spur gear

Project report on STATIC AND DYNAMIC ANALYSIS OF SPUR GEAR A major project work in the partial fulfillment of the degree BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING BY B.HARISH REDDY (07241A0387) G.SHIVA KUMAR (07241A0359) Under the guidance of RATNA KIRAN Assistant Professor Mechanical Department

DEPARTMENT OF MECHANICAL ENGINEERING GOKARAJU RANGARAJU ISNTITUTE OF ENGINEERING AND TECHNOLOGY BACHUPALLY, KUKATPALLY, HYDERABAD-90 (AFFILIATED TO J.N.T.U, HYDERABAD) APRIL 2011

DEPARTMENT OF MECHANICAL ENGINEERING GOKARAJU RANGARAJU ISNTITUTE OF ENGINEERING AND TECHNOLOGY BACHUPALLY, KUKATPALLY, HYDERABAD-90 (AFFILIATED TO J.N.T.U, HYDERABAD)

CERTIFICATE This is to certify that the thesis entitled “STATIC AND DYNAMIC ANALYSIS OF SPUR GEAR “ Submitted by MR B.HARISH REDDY, MR G.SHIVA KUMAR in the partial fulfillment of the requirements for the award of Bachelor of technology Degree in Mechanical Engineering Jawaharlal Nehru Technology University, Hyderabad is an authentic work carried out by him under my supervision and guidance. To the best of my knowledge, the matter embodied in the thesis has not been submitted to any other University / Institute for the award of any Degree.

Internal Guide RATNA KIRAN Assistant Professor Mechanical Department GRIET

Head of the Department Dr. KGK. MURTI Sr. Professor and HOD Mechanical Department GRIET

The accomplishment of this project has been lot easier owing to cooperation of Concurrent Analysis Pt. Ltd management of Gokaraju Rangaraju Institute of Engineering and Technology. We would like to thank the management of Concurrent Analysis Pt. Ltd for allowing us to take up this project under them. We would like to express our sincere thanks to our guide Mr. H.PRADEEP for helpful guidance. We would like to express our deepest gratitude towards our guide Mr.RATNA KIRAN (Associate Professor, Mechanical Department) for his constant help and encouragement during this project. We would like to thank Mr. Jandyala N Murthy (Principal, GRIET) and Mr. KGK Murthi (HOD, Mechanical Department) for permitting us to take up this project work. Lastly we would like to thank each and every person who helped directly or indirectly in the successful completion of this project. APRIL 2011 B.HARISH REDDY G.SHIVA KUMAR

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This thesis investigates the characteristics of a gear system including contact stresses, bending stresses, and the transmission errors of gears in mesh. Gearing is one of the most critical components in mechanical power transmission systems. The contact stresses were examined using 2-D FEM models. The bending stresses in the tooth root were examined using a 3-D FEM model. Current methods of calculating gear contact stresses use Hertz‘s equations, which were originally derived for contact between two cylinders. To enable the investigation of contact problems with FEM, the stiffness relationship between the two contact areas is usually established through a spring placed between the two contacting areas. This can be achieved by inserting a contact element placed in between the two areas where contact occurs. The results of the two dimensional FEM analyses from ANSYS are presented. These stresses were compared with the theoretical values. Both results agree very well. This indicates that the FEM model is accurate. This thesis also considers the variations of the whole gear body stiffness arising from the gear body rotation due to bending deflection, shearing displacement and contact deformation. Many different positions within the meshing cycle were investigated. Investigation of contact and bending stress characteristic of spur gears continues to be of immense attention to both engineers and researchers in spite of many studies in the past. This is because of the advances in the engineering technology that demands for gears with ever increasing load capacities and speeds with high reliability, the designers need to be able to accurately predict the stresses experienced the stresses experienced by the loaded gears.

Table of figures List of Symbols Literature review 1.0 Introduction 1.1 Introduction to Gears 1.2 Definitions 1.2.1 Advantages 1.2.2 Disadvantages 1.3 Applications 1.4 Materials for Spur Gear 2.0 Theory 2.1 Internal Spur Gear 2.2 External spur Gear 2.3 Spur Gear Nomenclature 3.0 Mathematical equations 4.0 Finite Element Analysis 4.1 Introduction to FEA

4.2 Basic steps involved in FEA 4.3 Types of finite elements 5.0 Introduction To Catia V5 5.1 Overview of Solid Modeling 5.2 General Operation 5.3 Creating a Solid Model 5.4 Introduction to Drafting 6.0 Spur Gear Analysis & Results 6.1 Gear Analysis 6.2 Dynamic Analysis 6.3 Harmonic Analysis 7.0 Conclusion 8.0 Bibliography

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Schematic Layout of Spur Gear Plastic Spur Gear in Film Winding Spur Gear in Automatic Packing Machine Spur Gear in Film Cutting Internal Spur Gear External Spur Gear Nomenclature of spur gear Properties Of Material Gear 3-D model Gear Meshed Model Boundary Conditions Vonmises stresses Linearised stress along high stress region Principal stress along X-axis Principal stress along Y-axis Principal stress along Z-axis. Deflection in Usum. Deflection along X-axis Deflection along Y-axis

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Deflection along Z-axis Model Analysis (Modes from 1-12) Graph 1 Frequency v/s Amplitude in X- Direction Gear location. Graph 2 Frequency v/s Amplitude in Y- Direction Gear location. Graph 3 Frequency v/s Amplitude in Z- Direction Gear location. Graph 4 Frequency v/s Amplitude in X,Y,Z- Direction Gear location. Graph 5 Frequency v/s Amplitude in X- Direction Gear Teeth location. Graph 6 Frequency v/s Amplitude in Y- Direction Gear Teeth location. Graph 7 Frequency v/s Amplitude in Z- Direction Gear Teeth location. Graph 1 Frequency v/s Amplitude in X,Y,Z- Direction Gear Teeth location.

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K Structural stiffness u Displacement vector F Applied load vector Pmax Maximum contact stress d1 Pinion pitch diameter d2 Gear pitch diameter Fi Load per unit width Ri Radius of cylinder i Φ Pressure angle i Poisson‘s ratio for cylinder i Ei Young‘s modulus for cylinder i σH Maximum Hertz stress. a Contact width r Any radius to involute curve rb Radius of base circle θ Vectorial angle at the pitch circle ξ Vectorial angle at the top of tooth φ Pressure angle at the pitch circle

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Bp Tooth displacement vectors caused by bending and shearing of the pinion Bg Tooth displacement vectors caused by bending and shearing of the gear Hp Contact deformation vectors of tooth pair B for the pinion Hg Contact deformation vectors of tooth pair B for the gear θp Transverse plane angular rotation of the pinion body θg Transverse plane angular rotation of the gear body pd Diametric pitch Y Lewis form factor Ka Application factor Ks Size factor Km Load distribution factor Kv Dynamic factor Ft Normal tangential load Yj Geometry factor θg Angular rotation of the output gear θp Angular rotation of the input gear

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There has been a great deal of research on gear analysis, and a large body of literature on gear modeling has been published. The gear stress analysis, the transmission errors, and the prediction of gear dynamic loads, gear noise, and the optimal design for gear sets are always major concerns in gear design. Errichello and Ozguven and Houser survey a great deal of literature on the development of a variety of simulation models for both static and dynamic analysis of different types of gears. The first study of transmission error was done by Harris. He showed that the behavior of spur gears at low speeds can be summarized in a set of static transmission error curves. In later years, Mark and analyzed the vibratory excitation of gear systems theoretically. He derived an expression for static transmission error and used it to predict the various components of the static transmission error spectrum from a set of measurements made on mating pair of spur gears. Kohler and Regan discussed the derivation of gear transmission error from pitch error transformed to the frequency domain. Kubo et al estimated the transmission error of cylindrical gears using a tooth contact pattern. The current literature reviews also attempt to classify gear model into groupings with particular relevance to the research. The following classification seems appropriate:

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Models with Tooth Compliance Models of Gear system Dynamics Models of A Whole Gearbox Models for Optimal Design of Gear Sets

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Spur Gears are the most common means of transmitting power in the modern mechanical engineering world. They vary from tiny size used in the watches to the large gears used in marine speed reducers; bridge lifting mechanism and railroad turn table drivers. They form vital elements of main and ancillary mechanism in many machines such as automobiles, tractors, metal cutting machine tools, rolling mills, hoisting and transmitting machinery and marine engines etc. The four major failure modes in gear systems are tooth bending fatigue, contact fatigue, surface wear and scoring. Two kinds of teeth damage can occur on gears under repeated loading due to fatigue; namely the pitting of gear teeth flanks and tooth breakage in the tooth root. Tooth breakage is clearly the worst damage case, since the gear could have seriously hampered operating condition or even be destroyed. Because of this, the stress in the tooth should always be carefully studied in all practical gear application. The fatigue process leading to tooth breakage is divided into crack initiation and crack propagation period. However, the crack initiation period generally account for the most of service life, especially in high cycle fatigue.

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The initial crack can be formed due to various reasons. The most common reasons are short-term overload, material defects, defects due to mechanical or thermal treatment and material fatigue. The initial crack then propagates under impulsive loading until some critical length is reached, when a complete tooth breakage occurs. The service life of a gear with a crack in the tooth root can be determined experimentally or numerically (e.g. with finite element method). The fatigue life of components subjected to sinusoidal loading can be estimated by using cumulative damage theories. Their extension to random load fatigue, through straightforward, may not be very accurate owing to inherent scatter exhibition by the fatigue phenomena. Due to the complexity in geometry and loading on the structure, the finite element method is preferably adopted.

1) MODULE: Module of a gear is defined as ratio of diameter to number of teeth.m= d/N 2) FACE WIDTH The width along the contact surface between the gears is called the face width. 3) TOOTH THICKNESS The thickness of the tooth along the pitch circle is called the tooth thickness. 4) ADDENDUM The radial distance between the pitch circle and the top land of the gear is called the addendum.3 5) DEDENDUM The radial distance between the pitch circle and the bottom land of the gear is called the dedendum. 6) PRESSURE ANGLE The angle between the line joining the centers of the two gears and the common tangent to the base circles.

1.2.1 ADVANTAGES ` Gear is one kind of mechanical parts. It can be widely used in industries. A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. ` Spur gear is the simplest type of gear which consists of a cylinder or disk. Its form is not straight-sided, thus, the edge of each tooth is straight and aligned parallel to the axis of rotation. Only gears fit to parallel axles can they rotate together correctly. ` As the most common type, spur gears are often used because they are the simplest to design and manufacture. Besides, they are the most efficient. When compared to helical gears, they are more efficient. The efficiency of a gear is the power output of its shaft divided by the input power of its shaft multiplied by 100. Because helical gears have sliding contact between their teeth, they produce axial thrust, which in turn produces more heat. This causes a loss of power, which means efficiency is lost. ` In addition to these, they also have many other advantages. Spur gears have a much simpler construction than helical gears because their teeth are straight rather than angular. Therefore, it is much easier to design and produce them. And they will not fail or break easily. And this makes them cheaper to purchase and to maintain which then leads to less cost.

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Simplicity Because their teeth are straight rather than angular, spur gears have a much simpler construction than helical gears. As such, they are easier to produce, and they tend not to break or fail as easily. This also makes them easier to find. Efficiency Spur gears are more efficient than helical gears. The efficiency of a gear is the power output of its shaft divided by the input power of its shaft multiplied by 100. Because helical gears have sliding contact between their teeth, they produce axial thrust, which in turn produces more heat. This causes a loss of power, which means efficiency is lost. Cost Because spur gears are simpler, they are easier to design and manufacture, and they are less likely to break. This makes them cheaper to purchase and to maintain.

1.2.3DISADVANTAGES `

Although they are common and efficient, spur gears have disadvantages as well. Firstly, they are very noisy when used at some speeds because the entire face engages at once. Therefore, they're also known as slow-speed gears. Secondly, they can only be used to transfer power between parallel shafts. They cannot transfer power between non-parallel shafts. Thirdly, when compared with other types of gears, they are not as strong as them. They cannot handle as much of a load because the teeth are small and situated parallel to the gear axis, rather than being large and situated diagonally as the teeth on a helical gear are.

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According to the above, we can conclude that spur gears have many advantages as well as some disadvantages. Although sometimes, its disadvantages may affect them a lot, their advantages still outweigh their disadvantages. That is to say, spur gears are still popular among many industries. And they can have good performances to meet people's requirements

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The image shows a Spur Gear and Plastic Spur Gears used in a film winding component.

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Image of Spur Gears used in automatic packing machine.

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Spur Gears are used in the film-cutting component.

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While coming to manufacturing materials for Spur gears, a wide variety is available. These includes Steel Nylon Aluminium Bronze Cast iron Phenolic Bakelite Plastics

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2.1 INTERNAL SPUR GEARS This is actually a type of Spur Gear. Internal Spur Gears are not much different from a regular spur gear. These gear by appearance shows pitch surface that is cylindrical. Here the tooth is parallel to the axis. In case of Internal Spur Gears, the gears are positioned to make internal contact. It is also referred to popularly as Ring Gears. The output rotation produced by the Ring gears is direction wise same as that of input rotation.

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As is clear from the figure the gear tooth are cut from inside. A typical Internal Spur Gear or Ring Gear consists of typically three or four larger spur gears referred to as planets. That surrounds a smaller central pinion referred to as sun. Normally, the ring gear remains stationary. This is quite like our own Planetary system, where the planets orbit round the sun in the same rotational direction. It is quite obvious that this class of gear is known as a planetary system. It is through a planet carrier that transmits the orbiting motion of the planets to the output shaft.

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In a different planetary arrangement, the ring may be left to move freely. This is done by restricting the planets from orbiting round the sun. This action results in the ring gear rotating in an opposite direction to that of the sun. Thus a differential gear drive is effected as a result of rotation of both the ring gear and the planet carrier. The output speed of the shafts are interdependent.

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External Spur Gears are the most popular and common type of spur gear. They has their teeth cut on the outside surface of mating cylindrical wheels. While the larger wheel is referred to as the gear and the smaller wheel is known as the pinion. Single reduction stage is the most basic type of arrangement of single pair of spur gears. Here the output rotation is in opposite direction to that of the input. In other arrangements of multiple stages higher net reduction can be achieved where the driven gear is connected rigidly to a third gear. This third gear in turn drives a

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mating fourth gear. This serves as the ideal output for the second stage. In this way, many output speeds on different shafts are produced starting from a just single input rotation. The image given below shows the inside of External Spur Gears.

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Working of External Spur Gears

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Actually the working of External Spur Gear is best explained with the help of Gear meshes. In the external mesh, the gears are made to rotate in directions that are opposite. The Figure below shows a simple spur gear mesh where the gears are meshing externally.

Checking the calculations: a): based on the compressive stress, σc=0.7(i+1)/a*√{(i+1/ib)*E[mt]} b): based on the bending stress, σb=0.7(i+1) (Mt) / {a x b x mn xYv} The theoretical design calculations are performed using the input parameters such as power for marine high speed engine, pinion speed, gear ratio, pressure angle etc. i.e Power P = 9000 KW, Speed of Pinion N = 3500 rpm, Gear Ratio i = 7, Minimum centre distance based on surface compression strength is given by a ≥ (7+1)√{.7/ σc}2x{E[Mt]/iψ}

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Table 3.1 properties of Material

¾Based on the Compressive Stresses ¾ σc = 0.7x ((i+1)/a) x√((i+1)/ib) x E[Mt] ≤ (σc) ¾Based on the Bending Stresses ¾ σb = 0.7x ((i+1)/abMnYv) x E[Mt]≤ (σc) ¾Based on the compressive stress ¾

σc = (0.7x8x325661.14) /(143x43x1. 8x0 .4205) = 150.303N/ mm2

¾Based on bending stress σb = 220.35 N/mm 2 ¾From the calculations, σc and σb are > [σc] & [σb] values of given material, i.e., Aluminum alloy [98%Al2O3, 0.40.7% Mn, 0.40.7& Mg]. Therefore our design is safe. ¾Addendum, mn = 18 mm, Dedendum = 1.25 x mn = 22.5 mm, ¾Tip circle diameter of the pinion ¾Tip circle diameter of gear ¾Root circle diameter of pinion ¾Root circle diameter of gear

= d1+ (2 x addendum) =357.4 + 36 = 393.4mm = d2 + (2 x addendum) = 2502.4+ 36 = 2538.46 mm = d1 (2 x addendum) = 357.4 – 36 = 321.4 mm = d2 (2 x addendum) = 2502.4– 36 = 2466.4 mm

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When the gear transmits the power P, the tangential force produced due to the power is given by Ft = (PxKs/v) V = (πxDpxNp) / (60x1000) = (πx357.4x3500)/(60000) = 65.51 m/s Ft = (9000x103x2)/65.51 =274749.26

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4.1Introduction The Basic concept in FEA is that the body or structure may be divided into a smaller elements of finite dimensions called “Finite Elements”. The original body or the structure is then considered as an assemblage of these elements connected at a finite number of joints called “Nodes” or “Nodal Points”. Simple functions are chosen to approximate the displacements over each finite element. Such assumed functions are called “shape functions”. This will represent the displacement with in the element in terms of the displacement at the nodes of the element. The Finite Element Method is a mathematical tool for solving ordinary and partial differential equations. Because it is a numerical tool, it has the ability to solve the complex problems that can be represented in differential equations form. The applications of FEM are limitless as regards the solution of practical design problems.

Due to high cost of computing power of years gone by, FEA has a history of being used to solve complex and cost critical problems. Classical methods alone usually cannot provide adequate information to determine the safe working limits of a major civil engineering construction or an automobile or an aircraft. In the recent years, FEA has been universally used to solve structural engineering problems. The departments, which are heavily relied on this technology, are the automotive and aerospace industry. Due to the need to meet the extreme demands for faster, stronger, efficient and lightweight automobiles and aircraft, manufacturers have to rely on this technique to stay competitive. FEA has been used routinely in high volume production and manufacturing industries for many years, as to get a product design wrong would be detrimental. For example, if a large manufacturer had to recall one model alone due to a hand brake design fault, they would end up having to replace up to few millions of hand brakes. This will cause a heavier loss to the company. `

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The finite element method is a very important tool for those involved in engineering design, it is now used routinely to solve problems in the following areas. Structural analysis Thermal analysis Vibrations and Dynamics Buckling analysis Acoustics Fluid flow simulations Crash simulations Mold flow simulations

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Mathematically, the structure to be analyzed is subdivided into a mesh of finite sized elements of simple shape. Within each element, the variation of displacement is assumed to be determined by simple polynomial shape functions and nodal displacements. Equations for the strains and stresses are developed in terms of the unknown nodal displacements. From this, the equations of equilibrium are assembled in a matrix form which can be easily be programmed and solved on a computer. After applying the appropriate boundary conditions, the nodal displacements are found by solving the matrix stiffness equation. Once the nodal displacements are known, element stresses and strains can be calculated.

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Discretization of the domain Application of Boundary conditions Assembling the system equations Solution for system equations Post processing the results. Descritization of the domain: The task is to divide the continuum under study into a number of subdivisions called element. Based on the continuum it can be divided into line or area or volume elements. Application of Boundary conditions: From the physics of the problem we have to apply the field conditions i.e. loads and constraints, which will help us in solving for the unknowns. Assembling the system equations: This involves the formulation of respective characteristic (Stiffness in case of structural) equation of matrices and assembly. Solution for system equations: Solving for the equations to know the unknowns. This is basically the system of matrices which are nothing but a set of simultaneous equations are solved. Viewing the results: After the completion of the solution we have to review the required results.

The first two steps of the above said process is known as pre-processing stage, third and fourth is the processing stage and final step is known as post-processing stage. ¾

What is an Element? Element is an entity, into which a system under study can be divided into. An element definition can be specified by nodes. The shape(area, length, and volume) of the element depends upon the nodes with which it is made up of.

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What are Nodes? Nodes are the corner points of the element. Nodes are independent entities in the space. These are similar to points in geometry. By moving a node in space an element shape can be changed.

0-D Element : This has the shape of the point, it requires only one node to define it

1-D Element : This has the shape of the line/curve and hence requires minimum of two nodes to define it.

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2-DElement: This is an n area element, which has the shape of the quadrilateral/triangle and hence requires minimum four/three nodes to define it.

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3-DElements: This is a volume element, can take the shape of a Hexahedron or a Wedge or a Tetrahedron. Hexahedron element requires 8 nodes to define its shape. A Penta element requires 6 nodes to define its shape. Similarly 4 nodes are

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required to define a Tetra element. The element is said to be linear or 1st order when it doesn’t have any mid side nodes. If the mid side nodes are present then those elements are called Quadratic or 2nd order elements. For linear elements the edge is defined by a linear function called shape function whose degree is one. For the elements having mid side nodes on the edge quadratic function called shape function whose degree is two is used. The higher order elements when over lapped on geometry can represent complex shapes very well within few elements. Also the solution accuracy more with the higher order elements. But higher order elements will require more computational effort and time

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Modal Analysis: This is used to determine the vibration characteristics, i.e., natural frequencies and mode shapes of a linear structure. It is also used as a starting point for other dynamic analysis Harmonic Response Analysis: This is used to determine the steady state response of a structure to loads that vary harmonically with time. Transient Dynamic Analysis: This is used to determine the response of the structure under the action of any general time dependent loads Spectrum Analysis: This is used to determine the response of the structure to random loading Brief Over View of Thermal Analysis: In thermal analysis we can simulate the system for the effects conduction, convection, and radiation. We can study the steady state response as well as transient response of the system subjected to temperature loading. In case of thermal analysis, the respective heat balance equations are solved.

5.1 Overview of Solid Modeling `

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CATIA V5 R14 is the worlds leading 3Dproduct development solution. This software enables designers and engineers to bring better products to the market faster. It takes care of the entire product definition to serviceability. CATIA delivers measurable value to manufacturing companies of all sizes and in all industries. CATIA is used in a vast range of industries from manufacturing of rockets to computer peripherals. With more than 1 lakh seats installed in worldwide many cad users are exposed to CATIA and enjoy using CATIA for its power and capability. CATIA MODULE CATIA design. CATIA production. CATIA shipbuilding. CATIA routed systems. CATIA foundation.

Start with a Sketch Use the Sketcher to freehand a sketch, and dimension an "outline" of Curves. You can then sweep the sketch using Extruded Body or Revolved Body to create a solid or sheet body. You can later refine the sketch to precisely represent the object of interest by editing the dimensions and by creating relationships between geometric objects. Editing a dimension of the sketch not only modifies the geometry of the sketch, but also the body created from the sketch. Creating and Editing Features Feature modeling lets you create features such as holes, extrudes and revolves on a model. You can then directly edit the dimensions of the feature and locate the feature by dimensions. For example, a Hole is defined by its diameter and length. You can directly edit all of these parameters by entering new values. You can create solid bodies of any desired design that can later be defined as a form feature using User Defined Features. This lets you create your own custom library of form features.

Associativity Associatively is a term that is used to indicate geometric relationships between individual portions of a model. These relationships are established as the designer uses various functions for model creation. In an associative model, constraints and relationships are captured automatically as the model is developed. For example, in an associative model, a through hole is associated with the faces that the hole penetrates. If the model is later changed so that one or both of those faces moves, the hole updates automatically due to its association with the faces. See Introduction to Feature Modeling for additional details. Positioning a Feature Within Modeling, you can position a feature relative to the geometry on your model using Positioning Methods, where you position dimensions. The feature is then associated with that geometry and will maintain those associations whenever you edit the model. You can also edit the position of the feature by changing the values of the positioning dimensions.

Reference Features You can create reference features, such as Datum Planes, Datum Axes and Datum CSYS, which you can use as reference geometry when needed, or as construction devices for other features. Any feature created using a reference feature is associated to that reference feature and retains that association during edits to the model. You can use a datum plane as a reference plane in constructing sketches, creating features, and positioning features. You can use a datum axis to create datum planes, to place items concentrically, or to create radial patterns. Expressions The Expressions tool lets you incorporate your requirements and design restrictions by defining mathematical relationships between different parts of the design. For example, you can define the height of a extrudes as three times its diameter, so that when the diameter changes, the height changes also.

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Modeling provides the design engineer with intuitive and comfortable modeling techniques such as sketching, feature based modeling, and dimension driven editing. An excellent way to begin a design concept is with a sketch. When you use a sketch, a rough idea of the part becomes represented and constrained, based on the fit and function requirements of your design. In this way, your design intent is captured. This ensures that when the design is passed down to the next level of engineering, the basic requirements are not lost when the design is edited.

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The strategy you use to create and edit your model to form the desired object depends on the form and complexity of the object. You will likely use several different methods during a work session. The next several figures illustrate one example of the design process, starting with a sketch and ending with a finished model. First, you can create a sketch "outline" of curves. Then you can sweep or rotate these curves to create a complex portion of your design.

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The Drafting application is designed to allow you to create and maintain a variety of drawings made from models generated from within the Modeling application. Drawings created in the Drafting application are fully associative to the model. Any changes made to the model are automatically reflected in the drawing. This associativity allows you to make as many model changes as you wish. Besides the powerful associativity functionality, Drafting contains many other useful features including the following: An intuitive, easy to use, graphical user interface. This allows you to create drawings quickly and easily. A drawing board paradigm in which you work "on a drawing." This approach is similar to the way a drafter would work on a drawing board. This method greatly increases productivity.

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Support of new assembly architecture and concurrent engineering. This allows the drafter to make drawings at the same time as the designer works on the model. The capability to create fully associative cross-sectional views with automatic hidden line rendering and crosshatching. Automatic orthographic view alignment. This allows you to quickly place views on a drawing, without having to consider their alignment. Automatic hidden line rendering of drawing views. The ability to edit most drafting objects (e.g., dimensions, symbols, etc.) from the graphics window. This allows you to create drafting objects and make changes to them immediately. On-screen feedback during the drafting process to reduce rework and editing. User controls for drawing updates, which enhance user productivity. Finally, you can add form features, such as chamfers, holes, slots, or even user defined features to complete the object.

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Assembly parts may be machined using the Manufacturing applications. An assembly can be created containing all of the setup, such as fixtures, necessary to machine a particular part. This approach has several advantages over traditional methods:

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It avoids having to merge the fixture geometry into the part to be machined.

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It lets the NC programmer generate fully associative tool paths for models for which the programmer may not have write access privilege.

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It enables multiple NC programmers to develop NC data in separate files simultaneously.

6.1Gear Analysis ` The objective of the analysis is to perform Structural static analysis on the gear by applying tangential load and examine the deflections and stresses and calculate the factor of safety. `

e 3d model of the turbine blade is done in CATIA and converted into parasolid file.

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Figure 6.1 Gear 3D model

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The parasolid file is imported into ansys and is meshed with 8 node solid45 element type. The structure, number of nodes and input summary of the element is given below.

SOLID45 Element Description ` SOLID45 is used for the 3-D modeling of solid structures. The element is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. ` The geometry, node locations, and the coordinate system for this element are shown in Figure: "SOLID45 Geometry". The element is defined by eight nodes and the orthotropic material properties. Orthotropic material directions correspond to the element coordinate directions. The element coordinate system orientation is as described in Coordinate Systems.

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SOLID45 Input Summary Nodes I, J, K, L, M, N, O, P Degrees of Freedom UX, UY, UZ Material Properties EX, EY, EZ, PRXY, PRYZ, PRXZ (or NUXY, NUYZ, NUXZ), ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ), DENS, GXY, GYZ, GXZ, DAMP Surface Loads Pressures -Face 1 (J-I-L-K), face 2 (I-J-N-M), face 3 (J-K-O-N), face 4 (K-L-PO), face 5 (L-I-M-P), face 6 (M-N-O-P) Body Loads Temperatures -T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P) Solid 45 a Hexahedral element used for meshing. Total number of elements = 199800 Tangential Load of 274749N is applied on the gear teeth Total number of nodes = 398104

Aluminum Young’s Modulus = 3.4 E4 N/mm2 Poisson’s Ratio = 0.22 Ultimate tensile strength = 260 N/mm2 Yeild strength = 165 N/mm2

Boundary Condition Tangential Load along x-axis = 274749N Centre shaft location is arrested in all DOF. Results and discussion:

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Figure 6.4. Vonmises stresses

Figure 6.5 Linearised stress along high stress region Maximum stress observed = 140 N/mm2 which is a stress singularity and can be ignored. linearised stress at the high stress region = 49 N/mm2 which is within the design limit.

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The gear was meshed with solid 45 with a total number of elements = 199800 and 398104 nodes. Maximum vonmises stress observed in aluminum gear is 140 N/mm2 which is because of stress singularity and can be ignored. Maximum linearised vonmises stress observed in aluminum gear is 49 N/mm2 within the design limit with a factor of safety of 3. Maximum deflection of 0.4mm observed in the gear along xdirection.

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The 3d model of the gear is imported into ansys and modal analysis has been performed to calculate natural frequencies and mode shapes. Both Modal and Harmonic analysis have been performed on the turbine blade to see the structure behavior at different frequencies between the frequency range of 0 – 1500 Hz Modal analysis is used to determine the vibration characteristics (natural frequencies and mode shapes) of a structure or a machine component while it is being designed. It can also serve as a starting point for another, more detailed, dynamic analysis, such as a transient dynamic analysis, a harmonic response analysis, or a spectrum analysis.

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You use modal analysis to determine the natural frequencies and mode shapes of a structure. The natural frequencies and mode shapes are important parameters in the design of a structure for dynamic loading conditions. They are also required if you want to do a spectrum analysis or a mode superposition harmonic or transient analysis. You can do modal analysis on a prestressed structure, such as a spinning turbine blade. Another useful feature is modal cyclic symmetry, which allows you to review the mode shapes of a cyclically symmetric structure by modeling just a sector of it. First 10 natural frequencies have been calculated for the gear model using modal analysis.

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Aluminum Young’s Modulus = 3.4 E4 N/mm2 Poisson’s Ratio = 0.22 Density = 2700 kg/mm3 Ultimate tensile strength = 260 N/mm2 Yeild strength = 165 N/mm2 Element Type: 8 node Solid 45 Shape of the element: Hexahedral No. of .dof: 3(ux, uy, uz) Results & Discussions: First 10 Natural frequencies

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Mode-5

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Mode7:

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Mode9:

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The harmonic analysis is performed on the gear between the range of 500 to 1600Hz and the structure behavior at different frequencies is observed due to applied tangential load of 274947N. Any sustained cyclic load will produce a sustained cyclic response (a harmonic response) in a structural system. Harmonic response analysis gives you the ability to predict the sustained dynamic behavior of your structures, thus enabling you to verify whether or not your designs will successfully overcome resonance, fatigue, and other harmful effects of forced vibrations. Harmonic response analysis is a technique used to determine the steadystate response of a linear structure to loads that vary sinusoidally (harmonically) with time. The idea is to calculate the structure's response at several frequencies and obtain a graph of some response quantity (usually displacements) versus frequency. "Peak" responses are then identified on the graph and stresses reviewed at those peak frequencies.

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Graph 1 of Frequency Vs Amplitude in X-direction at the gear location

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Graph 2 of Frequency Vs Amplitude in Y-direction at the gear location

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Graph 3 of Frequency Vs Amplitude in Z-direction at the gear location

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Graph 5 of Frequency Vs Amplitude in X-direction at the gear teeth location

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The maximum operating speed of the gear is 3000 rpm.i, e 3000/60=50Hz. From the above modal analysis the fundamental natural frequency is found at 504.92Hz. From the above analysis it is concluded that the gear model is free of vibrations in the operation speed of 0-50 Hz.

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Hanumanna. D, Narayanana. S, Krishnamurthy. S, (2001), “ Bending fatigue testing of gear teeth under random loading”’ Proc. Instn. Mech. Engrs, Vol.(215). Part C: pp 773-784 Glodez. S, Sraml. M, Kramberger. J, (2202), “A computational modelfor determination of service life of gears”, International Journal of fatigue, Volume 24, Issue 10, pp 1010-1020. Glodez. S, Abersek. B, Flasker. J, Ren. Z, (2004), “Evaluation of the service life of gears in regard to surface pitting”, Engineering Fracture Mechanics, Volume 71, Issue 4-6, pp 429-438. Direct Gear Design for Spur and Helical Involute Gears Alexander L. Kapelevich and Roderick E. Kleiss www.geartechnology.com • GEAR TECHNOLOGY • SEPTEMBER/OCTOBER 2002

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B. Abersek, J. Flasker, S. Glodez (2004), “Review of mathematical and experimental models for determination of service life of gears”, Engineering Fracture Mechanics, Volume 71, pp 439453. Q.J. Yang (1996), “Fatigue test and reliability of TLP tethers under random loading”, Marine structures, Volume 14, pp331-352. Statistical considerations in Fatigue (1996), “ Fatigue and Fracture”, ASM Handbook, Volume 19, pp 295-302. Structural life assessment Methods (2001), “ Failure Analysis and Prevention”, ASM Handbook, Volume 11, pp 225-289. Julius S. Bendat, Allan G. Piersol (1966), “ Measurement and Analysis of Random Data”, John wiley and sons, Inc. USA.