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FKlPl sin j (8-3Þwhere lPlis the stroke/connecting rod ratio (the quotient ofthe crank radius r and connecting rod length lPl). In a crankshaft-related reference system, the tangential or tor-sional force Ft acts on the crank’s crank pin:Ft ¼ FPl sinðj þ cÞ¼ FKsinðj þ cÞcos c(8-4ÞThe radial force Frad acts on the crank pin radially:Frad ¼ FPl cosðj þ cÞ¼ FKcosðj þ cÞcos c(8-5ÞWith the crank radius r as a lever arm,
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the tangential force Ftgenerates the crank torque M. Dependent on the piston sidethrust FKN and the instantaneous distance h between thepiston pin and crankshaft axis, it can also be defined as areaction torque in the cylinder crankcase
KNhh ¼ r cos j þ lPl cos c (8-6ÞThe bearing forces FPlL or FKWHL in the connecting rod andthe crankshaft bearings are obtained by adding the vectors ofthe connecting rod force FPlwith the related rotating inertialforces. In the case of the connecting rod bearing, this is theinertial force of the assumedmass component of the connect-ing rod FmPlrot rotating with the crank pin. In the case of thecrankshaft bearings, it is the entire inertial force Fmrot ofthe masses rotating with the crank. The latter are the totalof the rotating inertial forces of the connecting rod FmPlrot andthe crank FmKWrot :~ FPlL ¼ ~ FPl þ~ FmPlrot~ FKWHL ¼ ~ FPlL þ~ FmKWrot ¼ ~ FPl þ~ Fmrot(8-7ÞThe transmission of forces through adjacent cylinders – as afunction of their phase relation and distribution on the mainbearings of the crankshaft throw concerned – has to beallowed for in the statically indeterminate crankshaft sup-ports of multiple cylinder engines. Realistically, capturingevery effect (elastic deformation of the bearing bulkheadand crankshaft, different bearing clearances, hydrodynamiclubricating film formation in dynamically deformed bearingsand misalignment of the main bearing axis caused by manu-facturing) proves to be
commensurately difficult and complex(see [8-3–8-8]).At constant engine speed (angular frequency o), one crankangle j run through in the time t is j = ot. The followingrelationships deliver the correlation between the angles jand c:r sin j ¼ lPl sin csin c ¼ rlPlsinj ¼ lPl sin jsin j ¼ lPlr sinc ¼ 1lPlsin c(8-8Þsin2c þ cos2c ¼ 1cos c ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
sin2cq¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
l2Plsin2jq (8-9ÞThus, the equations containing the pivoting angle of theconnecting rod c may also be represented as a function ofthe crank angle j.Equation (8-9) only exactly applies to non-crankshaft offsetreciprocating piston engines, which additionally do not have two-stroke engine series can also range incrementally fromanI6 engine up through and including I11 to I12 engines andeven an I14 variant (e.g. MAN Diesel SE, model K98MCMK7). Medium speed diesel engines are manufactured in Vdesigns with different increments of up to twenty cylinders.8.1.3.4 Throw Configuration and Free Mass ActionsAppropriate configuration of the throws suffices to obtainquite good dynamic performance from a crankshaft assemblyin multiple cylinder engines. The first order free inertialforces are fully balanced in inline engines when the crankshaftis centrosymmetric (see Sect. 8.3.3.2 for a centrosymmetricfirst order star diagram). This is the case when the crank-shaft’s throw angle jK corresponds to one uniform ignitioninterval jz:jz ¼4pzðFour-stroke engineÞ jz ¼2pzðTwo-stroke engine)(8-11ÞThe firing sequence does not play a role at all. If the secondorder star diagram
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