-
Engineering Failure Analysis 18 (2011) 735746Contents lists
available at ScienceDirect
Engineering Failure Analysis
journal homepage: www.elsevier .com/locate /engfai lanalFailure
analysis of reciprocating compressor crankshafts
J.A. Becerra , F.J. Jimenez, M. Torres, D.T. Sanchez, E.
CarvajalHigh School of Engineering, University of Seville,
Spain
a r t i c l e i n f oArticle history:Received 13 July
2010Accepted 6 December 2010Available online 15 December 2010
Keywords:CrankshaftReciprocating
compressorFailureOverload1350-6307/$ - see front matter 2010
Elsevier Ltddoi:10.1016/j.engfailanal.2010.12.004
Corresponding author.E-mail address: [email protected] (J.A.
Becerra).a b s t r a c t
An analysis of the premature failure in a high number of
crankshafts from the same modelof a four cylinder reciprocating
compressor used in bus climate control systems has beencarried
out.The analysis included visual examination, crankshaft chemical
composition and hardness
analysis and a dynamical model of the system. The simulation
included several sub-mod-els:
Thermodynamic model of the refrigerating cycle. Compressor
torque dynamical model. Finite element model (FEM) of the
crankshaft. Dynamic lumped system model.
Results from the lumped model were incorporated into the FEM in
order to evaluate thestresses due to the torsional dynamic in the
crankshaft.Several conclusions can be drawn from this study:
Analysis of the compressor revealed that the torsional dynamic
controls the stress inthe crankshaft and that the influence of the
gas forces on the crankshaft stress is onlyminor.
The appearance of the fracture was consistent with a torque
overload. The maximum stress in the crankshaft, as obtained from
the FEM and lumped model,was located in the keyway, and this
location belongs to the fracture surface in mostof the broken
crankshafts. The influence of the stress concentration factor
imposedby this geometry is therefore very high.
The compressor speed range was found to continuously cross the
three lower resonancefrequencies.
The exhaust valve of the compressor should be redesigned in
order to reduce gas forces,power consumption and pressure drop.
2010 Elsevier Ltd. All rights reserved.1. Introduction
The first automobile to be equipped with air conditioning as we
know it today appeared in 1939 (Packard) and this tech-nology has
been under constant development ever since. Indeed, today around
70% of new automobiles world-wide incor-porate this system. In the
case of buses almost all vehicles are fitted with this technology.
One of the most important. All rights reserved.
http://dx.doi.org/10.1016/j.engfailanal.2010.12.004mailto:[email protected]://dx.doi.org/10.1016/j.engfailanal.2010.12.004http://www.sciencedirect.com/science/journal/13506307http://www.elsevier.com/locate/engfailanal
-
736 J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
735746components in an air conditioning system is the compressor,
which in many systems is a reciprocating volumetriccompressor.
Although crankshaft failure is not common in this type of
equipment, when such an event does occur it could affect all ofthe
components of the kinematic chain (connecting rod, cylinder head,
etc.).
An analysis of the failure of a reciprocating compressor
belonging to a bus climate system is described here. The
compres-sor consists of four cylinders (V arrangement) coupled to
the diesel engine of the bus through a V belt. The compressor
gen-erally operates at a variable speed between 1000 and 2000
rpm.
The location of the compressor, which is powered by the bus
engine through a V belt, is shown in Fig. 1 The compressor
isswitched on/off by an electromagnetic clutch located at the free
end of the crankshaft.
The most common cause of crankshaft failure is fatigue. In order
for fatigue to occur, a cyclic tensile stress and crack ini-tiation
site are necessary. The crankshafts run with harmonic torsion
combined with cyclic bending stress due to the radialloads of the
cylinder pressure transmitted from the pistons and connecting rods
to which inertia loads have to be added.Although crankshafts are
generally designed with high safety margins in order not to exceed
the fatigue strength of thematerial, high cyclic loading and local
stress concentration could lead to the formation and growth of
cracks even whenthe fatigue strength is not exceeded in terms of
average values. Pandey [1] analysed failures in the crankshafts of
35 hptwo cylinder engines used in tractors, where the fracture
plane was located between the main bearing and the journal.The
crack began to form at the crank-pin web region in a plane at
around 45 with respect to the rotational axis. This crackshowed
typical fatigue failure with beachmarks. The stress related to the
onset of fatigue was estimated to be 175 MPa,which is well below
the tensile stress (around 680 MPa) of the nodular cast iron
fromwhich the crankshafts were made. Tay-lor et al. [2] developed
two fatigue experiments for a crankshaft of a four cylinder engine
made of spheroidal graphite castiron, which has a tensile strength
of 440 MPa: one experiment was torsional and the other flexural.
The crankshafts under-went torsional and flexural cyclic loading
until failure and in both tests the same fracture angle of 45 with
respect to therotational axis was observed.
The work described here concerns a methodology that allowed the
cause of failure of a crankshaft to be established byconsidering
both torsional and bending loads. The approach involved the
evaluation of the von Mises stress at the crankshaftthrough dynamic
analysis.
This methodology is based on the results of a dynamic lumped
model developed jointly with a finite element model [3].2.
Crankshaft material and failure description
2.1. Crankshaft description and material composition
The crankshaft was made of 34CrMo4 (EN 10083-3:2002 number:
1.7220, BS 708M 32) low alloy steel forged as a singlepiece prior
to quenching and tempering. Each crank was connected with two
connecting rods.
A photograph of the crankshaft is shown in Fig. 2 and the
individual components are labelled.Chemical analysis data for three
of the broken crankshafts were obtained using a spectrometer and
the results are shown
in Table 1.The chemical composition results obtained in the
tests are consistent with typical 34CrMo4 values, although the
carbon
percentage was slightly lower than expected for 34CrMo4
steel.Fig. 1. The operating location of the compressor.
-
Fig. 2. Compressor crankshaft with common failure surface.
Table 1Chemical composition of the fractured crankshaft
(wt.%).
Crankshaft Id. 0 0 1 0 0 2 0 0 3 34CrMo4 steel
Carbon (%) 0.36 0.33 0.38 0.300.37 0.02Manganese (%) 0.73 0.84
0.78 0.600.90 0.04Silica (%) 0.23 0.24 0.23
-
Fig. 3. Appearance of the failure surface.
738 J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
735746Three forces act on the crankshaft:
Forces due to gas pressure in the cylinder Friction forces
Inertia forces
In order to evaluate the forces acting on the crankshaft due to
gas pressure within the cylinder, the pressure inside thecylinder
during a cycle needs to be estimated. For this purpose a
thermodynamic model of the evolution of the refrigeratinggas was
developed.
The cylinder volume was evaluated using the crank and rod
equation [4]. The inertia force was calculated from the crank-shaft
piston and the connecting rod geometry and material. The friction
force was estimated from a model developed by Re-zeka [5] and
adapted to this compressor.
Parameters included in the thermodynamic model were as
follows:Number of cylinders 4
Capacity per cylinder 148 cm3Bore 68.0 mm
Connecting rod length 105.0 mm
Stroke 40.0 mm
Geometric dead volume 2% of the total capacity
Fluid R 134a
High pressure 19.0 bar
Low pressure 2.5 barIntake and exhaust valve flow
characteristics were measured and a 0.70 discharge coefficient was
measured in a test rig. Themodel is dependent on the speed of the
compressor.
The evolution of the estimated pressure, mass and temperature of
the fluid inside the cylinder (at 1600 rpm) are repre-sented in
Fig. 4.
For the static analysis several speeds within operating range of
the compressor were studied.In all scenarios studied, an
overpressure in the exhaust process was observed (indicated in Fig.
4). The intensity of this
extra pressure increase has a detrimental effect on compressor
efficiency because it leads to a reduction in the COP coeffi-cient
of the refrigerating cycle and an overload in the whole system. An
insufficient cross area in the exhaust valve is respon-sible for
this behaviour and a redesign is required. Furthermore, an
insufficient cross area in the exhaust valve leads to adecrease in
the intake pressure and this finally reduces cylinder intake mass
through the diminution of volumetric efficiency.This effect is more
important as the environmental temperature and operating altitude
of the system increase.
The amplitudes of the first to fourth harmonics in the Fourier
series for the pressure are represented in Fig. 5.
4. Compressor torque dynamical model
The evolution of the gas pressure inside one cylinder and its
associated torque over the crank must be added in the orderof the
cylinders to obtain the total torque due to all four cylinders.
This value, combined with the friction and inertia torques,gives
the overall torque on the crankshaft.
The torque developed by gas pressure and inertia is shown in
Fig. 6A, the torque necessary to overcome friction forces isshown
in Fig. 6B and the total torque is shown in Fig. 6C.
-
Fig. 4. Estimated evolution of temperature, mass and pressure in
the cylinder for a speed of 1600 rpm. Max pressure 19.0 bar. Intake
pressure 2.5 bar.
Fig. 5. Harmonic amplitudes of the gas pressure inside the
cylinder at 1500 rpm.
J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
735746 739The mean torque required to overcome gas pressure and
inertia forces is 57.8 Nm and the value to overcome frictionforces
is 7.2 Nm (11% of the total mean torque). The maximum instantaneous
torque needed is 120 Nm.
The results for thermodynamic cycle power, mechanical power
losses and total power for some of the speed values stud-ied are
shown in Table 3.
Phase diagrams for compressor cylinders are shown in Fig. 7 and
it can be observed that in the fourth harmonic all cyl-inders are
in phase. Although the amplitude of the fourth harmonic is not very
high (Fig. 5), this fourth harmonic and itsmultiples would produce
the highest torque on the crankshaft.
-
Fig. 6. Mean torque related to gas and inertia forces (A),
friction forces (B) and total forces (C) at 1600 rpm.
Table 3Power results obtained from the torque acting on the
crankshaft for several shaft speeds.
RPM Thermodynamic cycle power (kW) Mechanical power losses (kW)
Total power (kW)
1000 5.4 0.4 5.81600 9.7 1.2 10.92000 11.2 1.3 12.5
Fig. 7. Phase diagram for compressor cylinders and for the first
to fourth harmonics.
740 J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
7357465. Dynamic torsional analysis
In order to estimate the stress level in the crankshaft due to
the dynamic behaviour of the system, a torsional lumpeddynamic
model of the system with five degrees of freedom (DOF) linked to a
finite element (FE) model was developed. Aschematic representation
of the procedure followed to evaluate the stress level in the
crankshaft is shown in Fig. 8.
The main contribution to the torque on each crank is due to the
pressure developed over the top of the piston of eachcylinder. This
pressure was simulated through the development of the thermodynamic
model for the refrigerating gas, asdescribed in the previous
section. Mechanical losses produced by friction [4] and inertia
torque were also considered.
-
Fig. 8. Methodology to evaluate the stress level in the
crankshaft due to the dynamic behaviour of the system.
J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
735746 741The excitation torque obtained in this step was
incorporated into a lumped model of the system. This lumped model
re-quires the stiffness of both cranks in which the crankshaft was
split to be included in the process. The stiffness values
wereobtained through an FE model of the crankshaft.
This step gives the relative angular displacement between
adjacent DOFs. The results (angular displacements) that in-volve
the crankshaft (DOFs 2, 3 and 4) were subsequently applied in the
FE model and in this way a von Mises stress contourin the
crankshaft could be obtained.
5.1. FE model description
The finite element model of the crankshaft was developed using
MSC/Nastran. The characteristics of the material (de-tailed in
Section 2) used in the model for the crankshaft are as
follows:Material 34CrMo4 Steel
Youngs modulus 210 GPa
Poisson coefficient 0.3
Yield threshold 550 MPaThe mesh of the finite element model used
to evaluate the stiffness of the crankshaft is shown in Fig. 9. The
same modelwas also used in the final step to evaluate the stress
level in the crankshaft. The boundary conditions applied during the
eval-uation of the stiffness were null radial displacement in
bearing regions.
5.2. Torsional lumped model
A scheme of the lumped model developed here is shown in Fig. 10
and the data involved are given in Table 4.The inertia of each
degree of freedomwas evaluated directly from the crankshaft
dimensions and material characteristics.The equivalent stiffness
for every crank segment was evaluated through a static finite
element analysis of the crankshaft
described above. V belt stiffness values were evaluated through
a Kozesnik model, K = AE/L, where A is the transverse area ofthe
belt, E is the equivalent Youngs modulus of the belt, and L is the
effective length. This model gives values for the
com-pressor-driven belt (A = 162 mm2; L = 1.075 mm) and for the
alternator band (A = 110 mm2; L = 370 mm). Equivalent Youngsmodulus
values were estimated by the manufacturer to be in the range 96140
MPa for both belts.
-
Fig. 9. Finite element mesh of the crankshaft.
Fig. 10. Lumped model of the system.
Table 4Stiffness and inertia parameters in the lumped model.
Degree of freedom Inertia (kg m2) Stiffness (Nm/rad)
1 Engine pulley Very high2 Crankshaft end (clutch side) 0.1017
K12 = 183.1261.13 Crankshaft intermediate 0.00177 K23 = 59,5004
Crankshaft end (oil pump side) 0.00177 K34 = 978005 Alternator
pulley 0.006 K25 = 90.3132.0
742 J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
735746The results obtained on solving this analytical model for the
system are the angular displacement between adjacent DOFs.These
data were then applied as external angular displacements in the
finite element model, thus allowing the von Misesstress contour to
be obtained. The torsional lumped system model was formulated as
follows:Jh C _h Kh Mfrict:h; _h;l; geometry Meffective Mcompressor
Minertiawhere J is the inertia matrix associated with elements that
rotate in the system (kg m2), h the acceleration vector for
eachdegree of freedom (rad/s2), K is stiffness matrix (Nm/rad), h
the angular displacement vector for each degree of freedom (rad),C
the damping matrix (Nm s/rad), _h the velocity vector for each DOF
(rad/s), l the oil lubrication dynamic viscosity (N s/m2),Mfric.
the mechanical losses for each DOF (Nm), Mcompressor the Compressor
torque (Nm), Minertia the inertial torque due toalternative parts
of the system (Nm), and Mindicated is the mean effective torque in
the engine shaft end (Nm)
A maximum power of 5 kW for the alternator was assumed to
include the charge in the alternator. Several resolutions inwhich
this value was varied were also carried out and appreciable
modifications in the system outputs were not observed.
5.2.1. Critical speeds analysisOn considering a free vibration
system, i.e. without forces acting, the system was solved (assuming
K12 = 200 Nm/rad)
and the torsional critical frequencies obtained in Hz were as
follows:
-
Fig. 11.colour
J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
735746 7436; 14; 612; 1814Due to the uncertainty in evaluating the
belt stiffness (K12), a sensitivity analysis was carried out and a
slight modifica-tion was observed for the first two critical
frequencies with a variation of up to 25% in the belt stiffness.
Such modificationswere not observed for the third and fourth
critical frequencies.
The first two critical frequencies intersect the main harmonic
(4 rpm), and multiples of it, at speeds below and far re-moved from
the lower limit of the operating speed range (1000 rpm) except for
start up and shut down processes. In thisway only in these latter
processes the critical frequencies can significantly affect the
system.
On the other hand, the third and fourth critical frequencies
intersect multiples of the main harmonic (20, 24, etc.)within the
nominal operation range of the compressor, as can be observed in
Fig. 11. The low amplitude associated withthese harmonics
(especially for those that affect the 4th critical speed) means
that even if these harmonics have the mostinfluence they would not
produce a high response in the system. The force-response model
developed in next paragraphallows an estimation of the response
level for each of the harmonic multiples.
5.2.2. Force response of the systemSolving the model including
torque imposed by the engine, compressor, inertia and finally the
friction torque, produces
the instantaneous angular oscillation of each degree of freedom
from which torsional loads in the whole crankshaft can
beestimated.
The relative angular displacements at 1500 rpm between adjacent
DOFs belonging to the crankshaft are shown in Fig. 12.These values
were subsequently applied to the finite element model of the
crankshaft in order to obtain the stress level in-duced at this rpm
level.
In order to evaluate the stress level in the crankshaft in the
worst case, the maximum amplitudes of these two DOFs with-in the
range 4003000 rpm were calculated. The results are shown in Fig. 13
(DOFs 23 and DOFs 34).
Three speeds were observed with high response amplification,
i.e. 1311 (28 1311 rpm = 3rd critical speed), 1530(24 1530 rpm =
3rd critical speed) and 1836 rpm (20 1836 rpm = 3rd critical
speed), and the maximum deformation oc-curred between DOFs 32,
where the cracks appeared. A maximum deformation of approximately
0.4 between DOFs 23could be sufficient to approach the yield point
of the material. However, this phenomenon alone does not explain
the cracksbecause the incorporation of damping into the model would
lead to a lower deformation value.
5.3. Finite element model
The model was meshed using a 4-node tetrahedral solid element.
Each journal was supported by its bearing, which al-lowed free
rotation. In this way the appropriate reaction could be considered
when the forces applied to each crankpin, jour-nal and bearings are
linked through non-linear gap elements. These elements develop
radial forces only when both surfacesare compressed. The same type
of element was used to transmit the forces from the connecting rod
big end to each crankpin.
Two different types of loads were applied simultaneously to the
crankshaft:
Torsional loads. These are derived from the lumped model
described above. The maximum angular displacement pro-duced by the
dynamic lumped model was imposed on each of the planes in which the
degrees of freedom belongingto the crankshaft are defined. The
angular displacement on both cranks is represented in Fig.
13.Critical 3rd and 4th frequencies of the system and Campbell
diagram (red lines = multiples of 4 RPM). (For interpretation of
the references toin this figure legend, the reader is referred to
the web version of this article.)
-
Fig. 12. Dynamic response of the system at 1500 rpm.
Fig. 13. Maximum angular deformation between adjacent DOFs of
the crankshaft in the operating speed range.
744 J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
735746 Radial loads. The connecting rod big end transmits gas
pressure from each cylinder to each crankpin as forces
distributedalong the pin surface. These forces can be decomposed
into tangential, which produce engine torque, and radial,
whichproduce bending of the crankshaft. The second type of force
must also be imposed to the crankshaft.
-
Fig. 14. Von Mises stress contours with a maximum angular
deformation of 0.4 between DOFs 23.
J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
735746 745The torsional loads described above were applied to the
FE model shown in Fig. 9. These loads, when applied simulta-neously
with the radial ones, represent an estimation of the dynamic loads
of the whole crankshaft and, therefore, the FEresults are close to
the stress behaviour of the system in operation.
A uniform force transmission throughout the keyway side area was
assumed. As a result, the stresses obtained in thiszone will be
underestimated.
The equivalent von Mises stress distribution obtained from the
FE analysis and including only the torsional loads is shownin Fig.
14. The model estimates the maximum stresses to be 425 MPa, which
is close to the yield point of the material(550 MPa). Furthermore,
the most loaded region is closest to the keyway that breaks and
this is commonly crossed.
The radial loads were subsequently applied simultaneously to the
torsional but significant increases in stress levels
alsoappeared.
The maximum stress value obtained has two main sources of
uncertainty:
The maximum stress was overestimated because damping effects
were not included. The boundary condition in the keyway region
(zero tangential displacement in one side) used for the static
resolutioncould lead to an underestimation of the maximum stress
value. This is because the dynamic effect of the alternate sideof
contact between the key and keyway side cannot be incorporated into
the static model.
Two factors may increase significantly this maximum stress level
in the crankshaft: Local defects in the material Stress transient
growth due to the engine acceleration/deceleration and clutch
engagement
Furthermore, it can be accepted that the torsional loads due to
the system dynamic are the main controlling factors of thestress
level in the crankshaft, and this issue in combination to the
geometry stress concentration factor in the keyway, andadditional
stress due to transient torques, are probably responsible for the
overload and leads to fracture.
In order to confirm the ideas outlined above and to study
possible solutions, a cold working process of shot peening
wasapplied to all crankshafts. It was found that cracks did not
appear in these processed crankshafts. This solution was adoptedby
the manufacturer and cracks have not appeared in the crankshafts
since.6. Conclusions
Torsional dynamics controlled the stress level response of the
crankshaft, with the values obtained higher than thosefound in a
static analysis (due only to gas pressure in the compressor
chamber).
Critical speed had values within the operating range of the
compressor and, as a result, this parameter always operatesnear
resonance during common operation.
Although the stress level estimated from the methodology
described here could be inadequate from a quantitative pointof view
(as it did not include damping), the friction model could not be
verified for the compressor (it was developed foralternative
engines) and dynamic effects between the key and keyway could not
be included. The results obtained fromthe FEM and forced response
of the system analysis, like the high increment in the torsional
displacement between DOFs2 and 3, are representative of the system
behaviour. In this way, the accuracy of the estimated critical
speed values isacceptable.
Higher stresses are located in the keyway region, where the
influence of the geometric stress concentration factor is
veryimportant. In this way, much of the broken crankshaft shows the
failure surface crossing this zone.
-
746 J.A. Becerra et al. / Engineering Failure Analysis 18 (2011)
735746References
[1] Pandey RK. Failure of diesel-engine crankshafts. Eng Fail
Anal 2003;10:16575.[2] Taylor D, Ciepalowiz AJ, Rogers P, Devlukia
J. Prediction of fatigue failure in a crankshaft using the
technique of crack modelling. Fatigue Fract Eng Mater
Struct Ltd. 1997;20:1321.[3] Becerra Villanueva JA, Metodologa
para el estudio de las causas de rotura de cigeales en motores de
combustin interna alternativos y compresores
alternativos. Aplicacin en un modelo de mantenimiento
predictivo. PhD Dissertation. Universidad de Sevilla; 2007.[4]
Rahnejat H. Multi-body dynamics. UK: Professional Engineering
Publishing; 1998.[5] Rezeka SF, Henein NH. A new approach to
evaluate instantaneous friction and its components in internal
combustion engines, SAE Paper 840179; 1985
Failure analysis of reciprocating compressor
crankshaftsIntroductionCrankshaft material and failure
descriptionCrankshaft description and material
compositionCrankshaft failure description
Thermodynamic model of the refrigerating cycleCompressor torque
dynamical modelDynamic torsional analysisFE model
descriptionTorsional lumped modelCritical speeds analysisForce
response of the system
Finite element model
ConclusionsReferences