearity problem can have many sources such as
Material nonlinearity where in the law of elasticity is invalid, Geometric nonlinearity arising from large
displacement and strain values, and nonlinearity due to the presence of contact zone which is generally
unknown. Also the Frictional contact exhibits more complexity as the energy is dissipated [6].
III. ANALYTICAL MODELING OF BOLTED DISK-DRUM JOINT
Reference [1] is used for analytical modeling of the bolted disk-drum joint. This includes the
mathematical expressions to determine the bending stiffness of the bolted joint and methodology to obtain the
modal frequencies of the rotor system analytically. Based on these expressions MATLAB codes are scripted for
both static and dynamic analysis.
Considering a linear dynamic model without any bolted joint, the equation of motion for the rotor
system without bolted joint can be expressed as:
𝑀𝛿 + 𝐶 + Ω𝐺 𝛿 + 𝐾𝛿 = 𝑓 (1)
Where, the ‘M’ is the mass matrix, ‘C’ is the damping matrix, ‘G’ is the Gyroscopic matrix and ‘δ’ is
the displacement matrix. Now by considering nonlinear model, the bending stiffness matrix ‘Kbe’ is added into
corresponding global stiffness matrix ‘K’. Dynamic equation of rotor for modal analysis considering bolted joint
is:
𝑀𝛿 + 𝐶 + Ω𝐺 𝛿 + (𝐾 + 𝐾𝑏𝑒 )𝛿 = 𝑓 (2)
IV. MODELING AND ANALYSIS
3.1 Solid modeling using CATIA v5
The rotor system considered for analysis has 3 disks and 2 drums and are joined using M6 bolts
conforming to ISO standard. To determine the bending stiffness of the bolted joint i.e. for static analysis the
CAD model is as shown in Fig.1. This includes only the middle disk bolted to the drums. The CAD model for
dynamic analysis involves all the 3 disks as shown in Fig.2
4. Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
Manuscript id. 45432600 www.ijstre.com Page 4
Fig. 1. CAD model of rotor with bolted joint
(for static analysis)
Fig. 2. CAD model of 3 rotors with bolted joint
(for dynamicanalysis)
3.2 FE Modeling & Analysis using ANSYS Workbench
The solid model of a bolted joint rotor, is imported to ANSYS Workbench and meshed using 3D-solid
tetrahedron elements. The total number of nodes were 46874 and total number of elements were 23202. Initially
all parameters are investigated with bolt preload value of 100N and then with a preload of 200N.
3.2.1 Bending Stiffness behaviour (Static Analysis)
In this paper the bending stiffness is investigated for different combination of bolt numbers and preload
values. The boundary conditions applied are shown in Fig.3 and as follows: The bolt pretension, in each bolt is
assigned a preload of 100N at first and then 200N. All the DOFs of the nodes on the right side surface of right
side drum are constrained to form a fixed support. This represents the rigidity provided from the welding of
drum to the outer disks. A bending moment, applied on the left drum shell surface indicates the bending load on
the rotor drum.
Fig. 3. FE model with boundary conditions (for static analysis)
To generate a contact pair the contact and target surfaces are assigned. The contact between the disk
and the drum flange represents a rigid-to-flexible and surface-to-surface contact. Here the target surface is
generally preferred to be of the rigid disk and the contact surface is from the flexible drum. In case of the
contact between the bolt head surface and the inner surface of the drum flange, a flexible-to-flexible contact is
represented where both the bodies in contact undergo deformation. Out of these two, bolt head surface is taken
as target surface and drum flange surface will become the contact surface to form a flexible-to-flexible contact
pair.
For different combination of bolt numbers, bolted joints with 30 bolts and 14 bolts are modeled. In a 30
bolted model, out of 62 contact pairs, the two contact pairs between the disk and the drum is considered to be a
frictional joint having a co-efficient of friction as 0.2. The remaining 60 contact pairs between 30x2 bolt heads
5. Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
Manuscript id. 45432600 www.ijstre.com Page 5
and drum flange are considered as bonded contact. This is because the bolt pretension load which is normal to
the contact surface will be very high compared to the tangential forces over the contact surface. Hence the
frictional forces are neglected at these 60 interfaces.
3.2.2 Dynamic Analysis
For dynamic analysis the boundary conditions applied are shown in Fig.4 and as follows: To restrict the
rotor in axial direction, the ends of the rotor shaft is fixed. The bearing are represented by elastic supports
having a stiffness of 2x107
N/m. The Bolt pretension, in each bolt is assigned a preload of 100N at first and then
200N. In dynamic analysis, the 30 bolted rotor model will have 2 additional contact pairs i.e. a total of 64
contact pairs. The two additional contact pairs are between left & right disks and the respective rotor drum
shells. This pair represents a bonded contact indicating the welded joint between left & right disks and their
respective rotor drums. The remaining 62 contact pairs are the same as in static analysis.
For rotordynamic analysis, to obtain the Campbell diagram, and perform the modal analysis, a
rotational velocity is applied on the rotor disks as shown in Fig.5. The axis of rotation also called as spin axis is
taken to be the x-axis. The operational speed range for the rotor under study is considered to be 1000 to 12000
rpm (104.72 to 1256.6 rad/s) and the velocity is incremented with a step of 1000 rpm.
Fig. 4. FE model with boundary conditions
(for dynamic analysis)
Fig. 5. FE rotor model with rotational velocity
3.2.3 Harmonic Analysis
For harmonic analysis, the excitation force considered is from the unbalance mass present in the middle
rotor disk. The unbalance force is given by Fb=mrω2
= F0 ω2
, where ‘m’ is the unbalance mass, ‘r’ is the location
of unbalance in the disk and ‘ω’ is the rotational velocity. This centrifugal unbalance force can be resolved
along y and z axes as shown in Fig.6.In this study, an unbalance mass of m=0.1kg, present at a radius of
r=0.25m in the middle-disk is considered. Hence the unbalance force of F0=2.5x10-2
N is applied on the middle
disk at a radius of 0.25m as shown in Fig.7.
6. Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
Manuscript id. 45432600 www.ijstre.com Page 6
Fig. 6. Unbalance excitation force in the rotor disk
Fig. 7. Unbalance force on middle disk of the
bolted joint rotor
V. RESULTS AND DISCUSSION
4.1 Bending stiffness behavior
The total deformation and von-misses stress distribution areas are shown in Fig. 8 & Fig. 9
respectively. For different bending loads, the total deformation ‘δ’ is measured at the outer edge of the drum
flange and the relative rotation angle ‘Φ’ is calculated. The respective bending stiffness is calculated as Kbe=M /
Φ. As in Fig.10, the plot of M vs Φ, shows a nonlinear behavior of the bending stiffness. As the bolt preload is
increased the slope of the line i.e. the stiffness increase. This is because the addition of preload reduces the
deformation or opening up of the drum at the joint interface and prevents the bolted joint to deform under
applied load. Also the increase in number of bolts induces more rigidity to the bolted joint.
Fig. 8. Total deformation of bolted disk-drum joint Fig. 9. Von-Mises stress distribution
Fig. 10. Graph of bending moment M vs. relative rotation angle Φ
7. Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
Manuscript id. 45432600 www.ijstre.com Page 7
For a maximum bending load of 5000 N-m the bending stiffness was found to be 1.12x107
N/m from
ANSYS simulation. A stiffness of 1.36 x 107
N/m was determined from MATLAB program. The stiffness
values for different preloads and number of bolts are compared in TABLE I.
TABLE I. BENDING STIFFNESS USING ANSYS AND MATLAB
Cases
14 Bolts,
P=100N
14 Bolts,
P=200N
30 Bolts,
P=100N
30 Bolts,
P=200N
ANSYS (N/m) 5.45x106
5.53x106
1.10x107
1.12x107
MATLAB (N/m) 5.74x106
5.96x106
1.23x107
1.36x107
4.2 Dynamic Analysis
4.2.1 Modal Analysis
The natural frequency of the rotor system for with bolt and without bolted disk-drum joint rotor
obtained from ANSYS simulation and MATLAB program are given in Table II and Table III respectively.
TABLE II. ANSYS MODAL FREQUENCIES (HZ) FOR
DIFFERENT JOINT STATUS AND DIFFERENT BOLT NUMBERS
No. of
Bolts
14 Bolts 30 Bolts
Joint
Status
Without
Bolted
With
Bolted
Without
Bolted
With
Bolted
1st
Mode 36.15 36.15 35.35 35.34
2nd
Mode 75.85 75.70 76.24 75.58
3rd
Mode 75.97 75.79 77.06 76.01
4th
Mode 81.76 81.43 94.13 92.97
5th
Mode 93.03 92.67 95.39 93.97
6th
Mode 105.50 105.18 102.69 102.69
TABLE III. MATLAB MODAL FREQUENCIES FOR
DIFFERENT JOINT STATUS AND DIFFERENT BOLT NUMBERS
No. of
Bolts
14 Bolts 30 Bolts
Joint
Status
Without
Bolted
With
Bolted
Without
Bolted
With
Bolted
1st
Mode 54.49 44.32 58.28 44.32
2nd
Mode 59.17 46.17 61.48 46.32
3rd
Mode 76.21 73.5 77.13 73.50
4th
Mode 83.18 78.62 84.23 78.62
5th
Mode 93.64 92.92 93.83 92.92
6th
Mode 104.33 103.63 104.38 103.63
From the above two tables it can be seen that the presence of bolted joint in the rotor model reduces the
rigidity making it a much more flexible rotor.
4.2.2 Critical speeds from Campbell diagram
Fig.11 shows Campbell diagram for a bolted rotor with 30 bolts. The variations in critical speeds
obtained from Campbell diagram are presented in Table IV and Table V. It can be seen that critical speeds
decrease due to softening of the joints. On the other hand, the increase in number of bolts increases the critical
speed by strengthening the bolted joint and making the rotor system relatively rigid.
8. Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
Manuscript id. 45432600 www.ijstre.com Page 8
Fig. 11. Campbell diagram for a bolted rotor with 30 bolts
TABLE IV. VARIATION IN CRITICAL SPEED IN BOLTED ROTOR
WITH 14 BOLTS
Mode #
Without Bolted With Bolted
Whirl
Direction
Critical Speed Critical Speed
rad/s Hz rad/s Hz
1 FW 227.16 36.17 227.16 36.17
2 BW 476.09 75.81 476.07 75.65
3 FW 478.21 76.15 477.19 75.99
4 BW 375.01 59.71 373.69 59.50
5 FW 647.7 103.14 631.38 100.54
TABLE V. VARIATION IN CRITICAL SPEED IN BOLTED ROTOR
WITH 30 BOLTS
Mode #
Without Bolted With Bolted
Whirl
Direction
Critical Speed Critical Speed
rad/s Hz rad/s Hz
1 FW 222.09 35.36 221.40 35.25
2 BW 480.89 76.57 478.76 76.24
3 FW 484.59 77.16 482.41 76.82
4 BW 406.30 64.70 403.35 64.23
6 BW 677.27 107.85 645.12 102.73
4.2.3 Harmonic analysis
For the excitation due to the unbalance mass of 0.1kg at a radius of 0.25m in the middle rotor, the
response amplitude of the outermost edge of the middle disk is recorded. The Amplitude vs. Frequency plot for
the middle disk considering both the case of without bolted rotor and with bolted joint rotor are as shown in
Fig.12 & Fig.13 respectively.The response amplitudes for different number of bolts are summarized in Table VI
and Table VII.
9. Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
Manuscript id. 45432600 www.ijstre.com Page 9
Fig. 12. Amplitude vs. Frequency plot for disk-drum
rotor without bolted joint
Fig. 13. Amplitude vs. Frequency plot for disk-drum
rotor with 30 bolts
TABLE VI. COMPARISON OF RESPONSE AMPLITUDES FOR
BOLTED DISK-DRUM ROTOR WITH 30 BOLTS
Response
Peak
With Bolted
Amplitude
(m)
Speed
rad/s
Amplitude
(m)
Speed
rad/s
1st
Peak 7.47 x 10-9
222.09 7.52 x 10-9
221.4
2nd
Peak 1.77 x 10-9
484.80 2.1 x 10-9
482.50
TABLE VII. COMPARISON OF RESPONSE AMPLITUDES FOR
BOLTED DISK-DRUM ROTOR WITH 14 BOLTS
Response
Peak
With Bolted
Amplitude
(m)
Speed
rad/s
Amplitude
(m)
Speed
rad/s
1st
Peak 1.01 x 10-7
227.32 1.01 x 10-7
227.16
2nd
Peak 2.91 x 10-8
477.01 2.92 x 10-8
476.01
From the above two tables, it is quite clear that the presence of bolted joint in the rotor experiences
relatively higher amplitudes of vibration at resonance frequencies(i.e. at critical speeds). Also from the
comparision of the response plots in Fig.14, it can be seen that the amplitude peak slightly shifts towards the left
as the rotor system exhibits lesser rigidity relative to the rotor system without bolted joints.
Fig. 14. Unbalance response comparison for rotor with 14 bolts
VI. CONCLUSION
The dynamic behaviour of a bolted disk-drum joint rotor discussed in this thesis considers the
nonlinearity effect due to the frictional contact at the joint interface. Based on the analytical model used, the
influence of bolted joint on dynamic parameters and the importance of these parameters are comprehended from
the results obtained by both analytical and FEA methods. The FEA results obtained showed good agreement
with analytical model. This study emphasizes the importance of understanding the nonlinear behavior of a
bolted joint and its dependent parameters in any rotor-bearing system. As the consideration of nonlinear effects
is more of a practical concern, the results obtained from this investigation are more of realistic values and are
10. Rotordynamic Analysis of Bolted Disk-Drum Rotor with Contact Nonlinearity
Manuscript id. 45432600 www.ijstre.com Page 10
reliable. Following are the vital conclusions that are drawn from this study.
1) The simulation results show that there is a decline in bending stiffness in case of a bolted disk-drum rotor.
Hence the modal frequency decreases in the bolted model as against the rotor model without bolted joint.
2) From the analytical model used, the bending stiffness at the joint, displays a nonlinear behavior at lower
bending loads, which is an obvious phenomena due to frictional losses in the contact zone as the tangential
forces are predominant at lower bending loads.
3) The increase in number of bolts, increases the joint stiffness as these additional bolts try to minimize the
deflection of the drum flange at joint interface. This additional stiffness causes the modal frequency to
increase. Hence optimum number of bolts should be considered that satisfies the joint strength requirements
and limits the joint deflection without much change in the modal frequency.
4) In a similar manner, the bolt preloads have little or no influence in modal frequencies. Increase in preload
increases joint stiffness and hence the modal frequency seems to be increasing, but no significantly.
5) Consideration of frictional contact between the joined parts decreases the critical speeds. Though the
critical speed increases comparatively, by increasing the number of bolts, there is an overall decline in
critical speed due to the presence of bolted joint.
6) In the case of bolted rotor model, the amplitude peak from harmonic response seems to increases relatively
at the resonance conditions due to slight decrease in the rigidity.
REFERENCES
[1] Q. K. H. ZY Qin, Analytical model of bolted disk-drum joints and its application to dynamic analysis of jointed rotor, Arch. Proc. Inst.
Mech. Eng. Part C J. Mech. Eng. Sci. 1989-1996 Vols 203-210, vol. 228, no. 4, pp. 646–663, 2014.
[2] M. Y. Liu Shuguo, Studies on dynamic characteristics of the joint in the aero-engine rotor system, Mech. Syst. Signal Process., vol. 29,
pp. 120–136, 2012.
[3] Guilherme de Oliveira Marcório, Tiago de Oliveira Vale, and João Carlos Menezes, Dynamical evolution of gas turbine rotors,
Instituto Tecnológico de Aeronáutica (ITA), São José dos Campos, São Paulo-2012.
[4] G. Genta, Dynamics of rotating systems (Springer Science & Business Media, 2007).
[5] Dr R Tiwari, Finite Element Analysis of simple rotor systems. Dept. of Mechanical Engg., IIT Guwahati.
[6] E. Zahavi, Nonlinear Problems in Machine Design(CRC-Press, 2000).