Machining vibrationsIn machining, vibrations, also called chatter, are the relative movements between the workpiece and the cutting tool. The vibrations result in waves on the machined surface. This affects typical machining processes, such as turning, milling and drilling, and atypical machining processes, such as grinding. A chatter mark is an irregular surface flaw left by a wheel that is out of true (off-center) in grinding, or regular marks left when turning a long piece on a lathe, due to machining vibrations.
Cauchy distributionThe Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.
ToolA tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates back hundreds of millennia, have been observed using tools to make other tools. Early human tools, made of such materials as stone, bone, and wood, were used for the preparation of food, hunting, the manufacture of weapons, and the working of materials to produce clothing and useful artifacts and crafts such as pottery, along with the construction of housing, businesses, infrastructure, and transportation.
Chemical engineeringChemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials into useful products. Chemical engineering uses principles of chemistry, physics, mathematics, biology, and economics to efficiently use, produce, design, transport and transform energy and materials.
Carbon-fiber-reinforced polymersCarbon fiber-reinforced polymers (American English), carbon-fiber-reinforced polymers (Commonwealth English), carbon-fiber-reinforced plastics, carbon-fiber reinforced-thermoplastic (CFRP, CRP, CFRTP), also known as carbon fiber, carbon composite, or just carbon, are extremely strong and light fiber-reinforced plastics that contain carbon fibers. CFRPs can be expensive to produce, but are commonly used wherever high strength-to-weight ratio and stiffness (rigidity) are required, such as aerospace, superstructures of ships, automotive, civil engineering, sports equipment, and an increasing number of consumer and technical applications.
Manufacturing resource planningManufacturing resource planning (MRP II) is a method for the effective planning of all resources of a manufacturing company. Ideally, it addresses operational planning in units, financial planning, and has a simulation capability to answer "what-if" questions and is an extension of closed-loop MRP (Material Requirements Planning). This is not exclusively a software function, but the management of people skills, requiring a dedication to database accuracy, and sufficient computer resources.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
EngineeringEngineering is the practice of using natural science, mathematics, and the engineering design process to solve problems, increase efficiency and productivity, and improve systems. Modern engineering comprises many subfields which include designing and creating infrastructure, machinery, vehicles, electronics, materials, and energy. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application.
Oxy-fuel welding and cuttingOxy-fuel welding (commonly called oxyacetylene welding, oxy welding, or gas welding in the United States) and oxy-fuel cutting are processes that use fuel gases (or liquid fuels such as gasoline or petrol, diesel, bio diesel, kerosene, etc) and oxygen to weld or cut metals. French engineers Edmond Fouché and Charles Picard became the first to develop oxygen-acetylene welding in 1903. Pure oxygen, instead of air, is used to increase the flame temperature to allow localised melting of the workpiece material (e.
Abelian varietyIn mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field.
