Crankshaft Failure in Compressor

Engineering Failure Analysis 18 (2011) 735–746

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Failure analysis of reciprocating compressor crankshafts J.A. Becerra ⇑, F.J. Jimenez, M. Torres, D.T. Sanchez, E. Carvajal High School of Engineering, University of Seville, Spain

a r t i c l e

i n f o

Article history: Received 13 July 2010 Accepted 6 December 2010 Available online 15 December 2010 Keywords: Crankshaft Reciprocating compressor Failure Overload

a b s t r a c t An analysis of the premature failure in a high number of crankshafts from the same model of a four cylinder reciprocating compressor used in bus climate control systems has been carried out. The analysis included visual examination, crankshaft chemical composition and hardness analysis and a dynamical model of the system. The simulation included several sub-models:

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 the stresses 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 in the crankshaft and that the influence of the gas forces on the crankshaft stress is only minor. 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 most of the broken crankshafts. The influence of the stress concentration factor imposed by this geometry is therefore very high. The compressor speed range was found to continuously cross the three lower resonance frequencies. The exhaust valve of the compressor should be redesigned in order to reduce gas forces, power consumption and pressure drop. Ó 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 technology has been under constant development ever since. Indeed, today around 70% of new automobiles world-wide incorporate this system. In the case of buses almost all vehicles are fitted with this technology. One of the most important ⇑ Corresponding author. E-mail address: [email protected] (J.A. Becerra). 1350-6307/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2010.12.004

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J.A. Becerra et al. / Engineering Failure Analysis 18 (2011) 735–746

components in an air conditioning system is the compressor, which in many systems is a reciprocating volumetric compressor. Although crankshaft failure is not common in this type of equipment, when such an event does occur it could affect all of the 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 compressor consists of four cylinders (V arrangement) coupled to the diesel engine of the bus through a V belt. The compressor generally 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 is switched 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 initiation site are necessary. The crankshafts run with harmonic torsion combined with cyclic bending stress due to the radial loads 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 the material, high cyclic loading and local stress concentration could lead to the formation and growth of cracks even when the fatigue strength is not exceeded in terms of average values. Pandey [1] analysed failures in the crankshafts of 35 hp two 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 crack showed 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 from which the crankshafts were made. Taylor et al. [2] developed two fatigue experiments for a crankshaft of a four cylinder engine made of spheroidal graphite cast iron, which has a tensile strength of 440 MPa: one experiment was torsional and the other flexural. The crankshafts underwent torsional and flexural cyclic loading until failure and in both tests the same fracture angle of 45° with respect to the rotational axis was observed. The work described here concerns a methodology that allowed the cause of failure of a crankshaft to be established by considering both torsional and bending loads. The approach involved the evaluation of the von Mises stress at the crankshaft through 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 single piece 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.

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Fig. 2. Compressor crankshaft with common failure surface.

Table 1 Chemical composition of the fractured crankshaft (wt.%). Crankshaft Id.

001

002

003

34CrMo4 steel

Carbon (%) Manganese (%) Silica (%) Sulphur (%) Phosphorus (%) Chromium (%) Molybdenum (%)

0.36 0.73 0.23 0.020 0.017 1.02 0.23

0.33 0.84 0.24 0.020 0.012 0.85 0.20

0.38 0.78 0.23 0.016 0.016 0.97 0.31

0.30–0.37 ± 0.02 0.60–0.90 ± 0.04 <0.40 ± 0.03 <0.035 + 0.005 <0.025 + 0.005 0.90–1.2 ± 0.05 0.15–0.30 ± 0.03

The Brinell hardness values of the broken crankshafts were also measured and the results are shown in Table 2. Two of the three crankshafts (0 0 1 and 0 0 3) show similar values but the result for the third is lower. These values drive to an estimation of the tensile strength show in the last row. 2.2. Crankshaft failure description At an operating time in the range 4000–6000 h, which is within the warranty period, a high number of compressor crankshafts broke and this failure led the manufacturer to re-evaluate the design. The common failure surface location is indicated in Fig. 2. A broken crankshaft is shown in Fig. 3 along with the failure region. The failure surface is at an angle of approximately 45° to the crankshaft rotation axis. This value appears to be the same in almost all of the broken crankshafts and is consistent with a torsional overload or fatigue being responsible for the failure. Fracture surfaces commonly cross the keyway and in this way geometric stress concentrations must influence the crack. Beachmarks were not observed around the area of failure and it also shows a brittle appearance. 3. Thermodynamic model of the refrigerating cycle A static and dynamic analysis of the system provided an insight into the stress level on the crankshaft. Based on the results of this analysis, it is possible to establish whether overload could be responsible for the failure or fatigue is the main factor responsible.

Table 2 Brinell hardness and tensile strength estimation. Crankshaft Id.

001

002

003

Brinell hardness Tensile strength (MPa)

286 979

252 855

289 993

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Fig. 3. Appearance of the failure surface.

Three 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 the cylinder during a cycle needs to be estimated. For this purpose a thermodynamic model of the evolution of the refrigerating gas was developed. The cylinder volume was evaluated using the crank and rod equation [4]. The inertia force was calculated from the crankshaft piston and the connecting rod geometry and material. The friction force was estimated from a model developed by Rezeka [5] and adapted to this compressor. Parameters included in the thermodynamic model were as follows: Number of cylinders Capacity per cylinder Bore Connecting rod length Stroke Geometric dead volume Fluid High pressure Low pressure

4 148 cm3 68.0 mm 105.0 mm 40.0 mm 2% of the total capacity R 134a 19.0 bar 2.5 bar

Intake and exhaust valve flow characteristics were measured and a 0.70 discharge coefficient was measured in a test rig. The model 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 represented 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 coefficient of the refrigerating cycle and an overload in the whole system. An insufficient cross area in the exhaust valve is responsible for this behaviour and a redesign is required. Furthermore, an insufficient cross area in the exhaust valve leads to a decrease 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 order of 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 is shown in Fig. 6B and the total torque is shown in Fig. 6C.


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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.

The mean torque required to overcome gas pressure and inertia forces is 57.8 Nm and the value to overcome friction forces 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 studied 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 cylinders are in phase. Although the amplitude of the fourth harmonic is not very high (Fig. 5), this fourth harmonic and its multiples would produce the highest torque on the crankshaft.

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Fig. 6. Mean torque related to gas and inertia forces (A), friction forces (B) and total forces (C) at 1600 rpm.

Table 3 Power 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 1600 2000

5.4 9.7 11.2

0.4 1.2 1.3

5.8 10.9 12.5

Fig. 7. Phase diagram for compressor cylinders and for the first to fourth harmonics.

5. Dynamic torsional analysis In order to estimate the stress level in the crankshaft due to the dynamic behaviour of the system, a torsional lumped dynamic model of the system with five degrees of freedom (DOF) linked to a finite element (FE) model was developed. A schematic 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 each cylinder. This pressure was simulated through the development of the thermodynamic model for the refrigerating gas, as described in the previous section. Mechanical losses produced by friction [4] and inertia torque were also considered.

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Fig. 8. Methodology to evaluate the stress level in the crankshaft due to the dynamic behaviour of the system.

The excitation torque obtained in this step was incorporated into a lumped model of the system. This lumped model requires the stiffness of both cranks in which the crankshaft was split to be included in the process. The stiffness values were obtained through an FE model of the crankshaft. This step gives the relative angular displacement between adjacent DOFs. The results (angular displacements) that involve the crankshaft (DOFs 2, 3 and 4) were subsequently applied in the FE model and in this way a von Mises stress contour in 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 (detailed in Section 2) used in the model for the crankshaft are as follows: Material Young’s modulus Poisson coefficient Yield threshold

34CrMo4 Steel 210 GPa 0.3 550 MPa

The mesh of the finite element model used to evaluate the stiffness of the crankshaft is shown in Fig. 9. The same model was also used in the final step to evaluate the stress level in the crankshaft. The boundary conditions applied during the evaluation 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 freedom was 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 of the belt, E is the equivalent Young’s modulus of the belt, and L is the effective length. This model gives values for the compressor-driven belt (A = 162 mm2; L = 1.075 mm) and for the alternator band (A = 110 mm2; L = 370 mm). Equivalent Young’s modulus values were estimated by the manufacturer to be in the range 96–140 MPa for both belts.

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Fig. 9. Finite element mesh of the crankshaft.

Fig. 10. Lumped model of the system.

Table 4 Stiffness and inertia parameters in the lumped model.

1 2 3 4 5

Degree of freedom

Inertia (kg m2)

Stiffness (Nm/rad)

Engine pulley Crankshaft end (clutch side) Crankshaft intermediate Crankshaft end (oil pump side) Alternator pulley

Very high 0.1017 0.00177 0.00177 0.006

K12 = 183.1–261.1 K23 = 59,500 K34 = 97800 K25 = 90.3–132.0

The 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 Mises stress contour to be obtained. The torsional lumped system model was formulated as follows:

_ l; geometryÞ þ M effectiv e þ Mcompressor þ Minertia J €h þ C h_ þ Kh ¼ M frict: ðh; h; h the acceleration vector for each where J is the inertia matrix associated with elements that rotate in the system (kg m2), € degree 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 to alternative 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 in which this value was varied were also carried out and appreciable modifications in the system outputs were not observed. 5.2.1. Critical speeds analysis On 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:


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6; 14; 612; 1814 Due to the uncertainty in evaluating the belt stiffness (K12), a sensitivity analysis was carried out and a slight modification was observed for the first two critical frequencies with a variation of up to 25% in the belt stiffness. Such modifications were 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 removed from the lower limit of the operating speed range (1000 rpm) – except for start up and shut down processes. In this way 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 with these harmonics (especially for those that affect the 4th critical speed) means that – even if these harmonics have the most influence – they would not produce a high response in the system. The force-response model developed in next paragraph allows an estimation of the response level for each of the harmonic multiples. 5.2.2. Force response of the system Solving 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 be estimated. 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 induced 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 within the range 400–3000 rpm were calculated. The results are shown in Fig. 13 (DOFs 2–3 and DOFs 3–4). 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 occurred between DOFs 3–2, where the cracks appeared. A maximum deformation of approximately 0.4° between DOFs 2–3 could be sufficient to approach the yield point of the material. However, this phenomenon alone does not explain the cracks because 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 allowed free rotation. In this way the appropriate reaction could be considered when the forces applied to each crankpin, journal and bearings are linked through non-linear gap elements. These elements develop radial forces only when both surfaces are 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 produced by the dynamic lumped model was imposed on each of the planes in which the degrees of freedom belonging to the crankshaft are defined. The angular displacement on both cranks is represented in Fig. 13.

Fig. 11. Critical 3rd and 4th frequencies of the system and Campbell diagram (red lines = multiples of 4 RPM). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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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.

Radial loads. The connecting rod big end transmits gas pressure from each cylinder to each crankpin as forces distributed along the pin surface. These forces can be decomposed into tangential, which produce engine torque, and radial, which produce bending of the crankshaft. The second type of force must also be imposed to the crankshaft.


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Fig. 14. Von Mises stress contours with a maximum angular deformation of 0.4° between DOFs 2–3.

The torsional loads described above were applied to the FE model shown in Fig. 9. These loads, when applied simultaneously with the radial ones, represent an estimation of the dynamic loads of the whole crankshaft and, therefore, the FE results 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 this zone will be underestimated. The equivalent von Mises stress distribution obtained from the FE analysis and including only the torsional loads is shown in 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 also appeared. 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 resolution could lead to an underestimation of the maximum stress value. This is because the dynamic effect of the alternate side of 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 the stress level in the crankshaft, and this issue in combination to the geometry stress concentration factor in the keyway, and additional 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 was applied to all crankshafts. It was found that cracks did not appear in these processed crankshafts. This solution was adopted by 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 those found 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 operates near resonance during common operation. Although the stress level estimated from the methodology described here could be inadequate from a quantitative point of view (as it did not include damping), the friction model could not be verified for the compressor (it was developed for alternative engines) and dynamic effects between the key and keyway could not be included. The results obtained from the FEM and forced response of the system analysis, like the high increment in the torsional displacement between DOFs 2 and 3, are representative of the system behaviour. In this way, the accuracy of the estimated critical speed values is acceptable. Higher stresses are located in the keyway region, where the influence of the geometric stress concentration factor is very important. In this way, much of the broken crankshaft shows the failure surface crossing this zone.

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References [1] Pandey RK. Failure of diesel-engine crankshafts. Eng Fail Anal 2003;10:165–75. [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;20:13–21. [3] Becerra Villanueva JA, Metodología para el estudio de las causas de rotura de cigüeñales en motores de combustión interna alternativos y compresores alternativos. Aplicación 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

Crankshaft Failure in Compressor

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