Basic Types, shapes, Grid and Geometry Mesh used in CFD

Basics of Meshing in CFD

Discretizing a domain into small elements or cells is known as meshing. Meshing is a very important part of numerical analysis. If the number of cells in a meshed domain are high the accuracy of analysis will be greater. Mesh is kept fine in the areas where capturing the physics of phenomenon is important. Mesh independence is one of the most important step in meshing. Mesh Independence is achieved by refining the mesh till the value of required variable becomes constant. Mesh refining requires high computational capabilities. Mesh can be classified into different types based on the uniformity and shape. Definitions of some elementary terms of meshing are given below (D. J. 1996).

Node: Point where two or more edges meet.

Edge: Boundary of a face

Face: Boundary of a cell

Cell: Control volume into which the domain is discretized.

Zone: Grouping of nodes faces and cells

Material data and source terms are assigned to cell zone whereas boundary conditions are applied on face zones.

Order of Meshing:

Mesh is generated in the order given below.

• Edge mesh

• Boundary mesh

• Face mesh

• Volume mesh

Mesh Independence:

Mesh independence is performed to see whether the size of mesh affects the solution or not. In this process, an initial mesh is generated and results are analysed for the conversion. If the conversion is not achieved, mesh is regenerated and checked to accomplish convergence. When the solution converges, mesh is refined (No of cells or elements are increased) to obtain better results. A residual limit can be set based on the problem to check for the error. With each refinement, results are obtained and compared to the results obtained with the previous mesh. If the results of two consecutive meshes are not same, mesh is refined again and again till the results become same. When the results for the two consecutive refinements are same, the previous mesh is believed to be generating accurate results.

TYPES of Meshing Based on Cell shape and Dimension:

A mesh can be two or three dimensional (D. J. 1996)

1) Two Dimensional Mesh:

            Two dimensional mesh can comprise of triangular or quadrilateral elements.

Triangular mesh:

In this type of mesh, cells are of triangular shape. Comparatively a very small amount of effort and time is usually required to generate this type of mesh. Triangular mesh is usually used in the domain areas where the physics of the problem is not very important.             

Quadrilateral Mesh:

In this type of mesh, cells are in rectangular shape. This shape is common in two dimensional structured mesh.             

 

Figure 9 types of 2D mesh

2) Three Dimension

In three dimensional meshing, a cell can have a shape of quadrilateral pyramid, tetrahedron, hexahedron or triangular prism. All of them have quadrilateral and triangular faces.               

Two dimensional extruded models can be represented completely by the hexahedron and prisms as extruded quadrilaterals and triangles.

In three dimensional meshing, quadrilateral faces might not be impeccably planar. A thin tetrahedron which is shared by two elements can be thought of a non-planar quadrilateral face.

Tetrahedron:

In geometry, a tetrahedron also known as a triangular pyramid, consists of four triangular faces, four vertices, four sides and six edges. This form of mesh can be auto-generated

Pyramid

This shape have four triangular faces, one quadrilateral face, eight edges and five vertices. They are utilized as transition elements between triangular and square elements. They are also used in hybrid grids.

Triangular prism:

This type of cell have six vertices and nine edges bounded by three quadrilateral faces and two triangular faces. It is very effective in resolving boundary layer.

Hexahedron

This type of cell have eight vertices and twelve edges bounded by six quadrilateral faces. Hexahedron mesh is considered best among all and it give the solution with highest accuracy. 

The triangular prism and pyramid zones can be considered computationally as degenerate hexahedrons, wherein some edges were decreased to 0. Other degenerate sorts of a hexahedron may also be represented.

Advanced Cells (Polyhedron)

It is a three dimensional element which can have any number of edges, faces and vertices. Large number of calculations are performed due to large number of neighbouring cells. This mesh is created to obtain more accuracy in calculations.

Figure 10 types of mesh

Uniform and Non Uniform Meshing:

In a uniform mesh, shape of cells throughout the domain is same whereas non-uniform mesh uses a blend of different mesh shapes. All the numerical approaches are designed to produce as small amount of errors as possible. These errors arises due to non-linear behaviour of the solution and large gradients of the physical properties in some places of the domain. This means that we need to handle small large-scale physical phenomena at the same time and these different phenomena can have a strong coupling with each other (D. J. 1996).

Grids:

The grid labels the elements or cells on which the flow is being solved.

• Represent the domain in a discrete manner

• Elements are grouped into boundary zones where boundary conditions has to be applied. 

• The mesh affects the rate of convergence, computational time and accuracy of the solution.

• Following parameters of the mesh are very important to obtain an accurate solution i.e. adjacent cellular extent/duration ratios, grid density, Tetrahedral vs. Hexahedral, skewness, mesh refinement thru adaption and Boundary/Inflation layer mesh.

Structured grids:

A structural grid spreads over a domain in a regular manner. In two dimensional meshing, structural grids have quadrilateral elements whereas in three dimensional structural meshing the elements are of hexahedron type. Structural gird is extremely space efficient. They display better solution convergence and generate accurate numerical results.

Unstructured grids:

Unstructured grids spread over a domain in an irregular manner. This type of mesh can be generated using any type of elements. The values at the nodes of unstructured mesh are very difficult to be represented in two or three dimensional arrays. Comparatively, an unstructured mesh is less space efficient. In two dimensional unstructured mesh, triangular shaped elements are used whereas in three dimensional unstructured mesh the elements are of tetrahedral shape

Figure 11  structured and non-structured Grid

Hybrid grids:

A hybrid mesh have both structured and unstructured mesh patches spread over the entire domain in a well-organized way. In the hybrid mode of meshing, structured grid is generated in the plain areas while unstructured meshing is generated in the areas where geometry is complex

CFD analysis of Tesla Turbine

CFD Studies of Tesla Turbine

In Jung (2014) work the flow rate was chosen as 0.0001. Iteration of disc outer radius and fluid angular velocity was done to find the volumetric flow rate for single disc spacing. In order to obtain the overall volumetric flow rate, the disk configuration was multiplied by the overall number of discs, giving appropriate efficiency and torque values. There was an iteration of head and flow speeds. Via the nozzle, fluid makes its way and is guided between the discs. The fluid hits the disc at an inclination nearly tangentially to the outside of the rotor, locating the jet's absolute and radial velocity. It measured the torque and generated power.

Jung (2014) worked on a CFD model of a Tesla turbine based on the design parameters mentioned above. In Solidworks2013, 2 domains were formed. The revolving domain comprised of a rotor assembly and the stationary domain composed of a simplistic nozzle in the outer casing. Figure below illustrates the layout of two domains.

 

Figure 3 Tesla Turbine CAD model for CFD

In Jung (2014) work fluid parameters are provided to illustrate the contact of the disc with water. The value of the dimensionless structure constant R was found to be -0.042, which implies reasonable model precision and important viscous effects. The performance of the streamlined nozzle was 77.7%. The velocity streamlines and pressure gradient are seen in Figures below:

 

Figure 4 Velocity Streamline of Tesla Turbine

 

Figure 5: Pressure gradient of Tesla Turbine

Lampart (2011) employed a CFD tool to observe the dependency of different operating parameters on the total sum of injecting nozzles. Nitrogen was the working fluid used in Organic Rankine Cycle. Three sum of nozzles 2, 4 and 6 were used in the study. The nozzles were located along the perimeter of flow inlet and were at equal distance and are tilted at 10° from the tangent of the circumference.  The results of the study showed a good correlation between less number of nozzles and higher flow efficiency under different operating conditions. The indicative of relatively low power transfer efficiency and losses occurring under same flow entrance locations, yielded the shortest flow path of six nozzles turbine that happen inside the flow space that leads to relatively low power output as compared with the lesser amount of nozzles alongside turbine. For the off-design operating mass flow situations, the stimulated models show the increased efficiency of flow. This happens to be in agreement with the interpretation of better efficiencies being accomplished at smaller flow directions proposed by Rice et al. However, at low flow rates in the vicinity of 0 kg/s, the study could not achieve the functioning features of the friction-type micro turbine. Moreover, the characteristics of operation of the turbine as soon as flow approximates to 0 kg/s and established the efficiency to react 0 at such conditions explored by many other investigators including Harwood (2008). The contradictions are made on the research work of Rice and Crawford (1974) to keep increasing the turbine’s efficiency as the flow reaches the zero flow rate state.

A numerical approach is used to study the effect of two geometric parameters, the thickness of disc and distance between disc spacing, that influences the performance of Tesla multichannel turbines. Two types of turbines were under study; 1st was a one-to-one turbine and 2nd was a one-to-many turbine, to check the aerodynamic performance and flow behavior in terms of geometric variations. The outcomes show the reduction in isentropic efficiency of the one-to-one turbine to some extend while the one-to-many turbine becomes significantly inefficient. For instance, the turbine having a 0.5 mm distance between disk, the drop is below 7%, and afterward, the variations in the thickness of the disc from 1 mm to 2 mm, resulting in the drop of 45% to its actual value. The increment between the distance of disc spacing results in the variation in isentropic efficiency of both turbines in the manner of initial increment than decrement later on. An ideal value and higher range of efficacy exist to attain maximum isentropic efficiency and to maintain it at the upper level. The ideal distance of disc spacing in the one-to-one turbine is 0.5mm that is relatively lower than a one-to-many turbine having disc spacing of 1mm with a constant thickness of discs that is 1mm. The summary for designing a multichannel Tesla turbine is that the distance between disc spacing must be in the range of its higher efficiency level and the criteria for selecting the thickness of disc must be balanced on the parameters of aerodynamic performance and mechanical stresses. 

 

Figure 6 CFD analysis of tesla turbine

The flow pattern in the Tesla turbine is illustrated in the figure below, having an inlet flow rate of about 1.32 Kg/s and 0..6Kg/s respectively. It is concluded that by keeping the inlet flow rate constant, there is a reduction in rotational speed. The increase in width of the distribution region of high-speed fluid towards the outer rim of turbine discs also increases the region and capacity of liquid doing-work. There is high-speed fluid flow from the outer rim to the center when the inlet flow rate is larger. This results in a lowering of fluid capacity and region. That is the reason why the rotational speed must be low to enhance the efficiency of the Tesla turbine for converting energy. 

 

Figure 7 velocity and pressure distribution inside tesla turbine

A figure provided below shows the domain pressure of fluid having an inlet flow rate of 1.32Kg/s. The increment in domain pressure of the fluid is observed by increasing the radius of the disc. The maximum pressure at the inlet of the turbine always appears near the outer rim. The maximum pressure continuously increased by an increment in speed of rotation and there is an absolute fluctuation in the distribution of pressure at the outlet while the fluctuations in velocity are significant at a higher rotation speed. There are small variations in domain pressure distribution of fluid between several flow rates.

 

Figure 8 Pressure distribution inside tesla turbine

Practical Designs, Numerical, Analytical and Experimental Studies of Tesla Turbine

Numerical and Analytical studies of Tesla Turbine

Many analytical and numerical attempts by various investigators were made during mid-nineteenth century to describe behavior of turbulent and laminar flow areas for flow between the tesla turbine’s disks. At times, computational tool capability was very limited that is why most of their studies had to rely on simple flow assumptions. Prof. W. Rice is one of the investigators who by employing different set of formulations has made his great efforts in describing and making a mathematical model of characteristics of operation and summation of parameters of multi-disk turbo machinery. He published an article in 1963 for the selection of quantity of disks of air-based friction compressors & pumps based on an incompressible and steady state flow in single inter-disk space by the determination of surface force and solution of the respective motion equations in tangential and radial coordinates. This study established the higher limit on parameters of performance like efficiency and total non-dimensional pressure rise of the pump by allocating losses due to friction to happen only among the disk spaces (i.e. entry & exit losses, wind age losses, housing and bearing are neglected). As the study continues, several derivations have been performed as for pumps in reverse operation (Multi disk Tesla Turbine) in 1965 having identical flow considerations.  It has been derived from the results of study that maximum level of pressure drop and efficiency of turbine is obtained at the inner fluid exit recess and as non-dimensional parameter of flow (Q/ωro 3) increases, the tendency of efficiency decreases. There are some other studies by W. Rice (1968). 

Many studies by Hasinger (1963) have elaborated pressure losses of different types which occur at the numerous points of the turbo machines. On the basis of previous studies for maximum attainable efficiency and power by W. Rice and his associates the existing knowledge gap in calculation of accurate performance characteristics of the device was filled by the determination of different frictional losses.  The swept path of spiral fluid particle travelling from fluid inlet of rotor to exhaust has been analytically traced out by (Jeffery, 1990). Some other investigators have also achieved the same goal by the use of other tools commercial CFD packages (Jedrzejewski, 2011) and (Piotr, 2009). Various solutions using two dimensional incompressible flow approaches have been proposed by different investigators for solving equations about various flow quantities like Reynolds number, regional shear force, tangential and radial components of velocity, pressure drop as compared with inlet conditions, flow paths of particle, etc. (Waren, 1965). Soo, (1957) has used first and second order approximation to Reynolds number for calculating the axial and radial velocity profiles of incompressible fluid flowing from a stationary and the other rotating disk plates for radially outward and inward flows. Some investigators have also tried to approach analytically by some other means such as by using numerical methods: Breiter and Pohlhausen (1962) presented calculation of outward radial flow between co-rotating disks using finite difference scheme. Boyd and Rice copied the same method for calculating radially inward flow. He modeled inlet region of turbine that grow an asymptotic flow for large Reynolds number.

Practical Designs and Experimental Studies of Tesla Turbine

N. Tesla is the person who has conducted the experiments and gave his undertakings. He conducted his experiments from 1906 to 1914 on turbine to check and investigate behavior of turbine for several different working conditions. According to him the turbines can be more than 95 % efficient exceeding conventional turbo machines of the day. He wanted to introduce a more reliable and efficient combustion engine in replacement of piston cylinder combustion engine using his technology. In their conversion of fuel to work the best available engines were not able to give more than 27 to 28 percentage efficiency. In 1966, a 6 inch wind turbine was tested by varying different conditions such as supply pressure varying from 6895Pa to 27,579 Pa, angular velocity varying from 4,000rmp to 18,000rpm and design variable such as disk spacing. He came up with observation that steam turbine with specific speed of 0.1 rpm is more efficient and give around 40-45% efficiency if it is compared with single stage turbine of same specific speed that gives efficiency up to 24% maximum. He also established a robust relation between flow rate and torque applied on disk of rotor of Tesla Turbine due to decrease in tangential velocity. 

Prof Warren Rice, in 1965, rechecked performance merit stated by tesla. For this he conducted number of experiments. Visco- Geometric properties were replicated under which preceding steps were made. His test results confirm that turbine can be operated at nearly pure impulse to solely reactive mode and the deviation of the results from N. Tesla’s claim of turbine merits at various speed , flow rate and geometry combinations. Adam (1970) tried to verify the research provided by Boyd and Rice (1968). He observed patterns of pressure drops in radial direction from inlet to outlet with partial flow admission for a narrowly separated pair of disks. An analytical model with a good agreement was reached for laminar flow. Pater (1974) made some improvements in the study provided by Adam et al. In his research and study he tried to determine fluid particle streamlines, pressure distribution and various fluid regimes. They described that multiple disk turbo machines may be designed by the combination of kinematic viscosity constant (ν), operating angular speed and flow rate, and if the flow is inside the laminar flow range and ri, ro, and b remaining are kept constant.

Advantages and Disadvantages of Tesla Turbine

Advantages of Tesla Turbine

There are numerous technological and operational advantages of the Tesla turbine. Some of them are listed below. 

• Extreme simplicity, reliability and dependability 

• Better stability owing to the uniform distribution of the mass of the rotor on the rotation axis

• Owing to its compact scale and low periphery speeds, small mechanical stress are produced in the turbine.

• Only radial and tangential fluid forces act on the rotating portion of the turbine, and it faces no axial load.

• Within the housing the internal static pressure is very little, so heavy cast housing is not needed to ensure the structural rigidity(Andrés, 2004) 

• As flow does not impinge directly on the surface of disk and there is a marginal static pressure differential inside the disk-casing assembly among the disks sides, the rotors are not much vulnerable to undergo cavitation (disks).

• Exotic fluid handling ability, e.g., high viscosity fluids, mixtures of gas and liquid, suspensions and commercial slurries with high concentration, non-Newtonian fluids and by-products of combustion. 

• Medium transfers fluently along the turbine with no slacking (Petrbloudicek 2007) 

• Higher theoretical turbine efficiency.

• Longer lifespans 

• The rotor is best suited for complex balance and avoids distracting forces by rubbing friction to ensure quieter running

• Tesla equipment does not have inherent valve faults typical to traditional turbo machinery. 

• Due to high acceleration of fluid, fluid separation doesn’t occur between the co-rotating disks. Due to this reason unstable flow and resulting unwanted vibrations are not present (Andres, 2004).

• By mounting separate nozzle systems on opposite casing sides, the operation in counterclockwise and clockwise directions can be accomplished.

• Components of Tesla Turbine tends to implode inside the assembly casing and blast out of the central exhaust recess, contrary to the explosion mode of failure that threatens human and machinery reliability during over speeding of equipment in traditional turbo machines. This makes it possible to run Tesla turbines in serious scenarios. 

Good capacity for load switching of Tesla Turbine

This turbine may also be applied successfully to high vacuum condensing plants. In this case, the exhaust mixture would be at a very low temperature which is ideal to enter a condenser because of the very high expansion ratio.

Disadvantages of Tesla Turbine

Prof. Rice concluded in his review paper of 2003, that the turbine would be better suitable for applications that demands high angular velocity, low mass flow rate and low torque. The disks of rotor should be expanded to satisfy the additional operating fluid movement if the need for higher power occurs. In essence, this will lead to larger tangential inlet velocities due to discs being radially increased. Therefore, dissipation of energy on the profile faces and outer edge of the rotor takes place. The combined effects of this will be the slowdown of the operation due to velocity producing moment of momentum. 

The optimal configuration and turbine’s operating point relies heavily on the motive fluid's inlet viscosity and pressure. In comparison, with the traditional bladed turbines, there is no unitary system of design that would be able to control the process of sizing. Using intuition and basic formulas or scientific knowledge and thumb laws, most Tesla model turbines and pumps have been developed. Turbulent flow in the disk spacing has led to use larger disk spacing (Warren Rice, 1991). The established design methodologies provided in numerous book, patents and articles are often contradictory (Jedrzejewski, 2011), thus generating a decreased understanding and interest in the friction turbine.

Geometry, Working and Application of Tesla Turbine

A bladeless turbine called Tesla turbine comprised of a sequence of Nozzle discs from which gas or liquid flows to the disc edge. Related to fluid properties of viscosity and adhesion, momentum transformation among fluid and disc occurs. Discs and washers are mounted on a sleeve with individual discs, fixed at the top, and nuts are used to keep dense top plates intact. There is a void in the sleeve which fits tightly onto the shaft. To connect with exhaust ports founded on the edge of the casing, holes are carved out across the middle of the discs. Therefore, a multi-disk tesla turbine is known as a shear force or secondary flow turbo equipment that operates with compressible and incompressible fluid. Fluid arrives radially then through the channels exits axially. The benefits of the Tesla turbine are ease of development, flexibility and low servicing. Vapor or water can be the fluid used. Owing to the absence of vanes, it is untouched by sediment erosion. Low performance is a problem associated with Tesla turbines. For optimum configuration, the Tesla turbine states higher torque performance, yet quantitatively several complexities were identified in achieving high productivity gains in nozzles and rotors. 

 

Figure 1 Tesla Turbine

In 1903, Nikola Tesla invented the Tesla Turbine. The turbine was using 22.5 cm disc, and the complete rotor was 5 cm thick, generating 110 horsepower, and steam is the percussive fluid. In 1909, the Tesla pump was invented using smooth spinning discs on volute casing. Between 1906 and 1914, Tesla carried out experiments with his turbine, but then there were few developments in this field until a resurgence of interest started in the beginning of 50s (Matej, 1993). 

Geometry of Tesla Turbine

The Tesla turbines are made up of rigid flat disk type rotors usually mounted on a revolving shaft parallel to each other. The disk thickness should be minimum as per theory.  Thin spacers are used to provide passage for movement of fluid among each disk. Spacers could either be disk-shaped or they can be constructed of thin magnets of cylindrical shape. In the latter case, the spacers are arranged in a round pattern about the point of entry. In this case, they are a cause of disturbance to the entering flow. It is pertinent to highlight that, after the commencement of motion of whole pack, there might be insignificant motion between spacers and disks. Rice [9] noted that, the maximum efficiency is obtained when the gaps are approximately two times the thickness of boundary layer. The existing flow situations and the working fluid’s physical properties are the deciding factors of the gap between the disks. Other factors upon which the gap depends upon are; the strength of material, manufacturing technology and assembly. The spacer assembly and the disk bank are shown in Figure below. 

 

Figure 2 Tesla Turbine Geometry

The assembly and the disk bank are locked together by a nut, which in turn is fastened by thread at one end shaft and on the other end it is fastened to a sleeve integrated into the shaft. The shaft, on both ends, is inserted into radial bearings. Bearings seats are used alongside radial bearing for smoother operation and are a part of external casing. The fluid is introduced into the row of blades using nozzle exit. The supply nozzles are positioned across the circumference. The nozzles placed at a specific angle with the disk’s tangent. When the nozzles are placed in opposing directions, the direction of rotation is defined by selecting the specific nozzle which needs to be rotated in a specific direction. The turbine’s performance depends strongly upon the nozzle efficiency and interaction of rotor and nozzle (Warren Rice, 1991).

Working Principle of Tesla Turbine

The fluid arrives in the chamber in the tangential direction through the inlet and travels over the disk surface through the spacing of the disk. Momentum exchange between discs and fluid takes place because of viscosity. Energy transfer between disc and fluid decreases the fluid velocity and it travels toward exhaust due in a spiral manner. As there are no projections on the rotor, it is quite durable. Flat discs that have exhaust ports close to their centers are piled up on a shaft and have thin spacers between them. By directing any fluid (air, exhaust gas or water) between them, these discs are rotated due to the development of fluid boundary layer on the surface of the disks which pushes them around when the fluid arrives in from the disk’s outer edge and move outwards from the central vent holes. The working fluid starts moving in lengthier spiral paths due to greater centrifugal force as disks begin to rotate and their velocity increases. Some part of the energy of fluid is converted into mechanical work by this phenomenon, resulting in the rotation of the shaft and disk.

Application of Tesla Turbine

Application of this system is typically in the narrower power ranges for turbines and compressors. This device has applications in compressing the slurries and fluids having significantly abrasive, solid, viscous, sensitive shear or in other words, any fluids which are hard to manage with centrifugal or vane pumps. Miller (1992) demonstrated successfully that the Tesla pump can be used in the human heart as an artificial ventricle. As the Tesla pump does not have a valve, voltage control of a DC drive motor can operate the pump in pulsating mode. Valente (2008) reported that the Tesla turbine could be successfully used for the reducing the pressure of hydrocarbon gases in gas liquefaction plants. We can liquefy Hydrocarbon gases almost isothermally with the integration of Tesla Turbine in liquefaction series. The ability of Tesla turbine for exploiting wind energy has been recognized in the recent years. In order to generate lift and apply more torque to the spinning shaft, the design incorporates a spacer of airfoil shape near the perimeter of the disk (Fuller 2010).

The general fields of use of Tesla turbo machinery are listed below.

• Power plants fueled by biomass

• Heat recover installations

• Systems using co-generation technology

• Solar energy systems

• Systems using exhaust heat

• Low-temperature geothermal medium plants 

Several other uses that use the concepts of the Tesla turbine are air motor motors, dentist drills, air compressors, vacuum exhausters and small expandable arms propulsion systems i.e. torpedoes. 

Understand the material hardness and effect of carbon content and heat treatment on hardness

Aim

“Understand the material hardness and effect of carbon content and heat treatment on hardness”

Aim of this lab work is to understand the material hardness of different materials and effect of carbon content present in material on material hardness and effect of heat treatment of material on material hardness.

Objectives

In order to achieve the aim of this lab work the following mention objectives have to be completed in said sequence

1.      Develop a comprehensive understanding of methods used for measuring material hardness

2.      Develop a comprehensive understanding of effect of carbon percentage on material hardness

3.      Develop a comprehensive understanding of effect of heat treatment on material hardness

4.      Perform hardness test to measure material hardness

5.      Perform hardness test after increasing carbon content

6.      Perform hardness test after heat treatment of material

7.      Develop a comprehensive conclusion about work

Theory

Hardness

Material hardness can be defined as the material ability to resist indentation. In more details it can be define as the material ability to resist the localized plastic deformation which is in the shape of indention and scratch. Material hardness is also a great way to understand the material wear resistance as it is observed that greater the material hardness greater is the material wear resistance. Another important relation of hardness with material is that the material hardness is roughly proportional material strength.

Hardness testing

Material hardness tests are very simple, easy and straight forward to perform as the only thing needed to be done in material hardness test is to produce a dent in material and then the force or load needed to product dent in material is used to measure the material, hardness. Hardness measure during the experiment is usually a dimension less number only that defines the level of hardness of material means hardness is a unit less quantity. Hardness test are destructive test by their nature of testing material but in some case these tests can be considered as non-destructive test as they only create a small dent on material surface and material can be used in any way possible after the test.

There are three different hardness testing methods namely as Brinell hardness test, Rockwell hardness test, and Vicker hardness test. Difference in type of hardness test tis based on the type indenter used in the experiments, load applied during the experiments and manner in which load is applied during the experiment. There are three different types of indenters used for the hardness test. First is the ball indenter made from the steel and has the diameter of 10 mm in most of the cases. Second the diamond cone and third is diamond pyramid.

Material Sample

In order to check the effect of carbon content and heat treatment on the material, different samples of material are provided as per below mention details

Procedure

Following are the steps needed to perform a hardness test on material

• First step is the setting up of the apparatus for the experiment and this includes ensuring that apparatus is placed on horizontal surface, no initial load is applied on the machine, related indenter is installed properly
• Second step is the preparing the sample for the test and that includes making a clean horizontal surface with dimensions as per standard provided.
• Third step is to place the sample material on the anvil of the machine in the manner that it is directly below the indenter
• Fourth step is to move the elevation screw of the machine to move the anvil up so that indenter and work piece almost touches each other
• Fifth step is to select the load as per type of indenter and then apply the load for few second
• In the case of Brinell hardness and Vicker hardness manual reading of the dent diameter and diagonal end will be taken respectively and they will be used to calculate the respective hardness number. In Rockwell case hardness number will be available directly on the screen of the machine
• Repeat the process for different sample of material provided for the test and record data of each material in the table provided 

Discussion

Figure 1 Rockwell hardness vs carbon content

 

Rockwell hardness test was performed using the basic method and procedure mention above in procedure section and results were recorded in Rockwell section of provided table. Two different values were taken and an average of these values was calculated and then that averaged value was used a hardness value of the material. Graph one shows the comparison of carbon content in material with the material hardness with carbon content on x axis and hardness on y axis. Graph show that by increase in carbon content in material the hardness of the material increase but this increase is up to a certain limit and after that material hardness start to decrease. This is due to the fact that steels that has more than 0.8 percent Carbon, has a combination of cementite and pearlite in it. When more carbon is added steels, cementite which is formed and it is brittle but hard, so it increases hardness of material. After a certain limit addition of carbon start to make material brittle enough to decrease its hardness.

Figure 2 Vicker hardness and carbon content

Vicker hardness test was performed using the basic method and procedure mention above in procedure section and results were recorded in Vicker section of provided table. X and Y values were taken and an average of these values was calculated and then that averaged value was used to calculate the hardness of the material. Graph two shows the comparison of carbon content in material with the material hardness with carbon content on x axis and Vicker hardness on y axis. Graph show that by increase in carbon content in material, the Vicker hardness of the material increase but this increase is up to a certain limit and after that material Vicker hardness start to decrease. This is due to the fact that steels that has more than 0.8 percent Carbon, has a combination of cementite and pearlite in it. When more carbon is added steels, cementite which is formed and it is brittle but hard, so it increases hardness of material. After a certain limit addition of carbon start to make material brittle enough to decrease its hardness.

Figure 3 Rockwell hardness and tempering temperature

 

In order to check the effect of tempering temperature on material Rockwell hardness, Different material samples were prepared at different tempering temperatures. Value of each sample was recorded and noted again the respective temperature column present in table provided. Graph three was generated for the effect of temperature on Rockwell hardness with temperature on x axis and Rockwell hardness on y axis. Graph show that increase in tempering temperature has very small effect on hardness initially where hardness increase very little. This small increase in hardness is up to 550 degree temperature and after that for 600 and 700 degree temperature hardness start to decrease steadily but continuously. Increase in material hardness is due to the fact that temperature removes the internal stress and allows material to have stronger bond between atoms but this is up to a certain limit after that increase in temperature makes material soft which reduce hardness.

 

Figure 4 Vicker hardness and tempering temperature

Different material samples were prepared at different tempering temperatures, in order to check the effect of tempering temperature on material Vicker hardness. Hardness Value of each sample was recorded and noted again the respective temperature column present in table provided. Graph four was generated for the effect of temperature on Vicker hardness with temperature on x axis and Vicker hardness on y axis. Graph show that increase in tempering temperature has very sharp effect on hardness lately where hardness increase very sharply. This sharp increase in hardness is at 500 and 550 degree temperature and after that for 600 and 700 degree temperature hardness start to decrease steadily and continuously. Increase in material hardness is due to the fact that temperature removes the internal stress and allows material to have stronger bond between atoms but this is up to a certain limit after that increase in temperature makes material soft which reduce hardness.

 Conclusion

Aim of this lab work was to understand the material hardness of different materials and effect of carbon content present in material on material hardness and effect of heat treatment of material on material hardness. In order to check the effect of carbon content and heat treatment on the material, different samples of material were provided with the following carbon contents (in weight %): 0.18, 0.35, 0.60, 0.90, 1.20 and sample hardened and quenched  at 1300 C and set of samples tempered and quenched for one hr at temperatures range from 200 C to 700 C. Graph show that by increase in carbon content in material the hardness of the material increase but this increase is up to a certain limit and after that material hardness start to decrease. This is due to the fact that steels that has more than 0.8 percent Carbon, has a combination of cementite and pearlite in it. When more carbon is added steels, cementite which is formed and it is brittle but hard, so it increases hardness of material. Graph show that increase in tempering temperature has very sharp effect on hardness lately where hardness increase very sharply. This sharp increase in hardness is at 500 and 550 degree temperature and after that for 600 and 700 degree temperature hardness start to decrease steadily and continuously. Increase in material hardness is due to the fact that temperature removes the internal stress and allows material to have stronger bond between atoms but this is up to a certain limit after that increase in temperature makes material soft which reduce hardness.

Lab Report Bending of a simply supported beam

Aim

“To study deflection in a simply supported beam”

This lab is aimed to study the behavior of simply supported beam under the action of a point load.

Objectives

The goal of comprehending the simply supported beam in an effective way can be achieved through step by step approach. It is very important that we follow the below given steps in the same order as they are listed.

Grasp the basic design of the beam and its working

Strain produced in the beam under the action of load

Perform experiment to study the strain produced in the beam and using strain gauge to measure strain

Introduction

Beam

Beam is one of the simplest but very important component of every structure or building. A simply supported beam has supports at both ends. It features roller support at one end and pinned support at the other. These beams can undergo both bending and shear stress. Therefore, these beams should be designed such that they are able to bear shear and bending stress applied on them.

Bending stresses in beam

When a beam is under the action of any load, reactions are produced at its supports which subsequently generate stresses within the beam. These stresses act to curve the beam about its supports. Therefore, these stresses are called bending stresses. Moreover, in bending the layers above neutral axis of the beam will be subjected to compression whereas bottom layers will be subjected to tension. 

Deflection of beam

Once the bending stress produced in the beam surpasses a certain value, beam starts to alter its shape and it moves in the direction of applied load. This deformation phenomenon is known as deflection of the beam. Mathematically, it can be expressed as,

Maximum deflection=  (W × L^3)/(48 × E × I)  

Where 

L is the length of the beam

W is the applied load

I is the moment of inertia of the beam

E is the modulus of elasticity of the beam

Modulus of elasticity

Young’s Modulus of elasticity of a material defines its ability to withstand the applied load remaining within its elastic limit. In a way, this property can also indicate the strain produced in a material. Mathematically, this can be obtained by simply dividing stress by strain. 

modulus of elasticity=E=Stress/Strain  

Moment of inertia

It is the geometric property of the beam. This property tells us about the resistance that a beam offers against angular motion when it is subjected to a stress.

 Mathematically, it is expressed as,

I =  1/12  × b × h^3  

Procedure

Experiment to find the deflection in a simply supported beam has following steps:

First of all, place the apparatus on a flat horizontal surface. Carefully, mount the dial gauge and attach load hanger to the apparatus. 

Take all necessary measurements of the beam and also measure the distance of the point where the force or load is being applied. Use the above formulas to calculate the deflection theoretically.

Now, use load hanger to exert a load of 100 grams at the center of the beam.

Use strain gauge to note the value strain produced.

Repeat step iii and iv for different weights available in the laboratory and compare the experimental reading with the theoretical readings.

Discussion

Strain in beam was measured using strain gauge for different load ranging from 100 gram to 1000 grans or 1 kg. Reading from strain gauge circuit were taken for each different load and when graph was plotted for loading condition it show that the relationship between strain and load applied is directly proportional. Means the strain and load applied are directly proportional to each other because as load on the beam was increased from 100 g to the value of 1000 grams the value of strain was increased from 15 to 181 linearly.  When this case of loading of beam was compared with the reference value of strain in beam for the same loading condition, result show vary small difference in the value of strain obtain form the class experiment and that obtained from the reference value.

Graphs shows that the value of strain obtained from class results were greater than that of the reference value. This difference can be due to number of reasons; first is that the beam used for the class experiment was already deformed and has a small value of strain in it even before the strain circuit was installed and experiment was conducted. Second can be defect in strain gauge circuit due to which it shows greater value of strain as compared to the actual value. Third can be due to human error means operator performing the experiment does not have proper experience and knowledge and is not performing the experiment correctly.

When the strain value loading case of beam where strain of beam was recorded for every increase in load, was compared to the unloading condition where strain of beam was recorded for every decrease in load from the maximum value shows that the this loading and unloading condition of beam was in the elastic region of the beam material as when load was removed the strain produce in beam also disappear fully and beam regain its original shape. This also show that beam loading as well as unloading case have directly proportional relation between strain and load applied and removed.

Cutting force monitoring using strain guage

Force monitoring

An electric circuit, that is fit for estimating the exceptionally little changes in resistance comparing to strain. This circuitry is utilized to quantify the strain with fortified opposition strain gauges. Typically, four strain gauge components are electrically associated with structure a Wheatstone bridge circuitry. 

A Wheatstone bridge is a separated bridge circuit utilized for the estimation of static or dynamic electrical opposition. The yield voltage of the Wheatstone bridge circuit is as milli volts (mv) yield per volt input. The Wheatstone circuit is likewise appropriate for temperature compensation. The numerical representation of the Wheatstone bridge, if R1, R2, R3, and R4 are equivalent, and a voltage, Vin , is applied between focuses A and C, at that point the yield between focuses B and D will show no expected distinction. Notwithstanding if R4 is changed to some esteem which doesn't rise to R1, R2, and R3, the bridge will become unequal and a voltage will exist at the yield terminals. In an alleged G-bridge setup, the variable strain sensor has opposition Rg, while different arms are fixed worth resistors. The sensor, in any case, can involve one, two, or four arms of the Wheatstone bridge, contingent upon the application. The all out strain, or yield voltage of the circuit (Vout) is equal to the contrast between the voltage drop across R1 and R4, or Rg.

 

Strain Gauge location

Example 1

The reason for this model is to ascertain the load force P, as appeared in Figure 2, with the assistance of two strain gages introduced on a rectangular pillar. Remembering that this pillar could be either the cutting tool holder, or it tends to be the cutting tool shank, and the edge or tip of the cutting tool is the main point of activity of the loal P. The two strain gages are locked in on the outside of the cantilever pillar as appeared in the figure. These strains mounted on a superficial level are in pressure when the load P is applied toward the finish of bar. These strain gages must be associated with a Wheatstone bridge in the manner R and R2, or R1 and R3, as appeared in Figure 1, to finish the bridge circuit other two resistors must be added, remembering that these resistors have same ostensible estimation of resistance as that of strain gages. The reason for doing so is to keep the bridge be as equilibrium as could be expected under the circumstances (Vο= 0) when the gages are unreformed.

 

Example 2

The purpose of dynamometer in dynamometer based system was to measure the cutting force. So dynamometer was installed in tool shank so that it can measure the cutting force involve in the turning process. The best feature of this process is that the dynamometer can be installed very easily on the tool shank. Other than this its customization is very easy as the data transmission happen through wireless setup. In order to avoid thermal effect of cutting operation and to increase the sensitivity of the apparatus, the installation of strain gauge is done away from the tip of the cutting tool cutting tip. This helps protect the dynamometer from damages when the tool failure occur. In order to achieve an amplified strain in results most strain gauges are placed at the hole of the tool shank or at the place of high stress concentration. This is done to avoid compromising the stiffness of the tool shank.

 

In above mention circuit of dynamometer based setup, the volte value provided by the Wheatstone Bridge is first amplified about 200 times more the original one and then it is transferred to frequency from voltage by an IC. Then these signals are delivered to an IR Emitter diode that is placed at the back side of shank of tool. After this stage the signal which are in frequency form are then again converted into voltage once again and that voltage is proportional to the strain value of the tool. The offset value of the voltage which is due to the unbalancing of the bridge is considered as the final output value.

Example 3

At the point when load P and Q are applied toward the end rectangular cross sectional zone of the instrument holder, minutes Mp and Mq and powers. Which bring with strain in strain gauges which are mounted on the rectangular cross sectional territory of the cutting tool holder. The circular drill is made at the focal point of cross sectional region, this is where strain gauges are introduced. There are two reason for doing this. First increment the affectability of the dynamometer, second design is to keep the solidness of hardware holder for all intents and purposes unaltered. 

Thinking about the accompanying conditions for this model: 

a) Strain gages with an ostensible resistance estimation of R, 

b) Strain gages of segments 1 and 2 (base and excellent condition) a full bridge with yield voltage V01, 

Considering that the instrument holder is made of a decent thermally conductive material, for example, aluminum, remembering the reality given above it is sensible suspicion that the temperature of all the strain gages is nearly the equivalent. Therefore, variety in temperature influences the affectability of all the strain gages similarly, dropping its impact on the last estimation. Extra strain gages must be introduced to quantify the pivotal power R,

Explain single point cutting tool geometry, angles and materials properties

Tool Geometry
Cutting Tool Geometry

1. Shank:

It is the body of the tool. It includes the part of tool which is inserted in tool post to hold the tool in machine. In simple words, it joins the handle and operational end.

2. Flank:

The surface of the tool adjacent to and facing work piece is called flank. A tool have two types of flanks i.e. major and minor flank. Major flank is also called side flank whereas minor flank is also called end flank. Minor flank is the end face of the tool which is facing the work piece while major flank is the adjacent surface to the minor flank.

3. Base:

The opposite side of shank with respect to the top side of tool is known as base.

4. Face:

Rake surface is also called tool face. This allows the chips of work piece to flow over the tool. 

5. Cutting edge:

The edge of tool that removes material by coming into contact with work piece is known as cutting edge. A tool have two cutting edges. 

i. Side cutting edge: Top edge of side flank is knows as side cutting edge.

ii. End cutting edge: Top edge of end flank is known as end cutting edge.

6. Nose or cutting point:

The point on the tool that separates end cutting edge from side cutting edge is known as nose.

7. Nose radius:

The point where end and side cutting edge meet is given a rounded. The radius given to the intersection point is called nose radius. Nose radius determines the surface quality of the work piece. It also has an effect on tool’s life.

8. Heel:

Intersection of flank and base is called tool heel.

Angles of Single Point Cutting Tool

There are several types of angle in a cutting tool. Each angle have its own importance and function.

1. End Cutting Edge Angle:

It is the angle formed between end face of the tool and plane normal to the side of shank.

2. Side Cutting Edge Angle:

The angle formed between major flank and the longitudinal axis of the tool is known as side cutting edge angle.

3. Back Rake Angle:

The angle made by the face of the tool and plane parallel to the base of tool is known as back rake angle. If the angle is measured in the direction of shank then it is called back rake angle and if it is measured in a direction perpendicular to the shank then it is called side rake angle.

4. End Relief Angle:

It is the angle between side flank and the plane perpendicular to the tool base is known as end relief angle. It prevents the tool from rubbing against the job.

5. Lip Angle/ Wedge Angle:

Angle between the face of tool and end flank is known as lip or wedge angle.

6. Side Rake Angle:

The angle between the face of the tool and plane normal to shank is known as side rake angle. 

7. Side Relief Angle:

The angle between portion of side flank immediately below the side cutting edge and line perpendicular to base of tool measured at right angle to side is known as side relief angle. It prevents interference when tool enters the material.

Single Point Cutting Tool Material Properties

Tool can be made of different materials depending upon the material which is being machined. Three important properties of tool material are given below.

• Hardness: Hardness is the property of the material with which it resists to indentation. The strength exhibited by the tool is directly related to the hardness of material with which the tool is made. Hot hardness is the ability of a material to maintain its hardness at high temperature.

• Toughness: Toughness tells us the about the energy which a material absorbs prior to its fracture. It is usually characterized by a combination of strength and ductility in the material. A material with high value of toughness exhibits good resistance against shock load, fracturing and chipping. For a tool, toughness and hardness vary opposite to each other.

• Wear resistance: A material with high hardness show good wear resistance. Moreover, a tool with good surface finish exhibits good wear resistance due to lower coefficient of friction. The property of wear resistance seems simple but most of the people can’t comprehend it properly. Wear resistance decides the life of tool before its replacement.