Machine tools have played a fundamental role in the technological development of the world to the point that it is not an exaggeration to say that the rate of machine tool development directly governs the rate of industrial development.
Thanks to the use of the machine tool, it has been possible to carry out in a practical way, machinery of all kinds that, although conceived and realized, could not be commercialized due to the lack of adequate means for its industrial construction.
Thus, for example, if for the total mechanization of a number of pieces it were necessary to carry out the operations of milling, boring and drilling, it is logical that the greatest efficiency would be achieved if this group of machine tools were grouped, but a greater efficiency would be achieved even if all these operations will be carried out on the same machine. This need, added to numerous and new requirements that appeared day by day forced the use of new techniques that will replace the human operator. In this way, numerical control was introduced in manufacturing processes, imposed for several reasons:
Need to manufacture products that could not be obtained in sufficient quantity and quality without resorting to automation of the manufacturing process. Need to obtain products that were previously impossible or very difficult to manufacture, as they are excessively complex to be controlled by a human operator. Need to manufacture products at low enough prices.
Initially, the predominant factor that conditioned all automation was the increase in productivity. Later, due to the new needs of the industry, other no less important factors appeared, such as precision, speed and flexibility.
Around 1942, what could be called the first true numerical control emerged, due to a necessity imposed by the aeronautical industry for the realization of helicopter propellers of different configurations.
INTRODUCTION TO CAD / CAM
CAD / CAM, a process in which computers are used to improve the manufacturing, development and design of products. These can be manufactured faster, more accurately or at a lower price, with the proper application of computer technology.
Computer Aided Design (CAD) systems can be used to generate models with many, if not all, of the characteristics of a given product. These characteristics could be the size, contour and shape of each component, stored as two and three-dimensional drawings. Once these dimensional data have been entered and stored in the computer system, the designer can more easily manipulate or modify the design ideas to advance product development. In addition, the combined ideas of various designers can be shared and integrated, as data can be moved within computer networks, allowing designers and engineers located at distant locations to work as a team.CAD systems also allow simulating the operation of a product. They make it possible to verify whether a proposed electronic circuit will function as intended, whether a bridge will be able to support predicted loads safely, and even whether a tomato sauce will flow properly from a newly designed container.
When CAD systems are connected to also computer-controlled manufacturing equipment, they form an integrated CAD / CAM system (CAM, short for Computer Aided Manufacturing).
Computer Aided Manufacturing offers significant advantages over the more traditional methods of controlling manufacturing equipment with computers rather than with human operators. CAM equipment typically involves eliminating operator errors and reducing labor costs. However, the constant precision and optimal use of the equipment represent even greater advantages. For example, blades and cutting tools will wear out more slowly and break down less frequently, further reducing manufacturing costs. Faced with this saving, the higher costs of capital goods or the possible social implications of maintaining productivity with a reduction in the workforce can be argued.CAM equipment is based on a series of numerical codes, stored in computer files, to control manufacturing tasks. This Computer Numerical Control (CNC) is obtained by describing the operations of the machine in terms of the special codes and the geometry of the shapes of the components, creating specialized computer files or part programs. Creating these parts programs is a task that is largely done today by special computer software that creates the link between CAD and CAM systems.creating specialized computer files or part programs. Creating these parts programs is a task that is largely done today by special computer software that creates the link between CAD and CAM systems.creating specialized computer files or part programs. Creating these parts programs is a task that is largely done today by special computer software that creates the link between CAD and CAM systems.
The characteristics of CAD / CAM systems are used by designers, engineers and manufacturers to adapt them to the specific needs of their situations. For example, a designer can use the system to quickly create a first prototype and analyze the feasibility of a product, while a manufacturer may use the system because it is the only way to accurately manufacture a complex component. The range of features offered to CAD / CAM users is constantly expanding. Garment manufacturers can design the pattern of a garment in a CAD system, a pattern that is automatically placed on the fabric to minimize the waste of material when cut with a saw or a CNC laser. In addition to the CAD information that describes the outline of an engineering component,it is possible to choose the most suitable material for its manufacture in the computer database, and to use a variety of combined CNC machines to produce it. Computer Integrated Manufacturing (CIM) fully exploits the potential of this technology by combining a wide range of computer-aided activities, which may include inventory control, material cost calculation, and full control of each production process. This offers greater flexibility to the manufacturer, allowing the company to respond more quickly to market demands and the development of new products.Computer Integrated Manufacturing (CIM) fully exploits the potential of this technology by combining a wide range of computer-aided activities, which may include inventory control, material cost calculation, and full control of each production process. This offers greater flexibility to the manufacturer, allowing the company to respond more quickly to market demands and the development of new products.Computer Integrated Manufacturing (CIM) fully exploits the potential of this technology by combining a wide range of computer-aided activities, which may include inventory control, material cost calculation, and full control of each production process. This offers greater flexibility to the manufacturer, allowing the company to respond more quickly to market demands and the development of new products.allowing the company to respond more quickly to market demands and the development of new products.allowing the company to respond more quickly to market demands and the development of new products.
Future developments will include even greater integration of virtual reality systems, which will allow designers to interact with virtual prototypes of products using the computer, rather than having to build expensive models or simulators to test their feasibility. The area of rapid prototyping is also an evolution of CAD / CAM techniques, in which three-dimensional computerized images are converted into real models using specialized manufacturing equipment, such as a stereolithography system.
CHIP START MANUFACTURING PROCESSES
The application of numerical control covers a wide variety of processes. Applications are divided into two categories here: (1) machine tool applications, such as drilling, rolling, turning, etc., and (2) machine tool-less applications, such as assembly, plotting, and inspection. The principle of operation common to all numerical control applications is the control of the relative position of a tool or processing element with respect to the object to be processed.
| Process | Process definition | Equipment |
| Turning | It is a machining process in which a single pointed tool removes material from the surface of a rotating cylindrical workpiece | Turning is traditionally carried out on a machine called a lathe |
| Team Definition | Team classification | Tool |
| The lathe is a machine, which supplies the power to turn the part at a determined speed of rotation with advance of the tool and depth of cut specified | Tool lathe
Speed Lathe Revolver Lathe Mandrill Lathe Automatic Bar Machine Numerically controlled lathes |
Single point tools are used, for the threading operation, it is executed with a design with the shape of the rope to be produced. Shape turning is performed with a specially designed shape turning tool. |
| Define Tool | Tool Classification | Turning Related Operations |
| A cutting tool with a single cutting edge is used to remove material from a rotating workpiece to form a cylinder. | Head
Counterpoint Cakes Transverse Carriage Main car |
Facing
Tapered or tapered turning Contour Turning Turning Shapes Chamfered Parting Threaded Drilled Drilled Knurled |
| Process | Process definition | Equipment |
| Boring | It is a machining operation that is used to create round holes in a work part | Drill Press |
| Team Definition | Team classification | Tool |
| The Press Drill is the standard machine for drilling. | Vertical Drill
Bench Drill Drill radial Multiple Drill |
Drill |
| Define Tool | Tool Classification | Drilling Related Operations |
| Various cutting tools are available for drilling holes, but the twist drill is by far the most common. Their diameters fluctuate from 0.006 in. Up to bits as large as 3.0 in. Twist drills are widely used in the industry to produce holes quickly and inexpensively. | Twist Drill | Reaming
Internal Threading Flared Countersunk Centered Facing |
| Process | Process definition | Equipment |
| Brushed | Process to produce flat surfaces by means of a single-edge cutting tool. | Brush |
| Team Definition | Team classification | Tool |
| The brushing machine tool is called a brush. Cutting speed is achieved through one month of oscillating work that moves the back of a single point cutting tool | Side-open table brushes
Double Column Brushes |
The cutting tool used in planing are single point tools |
| Define Tool | Tool Classification | Brushing Related Operations |
| Process in which a blade is passed through the part to eliminate material. | Cross rail
Tool head Work table Column Base |
Brushing can be used to machine surfaces other than flat. The restriction is that the surfaces must be straight. |
| Process | Process definition | Equipment |
| Sawing | It is a process in which you cut a narrow gap within the working part by means of a tool that has a series of closely spaced teeth | Mowing |
| Team Definition | Team classification | Tool |
| The saw cut involves a reciprocating linear movement of the saw against the work. Band Sawing involves a continuous linear movement using a saw blade made of a flexible endless band with teeth on one of its edges. The circular saw uses a rotating circular saw to provide continuous tool movement in front of the job. | Mowing
Sierra Banda Circular saw |
Sierra leaf |
| Define Tool | Tool Classification | Operations Related to Sawing |
| Saw blades have certain common characteristics including the shape of the teeth, their spacing and their arrangement | Tooth shape
Spacing between teeth Teeth Arrangement |
Openwork
Grooved Abrasive cut Friction Sawing |
| Process | Process definition | Equipment |
| Rectified | It is an abrasive process executed by a set of bonded abrasive bars | Grinding machine |
| Team Definition | Team classification | Tool |
| The movement of the equipment is a combination of rotation and linear oscillation, regulated in such a way that a given point on the abrasive bar does not repeat the same path | Set of bonded abrasive bars | |
| Define Tool | Tool Classification | Operations Related to Grinding |
| Four bars are used, but their number depends on the size of the hole | Universal Joints
Driving |
Lapping or polishing
Superfinish Polished Polished |
| Process | Process definition | Equipment |
| Milling | It is a machining operation in which a working part is passed in front of a rotary cylindrical tool with multiple cutting edges or edges. | Milling machine |
| Team Definition | Team classification | Tool |
| The classification of cutters for milling machines or milling cutters as they are commonly known, is closely associated with the milling operations just described. | Cylindrical cutters or flat milling cutters
Forming cutters or forming cutters Face cutters or face cutters Finishing cutters or end mill |
Rotary spindle
Table to hold |
| Define Tool | Tool Classification | Milling Related Operations |
| Milling machines must have a rotary spindle for the cutter and a table to clamp, position and advance the work part. | Vertical milling machine
Horizontal milling machine Knee and column Bed type Brush type Plotters CNC milling machines |
Turning
Boring Profiling Brushed Reaming Sawing |
INTRODUCTION TO COMPUTERIZED NUMERICAL CONTROL
The CNC originated in the early 1950s at the Massachusetts Institute of Technology (MIT), where a large milling machine was first automated.
At this time computers were in their infancy and were so large that the space occupied by the computer was greater than that of the machine.
Nowadays computers are becoming smaller and cheaper, with which the use of the CNC has been extended to all types of machinery: lathes, grinding machines, electric erosion machines, sewing machines, etc.
CNC stands for "Computer Numerical Control."
In a CNC machine, unlike a conventional or manual machine, a computer controls the position and speed of the motors that drive the axes of the machine. Thanks to this, you can make movements that cannot be achieved manually like circles, diagonal lines and complex three-dimensional figures.
CNC machines are capable of moving the tool at the same time on all three axes to execute three-dimensional trajectories such as those required for machining complex molds and dies as shown in the image.
In a CNC machine a computer controls the movement of the table, the carriage and the spindle. Once the machine has been programmed, it performs all the operations by itself, without the need for the operator to operate it. This allows for better use of staff time to be more productive.
The term "numerical control" is because the orders given to the machine are indicated by numerical codes. For example, to instruct the machine to move the tool describing a 10 mm square per side, the following codes would be given:
G90 G71
G00 X0.0 Y0.0
G01 X10.0
G01 Y10.0
G01 X0.0
G01 Y0.0
A set of commands that follow a logical sequence constitutes a machining program. By giving the appropriate orders or instructions to the machine, it is capable of machining a simple groove, an irregular cavity, the face of a person in high or low relief, an artistic engraving, an injection mold of a spoon or a bottle… want.
At the beginning, making a machining program was very difficult and tedious, since it was necessary to plan and manually indicate to the machine each of the movements it had to make. It was a process that could take hours, days, weeks. Still it was a time saver compared to conventional methods.
Currently many of the modern machines work with what is known as "conversational language" in which the programmer chooses the operation he wants and the machine asks him what data is required. Each instruction in this conversational language can represent dozens of numeric codes. For example, machining an entire cavity can be done with a single instruction specifying length, height, depth, position, corner radii, etc. Some controls even have on-screen graphics and gerometric help functions. All this makes programming much faster and easier.
CAD / CAM systems that automatically generate the machining program are also used. In CAD (Computer Aided Design) the part to be machined is designed on the computer with drawing tools and solid modeling. Subsequently, the CAM system (computer-aided manufacturing) takes the design information and generates the cutting path that the tool must follow to manufacture the desired part; From this cutting path, the machining program is automatically created, which can be entered into the machine by means of a disk or sent electronically.
Today, CNC equipment with the help of conversational languages and CAD / CAM systems allow companies to produce much faster and with greater quality without the need for highly specialized personnel.
NUMERICAL CONTROL IN INDUSTRIAL ENGINEERING
General definition:
Numerical control is considered to be any device capable of directing positions of a mobile mechanical organ, in which the orders related to the movements of the mobile are drawn up fully automatically from defined numerical information, either manually or by means of a program.
SCOPE OF NUMERICAL CONTROL:
As already mentioned, the four fundamental variables that affect the goodness of an automation are: productivity, speed, precision and speed.
According to these variables, we are going to analyze which type of automation is the most convenient according to the number of parts to be manufactured. Manufacturing series:
Large series: (greater than 10,000 pieces)
This production is currently covered by the transfer machines, carried out by several automatisms working simultaneously in synchronization. Average series: (between 50 and 10,000)
There are several automatisms that cover this range, including copiers and numerical controls. The use of these automatisms will depend on the precision, flexibility and speed required. The numerical control will be especially interesting when the fabrications are kept in series comprised between 5 and 1,000 pieces that must be repeated several times during the year. Small series: (less than 5 pieces) For these series, the use of the numerical control is usually not profitable, unless the piece is complex enough to justify its programming with the help of a computer. But in general, for productions of less than five pieces, machining on conventional machines turns out to be more economical. Next, we can see a graph that clearly illustrates what was previously expressed.
ADVANTAGES OF NUMERICAL CONTROL:
The advantages, within the production parameters explained above are:
Possibility of manufacturing impossible or very difficult parts. Thanks to the numerical control, very complicated parts have been obtained, such as the three-dimensional surfaces necessary in the manufacture of aircraft.
Security. Numerical control is especially recommended for working with dangerous products.
Precision. This is due to the greater precision of the numerical control machine tool compared to the classic ones.
Increased machine productivity. This is due to the decrease in the total machining time, due to the decrease in the empty travel times and the speed of the positioning provided by the electronic control systems.
Reduction of controls and waste. This reduction is mainly due to the high reliability and repeatability of a numerically controlled machine tool. This reduction of controls practically eliminates all subsequent human operations, with the subsequent reduction in costs and manufacturing times.
CLASSIFICATION OF NUMERICAL CONTROL SYSTEMS.
They are mainly divided into:
Numerical control equipment for positioning or point to point.
Numerical control equipment of contouring.
Let us suppose a piece placed on the table (see figure), and that at point A you want to drill. Let the X axis be the longitudinal axis of the table and the Y axis be the transverse axis. B represents the projection of the tool axis on the table. The problem of bringing point A to point B can be solved in the following ways:
Actuate the Y axis motor until reaching point A´ and then the X axis motor until reaching point B.
Analogous to the previous one, but first driving the longitudinal axis motor and then the transversal axis motor. These two positioning modes are called sequential positioning and are normally performed at the maximum speed supported by the machine.
Actuate both motors at the same time and at the same speed. In this case, the path followed will be a 45º straight line. Once the height of point B has been reached, the Y axis motor will be stopped to continue exclusively the X axis motor until reaching point B. This type of positioning is called simultaneous positioning (point to point).
Sequential actuation of the motors but always approaching a point in the same direction. This type of approach is called a unidirectional approach and is used exclusively in point-to-point positions.
In a point-to-point system, the control determines, from the information provided by the program and before starting the movement, the total path to travel. Subsequently, such positioning is carried out, regardless of the path traveled, since the only thing that matters is reaching the point in question accurately and quickly.
Whenever you want to make trajectories that are not paraxial (straight along the axes) it is necessary that the control system has special characteristics.
The equipments that allow curves to be generated are called contour equipments.
The systems of contouring govern not only the final position but also the movement at each moment of the axes in which the interpolation is carried out. In these equipment there must be a perfect synchronization between the different axes, therefore controlling the actual path that the tool must follow. With these systems, routes such as lines with any slope, arcs of circumference, conics or any other mathematically definable curve can be generated. These systems are used, above all, in complex milling, turning, etc.
Lastly, it can be said that a paraxial numerical control equipment can carry out the work carried out by a point-to-point equipment and a contouring equipment can carry out the work carried out by the point-to-point and paraxial equipment.
GENERAL ARCHITECTURE OF A NUMERICAL CONTROL.
We can distinguish four functional subsets:
Data input - output unit.
Internal memory unit and interpretation of orders.
Calculation unit.
Link unit with the machine tool and servomechanisms.
A simplified functional diagram of a three axis contour numerical control is shown in the figure on the next page.
INPUT UNIT - DATA OUTPUT
The data entry unit is used to enter the machining programs in the numerical control equipment, using an intelligible language for it.
In older systems, tab-type systems (Data Modul) or preselectors (coded rotary switches) were used for data entry; the great disadvantages that these methods presented, especially in extensive programs, caused their total elimination.
Subsequently, the perforated tape (paper, milar or aluminum) was used for this purpose, so the tape reader became the main data entry device.
This tape was previously punctured using a tape puncher or a teletypewriter. The maximum number of holes for each character was eight (eight channel tape). In addition to these holes, there was another one of a smaller size, located between channels 3 and 4 that allowed the belt to drag.
The first tape readers were electromechanical; which used a system of probing needles that determined the existence of holes or not in each channel of the tape, then this acted on a switch whose contacts open or close depending on the existence or not of said holes.
Then photoelectric tape readers were used, which allowed a much higher tape reading speed. They consisted of photoelectric cells, photodiodes or phototransistors as sensor elements. These light sensitive elements, located under each channel of the belt (even under the channel of the drag). A light source was placed on the tape, in such a way that each sensor produced a signal indicating the presence of a hole that would be amplified and supplied to the control equipment as input data.
Another medium that was used for data entry was the cassette, robust and small, it was easier to use, save and transport than tape, being optimal for use in hostile media. Its capacity varied between 1 and 5 Mb.
Then the floppy disk began to be used. Its most important feature was that of having random access, which allowed access to any part of the disk in less than half a second. The data transfer rate varied between 250 and 500 Kb / s.
With the appearance of the keyboard as an organ of data entry, the problem of modifying the program, which could not be done with the perforated tape, was solved, in addition to a fast editing of programs and a comfortable insertion and deletion of blocks, searching for a address in memory, etc.
INTERNAL MEMORY UNIT AND INTERPRETATION OF ORDERS.
In both manual programming and mixed programming equipment (tape or cassette and keyboard), the internal memory unit stored not only the program but also the machine data and the compensations (acceleration and deceleration, compensations and corrections of the tool, etc.). These are the so-called commissioning data.
On machines that only had perforated tape as data input, buffer memories were used.
Then, with the emergence of the keyboard and the need to significantly expand memory (because a complete machining program had to be stored in it), non-volatile memories began to be used (their information remains stored even if the power source of the circuit, for example in the case of a network failure) of random access (called RAM) of the CMOS type.
They also had a battery called a buffer, generally nickel-cadmium, which fulfilled the function of storing for a few days (at least three) all machine data in the event of a network failure.
Once the program is stored in memory, it starts reading for later execution.
The blocks are read sequentially. They contain all the information necessary for the execution of a machining operation.
CALCULATION UNIT: Once an information block has been interpreted, this unit is in charge of creating the set of commands that will be used to govern the machine tool.
As already stated, this information block supplies the information necessary for the execution of a machining operation. Therefore, once the program is in memory, it starts executing. The control reads a number of blocks necessary to carry out a duty cycle. These program blocks are interpreted by the control, which identifies:
the new height to be reached (x, y, z of the new point in the case of a three-axis equipment), forward speed with which the route will be made, how to make the route, other information such as tool compensation, change useful, rotation or not thereof, direction, cooling, etc.). The calculation unit, according to the new level to be reached, calculates the way to go along the various axes.
SERVOMECHANISMS: The main function of a numerical control is to control the motors (servomotors) of a machine tool, which cause a relative displacement between the tool and the part on the table. If we consider a displacement in the plane, it will be necessary to drive two motors, in space, three motors, and so on.
In the case of a point-to-point and paraxial numerical control, the orders supplied to each of the motors have no relation to each other; instead in a numerical control of contouring, the orders must be related according to a well defined law.
Two types of servo mechanisms can be used to control the machine tool motors, open-loop and closed-loop.
In open-loop machines, orders to the motors are sent from the information supplied by the calculation unit, and the servo mechanism does not receive any information about the actual position of the tool or its speed.
Not so in a closed-loop system, where the orders supplied to the motors depend both on the information sent by the calculation unit and on the information supplied by a system for measuring the actual position by means of a position sensor. (generally an encoder), and an actual speed measurement (tachometer), both mounted on the machine.
PROGRAMMING IN THE NUMERICAL CONTROL:
Two methods can be used: Manual Programming:
In this case, the part-program is written only by means of reasoning and calculations carried out by an operator.
Automatic Programming: In this case, the calculations are carried out by a computer, which supplies the part program in machine language at its output. For this reason it is called computer-assisted programming. We will talk about this method later.
Manual programming:
The machine language includes all the data set that the control needs for the machining of the part.
The set of information that corresponds to the same phase of machining is called a block or sequence, which are numbered to facilitate its search. This set of information is interpreted by the shell.
The machining program contains all the instructions necessary for the machining process.
A sequence or program block must contain all the geometric functions, machine functions and technological functions of the machining, in such a way, a program block consists of several instructions.
The beginning of numerical control has been characterized by an anarchic development of programming codes. Each builder used his own.
Subsequently, the need to standardize the programming codes was seen as an indispensable condition so that the same program could be used for different machines as long as they were of the same type.
The most commonly used characters, governed by DIN 66024 and 66025 are, among others, the following:
N is the address corresponding to the block or sequence number. This address is usually followed by a three or four digit number. In the case of the N03 format, the maximum number of blocks that can be programmed is 1000 (N000 N999).
X, Y, Z are the directions corresponding to the dimensions along the X, Y, Z axes of the machine tool. These dimensions can be programmed in an absolute or relative way, that is, with respect to the zero part or with respect to the last dimension respectively.
G is the address corresponding to the preparatory functions. They are used to inform the control of the characteristics of the machining functions, such as the shape of the trajectory, type of tool correction, timed stop, automatic cycles, absolute and relative programming, etc. Function G is followed by a two-digit number that allows you to program up to 100 different preparatory functions.
Examples:
G00: The programmed route is carried out at the maximum possible speed, that is, at the rapid traverse speed.
G01: The axes are governed in such a way that the tool moves along a straight line.
G02: Linear interpolation clockwise.
G03: Linear interpolation counterclockwise.
G33: Indicates automatic threading cycle.
G77: It is an automatic cycle that allows turning a cylinder, etc., with a single block.
M is the address corresponding to the auxiliary or complementary functions. They are used to indicate to the machine tool that operations must be carried out such as: programmed stop, spindle rotation clockwise or counterclockwise, tool change, etc. Address m is followed by a two-digit number that allows you to program up to 100 different auxiliary functions.
Examples:
M00: Causes unconditional program stop, stops spindle and cooling.
M02: Indicates the end of the program. It must be written in the last block of the program and makes it possible to stop the control once the rest of the operations contained in the same block have been executed.
M03: It allows to program the rotation of the spindle clockwise.
M04: Allows programming the spindle rotation counterclockwise, etc.
F is the direction corresponding to the forward speed. It is followed by a four-digit number indicating the feed rate in mm / min.
S is the direction corresponding to the rotation speed of the main spindle. It is programmed directly in revolutions per minute, using four digits.
I, J, K are addresses used to program arcs of circumference. When interpolation is performed in the XY plane, the I and J directions are used. Similarly, in the XZ plane, the I and K directions are used, and in the YZ plane, the J and K directions.
T is the address corresponding to the tool number. It is followed by a four-digit number in which the first two indicate the tool number and the last two indicate the correction number.
THE FAMOUS BLOCKS IN CN
Block structure
It is the way of giving orders to the machine so that they are executed it has certain characteristics that must be fulfilled.
The machine executes the orders (operations) in a different way, so each order has a defined structure; each order is called a block or program block.
In general, each block has the following structure:
- a) Number of operations b) Configuration order code c) Coordinate points or coordinates d) Complementary parameters
Block format
The basic way of communicating with the machine tool is through the elements that form the structure of an instruction block, where each of the alphanumeric characters has its own meaning and representation.
Original text
| to | b | c | d | ||
| O001 | |||||
| N010 | G21 | Header | |||
| N020 |
DATA ABOUT THE AUTHOR: industrial engineering UPIICSA - IPN e-mail: [email protected] Note: If you want to add a comment or if you have any doubts or complaints about any work (s) published in monographs.com , you can write me to the emails indicated, indicating which work you reviewed by writing the title of the job (s), also where you are from since you are dedicated (if you study or work) Being specific, also the age, if you do not indicate them in the email, I will delete the email and I will not be able to help you , thank you. High School Studies: Atoyac School Center (Incorporated at UNAM) University Studies: Interdisciplinary Professional Unit of Engineering and Social and Administrative Sciences (UPIICSA) of the National Polytechnic Institute (IPN) www.upiicsa.ipn.mx Hometown: Mexico. Download the original file
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