The Importance of Water and the Hydrologic Cycle Essay

The Importance of Water and the Hydrologic Cycle - Essay Example NRDC arranged to test 1000 portable water bottles comprising of 103 brands available in the US market. NRDC conducted a detailed investigation that lasted for four years. Usually, producers of the bottled water maintain that their products are free of any chemical contaminants. Some of the samples collected were found to be contaminated with E-coli Bacteria, Arsenic, Nitrate, chloroform, phthalates, and some other kinds of bacteria that can cause serious illnesses to those who consume it. Infection with E-Coli bacteria can cause diarrhea, and vomit to children, elderly people and those who body immune system is weak. Substances such as Arsenic are considered carcinogenic and can lead to nervous, skin and reproductive issues. Nitrate interferes with blood's oxygen intake ability, especially in infants. Nitrates also increase cancer risk. The substance such as chloroform can cause cancer of the pancreas, colon; it may also cause miscarriage or birth defects in newborns (NRDC, 2013).NRD C clarifies that not all brands were contaminated with harmful substances. Almost 25% of the bottled water, with at least one sample tested of each brand, was found to be violating state standards. Some of them were comparable to tap water; however, NRDC clarifies that these brands are not without risk because most brands were tested only a few times; NRDC has called their tests as 'snapshot' tests. It is also likely that source water quality due to different surface water sources varies significantly time to time.

Drugs of Abuse Essay Example | Topics and Well Written Essays - 1000 words

Drugs of Abuse - Essay Example ay and white matter and is the focal point of all human activity—controlling all movements and coordination when a person need to breathe, drive a car, eat some snacks, create some artistic masterpiece, and many other things. Note that, human brain has three very vital areas that can be damaged by drug abuse. The brain stem, which controls basic functions crucial to life, examples include: breathing, heart rate, and sleeping; The limbic system, which consist of the brain’s reward circuit, whereby brain structures are link together, control and regulate a person’s ability to sense pleasure as well as motivates to repeat behaviors like eating. Then, the limbic system that is practically activated the moment people perform activities including drugs of abuse. Furthermore, the limbic system is accountable for perception of other emotions, whether it is positive or negative, and this explains the mood-altering characteristics of many drugs. Probably, the most essential part of the brain is the cerebral cortex, since this area is occupied by structures controlling the senses, enabling people to see, feel, hear, and also to taste. Cerebral cortex is also the â€Å"thinking† area of the brain, very essential for memory, association of facts and events and also for decision making process. Entirely, the brain basically regulates individuals’ basic body functions, including the process of interpreting facts as well as responding to experiences, emotions, and even behavior. Indeed, the brain is composed of many parts which all work together as one team and these parts are responsible for coordinating and conducting particular functions. However, drugs can modify important brain areas which are essential for life-sustaining functions; it can drive the uncontrollable drug abuse which marks addiction. The areas of the brain are certainly affected by drug abuse (National Institutes of Health - U.S. Department of Health and Human Services, 2008; p 15). Drugs are

Business law concepts Essay Example | Topics and Well Written Essays - 250 words

Business law concepts - Essay Example An employer has to pay wages even if no work is there for the employee to do. The common principle is that wages has to be paid if an employee is accessible for work. This again depends on whether the terms in the contract are expressed or implied. The case on hand with regard to Lessex Police Constabulary agree with Highspots Nightclub is similar to the case of Scottbridge Ltd v Wright wherein a night-watchman was called for to be on the building between 5 pm and 7 am every night. Other than some minor duties the watch man was mainly required to be in the premises to prevent any intruders. When the night watch-man claimed his wages the employer refused to pay saying that he had no work. The Court of Session preserved the EAT judgment that he has to be paid at least the national minimum wage rate for the hours he was at work. It was in the hands of the employer to render him with work and just because he did not have any work to do will not nullify his right to be paid.

Privatization in developing countries Assignment

Privatization in developing countries - Assignment Example They start to register losses and the management fails at delivering their goals (Gianaris 57). Each of the management cycle and rules comes with certain advantages and disadvantages; likewise the concept of privatization also comes with certain advantages and disadvantages. If we look at the pros we would conclude that privatization places its operations in the ownership of private enterprise, these are more responsive to customer services because they deal with great competition in the industry and they have to perform well to gain market share. The Government cannot take undue advantage of the industry and they are not bound to perform under limitations. Privatization also provides a one off boost of cash flows to the government and the same money can be invested in other projects or to meet short term liabilities. Privatization of the industry loses its monopoly and that is why the same product could be sold at a much competitive price with enough supply to meet the demand. Another advantage of the concept is it leads to innovation in the product and other features that le ads to a better understanding of the customer needs and requirements Few of the disadvantages that are related to privatization are the cost of transaction is too high, the public monopolies are now private monopolies and the competition is still less in few of the industries, Government privatizes its industries because they are short of cash flows or are high on debt and for that reason they sell their industries for a much cheaper cost and value than it would have been sold under normal circumstances, the private business closes down the operations which are performing well and so a lot of jobs are lost and sections are closed and the investment goes in the hand of few even though it is sold to a huge majority. Margaret Thatcher was one of those people who introduced

Mobile Phone Addiction Essay Example for Free

Mobile Phone Addiction Essay The mobile phone is one of the greatest invention in 20th century. We can not imagine how is our life without the mobile phone. It is an obvious truth that the mobile phone gives us benefits in some aspects of life. Using mobile phone distributes our communication to make it easier than before. Besides a mobile phone can provide us with a lot of functions like relaxing with music, chatting or playing games. However, today people especially young people are becoming addicted to using the mobile phone. They can not stay away from their phones, even for a minute. Perhaps, because of the benefits of the mobile phones, most people do not realize lots of negative effects that the mobile phone has brought to us. Using mobile phones too much not only affects our health seriously but also causes some personal problems and limiting communication face to face. In the high-tech world, the mobile phones are equipped with all necessary functions. People can chat together for hours whenever they have time. They talk together from hour to hour, from day to day. As a result, using mobile phone for a long time affects our hea lth. Do you know how dangerous the wave from the cell phone is for our brain? The waves from cell phone are very harmful to our physical body such as our heart and brain. A recent study tells that our brain is seriously damaged when using mobile phone too much. Have you ever experienced the headache with talking on the cell phone for a long time? It is the wave from the mobile phone that causes the headache. Due to the danger of the cell phone wave to our brain, using phones too much can cause a poor memory. Besides, the wave of cell phones is very strong so it can cause heart disease if we keep cell phone near our body, especially under the pillow while sleeping. With many functions of the cell phone, the young can listen to music anytime they want. By using a headphone, people can enjoy some video, some music all time without annoying anyone. However, one effect of listening by earphones for a long time is that it damages our ear, even it can cause deaf. Moreover, the excessive use of cell phones causes teens and young adults to experience restlessness and it can make them feel difficult to fall asleep. It is an obvious fact that using cell phones too much can affect our brain, because sleep loss and damage our ears. Our life is becoming more and more convenient and the mobile phone has become an indispensable and inseparable object. People use mobile phones in every place, every time to manage their business. They talk on the cell phone when working, even when they are on the road. A lot of drivers listen to cell phone conversations while they are driving on the road. Consequently, they can cause dangerous accidents for other drivers on the road. Getting caught up in conversations on a cell phone can lead to the loss of focusing and highly distracted driving. Furthermore, it is generally observed that drivers using cell phones often forget to give proper signals disobey street signs and tend to cut lanes without warning. It is such a careless driving that results in many crashes and fatalities every day. Therefore, our government should give the law to ban drivers from using mobile phones while driving. Besides, another result of using phones too much is the expenses for cell phone cards every month. We often spend a lot of money using mobile phone. Not only the expenses for cell phone cards, sometimes using phones in a public places also causes some problems. We can see some rude people who speak loudly in public places, particularly in libraries, trains and theatres, which disturb other people a lot. For example, the camera of mobile phones sometimes disturbs a persons privacy. Some people use the Bluetooth and the camera in a bad purpose. In short, using mobile phone can cause some personal problem like accidents on the road, money for cell phone cards and some trouble in public places. Mobile phone has become crucial part of our life. One of the most important functions of the phone is that it helps the communication become easier and quicker. However it also causes a lot of problem in communicating. Firstly, cell phone use has effects on the direct human to human interaction. Talking on the cell phones is gradually replacing the communication face to face between people. There was a time when the purpose of a telephone was to convey the important messages and not many people owned telephones. Thus, to talk together about something, they often met directly. Today owning a cell phone is held as a necessity and anyone including children have their cell phone. Therefore, the communication face to face between people is limited. Nowadays parents can be at the work place to talk to their children, to remind them of studying at school. Friends like chatting together for hours by mobile phone so they do not have anything to tell together when meeting at school. It seems that using cell phones too much destroys the pleasure of direct interaction. Another effect in communicating by mobile phone is misunderstanding between people. Always, people send messages to ask for information or congratulate someone. And the problem is that sometimes they forget to type the punctuation marks or they misspell, which makes the receiver misunderstand. More seriously, this can destroy the relationship between them. Therefore, to avoid some problem in communicating by cell phone, people should be careful in using it. Mobile phone is really necessary for our life because of many convenient functions of it. However, sometimes mobile phone can cause us many problems. The advantages or disadvantages of using mobile phones depend on the way how we can use it in right ways or in wrong ways.

Dystopian Disaster Essay Example for Free

Dystopian Disaster Essay A Dystopian Masterpiece In his short story, â€Å"Harrison Bergeron†, author Kurt Vonnegut, Jr. tells about a society, or America, in the future being ruled by a totalitarian government, whose number one law, is equality. Everyone is treated equally by law; no one is smarter, faster, stronger or more beautiful than another. The people of the society are forced to conform to handicaps by wearing weights around their neck or masks to hide a beautiful face. Vonnegut shows how far people are willing to go for equality and putting people in degrading situations just to make them equal. Is someone truly equal in a dystopian society, where being above average is not normal and being almost dumb is almost completely normal? In order to demonstrate Harrison Bergeron is living under dystopian society, the reader must examine a society were there are too many laws, in which is the public is being regulated by the state, everyone being forced to conform. One of the qualities of a dystopian society is being regulated by the state; every move made by the public is being watched, making sure that no one is above equality. Equality is taken very seriously, so serious that it became â€Å"the 211th, 212th and the 213th amendment to the Constitution† (1). This shows that at least a few centuries ago when the constitution was written there were just enough amendments but now in 2081 there is more then two hundred. So many amendments, each time a new amendment is added little of equality is taken away. Anyone who was of above average intelligence, beauty, or strength was required to wear a handicap, weights around their neck or an earpiece tuned to the government. Tampering with these weights would automatically give â€Å"two years in prison and a two thousand dollar fine† (2). These weights weighed over forty-five pounds, who would not want to rid that, but is that the price they must pay for equality. Vonnegut character Harrison Bergeron who was above average intelligence, physical strength and beauty was required to wear a handicap, by the state. Harrison wore scrap metal around his neck and â€Å"rubber nose† to hide his beauty. People weren’t allowed to do anything without the government being involved, not even a train of thought. They had to bare those heavy weights, all day for their rest of their lives. Vonnegut short story takes equality a step up from the stairs of equality, putting the public in dehumanized and degrading situation. Hazel being of average intelligence was considered normal although she â€Å"couldn’t think about anything but in short bursts† (1) which goes to show she is to dumb to pose a threat to the handicap generals. While Harrison on the other hand, was above average, had to wear heavy handicaps such as â€Å"tremendous pair of head phones and spectacles with thick lenses† (3 Vonnegut). This was all to weigh him down because he posed a threat with his above average intelligence and physical strength. The state was so afraid of people like him they made him wear those handicaps, now is that really fair. Someone is slightly larger slightly beautiful they have to hide it. Where does that put people, making them dumber rather then helping them, or keeping someone caged up to the point he will rebel. Then there’s the ballerina how had to wear a â€Å"hideous mask† (1 Vonnegut) to hide her above average beauty, had to apologize for her voice. When she spoke it was with â€Å"a very unfair voice for a woman† (3). If your voice is lovely or soothing you cannot use it, it is unfair and possibly punishable by law. Equality is taken a bit too extreme when someone has to apologize for tone of voice. In a utopian society there are not many laws, in â€Å"Harrison Bergeron†, there are too many laws with all those amendments. George Bergeron being above average intelligence is â€Å"required by law to wear it at all times† (1) to wear an ear piece, it is tuned to the government so they’d and goes off â€Å"every twenty seconds† (1) forbidding him to have a train of thought. George cant even remember his son or think about something without a noise going off in his ear. How can someone have a proper conversation with a noise going off in the ear every twenty seconds? This shows a dystopian quality, independent thought being limited or restricted. In this society breaking the law can even cause death. By the time Harrison removed his weights and escaped and took over a television broad cast to dance with a ballerina, at that point â€Å"Diana Glump Handicapper General came in to the studio with a double barrel gun and shot twice†(3). They dies instantly, a world with no jurisdiction or chances, the ballerina did not even have a say in it, it could have been handled differently. Instead, the situation is handled with violence, yet another dystopian quality. A dystopian society has laws, and is ruled by the government, Harrison Bergeron shows this, in no way is it utopian. This goes on to show that Harrison Bergeron is indeed a dystopian society. Its is controlled by a totalitarian government, and their behaviors are regulated by the state. Vonnegut wanted to show American in the future as a dystopia society, showing that America will go overboard for equality. Also by making people lead a dehumanized live by being handicapped forever. This short story contains all the qualities of a dystopian society, not being able to think or under watch of the state, but everyone is used to it. Vonnegut showed that people can let things get out of hand and be taken to extreme levels. One by one, tweak this hear tweak that there, when will it stop.

Prediction Of Cutting Forces In Broaching Operation Commerce Essay

Prediction Of Cutting Forces In Broaching Operation Commerce Essay According to variety of workpiece profiles in broaching, the geometry of cutting edge varies from simple line to very complicated curves. Wide range of cutting edge geometry in broaching imposes complexity to the distribution of the chip load along the cutting edge. Hence, prediction of cutting forces in broaching is not as simple as other machining processes. Due to this complexity, introducing an applicable force model for all of the orthogonal and oblique broaching cutters can be problematic. In this paper, an attempt is made to present a new force model for broaching. The newly proposed force model expresses the cutting edge as a B-spline parametric curve and uses their flexibility to calculate the chip load as well as cutting forces for orthogonal and oblique broaching. Verified by experimental results, the presented model has a great capability to simulate broaching cutter geometry along with cutting forces and it can be applied for the entire broaching cutters. 1. Introduction Broaching is a powerful process for the production of complex internal and external profiles. As a machining process, it is commonly used for the machining of a broad range of profiles such as keyways, guide ways, holes and fir-tree slots on turbine discs. Broaching has considerable advantages in comparison to other machining processes. Roughing, semi finishing and finishing of a complex profiles can be done in one stroke of the machine which would require many passes in other conventional processes such as turning, milling, slot milling, etc. It can also produce parts with high surface quality and high geometrical and dimensional tolerances in one stroke. Since the number of simultaneously engaged cutting edges with the workpiece is higher than the other cutting tools, the chip load on each of them will be smaller and tool life is distinctively longer in comparison to other machining processes such as milling and turning [1]. It can be also mentioned that broaching machines are not as complicated as CNC milling or CNC turning machines and thus considered as a simple operation that requires not a highly skilled operator. In other commonly used machining processes such as milling and turning, final geometry of workpiece is generated by combination of tool and workpiece motion and there is no similarity between final geometry of workpiece and cutting tool geometry. In broaching, the geometry of machined part is derived directly by the inversion of broaching cutter geometry. Therefore unlike other machining processes, broaching cutters have a wide range of geometries as well as parts. Consequently, chip load has a complicated non-uniform 2D or 3D geometry depending on the profile complexity of workpiece. A unique feature of broaching operation is that it is not possible to change any of the cutting parameters during process but the cutting speed. That is because all other cutting parameters such as feed, depth of cut and width of cut are built in features of broac hing tool geometry which makes the tool design the most important aspect of broaching. Although broaching is well defined in industry, just a limited number of researches have reported work in the open literatures. In 1960 Monday [2] presents the most comprehensive source on broaching. A detailed description of broaching technology can be found in his book. Kokmeyer [3] edited collection of works on broaching representing the usefulness of the process. Gilormini et al. [4] analyzed the cutting forces on a single broaching and compared them to the forces in slotting and tapping process. Terry et al. [1] presented a system for optimal design of broaching tools. They presented the factors that affect productivity in broaching and explained the design constraints, their importance and how they are selected. Finite element was used to predict the tooth deflection and experimental data in order to create the general rules for designing. Sutherland et al. [5] presented a force model for broaching based on the oblique analysis to determine the forces in the gear broaching proc ess. Their model showed the relationship between contact area, chip load and cutting force. Sajeev et al. [6, 7] investigated the effects of broaching parameters on the tool and workpiece deflections and the final shape of the broached geometry. Budak [8] examined the performance of broaching tools used for broaching of waspaloy turbine discs with fir-tree profile based on the monitoring of force and power. It has been demonstrated that for most of the investigated tools, the load distribution among the broaching sections were non-uniform resulting in uneven wear. Recently Ozturk and Budak [9, 10] performed Finite Element Analysis to calculate the stresses in the broaching tool during the cutting process. The developed model is used to simulate the broaching process and predict the generated stresses in the tool to improve the tool design. He studied fir-tree profiles, simulated the broaching process forces and the tool stresses to improve the tool design. Later Kokturk and Budak [1 1, 12] performed an optimization on the geometry of the broaching tool cutting edges. In their study the cutting conditions are changed until they can satisfy the preset constraint. They also used the optimized conditions to improve the broaching process. Yussefian et al. [13] applied B-Spline parametric curves in modeling of boring process. Recently Hosseini and Kishawy [14] presented a general force model for orthogonal broaching using B-spline interpolation of cutting edge. By taking geometric flexibility of B-spline curves, their model was capable of modeling any arbitrary orthogonal broaching cutting edge geometry as well as computing the chip load for various cutting conditions. This paper proposes a 3D general force model for the broaching process. The proposed force model is capable of modelling of three force components using B-Spline interpolation of the cutting edge. Each cutting edge is first modeled by B-Spline parametric curves then the chip load is calculated by integ ration of area between two successive edges. The proposed force model for orthogonal and oblique broaching can calculate the chip load for any arbitrary geometry of cutting edge from the simplest to the most complicated. The proposed method is used to calculate the generated forces and the results are compared to the measured data. 2. Broaching tool geometry Broaching tool is a straight multi tooth cutter in which several cutting edges engage with the workpiece simultaneously and each tooth removes a portion of material from workpiece surface. Broaching cutter has a tapered flat or round profile with a series of teeth on its surface [4]. Each successive tooth in a broaching tool is higher than the preceding one to perform the cutting action and remove material from workpiece surface. Broaching cutters in their general form can be geometrically divided into three categories of teeth, namely, roughing, semi-finishing and finishing teeth. Roughing teeth remove the bulk of material from workpiece, semi finishing teeth produce the basic surface finish (surface quality), and finishing teeth provide the final surface finish and set geometrical and dimensional tolerances [4]. Figure (1) shows a typical broaching cutting tool. Figure 1: Schematic view of broaching tool Normally the maximum rise per tooth in broaching tool belongs to the roughing teeth which perform the major part of metal removal. The rate of rising per tooth slightly decreases in semi finishing teeth as they only remove a small portion of material from workpiece surface to improve the dimensional accuracy and surface quality. In the finishing part, all of the teeth have the same height. These teeth are not cutting teeth and they provide the desired surface quality and adjust the geometrical and dimensional tolerances in the predefined range. Figure (2) illustrates the general mechanism of cutting in broaching. Figure 2: Mechanism of cutting in broaching When broaching cutter is accurately designed, broaching process can be faster and more accurate than many other machining processes. Although the initial cost of establishing for a broaching process is comparatively higher than that of other cutting processes, the production cost is commonly low because of the high production rates and the long tool life. Figure (3) presents some of the important geometrical parameters of broaching cutting tool. Figure 3: Broaching tool geometry In figure (3), and are rake angle, clearance (relief) angle, tooth height and land length respectively. The rake angle and clearance angle can be selected based on workpiece material. The rake angle is usually selected between to and clearance angle is usually selected between to [12]. The total length of the tool and number of simultaneously engaged cutting edges can be determined by the pitch length which is a linear distance between two successive cutting edges. Based on some previously conducted research [10, 12, 15], it is concluded that it is preferable to have at least two cutting edges in cut to have a dynamically stable cutting. Another geometric feature of broaching tool is gullet space which is the empty space between two following teeth. The main advantage of gullet space is to retain the chip during cutting until the tooth leaves the workpiece. Once the broaching tool engages with the workpiece, chip is captured between tool and workpiece and it is maintained there until each tooth finishes the cut and leaves the workpiece. Small gullet space may cause tool breakage because of no space to keep the removed chip. It can also lead to poor surface finish due to rubbing of removed chip to the machined surface. If the gullet space is chosen too large it makes the tool very slender and decreases the tool strength and stability. According to the above mentioned reasons, it is very important to design the gullet space accurately to achieve acceptable space and dynamic stability simultaneously. In order to perform a reasonable design it is necessary to have a good understanding of cutting forces during machining p rocess. If the force model can predict the cutting force truthfully the result of force simulation can be used as an input for design and optimization process. 3. Mechanics of metal cutting in broaching Similar to almost all of the cutting processes, the cutting force in broaching can be expressed generally by three differential components which are directly related to chip load area and the contact length between cutting edge and workpiece such that [16]: (1) Figure (4) depicts the main features of oblique broaching and shows the force components generated during the chip removal process. Figure 4: Mechanics of oblique broaching In equations (1), is the differential component of tangential force, is the differential component of feed force and is the differential component of radial force. and are chip thickness and length of the cut for infinitesimal element along the cutting edge respectively. and are cutting and edge constants while the subscript refer to the tangential, feed and radial directions. Similar to the other cutting mechanics, the radial component of force appears only during oblique broaching when cutting edge has an inclination angle with the cutting direction. The total tangential, feed and radial component of cutting force for each edge can be calculated by integrating of those components along the cutting edge. Equation (2) shows the force integration along the cutting edge from the start to the end of engagement. (2) In equation (2), represents a differential element of chip area which is removed by the cutting edge. Equation (2) can be written in this format: (3) In the above equation, is chip load along the cutting edge and is length of engagement between cutting edge and workpiece. Figure (5) demonstrates the infinitesimal element of cutting edge, chip load and contact length for an arbitrary fir tree broaching tool. Figure 5: Infinitesimal element of cutting edge Since the chip load may vary along the broaching edge, it must be segmented into elements for which local thickness can be assumed constant. The geometry of chip along the broaching cutting edge is complicated however, since there is no relative motion between successive edges the chip load remains constant. The common approach for simulation of cutting forces is dividing the cutting edge to infinitesimal elements and calculating the area for each element separately. If total chip area can be calculated, cutting forces are obtained without the need for dividing the edge to elements. However, due to the variety and the complexity of cutting edge profiles in broaching, it is difficult to express the edge by an explicit function. Hence, calculation of the above integration in equation (3) is not a straight forward procedure. Representing the broaching cutting edge by B-Spline curves is a powerful way to express the geometry with parametric relations which makes integration and derivatio n along the edge much easier process. 4. Cutting edge interpolation by B-spline parametric curves A series of data point can be obtained by collecting the coordinates for each point along the cutting edge using inspection method such as CMM, digitizing or laser scanning. The desired B-Spline of degree p defined by control points passes through all those data points and expresses the cutting edge by a parametric curve. This parametric representation of the cutting edge can be easily appllied to perform derivation and integration along the edge to find the chip load area and the total engagement length. The interpolated B-spline cutting edge of degree p can be expressed as below [17-19]: (4) Where is interpolating B-Spline curve of degree p, is control points which control the geometry of curve and is B-spline Basis functions which can be computed by: (5) In equation (5), is a B-spline knot which belongs to the knot vector of . The equation (4) has unknown control points. For this reason, it is necessary to have a parameter like to relate the control points to the data points. Since parameter corresponds to data point , plugging into the above equation yields the following [19]: (6) There are n+1 B-spline basis functions and parameters in equation (6). Substituting t in to , these values can be organized in a matrix N as shown as below: (7) Data points and control points can be expressed in similar way: (8) And (9) In equation (9) matrix D is input data points which are represents the points along the cutting edge and matrix N can be obtained by evaluating B-spline basis functions at the given parameters [19]. D and N both are known and the only unknown parameter is matrix P. Equation (9) is a system of linear equations with unknown P, solving for P yields the control points and the desired B-spline interpolation curve becomes available. Figure (6) shows control points and desired interpolated broaching cutting edge using B-spline curves. Figure 6: B-spline interpolation of cutting edge 5. Calculation of chip load and contact length In orthogonal broaching, all of the cutting edges are parallel together and perpendicular to the cutter axis therefore the third column of matrixes and in equation (8) are zero and only two parameters of and in equation (4) is needed to represent the cutting edge. Figures (7a) and (7b) depicts a typical Cartesian coordinates in orthogonal and oblique broaching. (a) Orthogonal broaching (b) Oblique broaching Figure 7: Cartesian coordinates In contrast with orthogonal broaching in which all teeth are perpendicular to the cutter axis, in oblique broaching cutting edges have an oblique angle with cutter axis but they are still parallel to each other. In this case , , and all of the coordinates in the third column of matrixes and are non zero. B-spline interpolation of 3D curves is possible but little bit time consuming so it is preferable to transform the 3D to 2D and use the same method for 3D after transformation. Coordinates of point in Cartesian coordinates can be expressed by in plane as follows: (10) The above transformation can be done for all of cutting edge data points and in the new coordinate system matrixes is as follows: (11) Once matrix presented in new coordinate system the interpolation process can be done the same as previous method for 2D curves. As soon as the cutting edge is presented by B-Spline curves, chip area and cutting length for each cutting edge can be calculated directly from B-Spline equations as follows [13]: (12) Where indicate start of the cut, end of the cut, current cutting edge and previous cutting edge respectively. Equation (12) has two coordinate parameters and it is applicable for calculation of chip load and contact length for orthogonal and oblique broaching. 6. Cutting forces simulation In order to compare the presented geometric model with a real case, a broach cutter was selected and its cutting edges were modeled using B-Spline curves. The geometry of cutter was chosen based on previously presented research by Kokturk [12] to validate the newly proposed model capability. Figure (8) demonstrates the cutter geometry. Figure 8: Cutter geometry The geometrical features of cutting edge can be found in table (1) [12]. Table 1: Geometry of broaching cutter [12] In the next step, selected cutting edges were interpolated using proposed approach. Similar to other interpolation methods, B-Spline interpolation is sensitive to the number of data points. Increasing the number of data points yields a better accuracy but it makes the running time of the algorithm longer. Decreasing the number of data points, accelerate the algorithm but it has a negative effect on the accuracy. It has been shown that smooth parts of the curve are not very sensitive to the number of data points because inaccuracy occurs in the sharp corners where the curve direction changes suddenly. As a result, it would be better to use more data points at the sharp corners and less data point at the other parts to increase the accuracy and time efficiency of the algorithm simultaneously. Figures (9a) and (9b) show the B-Spline presentation of two successive cutting edges. (a) B-spline representation of the first cutting edge (b) B-spline representation of the second cutting edge Figure 9: B-spline representation of two successive cutting edges It can be seen from the above figures that B-Spline curve follows the data point at the sharp corner with high accuracy. 7. Results and discussion Figure (10) shows the final geometry of workpiece. Cutting conditions and force coefficients which are used in simulation can be found in table (2). Figure 10: Final workpiece geometry Table 2: Cutting conditions [12] 5 Since the cutting edge without oblique angle doesnà ¢Ã¢â€š ¬Ã¢â€ž ¢t have radial component of cutting force it was assumed that for this special case. The edge coefficients of cutting force are always very small in comparison to cutting coefficients so it has been assumed that , and are negligible. Figure 11: Simulated and experimental cutting forces for orthogonal broaching Figure 12: Simulated and experimental resultant force for orthogonal broaching Figure 13: Simulated and experimental cutting forces for oblique broaching Figure 14: Simulated and experimental resultant force for oblique broaching It can be seen from figures (11) to (14) that the results of newly proposed model are in good agreement with the previously published results [12]. Since there is no oblique angle in orthogonal broaching the cutting edge engaged with workpiece suddenly with full length so there is a jump in force diagram when each tooth engaged with workpiece. Due to presence of oblique angle in oblique broaching the tooth engaged with workpiece smoothly so the cutting forces rise gradually from zero to its final value. Also, in oblique broaching, fluctuation of cutting forces in the steady state part of the cutting is less than orthogonal one because when one of the teeth leaving the workpiece another one engages smoothly but the average force is higher because of longer contact length. 8. Conclusion In this paper, a force model is developed to simulate the cutting forces in orthogonal and oblique broaching using B-spline representation of the cutting edge. The new model can interpolate broaching tool cutting edge without any limitations which offer the simulation of cutting forces for any desired input geometry. In order to validate the new force model, the predicted cutting forces are compared to previously measured data [12]. The comparison showed a good agreement in both measured and predicted data for orthogonal and oblique broaching. The simulated cutting forces can be used to have a better understanding of process and optimize the geometric features of broaching cutter to achieve more efficient cutting which is under investigation of authors. Acknowledgment The authors acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) for their support to the project.