Crankshaft Vibration

I.J. Image, Graphics and Signal Processing, 2011, 5, 22-29 Published Online August 2011 in MECS (http://www.mecs-press.org/)

Finite Element Analysis of 4-Cylinder Diesel Crankshaft

Jian Meng,

School of Traffic and Vehicle Engineering Shandong University of Technology, Zibo, Shandong, China e-mail: [email protected]

Yongqi Liu, Ruixiang Liu

School of Traffic and Vehicle Engineering Shandong University of Technology, Zibo, Shandong, China e-mail: [email protected]

Abstract—The stress analysis and modal analysis of a 4-cylinder crankshaft are discussed using finite element method in this paper. Three-dimension models of 480 diesel engine crankshaft and crankthrow were created using Pro/ENGINEER software The finite element analysis (FEM) software ANSYS was used to analyse the vibration modal and the distortion and stress status of the crankthrow.The maximum deformation, maximum stress point and dangerous areas are found by the stress analysis of crankthrow. The relationship between the frequency and the vibration modal is explained by the modal analysis of crankshaft. The results would provide a valuable theoretical foundation for the optimization and improvement of engine design. Index Terms—finete element analysis; modal analysis; strss analysis; crankshaft

I. INTRODUCTION

Crankshaft is one of the most important moving parts in internal combustion engine [1]. It must be strong enough to take the downward force of the power stroked without excessive bending. So the reliability and life of internal combustion engine depend on the strength of the crankshaft largely. And as the engine runs, the power inpulses hit the crankshaft in one place and then another. The torsional vebration appeas when a power impuls hits a crankpin toward the front of the engine and the power stroke ends. If not controlled, it can break the cuankshaft.

Srength caculation of crankshaft becomes a key factor to ensure the life of engine. Beam and space frame model were used to calculate the stress of crankshaft usually in the past. But the number of node is limited in these models. With the development of computer, more and more design of crankshaft has been utilized finite element method (FME) to calculate the stress of crankshaft. The application of numerical simulation for the designing crankshaft helped engineers to efficiently improve the process development avoiding the cost and limitations of compiling a database of real world parts. Finite element analysis allows an inexpensive study of arbitrary combinations of input parameters including design

parameters and process conditions to be investigated [2-5].

Crankshaft is a complicated continuous elastomer. The vibration performance of crankshaft has important effect to engine. The calculation of crankshaft vibration performance is difficult because of the complexity of crankshaft structure, the difficult determinacy of boundary condition. Dynamic matrix method and dynamic substructural method combined with FME were used to calculate the vibration of crankshaft. The method of three-dimensional finite element was carried to analysis dynamical characteristic of diesel crankshaft [6-9].

In the paper, 3-D finite element analyses are carried out on the modal analysis of crankshaft and the stress analysis of crankpin. And the FME software ANSYS was used to simulate the modal analysis and crankshaft. The results of natural frequencies and mode shape were obtained. And stress and deformation distributions of crankpin were obtained by using ANSYS software. The results are regarded as a theory basis to optimize the design of crankshaft and analysis the structure dynamics of crankshaft.

II. CRANKTHROW STRESS ANALYSIS

A. crankthrow model It is necessary to simplify the model in the stress

analysis of crankshaft using ANSYS software. Because the 480 disel crankshaft structure is symmetrical and all the crankthrow is identical, one crankthrow model, one-half crankthrow model and one-quarter crankthrow model can be used to compute the static strength instead of whole crankshaft model. The three models are the equivalent in computing the static strength of 480 disel crankshaft, and the one-quarter crankthrow model uses the least computer resources. But the large stress and stress gradient appear at the one-quarter model section. This phenomenon will lead to the inaccuracy of simulation results. In this paper, one crankthrow model was used to calculate the static strength of crankshaft. The model was created by Pro/ENGINEER software, (see Fig. 1). As shown in Fig. 1, some tiny structure characteristics which had barely effect for the simulation results, such as rounding chamfers and oilhole, were simplified in the

1 Footnotes: 8-point Times New Roman font; 2 Manuscript received January 1, 2008; revised June 1, 2008;

accepted July 1, 2008. 3 Copyright credit, project number, corresponding author, etc.

Copyright© 2011 MECS I.J. Image, Graphics and Signal Processing, 2011, 5, 22-29

mailto:[email protected]

Finite Element Analysis of 4-Cylinder Diesel Crankshaft 23

model. Then the model was imported to ANSYS software. The main physical dimensions of crankthrow are shown in Tab. I. The material of crankthrow is 42CrMn. The physical parameters used in the crankthrow simulation are list in Tab. II.

According to the structure of crankthrow, the crankpin model was meshed by solid45 which has 8 nodes tetrahedral feature. Fig. 2 shows the model after meshed by solid 45.

B. Boundary conditions The boundary conditions are the critical factors for the

correctness of calculation. The boundary conditions in the crankthrow model consist of load boundary condition and restriction boundary condition. The mechanics boundary conditions mainly involves: gravity, centrifugal force, crankpin neck surface force, various bending moment and torque,etc. Gravity, centrifugal force, various bending moment and torque can apply to the model with the distributed force, ANSYS software simulates the effects of guavity and centrifugal force itself based on the given gravity accelerative, angular velocity, density and physical dimension. So the load applying on the crankpin neck surface becomes the critical factor of load boundary condition. In the paper, kinetic method is used to calculate load. And the load applying on the crankpin surface is supposed as distributed load. The distributed load along the crankpin axis is a quadratic parabola distribution and along the radial direction within 120°is cosine distribution. Fig. 3 shows the distribution function form.

The quadratic parabola load distribution equation along

the crankpin axis is assumed by: 2

xQ ax bx c= + + . (1)

When x=±L, Qx=0; when x=0, Qx=Qmax, the above formula can be written as:

Figure 2. The crankpin finite element mesh

Figure 3. load distribution in the crankpin

TABLE I. CRANKTHROW MAIN PHYSICAL DIMENSIONS

Physical parameters Values

Crankpin diameter (mm) 50

Crankpin axial length (mm) 31

Crankthrow main journal diameter (mm) 58

Crank cheek thichness (mm) 19

Crank cheek height (mm) 112

TABLE II. PHYSICAL PARAMETERS USED IN SIMULATION

Physical parameters Values

Tensile strength ( MPa) 1080

Yield strength (MPa) 930

Elongation (%) 12

Reduction of cross sectional area (%) 5

Impacting energy (J) 63

Notched bar impact strength ( J/cm2) 78

Rigidity (HB) 217

Modulus of Elasiticity (GPa) 210

Poisson ratio 0.3

Density (g/cm3) 7.9

Figure 1. Crankthrow mode


24 Finite Element Analysis of 4-Cylinder Diesel Crankshaft

20 aL bL c= + + . (2) (3) 20 aL bL c= − + (4) maxQ = cThe a, b, c can be obtained by solving the (2), (3) and (4). The results are a=-Qmax/L2, b=0, c=Qmax. Accordingly, the load distribution along the crankpin axis can be obtained as follows:

2

max 21-xxQ QL

= （）

s

）

s

(5) (5)

where x = -L-L. where x = -L-L. The cosine load distribution equation along the radial

direction within 120°is supposed by: The cosine load distribution equation along the radial

direction within 120°is supposed by: ( ), coxQ x Q k( ), coxQ x Q kθ θ= × (6) where θ=-π/3-π/3. When θ=π/3, Q(x, θ)=0, the k can be calculated by (7):

3cos 0 /

3 2k kπ π= ⇒ = =

3 2π

(7)

Accordingly, the load distribution along the crankpin radial direction within 120°can be written as follows:

( )

2

2

3, cos2

3(1 ) cos2x

Q x QxxQL

θ θ

θ

= ×

= − × (8)

The total load applying on the crankpin neck surface can be caculated by the follow equation:

3

3

23

max 23

max

( , )

3(1 )cos( )2

169

L

c L

L

L

F Q x ds dx

xQ RL

RL Q

π

π

π

π

θ

θ θ

− −

− −

=

= −

= ×

∫ ∫

∫ ∫ d dx (9)

where ds=Rdθ, R is the crankpin radius. Qmax can be expressed in terms of (9) as the following expression,

max916

cFQ

RL= × (10)

Rewriting (6) as:

( )2

2

9 3, (1 ) co16 2

cF xQ xLR L

sθ θ= − × (11)

where Fc is the total load acting on the crankpin neck surface, x is crankpin load bearing length, x=-L-L [10,11]. The largest load was used in this paper when the crankpin working at the largest toque.

Base on (11), equation loaded method was used to exert the load on the crankpin surface. The selected crankpin surface area after exerting equation load is shown in Fig. 4.

The method to deal with the restriction boundary condition mainly based on the practical situation of crankshaft strcture. The degrees of freedom of X, Y, Z direction at the left crankthrow end surface are limited. While at the right crankthrow end surface the motion degrees of freedom of X, Y radial direction are limited. The scheme of the crankthrow model after exertting the boundary conditions completely is illustrated in Fig. 5.

C. Analysis

After defining the boundary conditions, the simulation can be started. As the number of elements is large, Pre-Condition CG solver was used in this paper. The results of simulation are given in Fig. 6 and Fig. 7.

Figure 6. Deformation distribution (MPa) on the crankpin at the

most critical loading condition

Figure 4. The diagram of selected area after exertting equation

load.

Figure 5. The scheme of the crankthrow model after exertting the boundary conditions completely



As shown in Fig. 6, the maximum deformation is 0.0685mm at the most critical loading condition. The maximum deformation appears at the center of crankpin neck surface. The stress distribution of crankthrow at the most critical loading condition is illustrated in Fig. 7. From Fig. 7, we note that the maximum stress is 103.974 Mpa. The maximum stress appears at the fillets between the crankshaft journal and crank cheeks, and near the central point. The edge of main journal is high stress area, so the oil hole or hole can not be ingrooved at this area. The simulation results corresponds to practical situation. The analysis of crankthrow deformation and stress provides a theoretical basis to optimize the design and fatigue life calculation.

Ⅲ. CRANKSHAFT MODEL FORMULATION

A. structure dynamic properties of finite element method

When the model was divided into finite element, the dynamical balance equation is [12,13]: (12) { } { } { } { ( )}i c sF F F F t+ + =

where {Fi} is inertia force vector quantity; {Fc} is damping force vector quantity; {Fs} is elastic force vector quantity; {F(t)} is dynamic load vector quantity. For the system without damp or ignoring damp, the balance equation can be written by: { } { } { ( )}i sF F F t+ = (13) The inertia force vector quantity can be substituted by quality matrix and node displacement vector. Then }{ iF

becomes:

( )2

2{ }iF M ttα∂

=∂

(14)

Where is node displacement vector, M is quality matrix. The elastic force vector can be substituted by node displacement vector and rigidity vector. Thus the

( )tα

}{ sF can be written by:

{ } ( )sF K tα= (15)

where K is rigidity vector, is node displacement. When the system is natural vibration, {F(t)l}= 0, and the (13) can be transformed as the follow

( )tα

( ) ( ) 0M t K tα α+ =&& (16) The characteristic equation based on (1) is given by 2( ) ( )K M tω ϕ 0− = (17) where ω is intrinsic frequency. ANSYS software provides several arithmetic, such as subspace arithmetic, Interactive arithmetic, Lanczos arithmetic, Reduction arithmetic, etc. Lanczos arithmetic is appropriate for calculating the huge and complicated structure. In this paper, with the powerful functions of high operation speed and high precision, Lanczos arithmetic is used to calculate the natural frequency and fundamental main modes.

Figure 7. stress distribution (MPa) on the camshaft at the most

critical loading condition

The derivation steps of Lanczos arithmetic are given by the follows.

Given vector xi (i=1, 2, 3,…, r). Then equation (18) can be solved by: 1i iK x Mx −=

uur (18)

Orthogonalization: 1 1 2 2i i i i i ix x x xα β− − − −= − −

uur (19)

where 1i i i 1x Mxα − −=

uur (20)

Regularization: /i ix x iβ= (21)

where . ( )1/ 2ˆ ˆi i ix Mxβ =Generalized eigenvalue problem ( )

translates into standard eigenvalue problem which is Lanczos vector towards to triangle matrix. Based on (16) to (21),

r rK MΦ = ΦΩ

1A K M−= can be solved by (22): 1 1 1i i i i i i i1 2Ax x x xβ α β− − − − −= + + (22) where (i=1, 2, 3,…, r), . }{0 0x =

(22) may be written as matrix form AX XT= (23) where

2

2 2 3

3 3 4

i

T

α ββ α β

β α β

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

L L

L L

, (24)

[ ]1 2 rX x x x= L (25) The equation between original characteristic matrices and Lanczos vector is written as: r XZΦ = (26) where [ ]1 2r rϕ ϕ ϕΦ = L . (27) Substitution (27) into original eigenvalues, use XTMK-1 premultiply and 1

rλ −= Ω post-multiply in equation two sides, then use (23) and TX MX I= obtains the equation: TZ Zλ= (28)



The eigen solution of (28) is [ ]1 2 1,r rZ z z z λ−= ΩL = . (29) Then r XZΦ = , 1

r λ−Ω = .

Accordingly, . 2 21/ ( 1, 2, , )i iW iλ= = L r

B. Crankshaft Model In the present research, a 480 diesel crankshaft was

studied. The crankshaft has four crankthrows, three rod journals and two main journals, and the mainly dimension parameters are shown in Table III. According to complicated structure of crankshaft, the integral crankshaft should be applied when performing finite element model analysis. In view of the structure shape characteristics of crankshaft, reducing the solution time and enhancing the simulation accuracy, the crankshaft model was simplified in establishment process. The premise of simplification is that it does not influence the dynamics characteristics of crankshaft. The 480 crankshaft model was created by Pro/ENGINEER software.

The structure of the crankshaft has more small fillets and fine oil hole. Considering these factors in establishment process, finite element mesh of crankshaft becomes very densely, the number of node equation increase greatly. These factors would extend the solution time, make the unit shape unsatisfactory and amplify the accumulative error. This would lower the simulation accuracy. Hence, in the paper, the real crankshaft was represented by a simplified model. In this simplified model, the chamfers which radius less than 5mm and the oil holes which diameter less than 12mm were ignored. The model of four-cylinder crankshaft is shown in Fig. 8.

Then the model was imported to the ANSYS software.

According to the structure of crankshaft, the crankshaft model was meshed by 8-node hexahedron unit solid45. the meshing accuracy is 3 grade. After automatic meshing, in order to enhance the simulation accuracy and avoid generating the macrocephalic mesh, the crankshaft dangerous areas were further tessellated. The 3-D crankshaft finite element grid model is shown in Fig. 9. The material of crankshaft is 42CrMn. The physical

parameters used in the crankshaft simulation were list in Tab. II.

C. Boundary Conditions

Figure 8. 3-D entity model of crankshaft

The crankshaft bears the constraints of main journals and longitudinal thrust bearing. Because of the effect of load, crankshaft main journals appear bend deformation between the lower main-bearing half and upper main-bearing half. And the longitudinal thrust bearing can prevent effectively the crankshaft axial movement and ensure the piston-and-connecting-rod assembly normally work. Five surface radial symmetry constrains were exerted on the five main journals surface respectively, axial displacement constrains were exerted on the two end face of crankshaft. Then the modal analysis was carried out using the ANSYS software [14].

D. Modal Analysis The vibration characteristic of crankshaft was obtained

with modal analysis. The former six modal parameters were list in Table. III.

The former six vibration modal diagrams of crankshaft are shown in Fig. 3-8. From the simulation results and the vibration modal shapes, the lowest frequency is 116.93 Hz, and with the increase of modal order, the frequency increase accordingly within the former six modes. Referring to Fig. 10 and Fig. 11, both the crankshaft first and second vibration modes are the firs-mode bending vibration in the mutually perpendicular plane YOZ and XOZ. As shown in Fig. 12, the crankshaft third vibration mode is the firs-mode bending vibration in XOZ plane, and the maximum distortion appears at the first crankpin. Fig. 13 and Fig. 14 show that the crankshaft fourth and fifth modes are the second-mode bending vibration in the YOZ and XOZ plane. As shown in Fig. 15, the sixth mode is third-mode bending vibration in the YOZ plane.

The maximum deformation of crankshaft appears at the third cylinder, the fourth cylinder and the crankpin between the third and fourth cylinder. As shown from the Fig. 10 to Fig. 14, the vibration is bending vibration under the low frequency, and the maximum bending

TABLE III. CRANKSHAFT MAINLY DIMENSIONS

Structure parameters Values

Crankshaft length (mm) 538

Crankthaft height (mm) 148

Crank radius (mm) 67.5

Main journal diameter (mm) 58

rod journal (mm) 58

Crankpin axial length (mm) 31

Main journal axial length (mm) 29.5

Counterweight radius (mm) 74

Crank cheek thickness (mm) 19

Figure 9. The crankshaft finite element mesh



deformation appears at the fillet between main bearing journal and crankpin.

Figure 12. Third vibration modal of crankshaft

Figure 10. First vibration modal of crankshaft

TABLE IV. THE FIRST SIX MODAL PARAMETERS

Modal orders 1 2 3 4 5 6

Frequency

(Hz) 116.93 124.1 234.7 316.58 344.14 354.82

Figure 13. Fourth vibration mode of crankshaft

Figure 11. Second vibration mode of crankshaft

Figure 14. Fifth vibration mode of crankshaft



Ⅳ. CONCLUSIONS In this paper, the crankshaft model and crankthrow

momal were created by Pro/ENGINEER software. Then the model created by pro/Engineer was imported to ANSYS software.

The maximum deformation appears at the center of crankpin neck surface. The maximum stress appears at the fillets between the crankshaft journal and crank cheeks, and near the central point.journal. The edge of main journal is high stress area.

The crankshaft deformation was mainly bending deformation under the lower frequency. And the maximum deformation was located at the link between main bearing journal and crankpin and crank cheeks. So this area prones to appear the bending fatigue crack. Base on the results, we can forecast the possibility of mutual interference between the crankshaft and other parts. The resonance vibration of system can be avoided effectively by Appropriate structure design The results provide a theoretical basis to optimize the design and fatigue life calculation.

ACKNOWLEDGMENT This research is partially supported by University

Science and Technology Program of Shandong Province of China under Grant J10LD62 and Natural Science Foundation of Shandong Province, China under Grant Y2006F63.

REFERENCES [1] J. Haats and S. Wambach, “Lightweight crankshaft drives by

forging,” Steel times, pp. 346-347, september 1999 [2] Myung-Rae,Dae-Yoon, and S.Hyuk, “Load Characteristics of

Engine Main Bearing Comparison Between Theory and Experiment,” KSME International Journal ， Vol. 16, pp.1095-1101, 2002.

[3] Z. P, Mourelatos, “A crankshaft system model for structural dynamic analysis of internal combustion engines,” Combustion and engines，vol. 79，pp. 2009-2027, 2001.

[4] O kamura. Experimental study of the correction between crankshaft vibrations, engine structure vibrations, and engine noise in high speed engines. SAE Paper, 951290, 1995.

[5] A. Alaswad, A.G. Olabi, K.Y. Benyounis, “Integration of finite element analysis and design of experiments to analysis the geometrical factors in bi-layered tube hydroforming ,” Materials and Design,

Figure 15. Sixth vibration mode of crankshaft

[6] O. kamura H, “A dynamic stiffnessmat rix approach to the analysis of three dimensional vibrations of automobile engine crankshaft,” Part 1-Background and application to free vibrations. Proceeding of Vehicle Noise, ASME, 1990, 9 (2) , pp. 899-908.

[7] J. Sun, C..L. Gui, and x. Li, “A Review of Crankshaft Strength Analysis for Internal Combustion Engines,” Transactions of Csice, 20(2), pp, 179-184,2002.

[8] Z. Mourelatos, “An analytical investigation of the crankshaft flywheel bending vibrations for a V6 engine,” SAE Paper 951276, 1995.

[9] Han Songtao, Hao Zhiyong, “Mode analysis of three-dimensional finite element and experimental study on a 6102B diesel engine crankshaft,” Transactions of the Chinese Society of Agricultural Machinery , vol.32(4) , pp. 74-77, 2001.

[10] Y. Y. Chun, “The Performance Analysis and Optimal Structural Design for Crankshaft,” [D], JiangSu, Jiangsu University, 2005.

[11] Liu Tao, “Strength Calculation of Engine Crankshaft,” [D]. ShanDong, Shandong University, 2000

[12] H. LI,” Influence of the Processing of Boundary Conditions on the Calculation of Crankshafet Strength”, Journal of Anqing Teachers College(Natural Science Edition), 12(2), pp, 35-37, 2006.

[13] S. T. Han, Z. Y. Hao, “Mode Analysis of Three dimensional Finite Element and Experimental Study on a 6102B Diesel Engine Crankshaft”, Transactions of The Chinese Society of Agricultural Machinery, 32(4), pp, 75-77, 2001.

[14] L. Wang, Y. Xiang, Y. H. Lu, W. F. Liu, “Modeling and Free Modal Analysis of the Crankshaft.” Journal of Luoyang Technology College, 14(1), pp, 8-10, 2004.

Jian Meng was born in P.R.China in 1979, earned his B.S.degree in the field of Agricultural Machinery and Automation in 2002 and M.S.degree in the field of Farm Machinery Engineering in 2005 from Shandong University of Agricultue, Tai'an city,P.R.China.

He is now a LECTURE of Thermal Energy and Power Engineering department in Shandong University of Technology since July, 2005. He was a co-author of Vehicle CAD Technology and Pro/E Application published by Beijing Industrial Press in 2009. His research interests include clean energy, engine simulation.

Now he takes part in a National 863 High-tech Programme of China under Grand No. 2009AA063202.

Yongqi Liu was born in P.R.China in 1965,earned his D.S.degree in the field of Power Machinery and Engineering from Shanghai University of Technology in 2003. He is now a PROFESSOR as well as the DEAN of Thermal Energy and Power Engineering department in Shandong University of Technology. He has

published 52 research papers since 2006 in the area of clean energy. At present time, he takes part in many research projects supported by Shandong Natural Science Foundation and now he is the chief of National 863 High-tech Programme of China under Grand No. 2009AA063202. His research interests include clean energy, lean methane oxidation and utilization.


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Ruixiang Liu was born in P.R.China in 1963. He got his D.S.degree from Dalian University of Technology in the field of Electronic Control Technology of Diesel Engine in 2005 and now

he is a ASSOCIATE PROFESSOR of Thermal Energy and Power Engineering department in Shandong University of Technology. His research interests include engine emission and control, Working process simulation, and lean methane oxidation and utilization


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