How to Make Biodiesel

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December 6th, 2007, 12:42 GMT| By Gabriel Gache

Incredibly or not, the first diesel engine didn't use petroleum diesel to power itself, but instead it used vegetable oil. Most of us recognize the German engineer, Rudolf Diesel, as the father of the diesel engine, but the truth is that the first internal combustion engine, which operated on a diesel cycle, has first been built by Herbert Akroyd Stuart and Charles Richard Binney, one year before Diesel built its first engine, and they have received a patent for their invention three years before Diesel.

Diesel engines represent a variation of the classical internal combustion engine running of Otto cycles, and is mostly distinctive through

its different ignition system which, unlike the classical gasoline engines that use spark plugs to light the fuel mixture, uses a compression ignition technique, in which the fuel-air mixture is being injected in the piston and compressed until the fuel self ignites.

Now, all the diesel powered cars use a diesel fuel, obtained through fractional distillation from petroleum oil; however, though the diesel engines have evolved from the original engine that was built in 1890, they are still able to work with multiple types of vegetable oil, or biodiesels.

If you want to spare yourself from a trip to the gas station and learn a bit of chemistry, you could use some items, which can be found in most of the supermarkets, in order to make your own biodiesel, to power your diesel engine car.

Here is what you need: 250 mililiters of fuel additive, or methanol, 4 grams of caustic solution, one litre of vegetable oil, protective equipment such as eyewear, rubber gloves, a container airtight seal, a 2 litre PET bottle, and a funnel.

Begin by mixing the methanol and caustic solution in the airtight seal container, preferable a glass jar, and shake it until the caustic solution completely dissolves in the methanol. Be advised, this mixture should be prepared in a well ventilated area!

After the methanol-lye solution has been prepared, heat up the vegetable oil to a temperature of 60 degrees Celsius, and pore it into the PET bottle by using the funnel, after which pore the methanol-lye solution that was prepared earlier, in the same bottle and shake it for 20 to 40 seconds.

The obtained solution will deposit a precipitation of Glycerin at the bottom of the PET bottle in the next twenty minutes, leaving behind an upper cloudy layer. Put the bottle aside for 1 to 2 days, after which the upper layer will become clear and can be drawn out of the bottle to extract the biodiesel.

2 HYDRODYNAMIC ASSESSMENT

The point of departure for any study on lubrication is the solution to the Reynolds

equation /1/, proposed by Sir Osborne Reynolds in 1886. There is no single general

analytic solution to the Reynolds equation. Partial analytic solutions have been obtained

by using analogies with electricity or numerical and graphical methods. One of the most

interesting approaches is the Mobility Method, the premises of which were first

formulated by Booker /2/ and which has since served as the basis for other solutions put

forward by authors, such as Goenka /3/.

In essence, the Mobility Method is based on ascertainment of the bearing’s polar load

diagram and allows for calculation of the journal orbit diagram, oil film pressure diagram

and other associated variables such as the required volume of oil flow or friction

horsepower loss. The polar load diagram (Figure l) represents the variation in the

resulting load which acts on the bearing during the course of one complete engine cycle.

Fig. 1: Polar load diagram for connecting rod big-end bearing

The journal orbit diagram (Figure 2) depicts the path traced by the journal center on

displacement within the bearing clearance during one complete engine cycle and

furnishes information on variations in oil-film thickness during said cycle. Dependent on

this latter value are factors of critical importance, such as wear, overheating, seizure,

friction horsepower loss, oil flow volume, etc. In the case of reciprocating engines,

bearing design must ensure that, under hydrodynamic lubrication conditions, minimum

oil-film thickness will never fall below a given safety factor during the operating cycle.

Fig. 2: Journal orbit diagram for connecting rod big-end bearingThe oil-film pressure diagram (Figure 3) represents the variation in oil-film pressure in

the bearing for each crank angle of the cycle, and determines the mechanical endurance

and fatigue strength which a bearing must possess if it is to perform satisfactorily. The

oil-film pressure diagram may also be used to determine the ideal position for oil holes,

in both shaft and bearing, so as to ensure adequate oil circulation.

Fig. 3: Oil-film pressure diagram for connecting rod big-end bearing

3 MAIN BEARING LOAD CALCULATION

Applied big-end bearing load is relatively simple to compute, since it depends on known

factors, such as the inertia of moving parts and gas pressure forces exerted on the

3 MAIN BEARING LOAD CALCULATION

Applied big-end bearing load is relatively simple to compute, since it depends on known

factors, such as the inertia of moving parts and gas pressure forces exerted on the

piston.

However, the loads appearing on the main bearings react on the crankshaft in opposition

to big-end bearing load and are more complicated to calculate. The reason for this is that

the crankshaft is a flexible structure which is statically indeterminate, so that the reaction

in any given main bearing will depend on the load exerted on the structure as a whole,

with the influence coefficients being unknown a priori. Furthermore, such loads are

variable in magnitude and direction throughout the engine cycle.

Calculation of the reaction forces on the main bearings can be approached via two

procedures: the first assumes the crankshaft to be isostatic which, while sacrificing

accuracy, allows for a determinate method to be applied; the second assumes the

crankshaft to be statically indeterminate and uses an indeterminate procedure to

compute the reaction forces.

3.1. DETERMINATE METHOD

The statically determinate method assumes that the crankshaft is simply supported at it

each of its main journal centers. Hence, the reaction of any given main bearing will

depend solely on the load exerted on the crankthrows adjacent to the journal in question.

The determinate method is thus not applicable to crankshafts where stiffness (or

flexibility) is an important design parameter.3.2. INDETERMINATE METHOD

The indeterminate method is based on a sequential solution to the structural equation

governing the crankshaft, written in terms of influence coefficients, and to the Reynolds

equation (the Mobility Method being used for the latter purpose). The structural equation

for the crankshaft can be expressed as follows:

(Fc) = (Kc) (uc) (1)

where: (Fc) is the vector of the forces (actions and reactions) that act on the crankshaft,

crankpins and main journals; (Kc), the matrix of crankshaft stiffness; and (uc), the vector

of crankpin and main journal displacements.

In its more developed form, equation (1) becomes:

(Ra) = (K) (ua) + (T) (Fm) + (C) ù

(2)

where:

(Ra) is the vector of the reaction forces exerted by the bearings on the crankshaft main

journals, and is the target to be calculated;

(Fm) is the vector of the loads applied by the connecting rod on the crankpins;

(ua) is the vector of main journal displacements;

ù is crankshaft rotation speed; and,

(K), (T) y (C) are the matrices of stiffness, transmissibility and centrifugal load influence

coefficients respectively. These matrices are obtained by appropriate application of loads,

displacements and rotation speed to a crankshaft model by finite element methods, as

shown in Figure 4.

Fig. 4: Crankshaft FE model

Figure 5 illustrates the difference between the two methods vis-à-vis the reactions

provoked by an applied crankpin load on the respective main bearing journals of a fourcylinder engine crankshaft.

For a more thorough discussion of this subject, see Law /4/, López /5/ and Galindo /6/.Fig. 5: Load transmissibility as per determinate and indeterminate methods

3.3 RESULTS OF THE DETERMINATE AND INDETERMINATE METHODS

A comparative study was carried out on the results obtained when both methods were

applied to the calculation of main bearings of a turbo-charged four-in-line diesel engine.

Values for maximum load (Fmax), minimum oil-film thickness (hmin) and maximum oilfilm pressure (Pmax) for the first three main bearings under operating conditions of

maximum torque (Mmax: 265 Nm, 2000 min

-1

) and maximum brake horsepower (Nmax:

87 kW, 3600 min

-1

) are shown in Table l.

Operating conditions: maximum TORQUE Operating conditions: max. BRAKE HPW.

COJINETE Fmáx (N) hmin (ìm)

Pmax

(MPa) Fmax (N) hmin (ìm)

Pmax

(MPa)

Det 38247 2,78 97 32241 3,55 62

Main

Indet

30981

(-19,0%)

3,30

(+18,5 %)

(-25,8 %)

24669

(-23,5%)

3,68

(+3,8%)

(-29,3 %)

Det 41986 2,29 123 40130 3,29 100

Main

Indet

56165

(+33,8%)

1,86

(-19,1 %)

177

(+44,0%)

54261

(+35,2%)

2,77

(-16,0%)

144

(+43,6 %)

Det 35584 2,57 86 23616 2,39 37

Main

Indet

37670

(+5,9%)

2,94

(+14,3 %)

(+10,3 %)

20117

(-24,8%)

2,43

(+1,6%)

(+8,6 %)

Table 1: Extreme values for the principal lubrication parameters in respect of the first

three main bearings of a four-in-line diesel engine, as yielded by statically determinate

and indeterminate methodsFigures 6 and 7 compare the polar and journal orbit diagrams plotted by each of the two

methods when applied to calculation of the first main bearing, under conditions of

maximum torque and maximum brake horsepower.

Fig. 6: Polar diagrams for main bearing 1 as per determinate (left) and indeterminate

(right) methodsFig. 7: Orbit diagrams for main bearing 1 as per determinate (left) and indeterminate

(right) methods

The influence on the target bearing of combustion in non-adjacent cylinders is evident in

the diagrams plotted with the indeterminate method. Logically, the greater the inertia

loop (higher engine speed), the more pronounced the effect on the polar curve will be,

whilst the journal orbit diagram will undergo ever greater modification as engine speed is

lowered.

In general, the indeterminate and determinate methods yield similar results for the

extreme main bearings, since these are influenced to a great extent by adjacent

cylinders 1 and 4. The influence of crankshaft flexibility is accentuated as regards the

intermediate bearings, with higher maximum load and lower oil-film values being

obtained when the indeterminate method is used. With respect to the results obtained

for the central bearing, in general, the extreme values for the parameters analyzed show

no appreciable degree of divergence as between the two methods.4 CRANKSHAFT STRESS CALCULATION

In much the same fashion as equation (1) above, the stress status at any given point

along the crankshaft will be given by the so-called structural stress equation, expressed

as:

(S) =(Kó)(ua) +(Tó)(Fm) +(Có) ù

(3)

where:

(S) is the vector of the stresses at the different calculation points; and,

(Kó), (Tó) and (Có) -the magnitude of which depends on that of (S)- are the equivalent

in terms of stress of matrices (K), (T) and (C) in terms of reaction forces, and are

likewise obtained by applying finite element methods.

Shown in Figure 8, by way of example, are the equivalent stress (óe) - crank angle (á)

diagrams in respect of the fillet radii of crankweb no. 1.

Fig. 8: Evolution of Von Mises’ equivalent stress in the fillet radii of crankweb no. 1 of the

crankshaft

In both crankwebs, maximum stress occurs at combustion TDC in cylinder 1. The

discontinuities seen in the curve 180º before and after this point, are due to combustion

in cylinders 2 and 3 (engine firing order: 1-3-4-2), and are more clearly observable in

the crankweb nearest these cylinders. Logically, these discontinuities will not appear if

the analysis is run using the determinate method.

Ascertainment of the stress pattern for each of the fillet radii by reference to the

different critical sections of the crankshaft, makes it possible for the mean and

alternating stresses at each point to be computed, thus leaving the fatigue safety factor

to be calculated by means of the modified Goodman criterion.

A further application of the indeterminate method is ascertainment, for each crank angle,

of the crankshaft’s elastic line, which enables edge loading to be studied in those

situations where a high degree of crankshaft flexibility might occasion sporadic contact

between journal and bearing edge.5 CONCLUSIONS

Set out in this paper is an advanced method for the calculation of crankshafts and sliding

bearings for reciprocating internal combustion engines.

The indeterminate method provides a valid tool for the design of crankshafts and slidingbearings, and enables calculation to come closer to real performance of same.

In general, the results furnished by the indeterminate method allow for use of a wider

range of criteria in the choice of fundamental design parameters.

Other aspects not taken into account in this model, such as main bearing elastic

deformation or cylinder block stiffness, would make for a more accurate picture of the

integrated performance of the crankshaft-bearing unit as a whole.

6 REFERENCES

1. Reynolds, O. “Theory of Lubrication”, Part I, Phil. Trans. Roy. Soc., London 1886

2. Booker, J.F. “Dynamically Loaded Journal Bearings: Mobility Method of Solution”,

Journal of Basic Engineering, Sept. 1965

3. Goenka, P.K. “Analytical Curve Fits for Solution Parameters of Dynamically Loaded

Journal Bearings”, Journal of Tribology, Vol. 106, 1984

4. Law, B. “Crankshaft Loading and Bearing Performance Analysis”, Design and

Applications in Diesel Engineering, Edited by Haddad, S. and Watson, N., Ellis Horwood,

1984

5. López, J.M. “Influencia de la flexibilidad del cigüeñal en el comportamiento

hidrodinámico de los cojinetes de fricción de motores” Tesis Doctoral, U.P.M. Julio 1993

6. Galindo, E. “Estudio comparativo de los métodos estáticamente determinado e

indeterminado para el cálculo de los principales parámetros de lubricación de los

cojinetes de bancada de un motor de combustión interna alternativo” Master en

Ingeniería de los Vehículos Automóviles, U.P.M. 1994

Automobile

Friday, January 21, 2011

How to Make Biodiesel

How to Make Biodiesel

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