FEA

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Finite element method From Wikipedia, the free encyclopedia   (Redirected from Finite element analysis) Jump to: navigation, search 2D FEM solution for a magnetostatic configuration (lines denote the direction and colour the magnitude of calculated flux density) 2D mesh for the image above (mesh is denser around the object of interest)  The finite element method (FEM) (its practical application often known as finite element analysis (FEA)) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler's method, Runge-Kutta, etc.  In solving partial differential equations, the primary challenge is to create an equation that approximates the equation to be studied, but is numerically stable, meaning that errors in the input and intermediate calculations do not accumulate and cause the resulting output to be meaningless. There are many ways of doing this, all with advantages and disadvantages. The Finite Element Method is a good choice for solving partial differential equations over complicated domains (like cars and oil pipelines), when the domain changes (as during a solid state reaction with a moving boundary), when the desired precision varies over the entire domain, or when the solution lacks smoothness. For instance, in a frontal crash simulation it is possible to increase prediction accuracy in "important" areas like the front of the car and reduce it in its rear (thus reducing cost of the simulation); another example would be the simulation of the weather pattern on Earth, where it is more important to have accurate predictions over land than over the wide-open sea.

History

The finite element method originated from the need for solving complex elasticity and structural analysis problems in civil and aeronautical engineering. Its development can be traced back to the work by Alexander Hrennikoff (1941) and Richard Courant (1942). While the approaches used by these pioneers are different, they share one essential characteristic: mesh discretization of a continuous domain into a set of discrete sub-domains, usually called elements. Starting in 1947, Olgierd Zienkiewicz from Imperial College gathered those methods together into what would be called the Finite Element Method, building the pioneering mathematical formalism of the method.
Hrennikoff's work discretizes the domain by using a lattice analogy, while Courant's approach divides the domain into finite triangular subregions to solve second order elliptic partial differential equations (PDEs) that arise from the problem of torsion of a cylinder. Courant's contribution was evolutionary, drawing on a large body of earlier results for PDEs developed by Rayleigh, Ritz, and Galerkin.
Development of the finite element method began in earnest in the middle to late 1950s for airframe and structural analysis and gathered momentum at the University of Stuttgart through the work of John Argyris and at Berkeley through the work of Ray W. Clough in the 1960s for use in civil engineering. By late 1950s, the key concepts of stiffness matrix and element assembly existed essentially in the form used today. NASA issued a request for proposals for the development of the finite element software NASTRAN in 1965. The method was again provided with a rigorous mathematical foundation in 1973 with the publication of Strang and Fix's An Analysis of The Finite Element Method, and has since been generalized into a branch of applied mathematics for numerical modeling of physical systems in a wide variety of engineering disciplines, e.g., electromagnetism, thanks to Peter P. Silvester and fluid dynamics.

Application


Visualization of how a car deforms in an asymmetrical crash using finite element analysis.
A variety of specializations under the umbrella of the mechanical engineering discipline (such as aeronautical, biomechanical, and automotive industries) commonly use integrated FEM in design and development of their products. Several modern FEM packages include specific components such as thermal, electromagnetic, fluid, and structural working environments. In a structural simulation, FEM helps tremendously in producing stiffness and strength visualizations and also in minimizing weight, materials, and costs.
FEM allows detailed visualization of where structures bend or twist, and indicates the distribution of stresses and displacements. FEM software provides a wide range of simulation options for controlling the complexity of both modeling and analysis of a system. Similarly, the desired level of accuracy required and associated computational time requirements can be managed simultaneously to address most engineering applications. FEM allows entire designs to be constructed, refined, and optimized before the design is manufactured.
This powerful design tool has significantly improved both the standard of engineering designs and the methodology of the design process in many industrial applications. The introduction of FEM has substantially decreased the time to take products from concept to the production line. It is primarily through improved initial prototype designs using FEM that testing and development have been accelerated. In summary, benefits of FEM include increased accuracy, enhanced design and better insight into critical design parameters, virtual prototyping, fewer hardware prototypes, a faster and less expensive design cycle, increased productivity, and increased revenue

Technical discussion

We will illustrate the finite element method using two sample problems from which the general method can be extrapolated. It is assumed that the reader is familiar with calculus and linear algebra.
P1 is a one-dimensional problem
\mbox{ P1 }:\begin{cases} u''(x)=f(x) \mbox{ in } (0,1), \\ u(0)=u(1)=0, \end{cases}
where f is given, u is an unknown function of x, and u'' is the second derivative of u with respect to x.
The two-dimensional sample problem is the Dirichlet problem
\mbox{P2 }:\begin{cases} u_{xx}(x,y)+u_{yy}(x,y)=f(x,y) & \mbox{ in } \Omega, \\ u=0 & \mbox{ on } \partial \Omega, \end{cases}
where Ω is a connected open region in the (x,y) plane whose boundary \partial \Omega is "nice" (e.g., a smooth manifold or a polygon), and uxx and uyy denote the second derivatives with respect to x and y, respectively.
The problem P1 can be solved "directly" by computing antiderivatives. However, this method of solving the boundary value problem works only when there is only one spatial dimension and does not generalize to higher-dimensional problems or to problems like u + u'' = f. For this reason, we will develop the finite element method for P1 and outline its generalization to P2.
Our explanation will proceed in two steps, which mirror two essential steps one must take to solve a boundary value problem (BVP) using the FEM.
  • In the first step, one rephrases the original BVP in its weak, or variational form. Little to no computation is usually required for this step. The transformation is done by hand on paper.
  • The second step is the discretization, where the weak form is discretized in a finite dimensional space.
After this second step, we have concrete formulae for a large but finite dimensional linear problem whose solution will approximately solve the original BVP. This finite dimensional problem is then implemented on a computer.

Variational formulation

The first step is to convert P1 and P2 into their variational equivalents, or Weak formulation. If u solves P1, then for any smooth function v that satisfies the displacement boundary conditions, i.e. v = 0 at x = 0 and x = 1,we have
(1) \int_0^1 f(x)v(x) \, dx = \int_0^1 u''(x)v(x) \, dx.
Conversely, if u with u(0) = u(1) = 0 satisfies (1) for every smooth function v(x) then one may show that this u will solve P1. The proof is easier for twice continuously differentiable u (mean value theorem), but may be proved in a distributional sense as well.
By using integration by parts on the right-hand-side of (1), we obtain
(2)\begin{align} \int_0^1 f(x)v(x) \, dx & = \int_0^1 u''(x)v(x) \, dx \\ & = u'(x)v(x)|_0^1-\int_0^1 u'(x)v'(x) \, dx \\ & = -\int_0^1 u'(x)v'(x) \, dx = -\phi (u,v). \end{align}
where we have used the assumption that v(0) = v(1) = 0.

 A proof outline of existence and uniqueness of the solution

We can loosely think of H_0^1(0,1) to be the absolutely continuous functions of (0,1) that are 0 at x = 0 and x = 1 (see Sobolev spaces). Such function are (weakly) "once differentiable" and it turns out that the symmetric bilinear map \!\,\phi then defines an inner product which turns H_0^1(0,1) into a Hilbert space (a detailed proof is nontrivial.) On the other hand, the left-hand-side \int_0^1 f(x)v(x)dx is also an inner product, this time on the Lp space L2(0,1). An application of the Riesz representation theorem for Hilbert spaces shows that there is a unique u solving (2) and therefore P1. This solution is a-priori only a member of H_0^1(0,1), but using elliptic regularity, will be smooth if f is.

The variational form of P2

If we integrate by parts using a form of Green's identities, we see that if u solves P2, then for any v,
\int_{\Omega} fv\,ds = -\int_{\Omega} \nabla u \cdot \nabla v \, ds = -\phi(u,v),
where \nabla denotes the gradient and \cdot denotes the dot product in the two-dimensional plane. Once more \,\!\phi can be turned into an inner product on a suitable space H_0^1(\Omega) of "once differentiable" functions of Ω that are zero on \partial \Omega. We have also assumed that v \in H_0^1(\Omega) (see Sobolev spaces). Existence and uniqueness of the solution can also be shown.

 Discretization


A function in H10, with zero values at the endpoints (blue), and a piecewise linear approximation (red).
The basic idea is to replace the infinite dimensional linear problem:
Find u \in H_0^1 such that
\forall v \in H_0^1, \; -\phi(u,v)=\int fv
with a finite dimensional version:
(3) Find u \in V such that
\forall v \in V, \; -\phi(u,v)=\int fv
where V is a finite dimensional subspace of H_0^1. There are many possible choices for V (one possibility leads to the spectral method). However, for the finite element method we take V to be a space of piecewise polynomial functions.
For problem P1, we take the interval (0,1), choose n values of x with 0 = x0 < x1 < ... < xn < xn + 1 = 1 and we define V by
\begin{matrix} V=\{v:[0,1] \rightarrow \Bbb R\;: v\mbox{ is continuous, }v|_{[x_k,x_{k+1}]} \mbox{ is linear for }\\ k=0,...,n \mbox{, and } v(0)=v(1)=0 \} \end{matrix}
where we define x0 = 0 and xn + 1 = 1. Observe that functions in V are not differentiable according to the elementary definition of calculus. Indeed, if v \in V then the derivative is typically not defined at any x = xk, k = 1,...,n. However, the derivative exists at every other value of x and one can use this derivative for the purpose of integration by parts.

A piecewise linear function in two dimensions.
For problem P2, we need V to be a set of functions of Ω. In the figure on the right, we have illustrated a triangulation of a 15 sided polygonal region Ω in the plane (below), and a piecewise linear function (above, in color) of this polygon which is linear on each triangle of the triangulation; the space V would consist of functions that are linear on each triangle of the chosen triangulation.
One often reads Vh instead of V in the literature. The reason is that one hopes that as the underlying triangular grid becomes finer and finer, the solution of the discrete problem (3) will in some sense converge to the solution of the original boundary value problem P2. The triangulation is then indexed by a real valued parameter h > 0 which one takes to be very small. This parameter will be related to the size of the largest or average triangle in the triangulation. As we refine the triangulation, the space of piecewise linear functions V must also change with h, hence the notation Vh. Since we do not perform such an analysis, we will not use this notation.

Choosing a basis


Basis functions vk (blue) and a linear combination of them, which is piecewise linear (red).
To complete the discretization, we must select a basis of V. In the one-dimensional case, for each control point xk we will choose the piecewise linear function vk in V whose value is 1 at xk and zero at every x_j,\;j \neq k, i.e.,
v_{k}(x)=\begin{cases} {x-x_{k-1} \over x_k\,-x_{k-1}} & \mbox{ if } x \in [x_{k-1},x_k], \\ {x_{k+1}\,-x \over x_{k+1}\,-x_k} & \mbox{ if } x \in [x_k,x_{k+1}], \\ 0 & \mbox{ otherwise},\end{cases}
for k = 1,...,n; this basis is a shifted and scaled tent function. For the two-dimensional case, we choose again one basis function vk per vertex xk of the triangulation of the planar region Ω. The function vk is the unique function of V whose value is 1 at xk and zero at every x_j,\;j \neq k.
Depending on the author, the word "element" in "finite element method" refers either to the triangles in the domain, the piecewise linear basis function, or both. So for instance, an author interested in curved domains might replace the triangles with curved primitives, and so might describe the elements as being curvilinear. On the other hand, some authors replace "piecewise linear" by "piecewise quadratic" or even "piecewise polynomial". The author might then say "higher order element" instead of "higher degree polynomial". Finite element method is not restricted to triangles (or tetrahedra in 3-d, or higher order simplexes in multidimensional spaces), but can be defined on quadrilateral subdomains (hexahedra, prisms, or pyramids in 3-d, and so on). Higher order shapes (curvilinear elements) can be defined with polynomial and even non-polynomial shapes (e.g. ellipse or circle).
Examples of methods that use higher degree piecewise polynomial basis functions are the hp-FEM and spectral FEM.
More advanced implementations (adaptive finite element methods) utilize a method to assess the quality of the results (based on error estimation theory) and modify the mesh during the solution aiming to achieve approximate solution within some bounds from the 'exact' solution of the continuum problem. Mesh adaptivity may utilize various techniques, the most popular are:
  • moving nodes (r-adaptivity)
  • refining (and unrefining) elements (h-adaptivity)
  • changing order of base functions (p-adaptivity)
  • combinations of the above (hp-adaptivity)

Small support of the basis


Solving the two-dimensional problem uxx + uyy = − 4 in the disk centered at the origin and radius 1, with zero boundary conditions.
(a) The triangulation.

(b) The sparse matrix L of the discretized linear system.

(c) The computed solution, u(x,y) = 1 − x2 − y2.
The primary advantage of this choice of basis is that the inner products
\langle v_j,v_k \rangle=\int_0^1 v_j v_k\,dx
and
\phi(v_j,v_k)=\int_0^1 v_j' v_k'\,dx
will be zero for almost all j,k. (The matrix containing \langle v_j,v_k \rangle in the (j,k) location is known as the Gramian matrix.) In the one dimensional case, the support of vk is the interval [xk − 1,xk + 1]. Hence, the integrands of \langle v_j,v_k \rangle and φ(vj,vk) are identically zero whenever | j − k | > 1.
Similarly, in the planar case, if xj and xk do not share an edge of the triangulation, then the integrals
\int_{\Omega} v_j v_k\,ds
and
\int_{\Omega} \nabla v_j \cdot \nabla v_k\,ds
are both zero.

Matrix form of the problem

If we write u(x)=\sum_{k=1}^n u_k v_k(x) and f(x)=\sum_{k=1}^n f_k v_k(x) then problem (3) becomes
-\sum_{k=1}^n u_k \phi (v_k,v_j) = \sum_{k=1}^n f_k \int v_k v_j for j = 1,...,n. (4)
If we denote by \mathbf{u} and \mathbf{f} the column vectors (u1,...,un)t and (f1,...,fn)t, and if we let
L = (Lij)
and
M = (Mij)
be matrices whose entries are
Lij = φ(vi,vj)
and
M_{ij}=\int v_i v_j
then we may rephrase (4) as
-L \mathbf{u} = M \mathbf{f}. (5)
As we have discussed before, most of the entries of L and M are zero because the basis functions vk have small support. So we now have to solve a linear system in the unknown \mathbf{u} where most of the entries of the matrix L, which we need to invert, are zero.
Such matrices are known as sparse matrices, and there are efficient solvers for such problems (much more efficient than actually inverting the matrix.) In addition, L is symmetric and positive definite, so a technique such as the conjugate gradient method is favored. For problems that are not too large, sparse LU decompositions and Cholesky decompositions still work well. For instance, Matlab's backslash operator (which uses sparse LU, sparse Cholesky, and other factorization methods) can be sufficient for meshes with a hundred thousand vertices.
The matrix L is usually referred to as the stiffness matrix, while the matrix M is dubbed the mass matrix.

General form of the finite element method

In general, the finite element method is characterized by the following process.
  • One chooses a grid for Ω. In the preceding treatment, the grid consisted of triangles, but one can also use squares or curvilinear polygons.
  • Then, one chooses basis functions. In our discussion, we used piecewise linear basis functions, but it is also common to use piecewise polynomial basis functions.
A separate consideration is the smoothness of the basis functions. For second order elliptic boundary value problems, piecewise polynomial basis function that are merely continuous suffice (i.e., the derivatives are discontinuous.) For higher order partial differential equations, one must use smoother basis functions. For instance, for a fourth order problem such as uxxxx + uyyyy = f, one may use piecewise quadratic basis functions that are C1.
Another consideration is the relation of the finite dimensional space V to its infinite dimensional counterpart, in the examples above H_0^1. A conforming element method is one in which the space V is a subspace of the element space for the continuous problem. The example above is such a method. If this condition is not satisfied, we obtain a nonconforming element method, an example of which is the space of piecewise linear functions over the mesh which are continuous at each edge midpoint. Since these functions are in general discontinuous along the edges, this finite dimensional space is not a subspace of the original H_0^1.
Typically, one has an algorithm for taking a given mesh and subdividing it. If the main method for increasing precision is to subdivide the mesh, one has an h-method (h is customarily the diameter of the largest element in the mesh.) In this manner, if one shows that the error with a grid h is bounded above by Chp, for some C<\infty and p > 0, then one has an order p method. Under certain hypotheses (for instance, if the domain is convex), a piecewise polynomial of order d method will have an error of order p = d + 1.
If instead of making h smaller, one increases the degree of the polynomials used in the basis function, one has a p-method. If one combines these two refinement types, one obtains an hp-method (hp-FEM). In the hp-FEM, the polynomial degrees can vary from element to element. High order methods with large uniform p are called spectral finite element methods (SFEM). These are not to be confused with spectral methods.
For vector partial differential equations, the basis functions may take values in \mathbb{R}^n.

Comparison to the finite difference method
The finite difference method (FDM) is an alternative way of approximating solutions of PDEs. The differences between FEM and FDM are:
  • The most attractive feature of the FEM is its ability to handle complicated geometries (and boundaries) with relative ease. While FDM in its basic form is restricted to handle rectangular shapes and simple alterations thereof, the handling of geometries in FEM is theoretically straightforward.
  • The most attractive feature of finite differences is that it can be very easy to implement.
  • There are several ways one could consider the FDM a special case of the FEM approach. One might choose basis functions as either piecewise constant functions or Dirac delta functions. In both approaches, the approximations are defined on the entire domain, but need not be continuous. Alternatively, one might define the function on a discrete domain, with the result that the continuous differential operator no longer makes sense, however this approach is not FEM.
  • There are reasons to consider the mathematical foundation of the finite element approximation more sound, for instance, because the quality of the approximation between grid points is poor in FDM.
  • The quality of a FEM approximation is often higher than in the corresponding FDM approach, but this is extremely problem dependent and several examples to the contrary can be provided.
Generally, FEM is the method of choice in all types of analysis in structural mechanics (i.e. solving for deformation and stresses in solid bodies or dynamics of structures) while computational fluid dynamics (CFD) tends to use FDM or other methods like finite volume method (FVM). CFD problems usually require discretization of the problem into a large number of cells/gridpoints (millions and more), therefore cost of the solution favors simpler, lower order approximation within each cell. This is especially true for 'external flow' problems, like air flow around the car or airplane, or weather simulation in a large area.

Various types of finite element methods

Generalized finite element method

The Generalized Finite Element Method (GFEM) uses local spaces consisting of functions, not necessarily polynomials, that reflect the available information on the unknown solution and thus ensure good local approximation. Then a partition of unity is used to “bond” these spaces together to form the approximating subspace. The effectiveness of GFEM has been shown when applied to problems with domains having complicated boundaries, problems with micro-scales, and problems with boundary layers.

hp-FEM

The hp-FEM combines adaptively elements with variable size h and polynomial degree p in order to achieve exceptionally fast, exponential convergence rates.

hpk-FEM

The hpk-FEM combines adaptively elements with variable size h, polynomial degree of the local approximations p and global differentiability of the local approximations (k-1) in order to achieve best convergence rates.

XFEM

Main article: Extended finite element method

Spectral methods

Main article: Spectral method

 Meshfree methods

Main article: Meshfree methods

Discontinuous Galerkin methods

Main article: Discontinuous Galerkin method

Finite element limit analysis

Main article: Finite element limit analysis

Other applications of finite elements analysis

FEA has also been proposed to use in stochastic modelling, for numerically solving probability models. See the references list

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Mech Topics

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Combustion chambers

Main article: Combustion chamber
 
Internal combustion engines can contain any number of combustion chambers (cylinders), with numbers between one and twelve being common, though as many as 36 (Lycoming R-7755) have been used. Having more cylinders in an engine yields two potential benefits: first, the engine can have a larger displacement with smaller individual reciprocating masses, that is, the mass of each piston can be less thus making a smoother-running engine since the engine tends to vibrate as a result of the pistons moving up and down. Doubling the number of the same size cylinders will double the torque and power. The downside to having more pistons is that the engine will tend to weigh more and generate more internal friction as the greater number of pistons rub against the inside of their cylinders. This tends to decrease fuel efficiency and robs the engine of some of its power. For high-performance gasoline engines using current materials and technology, such as the engines found in modern automobiles, there seems to be a point around 10 or 12 cylinders after which the addition of cylinders becomes an overall detriment to performance and efficiency. Although, exceptions such as the W16 engine from Volkswagen exist.
  • Most car engines have four to eight cylinders with some high performance cars having ten, 12 — or even 16, and some very small cars and trucks having two or three. In previous years, some quite large cars such as the DKW and Saab 92, had two-cylinder or two-stroke engines.
  • Radial aircraft engines had from three to 28 cylinders; examples include the small Kinner B-5 and the large Pratt & Whitney R-4360. Larger examples were built as multiple rows. As each row contains an odd number of cylinders, to give an even firing sequence for a four-stroke engine, an even number indicates a two- or four-row engine. The largest of these was the Lycoming R-7755 with 36 cylinders (four rows of nine cylinders), but it did not enter production.
  • Motorcycles commonly have from one to four cylinders, with a few high performance models having six; although, some 'novelties' exist with 8, 10, or 12.
  • Snowmobiles Usually have one to four cylinders and can be both 2 stroke or 4 stroke, normally in the in-line configuration however there are again some novelties that exist with V-4 Engines
  • Small portable appliances such as chainsaws, generators, and domestic lawn mowers most commonly have one cylinder, but two-cylinder chainsaws exist.
  • Large reversible two cycle marine diesels have a minimum of three to over ten cylinders. Freight diesel locomotives usually have around 12 to 20 cylinders due to space limitations as larger cylinders take more space (volume) per kwh, due to the limit on average piston speed of less than 30 ft/sec on engines lasting more than 40000 hours under full power.

Ignition system

Main article: Ignition system
The ignition system of an internal combustion engines depends on the type of engine and the fuel used. Petrol engines are typically ignited by a precisely timed spark, and diesel engines by compression heating. Historically, outside flame and hot-tube systems were used, see hot bulb engine.

Spark

Main article: Ignition system
The mixture is ignited by an electric spark from a spark plug — the timing of which is very precisely controlled. Almost all gasoline engines are of this type. Diesel engines timing is precisely controlled by the pressure pump and injector.

Compression

Ignition occurs as the temperature of the fuel/air mixture is taken over its autoignition temperature, due to heat generated by the compression of the air during the compression stroke. The vast majority of compression ignition engines are diesels in which the fuel is mixed with the air after the air has reached ignition temperature. In this case, the timing comes from the fuel injection system. Very small model engines for which simplicity and light weight is more important than fuel costs use easily ignited fuels (a mixture of kerosene, ether, and lubricant) and adjustable compression to control ignition timing for starting and running.

Ignition timing

Main article: Ignition timing
For reciprocating engines, the point in the cycle at which the fuel-oxidizer mixture is ignited has a direct effect on the efficiency and output of the ICE. The thermodynamics of the idealized Carnot heat engine tells us that an ICE is most efficient if most of the burning takes place at a high temperature, resulting from compression — near top dead center. The speed of the flame front is directly affected by the compression ratio, fuel mixture temperature, and octane rating or cetane number of the fuel. Leaner mixtures and lower mixture pressures burn more slowly requiring more advanced ignition timing. It is important to have combustion spread by a thermal flame front (deflagration), not by a shock wave. Combustion propagation by a shock wave is called detonation and, in engines, is also known as pinging or Engine knocking.
So at least in gasoline-burning engines, ignition timing is largely a compromise between a later "retarded" spark — which gives greater efficiency with high octane fuel — and an earlier "advanced" spark that avoids detonation with the fuel used. For this reason, high-performance diesel automobile proponents, such as Gale Banks, believe that
There’s only so far you can go with an air-throttled engine on 91-octane gasoline. In other words, it is the fuel, gasoline, that has become the limiting factor. ... While turbocharging has been applied to both gasoline and diesel engines, only limited boost can be added to a gasoline engine before the fuel octane level again becomes a problem. With a diesel, boost pressure is essentially unlimited. It is literally possible to run as much boost as the engine will physically stand before breaking apart. Consequently, engine designers have come to realize that diesels are capable of substantially more power and torque than any comparably sized gasoline engine.

Fuel systems

Animated cut through diagram of a typical fuel injector, a device used to deliver fuel to the internal combustion engine.
Fuels burn faster and more efficiently when they present a large surface area to the oxygen in air. Liquid fuels must be atomized to create a fuel-air mixture, traditionally this was done with a carburetor in petrol engines and with fuel injection in diesel engines. Most modern petrol engines now use fuel injection too — though the technology is quite different. While diesel must be injected at an exact point in that engine cycle, no such precision is needed in a petrol engine. However, the lack of lubricity in petrol means that the injectors themselves must be more sophisticated.

Carburetor

Main article: carburetor
Simpler reciprocating engines continue to use a carburetor to supply fuel into the cylinder. Although carburetor technology in automobiles reached a very high degree of sophistication and precision, from the mid-1980s it lost out on cost and flexibility to fuel injection. Simple forms of carburetor remain in widespread use in small engines such as lawn mowers and more sophisticated forms are still used in small motorcycles.

Fuel injection

Main article: Fuel injection
Larger gasoline engines used in automobiles have mostly moved to fuel injection systems (see Gasoline Direct Injection). Diesel engines have always used fuel injection system because the timing of the injection initiates and controls the combustion.
Autogas engines use either fuel injection systems or open- or closed-loop carburetors.

Fuel pump

Main article: Fuel pump
Most internal combustion engines now require a fuel pump. Diesel engines use an all-mechanical precision pump system that delivers a timed injection direct into the combustion chamber, hence requiring a high delivery pressure to overcome the pressure of the combustion chamber. Petrol fuel injection delivers into the inlet tract at atmospheric pressure (or below) and timing is not involved, these pumps are normally driven electrically. Gas turbine and rocket engines use electrical systems.

Other

Other internal combustion engines like jet engines and rocket engines employ various methods of fuel delivery including impinging jets, gas/liquid shear, preburners and others.

Oxidiser-Air inlet system

Some engines such as solid rockets have oxidisers already within the combustion chamber but in most cases for combustion to occur, a continuous supply of oxidiser must be supplied to the combustion chamber.

Naturally-aspirated engines

When air is used with piston engines it can simply suck it in as the piston increases the volume of the chamber. However, this gives a maximum of 1 atmosphere of pressure difference across the inlet valves, and at high engine speeds the resulting airflow can limit potential output.

Superchargers and turbochargers

A supercharger is a "forced induction" system which uses a compressor powered by the shaft of the engine which forces air through the valves of the engine to achieve higher flow. When these systems are employed the maximum absolute pressure at the inlet valve is typically around 2 times atmospheric pressure or more.
A cutaway of a turbocharger
Turbochargers are another type of forced induction system which has its compressor powered by a gas turbine running off the exhaust gases from the engine.
Turbochargers and superchargers are particularly useful at high altitudes and they are frequently used in aircraft engines.
Duct jet engines use the same basic system, but eschew the piston engine, and replace it with a burner instead.

Liquids

In liquid rocket engines, the oxidiser comes in the form of a liquid and needs to be delivered at high pressure (typically 10-230 bar or 1–23 MPa) to the combustion chamber. This is normally achieved by the use of a centrifugal pump powered by a gas turbine — a configuration known as a turbopump, but it can also be pressure fed.

Parts

An illustration of several key components in a typical four-stroke engine.
For a four-stroke engine, key parts of the engine include the crankshaft (purple), connecting rod (orange), one or more camshafts (red and blue), and valves. For a two-stroke engine, there may simply be an exhaust outlet and fuel inlet instead of a valve system. In both types of engines there are one or more cylinders (grey and green), and for each cylinder there is a spark plug (darker-grey, gasoline engines only), a piston (yellow), and a crankpin (purple). A single sweep of the cylinder by the piston in an upward or downward motion is known as a stroke. The downward stroke that occurs directly after the air-fuel mix passes from the carburetor or fuel injector to the cylinder (where it is ignited) is also known as a power stroke.
A Wankel engine has a triangular rotor that orbits in an epitrochoidal (figure 8 shape) chamber around an eccentric shaft. The four phases of operation (intake, compression, power, and exhaust) take place in what is effectively a moving, variable-volume chamber.

Valves

Main article: valve
All four-stroke internal combustion engines employ valves to control the admittance of fuel and air into the combustion chamber. Two-stroke engines use ports in the cylinder bore, covered and uncovered by the piston, though there have been variations such as exhaust valves.

Piston engine valves

Main article: Piston engine valve
In piston engines, the valves are grouped into 'inlet valves' which admit the entrance of fuel and air and 'outlet valves' which allow the exhaust gases to escape. Each valve opens once per cycle and the ones that are subject to extreme accelerations are held closed by springs that are typically opened by rods running on a camshaft rotating with the engines' crankshaft.

[edit] Control valves

Continuous combustion engines—as well as piston engines—usually have valves that open and close to admit the fuel and/or air at the startup and shutdown. Some valves feather to adjust the flow to control power or engine speed as well.

Exhaust systems

Exhaust manifold with ceramic plasma-sprayed system
Main article: exhaust system
Internal combustion engines have to effectively manage the exhaust of the cooled combustion gas from the engine. The exhaust system frequently contains devices to control pollution, both chemical and noise pollution. In addition, for cyclic combustion engines the exhaust system is frequently tuned to improve emptying of the combustion chamber. The majority of exhausts also have systems to prevent heat from reaching places which would encounter damage from it such as heat-sensitive components, often referred to as Exhaust Heat Management.
For jet propulsion internal combustion engines, the 'exhaust system' takes the form of a high velocity nozzle, which generates thrust for the engine and forms a colimated jet of gas that gives the engine its name.

Cooling systems

Main article: Engine cooling
Combustion generates a great deal of heat, and some of this transfers to the walls of the engine. Failure will occur if the body of the engine is allowed to reach too high a temperature; either the engine will physically fail, or any lubricants used will degrade to the point that they no longer protect the engine. The lubricants must be clean as dirty lubricants may lead to over formation of sludge in the engines.
Cooling systems usually employ air (air cooled) or liquid (usually water) cooling while some very hot engines using radiative cooling (especially some Rocket engines). Some high altitude rocket engines use ablative cooling where the walls gradually erode in a controlled fashion. Rockets in particular can use regenerative cooling which uses the fuel to cool the solid parts of the engine.

Piston

Main article: piston
A piston is a component of reciprocating engines. It is located in a cylinder and is made gas-tight by piston rings. Its purpose is to transfer force from expanding gas in the cylinder to the crankshaft via a piston rod and/or connecting rod. In two-stroke engines the piston also acts as a valve by covering and uncovering ports in the cylinder wall.

Propelling nozzle

Main article: Propelling nozzle
For jet engine forms of internal combustion engines, a propelling nozzle is present. This takes the high temperature, high pressure exhaust and expands and cools it. The exhaust leaves the nozzle going at much higher speed and provides thrust, as well as constricting the flow from the engine and raising the pressure in the rest of the engine, giving greater thrust for the exhaust mass that exits.

Crankshaft

A crankshaft for a 4 cylinder engine
Main article: Crankshaft
Most reciprocating internal combustion engines end up turning a shaft. This means that the linear motion of a piston must be converted into rotation. This is typically achieved by a crankshaft.

Flywheels

Main article: flywheel
The flywheel is a disk or wheel attached to the crank, forming an inertial mass that stores rotational energy. In engines with only a single cylinder the flywheel is essential to carry energy over from the power stroke into a subsequent compression stroke. Flywheels are present in most reciprocating engines to smooth out the power delivery over each rotation of the crank and in most automotive engines also mount a gear ring for a starter. The rotational inertia of the flywheel also allows a much slower minimum unloaded speed and also improves the smoothness at idle. The flywheel may also perform a part of the balancing of the system and so by itself be out of balance, although most engines will use a neutral balance for the flywheel, enabling it to be balanced in a separate operation. The flywheel is also used as a mounting for the clutch or a torque converter in most automotive applications.

Starter systems

All internal combustion engines require some form of system to get them into operation. Most piston engines use a starter motor powered by the same battery as runs the rest of the electric systems. Large jet engines and gas turbines are started with a compressed air motor that is geared to one of the engine's driveshafts. Compressed air can be supplied from another engine, a unit on the ground or by the aircraft's APU. Small internal combustion engines are often started by pull cords. Motorcycles of all sizes were traditionally kick-started, though all but the smallest are now electric-start. Large stationary and marine engines may be started by the timed injection of compressed air into the cylinders — or occasionally with cartridges. Jump starting refers to assistance from another battery (typically when the fitted battery is discharged), while bump starting refers to an alternative method of starting by the application of some external force, e.g. rolling down a hill.

Heat shielding systems

Flexible ceramic heat shield commonly used on high-performance automobiles
Main article: Heat shield
These systems often work in combination with engine cooling and exhaust systems. Heat shielding is necessary to prevent engine heat from damaging heat-sensitive components. The majority of older cars use simple steel heat shielding to reduce thermal radiation and convection. It is now most common for modern cars are to use aluminium heat shielding which has a lower density, can be easily formed and does not corrode in the same way as steel. Higher performance vehicles are beginning to use ceramic heat shielding as this can withstand far higher temperatures as well as further reductions in heat transfer.

Lubrication systems

Internal combustions engines require lubrication in operation that moving parts slide smoothly over each other. Insufficient lubrication subjects the parts of the engine to metal-to-metal contact, friction, heat build-up, rapid wear often culminating in parts becoming friction welded together e.g. pistons in their cylinders. Big end bearings seizing up will sometimes lead to a connecting rod breaking and poking out through the crankcase.
Several different types of lubrication systems are used. Simple two-stroke engines are lubricated by oil mixed into the fuel or injected into the induction stream as a spray. Early slow-speed stationary and marine engines were lubricated by gravity from small chambers similar to those used on steam engines at the time — with an engine tender refilling these as needed. As engines were adapted for automotive and aircraft use, the need for a high power-to-weight ratio led to increased speeds, higher temperatures, and greater pressure on bearings which in turn required pressure-lubrication for crank bearings and connecting-rod journals. This was provided either by a direct lubrication from a pump, or indirectly by a jet of oil directed at pickup cups on the connecting rod ends which had the advantage of providing higher pressures as the engine speed increased.

Control systems

Most engines require one or more systems to start and shutdown the engine and to control parameters such as the power, speed, torque, pollution, combustion temperature, efficiency and to stabilise the engine from modes of operation that may induce self-damage such as pre-ignition. Such systems may be referred to as engine control units.
Many control systems today are digital, and are frequently termed FADEC (Full Authority Digital Electronic Control) systems.

Diagnostic systems

Main article: On Board Diagnostics
Engine On Board Diagnostics (also known as OBD) is a computerized system that allows for electronic diagnosis of a vehicles' powerplant. The first generation, known as OBD1, was introduced 10 years after the U.S. Congress passed the Clean Air Act in 1970 as a way to monitor a vehicles' fuel injection system. OBD2, the second generation of computerized on-board diagnostics, was codified and recommended by the California Air Resource Board in 1994 and became mandatory equipment aboard all vehicles sold in the United States as of 1996.

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