Crank Shaft Analysis

Appl. Math. Inf. Sci. 7, No. 1L, 313-321 (2013) 313

Applied Mathematics & Information SciencesAn International Journal

c⃝ 2013 NSPNatural Sciences Publishing Cor.

Numerical Analysis and Study of Crankshaft SystemHydrodynamic Lubrication and Dynamic CouplingSystem

Lin Qiong1, Meng Bin2, Yang Qinghua2

1College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, 310032, China2Key Laboratory of E &M, Zhejiang University of Technology, Hangzhou, 310032, China

Received: 28 Jul. 2012, Revised: 9 Oct. 2012, Accepted: 6 Jan. 2013Published online: 1 Feb. 2013

Abstract: Using finite element method and multi-body dynamics method, this study established an engine digitalized virtual prototypeembraced tribological characteristics in virtual prototype and MATLAB platform, and introduced Elastohydrodynamics theory into thesystem, wrote program with difference equation method, and solved the Reynolds Equation through shafting-bearing self-feedbackcontrol system, obtained the crankshaft main bearing reaction force which considered the system’s oil film dynamic lubricating frictionbehaviour, and also obtained data of main bearing’s load capacity, path of axle center and the minimum thickness of oil film. Thoughanalysis, it is found that engine crankshaft system’s oil film dynamic lubricating friction has certain impact on system’s dynamiccharacteristics, where using hydrodynamic lubrication coupling multi-body dynamic system for simulation could better reflect theengine’s actual working conditions, therefore the oil film dynamic lubricating friction behaviour of the system should be considered indynamic simulation calculations.

Keywords: hydrodynamic lubrication, coupling, dynamics, numerical simulation.

1 Introduction

Spurred by the more and more intense marketcompetition, the major car companies feel more pressureon the engine products’ development cycle, upgradingand updating. Therefore more and more attention is paidon engine system’s numerical simulating technology,expecting to complete the designing of products, virtualtesting, analysis and manufacture, as well as programimprovement under digitalized means-based conditions[1,3]. With the analysis and research on modern enginedigitalized simulation getting more in-depth, the couplingproblem of tribological and dynamic characteristics of theengine system needs to be resolved urgently; and thedynamic and kinematic transitive relation and boundaryconditions among components are important dataaffecting the accuracy of simulation analyze results.During the digitalized simulation analysis, the dynamicand kinematic transitive relation and boundary conditionsamong components are especially important dataaffecting the correctness of simulation analyze results.

And as an important dynamic behavior and boundarycondition, tribological system behavior commonly existsin major systems of engines; its features will undoubtedlyaffect the accuracy of the engine system’s digitalizedsimulation result [4,5]. However, in the engine digitalizedsimulation analysis process, the friction behavior is oftensimulated with simple mathematical models and definedwith empirical values, which will lead to error betweensimulation analyze result and the actual result. Thereforeit is necessary to carry out systematic study on enginedynamic system’s tribological behavior in order to betterguide the engine digitalized design work. As the pivot ofengine, crankshaft system’s components and body’sdynamic characteristics are not only related to thesystem’s dynamic characteristics, but also related to thetribological characteristics among them. The mainbearing oil film plays a role in supporting crankshaft andcarrying the pressure load of the cylinder, which is a veryimportant part of engine crankshaft system’s dynamicanalysis; its dynamic lubrication characteristics directlyaffect the dynamic coupling relation between crankshaft

∗ Corresponding author e-mail: [email protected]⃝ 2013 NSP

Natural Sciences Publishing Cor.

314 L. Qiong, M. Bin, Y. Qinghua: Numerical Analysis and Study of Crankshaft System...

system and the frame [6,7]. However, traditional analysisusually ignores the influence of hydrodynamiclubrication, and simplifies the main bearings to constraintbearings or linear bearings to analyze, thereby isolate thetribological problems and system dynamic problems forstudy. Because of the complexity of the load changes ofactual shafting, the coupling effect between the shaft andbearing should not be ignored, thus this kind of isolatedsimplified analysis has considerable error. This papertakes crankshaft system as study object, and engineflexible virtual prototype model and MATLABmathematic calculation software as simulation calculationplatform, carries out numerical calculation analysis oncrankshaft shafting and sliding bearing’s hydrodynamiclubrication and dynamic coupling behaviors; and predictsthe engine crankshaft system’s dynamic and kinematiccharacteristics fairly accurately, allowing a more accurateevaluation of engine dynamic characteristics andvibration levels.

2 Crankshaft shaft - bearing couplingdynamic model

The first thing of studying the crankshaft and the body’shydrodynamic lubrication effect using numerical analysisand virtual prototype is to establish the crankshaftsystem’s shaft-bearing flexible virtual prototype model. Incrankshaft systems, crankshaft is undoubtedly the pivot ofthe engine. When the engine is working, the elasticvibration deformation of crankshaft directly affects thefilmatic bearing’s loading and movement. Meanwhile, themain bearing’s bending moment caused by crankshaft’selastic deformation would affect the body and thecylinder’s loading. Therefore, this study uses flexiblecrankshaft while constructing the crankshaft systemvirtual prototype. Figure 2.1 presents the crankshaft’sfinite element model.

Fig. 2.1 Crankshaft finite element model

Considering that the flywheel in the system is alsolow stiffness component with lower connatural frequency,

it should not be treated as rigid body simply whenanalyzing crankshaft system’s vibrating characteristics,therefore infinite element model for flywheel is alsoconstructed. In past multi-body dynamic models,connecting rod is usually simplified as rigid componentwith big and small head qualities. However due to theuneven quality distribution of connecting rod, suchsimplification would definitely affects the correctness ofthe model. Therefore, same with crankshaft, connectingrod is defined as flexible component. Other componentsare all defined as rigid centralized quality. This study usesMSC.PATRAN to divide each component to finiteelement grid in hexahedral units, and uses MSC.Nastranto solve the free orthotropic modality.

When introducing finite element model intomulti-body dynamic software for virtual prototypesimulation, mode synthesis method is usually used. Forcomponents with complex structure, to reflect theirdynamic characteristics accurately, finite element modelwith large amount of degrees of freedom needs to beconstructed; hence the solving is very large-scale. Theadvantage of mode synthesis method is using a smallnumber of degrees of mode freedom to describecomponents’ macroscopic deformation, and encapsulatecomponents’ connatural features retained by modaltruncation in the calculation result of modal analysis. Thefinite element model of the flexible crankshaft, theflywheel and the connecting rod mentioned in this chapterare all introduced into the virtual prototype model usingmode synthesis technology. Figure 2.2 and 2.3 show thefinite element models of the flywheel and the connectingrod respectively.

Fig. 2.2 Flywheel finiteelement model

Fig. 2.3 Connecting rodfinite element model

By determining kinematic pairs according to actualkinematic relation, and simplifying each kinematic pair toideal constraints in multi-body dynamic softwareMSC/ADAMS, a complete kinematic structure could beconstructed. The main bearing constraints in the structureare replaced by oil film force, which is obtained bysolving the Reynolds Equation. Figure 2.4 represents thevirtual prototype model of this crankshaft system.

In this virtual prototype model, MSC/ADAMS Solveris used for solving and analysis. The solver constructs


Appl. Math. Inf. Sci. 7, No. 1L, 313-321 (2013) / www.naturalspublishing.com/Journals.asp 315

Fig. 2.4 Crankshaft three-dimensional model

kinematic constraint equations for multi-body system inthe form of a set of non-linear equations:

C(q, t) = 0 (2.1)

In which, q =[q1T q2T . . .qnbT

]T are the system’sgeneralized coordinates, nb is the number of thegeneralized coordinates; and C = [C1C2 . . .Cnc ]

T is thenumber of constraint equations. For the i -th flexible bodyor rigid body, list Lagrange Equation in following form:

ddt(

∂K∂ qi )

T

−(

∂K∂qi

)T

+CiTq λ = Qi (2.2)

Where, K is the system’s kinetic energy, qi is thegeneralized coordinate describing the system, Qi is thegeneralized force including the generalized force causedby unit flexibility deformation and the generalized forcecaused by additional loads (including loads among units),λi is Lagrange multiplier array, and CiT

q is kinematicconstraint. For the series of non-linear algebraic equationsabove, ADAMS solves them using amendedNewton-Raphson iterative algorithm.

3 Establishment of main bearing oil filmmathematic model

The crankshaft main bearings are radial cylinder filmaticbearings using dynamic lubrication; and the main bearingoil film perform supporting function for the crankshaft.Using cylindrical filmatic bearings for simulating thecrankshaft system’s main bearing constraints andhydrodynamic model for calculation could greatlyimprove the model’s accuracy.

3.1 Operating principle of hydrodynamiclubricating friction

In order to calculate the load capacity of the lubricatingfilm, its pressure distribution needs to be calculated. The

basic content of all kinds of hydrodynamic lubricationcalculation is the applying and solving of a special formof Navier-Stokes Equation – Reynolds Equation. Thegeneral form of Reynolds Equation is:

∂∂x

(ρh3

12µ∂ p∂x

)+

∂∂ z

(ρh3

12µ∂ p∂ z

)=

∂∂x

(ρUh

2

)+

∂∂ z

(ρWh

2

)−ρV +hρ

(3.1)

Where, U,V,W are the relative units of the velocitieson x,y,z directions respectively.

Fig. 3.1 Radical bearing diagram

For the radical bearing presented in Figure 3.1,x = rΦ indicates the circumferential direction coordinate,y is the radical direction coordinate, and z is the axialcoordinate. Assume the bearing journal moves around itscenter with angular velocity of Ω , horizontal shiftvelocity of Vh and vertical shift velocity of Vv . Thereby,U,V,W in equation (3.1) could be expressed as:

U = rΩ +Vv sinΦ −Vh cosΦV =−Vv cosΦ −Vh sinΦW = 0

Substitute them into Equation (3.1) and consideringVvr ,Vh

r << Ω , following equation is obtained:

1r2

∂∂Φ

(ρh3

12µ∂ p∂Φ

)+

∂∂ z

(ρh3

12µ∂ p∂ z

)=

Ω2

∂ (ρh)∂Φ

+ρ (Vv cosΦ +Vh sinΦ)+hρ(3.2)



When using the velocity on the eccentric direction Veand the velocity of the axle center moves around thebearing’s center Vθ to indicate the axle center velocity, theabove equation could be transformed to:

1r2

∂∂Φ

(ρh3

12µ∂ p∂Φ

)+

∂∂ z

(ρh3

12µ∂ p∂ z

)=

Ω2

∂ (ρh)∂Φ

+ρ (Ve cosϕ +Vθ sinϕ)+hρ(3.3)

3.2 Dimensionless form of the ReynoldsEquation

Assuming the operating temperature is 85 oC , and theviscosity coefficient is a constant. Usually the analyticalcalculation of oil film dynamic pressure bearings iscarried out in dimensionless form. Using dimensionlessform for calculation could simplify the calculationequation, and prevent the value of the variables in theequation from oversize or too small as far as possible, sothat error doesn’t appear in the process of submitting tocalculation. Reynolds Equation in the form of Equation(3.3) uses dimensionless form to represent the variables inthe equation.

λ = zl/2 ; H = h/c ;

h = c+ ecosϕ P = p/p0 p0 = 2Ω µ/ψ2

Vv =Vv/(cΩ),Vh =Vh/(cΩ)Ve =Ve/(cΩ),Vθ =Vθ/(cΩ)

∂∂ϕ

(H3 ∂P

∂ϕ

)+

(dl

)2 ∂∂λ

(H3 ∂P

∂λ

)= 3

∂H∂ϕ

+6(Ve cosϕ +Vθ sinϕ)(3.4)

In the above equations: h is the thickness of the oilfilm, z is the bearing axial coordinate, p is the oil filmpressure, r is the bearing radius, c is the bearing radiusinterval, and ψ = c/r ; p0 is the relative pressure, with thevalue of 2Ω µ/ψ2 , and e is the eccentricity, θ is the angleof displacement.

The oil film pressure could be obtained by solving theabove equation, and the oil film reaction force can beobtained through integration:

Fx = fx(e,θ ,Ve,Vθ ) =∫ ϕ2

ϕ1

∫ l/2−l/2 p(ϕ ,λ )dzsinϕdϕ

Fy = fy(e,θ ,Ve,Vθ ) =∫ ϕ2

ϕ1

∫ l/2−l/2 p(ϕ ,λ )dzcosϕdϕ

(3.5)

Where, l is the bearing width. And perform followingcoordinates changes to Equation (3.5):

e =√

x2 + y2

θ = arctan(y/x)Ve = xcosθ + ysinθ

Vθ = (xsinθ − ycosθ)/e

In which x,y and z are the crankshaft main bearing’s

horizontal, vertical and axial coordinates respectively.Then Equation (3.5) could be transformed to:

Fx = fx(x,y, x, y) =∫ ϕ2

ϕ1

∫ l/2−l/2 p(ϕ ,λ )dzsinϕdϕ

Fy = fy(x,y, x, y) =∫ ϕ2

ϕ1

∫ l/2−l/2 p(ϕ ,λ )dzcosϕdϕ

(3.6)

In the above equation, x,y, x, y are the axle centermovement parameters; they can be given by thecrankshaft system’s virtual prototype simulationcalculations. And then, through user-defined modules andADAMS virtual prototype combined simulation inMATLAB, the dynamic lubrication main bearing’s loadcapacity can be obtained.

3.3 Boundary conditions of oil film

When using MATLAB for integral calculation to solvethe pressure distribution of Reynolds Equation’s, pressureboundary conditions must be applied to determine theintegration constants, where the selection of differentboundary conditions would directly affect the accuracy ofthe solving result. For cylinder bearings of 360

,

convergent and divergent oil wedges may exist at thesame time, therefore there are several differentassumptions about the pressure boundary conditions.

The first kind of boundary condition is theSommerfeld boundary condition. This boundarycondition considers that there is complete oil film in thewhole oil film interval, with pressure distribution asshown in Figure 3.2. Positive pressure forms in theconvergent area, while negative pressure forms in thedivergent area, and the pressure distribution isanti-symmetric, i.e. pressure is 0 at the maximum intervalhmax and minimum interval hmin . Thus the pressure isperiodic function at circumferential direction:

p(Φ) = p(Φ +2π) (3.7)

Obviously, error of this assumption is large. Theactual oil film could not bear continuing negativepressure, and lubricating oil film can only bear shockwave of higher load or very small continuing negativepressure. Therefore it is not possible for complete oil filmto be existed in negative pressure area. However, sinceSommerfeld boundary condition could solve pressuredistribution conveniently, it can be used for the qualitativeanalysis of lubrication problems.

Another boundary condition is Reynolds boundarycondition assumption which is more reasonable. Itconsiders the ending edge of complete oil film is



Fig. 3.2 Cylinder bearing pressure distribution

determined by the Reynolds boundary condition p = pa ,and

∂ p∂Φ

= 0 (3.8)

The oil film starting point of this boundary conditionis at the maximum interval hmax , and p = pa . The endingpoint of the oil film is determined by the natural break ofthe film, its location is at some point in the divergent areaafter the minimum interval, and the point meets the twoconditions in equation (3.8) at the same time.

Reynolds boundary condition is the closest to actualcondition, however its oil film ending point must bedetermined by calculation and the calculation precision ishigh, while the model is relatively complex, and eachtime step requires repeating iterations of large amount ofcalculation. And since the iteration process requires thetime steps to be very small, the number of time steps inone work cycle of the engine would increase. Hence forthis method, the biggest challenge for current softwareand hardware conditions is the calculation size.Meanwhile when using half-Sommerfeld boundarycondition method to calculate, although the accuracywould be affected, this boundary condition is alreadyquite close to actual condition and the calculation size ismuch smaller. Therefore using this method would savecalculation time and improve the prediction efficiency.For the analysis in this study, the calculation of oil filmpressure makes use of half-Sommerfeld boundarycondition:

whenΦ = θandθ +π ,whenΦ = θ ∼ θ +π ,

p = 0p ≥ 0

(3.9)

And when Φ = θ +π ∼ θ +2π , p = pa

4 Sub-system Models

The crankshaft virtual prototype model is constructedwith MSC/ADAMS, the pressure distribution based oncrankshaft system’s virtual prototype model and thesolving of Reynolds Equation for oil film dynamiclubricating bearings is a self-feedback control system.Meanwhile, the Reynolds Equation for dynamiclubrication bearings is an elliptic partial differentialequation, which cannot be solved with analytical methodsin ordinary conditions. Thus using efficient and precisemathematical calculation software for numerical solvingbecomes an effective way for solving this problem.

Figure 4.1 represents the model of the crankshaftsystem’s control system. Under the cylinder firingpressure and the oil film supporting reaction force, themovement parameters of the main bearing’s axle centerwill change accordingly. And the location change of thefilmatic bearings’ axle center would definitely causechange of the oil film pressure. Apparently, the changesof the axle center’s location and the oil film reaction forcewill keep being fed back between the axis and thebearing, leading to further change of the entire system,and so forth. Hence, the system constructed by crankshaftsystem virtual prototype and main bearing is a typicalself-feedback system. The control system of crankshaftsystem and main bearing is presented by Figure 4.1.

Fig. 4.1 Control system model

Define the crankshaft system’s output variables as thebearing’s axle movement parameters, and the inputvariable is the oil film supporting reaction force obtainedby MATLAB calculation. Each change of the simulationstep axle center’s path will be calculated by ADAMS toget the axle center movement parameter at the moment,and input into MATLAB by ADAMS/CONTROLmodule. Build the main bearing sub-system model inMATLAB, and get the oil film pressure of the moment bycalculating equation (3.6), and thereby obtain the changedoil film reaction force. Feedback this oil film reactionforce to the crankshaft system through CONTROLmodule, and act it on the main bearing to get the new axlecenter path as the input of the next calculation. In thisway, through the signal feedback between the crankshaftsystem virtual prototype and the main bearing controller,



the main bearing’s support for crankshaft can be realized,and the crankshaft system’s dynamic and kinematicparameters within the simulation time could be obtained.

Set the Output as axle center movement parametersand Input as oil film reaction force inADAMS/CONTROL module to generate the crankshaftsystem’s sub-system module in MATLAB. Write theprogram to solve Reynolds Equation in MATLAB, andpack it into bearing sub-system module in SIMULINK.Use the packed crankshaft sub-system module and thebearing sub-system module to construct a completecrankshaft axle center- filmatic bearing self-feedbackcontrol system.

5 Numerical calculation method of dynamiclubrication bearings

Usually for the calculation of the crankshaft system’sdynamic response, the dynamic oil film lubricating mainbearings are simplified to linear spring - damping modelor nonlinear - spring damping model. This is because thepressure distribution of the main bearings withhydrodynamic model could not be solved by analyticmethods, and barely be solved by approximate analyticalmethods. Numerical methods to solve dynamic pressurebearings are mainly finite difference method and finiteelement method. Usually finite difference method couldalready allow obtaining accurate calculation results withlittle calculating time.

Using the finite difference method for solving is atransformation way to transform Reynolds partialdifferential equation to algebraic equation group. Thesolving principle is: divide the solution area into limitednumber of units as shown in Figure 5.1, and make eachunit as small as possible so that the oil pressures in theunits could be considered equal to each other or changeslinearly without causing substantial error. Then transformthe partial differential equation to be solved to a group ofdiscrete linear algebraic equations. And finally, get the oilfilm pressure distribution by solving this group ofalgebraic equations.

First of all, divide the solution area into equidistantgrids. As illustrated in Figure 8, column number along thebearing direction ϕ is indicated by i , and it is divided intom grids evenly on the direction; row number along thebearing direction λ is indicated by j , and it is dividedinto n grids evenly on the direction; there are(m + 1)× (n + 1) nodes in total. Usually in calculationm = 12 ∼ 25 , n = 8 ∼ 10 would fulfill the precisionrequirement, while sometimes to improve the calculationprecision, thin the grids in the solution area that thenumbers of unknown amount are dramatic, which meansto use uneven spacing grids or even proportion grids. InFigure 8, the location of each node is indicated by (i, j) ,and the dimensionless pressure value P at node (i, j) isindicated by P(i, j) . If using the central difference

Fig. 5.1 Grid Division

formula, then the first derivatives ∂P∂ϕ and ∂P

∂λ at node (i, j)can be expressed in the difference quotients of the valueits adjacent node’s P :

(∂P∂ϕ

)i, j

≈Pi+1,i −Pi−1, j

2∆ϕ ;(∂P∂λ

)i, j

≈Pi, j−1 −Pi, j+1

2∆λ

(5.1)

The second derivative on node (i, j) can be expressedin the central difference of the first derivatives of the insertpoint which is half step away:

[∂

∂ϕH3 ∂P

∂ϕ

]≈

(H3 ∂P

∂ϕ

)i+ 1

2 , j−(

H3 ∂P∂ϕ

)i− 1

2 , j

∆ϕ(5.2)

And the first derivatives in the equation can beexpressed by central difference as:

(H3 ∂P

∂ϕ

)i+ 1

2 , j≈ H3

i+ 12 , j

Pi+1, j −Pi, j

∆ϕ(H3 ∂P

∂ϕ

)i+ 1

−2 , j≈ H3

i− 12 , j

Pi, j −Pi−1, j

∆ϕ

(5.3)

Likewise, the isothermal and uncompressibledimensionless Reynolds Equation could be transformedto:

Ai, jPi+1, j +Bi, jPi−1, j +Ci, jPi, j+1+

Di, jPi, j−1 −Ei, jPi, j = Fi, j(5.4)

Where the coefficients are:



Ai, j = H3i+ 1

2Bi, j = H3

i− 12

Ci, j =(

dl ·

∆ϕ∆λ

)2H3

i, j+ 12

Di, j =(

dl ·

∆ϕ∆λ

)2H3

i, j− 12

Ei, j = Ai, j +Bi, j +Ci, j +Di, j

Fi, j = 3∆ϕ(

Hi+ 12 , j

−Hi− 12 , j

)

Based on the above equation, a set of equations which

apply to all internal nodes of i = 2 ∼ m, j = 2 ∼ n can beobtained, thus constituted a group of non-homogeneousalgebraic equations for (m−1)(n−1) internal nodes’ Pi, jvalues, and solved the value of each interval nodes’ Pi, j .Then, solve the equation group through iteration method.And to determine if the algebraic equation group’siteration result fulfill the precision requirement in order todecide the termination of iteration, following relativeconvergence principle is usually used:

m∑j=2

n∑

i=2

∣∣∣P(k)i, j −P(k−1)

i, j

∣∣∣m∑j=2

n∑

i=2

∣∣∣P(k)i, j

∣∣∣ ≤ δ (5.5)

Relative error value δ usually takes 10−3 . The flowchart in Figure 5.2 shows the process of solving oil filmsupporting reaction force using finite difference method.

6 Multi-body dynamic simulation and dataanalysis

In the engine’s operation process, the main bearing loadcaused by crankshaft force is the most important drivethat the body bears. The driving force generated by thecylinder firing is passed to the body through piston -connecting rod - crankshaft, thus the main bearing’smathematical model has important effect on thesimulation analysis of the body’s vibration and theradiated noise. Through co-numerical calculation ofADAMS/CONTROL and MATLAB, the parameters ofthe crankshaft system using oil film bearing forsimulation could be obtained.

During co-simulation, when solving the Reynoldsequation, in order to prevent irregular matrix causingunable to calculate, it is very important to define asuitable and minimal solving step length for thecrankshaft multi-body dynamic system. The fixed steplength INTERGRATOR \GSTIFF&FORMULATION\I3 solver in MSC \ADAMS is used here for calculation.The engine virtual prototype model uses flexiblecrankshaft for dynamic simulation; using flexiblecrankshaft could better reflect the crankshaft’s flexibledeformation, and also obtain the crankshaft’s stresses andstrains information, as well as the maximum dynamicstresses and strains location and amplitude, thereby

Fig. 5.2 Filmatic bearing pressure calculations

provide reference and determining criteria for thestructure’s improvement.

Figure 6.1 shows the main bearing loads of both thesimulation using oil film lubrication bearing and thesimulation turning the vice constraint bearing under thestandard condition of 2200rpm rotation speed. Mainbearing peak load value on y direction of the constraintbearing is 10.7% larger than the one of filmatic bearing,while the main bearing peak load value on x direction ofthe constraint bearing is 15.5% lower than the one offilmatic bearing. This shows that because of the filmaticbearing’s dynamic lubrication effect, the difference of themain bearing loads decreases, and main bearing loadstend to be stress-even in the working cycle time period.

Figure 6.2 shows the main bearing axle center’s pathsof the linear bearing under the speeds of 1000rpm and2200rpm, while Figure 6.3 shows the main bearing axlecenter’s path of filmatic bearing under the speeds of1000rpm and 2200rpm. As illustrated in the figures, there



Fig. 6.1 Load comparison of main bearing

is obvious difference between the axle paths of linearbearing and filmatic bearing. Meanwhile under high andlow speeds, linear bearing shows more different paths,while filmatic bearing’s paths are more consistent, and theoverall amplitudes under the two rotation speeds showsmall difference. This indicates that oil film bearing’smathematical model is more close to actual model thanthe model of linear bearing, therefore consideringbearing’s dynamic lubrication behavior in dynamicsimulation would help to better simulate the enginecrankshaft system under actual working conditions, andhave significant meaning for guiding engine’s dynamicdesign and structure design.

Fig. 6.2 Axle center paths of linear bearing

Figure 6.4 shows the pattern that engine crankshaft’smain bearings’ minimum oil film thickness changes alongwith the rotation speed. As shown in the picture, alongwith the speed’s increase, each main bearing’s minimumoil film thickness decreases. Take the main bearing 1 asexample, when speed is 1000rpm, the minimum oil filmthickness is 9.6µm, and when the speed increases to2200rpm, the thickness decreased to 3µm.

Fig. 6.3 Axle center paths of filmatic bearing

Fig. 6.4 Pattern of each main bearing’s minimum oil filmthickness’ changes with the rotation speed change

Meanwhile, the load film thickness of thehydrodynamic lubrication bearing is not simplydetermined by the bearing load and the journal speed, itmust be obtained by calculate each bearing’s axle centerpath. Figure 6.5 is the comparison chart of each bearing’smaximum load and minimum film thickness. Seen fromthe chart that the second main bearing’s maximum load is119KN while the first main bearing’s maximum load isonly 52KN, but the second main bearing’s minimum filmthickness is 6.2µm while the first main bearing’sminimum film thickness is 3µm. Although the first mainbearing bears smaller load, its minimum film thickness is3.2µm thinner than the second main bearing’s; hence itcan be seen that the first main bearing is easier to bedamaged.

Conclusion

With virtual prototype technology as simulation platform,this study made use of MSC/ADAMS and MATLAB andproposed a co-numerical calculation technology for the



Fig. 6.5 Comparison of each main bearing’s minimum oil filmthickness and maximum load

coupling of crankshaft system and oil film dynamiclubricating friction. The study introduced EHD(Elastohydrodynamics) theory into multi-body dynamicsimulation technology, using self-coded program, andconsidered the system’s oil film dynamic lubricatingfriction behavior, solved the Reynolds Equation andobtained the crankshaft’s main bearing reaction force.Through coupling calculation with the crankshaft systemvirtual prototype, this study also made relatively accurateprediction about the engine crankshaft system’s dynamicand kinematic characteristics. Following conclusionswere obtained:

First, the oil film dynamic lubricating frictionbehavior of the engine crankshaft system produces certainimpact on the system’s dynamic characteristics. It shouldbe considered in dynamic simulation calculations.

Second, simulations with hydrodynamic lubricationcoupling multi-body dynamic system could better reflectthe actual working conditions of engines, and provideeffective technology support for engine’s design anddevelopment.

References

[1] H. Y. Isaac Du . Simulation of Flexible Rotating Crankshaftwith Flexible Engine Block and Hydrodynamic Bearings fora V6 EngineNoise and Vibration Conference & ExpositionTraverse City, Michigan May 17-20, (1999).

[2] Lin Qiong, HAO Zhi-yong,JIA Wei-xin. Prediction methodof radiated noise by engine block. Journal of JiangsuUniversity(Natural Science Edition), 29(3), (2008).

[3] DU Aimin, LIANG Kun. Object-oriented DynamicalSimulation on Crank and Connection Mechanism of Engine.Journal of Tongji University(Natural Science), 38(5) (2010).

[4] Boedo,S. and Booker, J.F.A Mode-BasedElastohydrodynamic Lubrication Model with ElasticJournal and Sleeve ASME Journal of Tribology, Vol. 122,94-102 (2000).

[5] KIM,B.-J.,KIM .-W.Thermo-elastohydrodynamic analysis ofconnecting rod bearing in internal combustion engineASMEJournal of Tribology, vol. 123, 444-454 (2001).

[6] Wang Tao, Qin De, Hao Zhiyong. Advancements ofsimulative analysis and test method of bearings for I. C.EngineJournal of Tianjin Institute of Technology 19(1), 6-10(2003).

[7] Hsiao Kai-Long. Multimedia feature for unsteady fluidflow over a non-uniform heat source stretching sheet withmagnetic radiation physical effects. Applied Mathematics &Information Sciences, 6, 59-65 (2012)

Lin Qiong receivedthe PhD degree in PowerEngineering and EngineeringThermophysics fromZhejiang University in 2008.He is currently a Lecturein Zhejiang Universityof Technology. His researchinterests are in the areas ofstructure optimization, virtual

simulation and mechanism dynamics.


Crank Shaft Analysis

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