08-16-2017, 11:00 PM
Cummins Crankshaft and Bearing Analysis Process
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1. INTRODUCTION
This paper outlines the steps taken for the preliminary crankshaft and bearing design
analysis at Cummins. Major crankshaft dimensions must be chosen early in the engine design
process because they affect overall engine dimensions. Proper selection of the crank dimensions
requires multiple design iterations to avoid design alterations during the development stage when
any change is very costly. Therefore, the crankshaft and bearing analysis should be not only
quick, but also accurate and robust because some of the parameters may not yet be well defined
at this preliminary stage.
A number of considerations need to be addressed in the preliminary crankshaft and
bearing design analysis. Among these considerations are crank stress, bearing performance,
integrity of the crankshaft joints, and the impact of the crank on the block stress and deformation.
Though each consideration may require a detailed and complicated analysis, simplified
approaches have been developed over the years by the industry and successfully applied at
Cummins.
This paper describes a two-stage process adopted by Cummins for crankshaft analysis.
The first stage is a simplified analysis, which combines a quasi-static crankshaft model and a
rigid hydrodynamic bearing model to address crankshaft fillet bending stress and bearing
performance characteristics. The torsional vibration effects are accounted for independently
based on a simple one-dimensional dynamic mass-elastic model. At the second stage, the
crankshaft bending loads are combined with the torsional loads to simulate stress at any location
in the crankshaft finite element (FE) model. Stresses at various locations in the crank are
calculated by using sets of unit load cases applied to a single throw FE model. The appropriate
unit load cases are scaled according to the load, and combined to calculate the stresses in the
crank. The process is repeated in an efficient manner to simulate multiple engine conditions for
rapid crankshaft and bearing preliminary design.
2. CRANKSHAFT ANALYSIS HISTORY
Figure 1 gives a brief overview of the major developments in crankshaft analysis.
Historically, the major concern has been around crankshaft fillet stress associated with crank
bending. A so-called statically determinate scheme was utilized in the early days of diesel
engine development. Each throw was considered separately without interaction with
neighboring throws. This allows the calculation of bending moments in the webs, which, in
conjunction with stress concentration factors, allow for stress calculation in the fillets. The
simplicity and conservative nature of this scheme made it very popular. Application to multicylinder
engines, particularly marine, led to developments in the crankshaft torsional vibration
analysis focused on the stress calculation around oil holes in the pin journals.
The first applications of a statically indeterminate scheme were based on a rigid block.
Unloading action of the bending moments in the main journals caused significant reduction of
the calculated bending stress. Accounting for realistic main bearing support stiffness led to some
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Figure 1: Timeline of Crankshaft Analysis Processes
Statically Indeterminate Scheme -
Non-Linear Supports
1985 Cummins Coupled Solution
=88% t=10
1984 Goenka s Approximation
1983 Booker/Welsh - Coupled Solution
1975 Booker s Mobility/Impedance Method
1970s
1960s
1940s
1899
1999 Virtual Engine t=150
Statically Determinate Scheme
=100% t=1
Statically Indeterminate Scheme -
Rigid Supports =80% t=2
Statically Indeterminate Scheme -
Elastic Supports =87% t=4
2000
1920s Torsional Analysis t=1
Late
1960s
Bending + Torsion in Fillet only =104%
Combined Stress =102% (VM)
=109% (SP)
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increase in the fillet stress.
Since the 60s, combining the bending stress in the fillet calculated based on the quasistatic
statically indeterminate scheme, with the torsional stress calculated based on a dynamic
model using stress concentration factors has become a standard. In the 70s attempts were made
to model main bearings as nonlinear springs [1]. But with the development of quick and
efficient methods of bearing analysis [2,3], a coupled, quasi-static crank model and
hydrodynamic bearing model became a viable alternative, particularly since the publication of
Goenka s mobility curve fits [4]. This technique was implemented in the mid-80s [5]. As Figure
1 shows, the crankshaft fillet bending stress has further increased due to allowance for the
journal motion within the clearance space.
Major developments in commercial multi-body dynamics software in the late 90s made it
possible to consider crankshaft dynamics along with the block dynamics, coupled through the
non-linear hydrodynamic bearings [6,7]. Although modern high-speed computers have enough
power to carry out this kind of simulation in a matter of hours, current traditional methods
remain attractive because of their relative simplicity and because of the efficiency with which
they solve. Cummins has worked with the ADAMS/Engine consortium to develop a virtual
engine model, which allows NVH analysis in addition to crankshaft stress analysis. While this
approach looks promising for future application, incorporating simpler models into ADAMS/
Engine may allow preliminary crankshaft analysis to be performed quickly within a common
environment.
2.1. Historical Cummins Procedure
The current procedure, which has been in place for about 20 years, follows the major
failure modes: (a) fatigue through the crank web, with the crack initiation starting at the main or
pin fillet. This failure mode is caused by an excessive normal stress in the fillet associated with
bending of the crank throw in its plane; (b) fatigue through the pin journal, with the crack
initiation starting at the oil hole. This failure mode is caused by an excessive shear stress
associated with the throw torsion.
To address these issues, two independent procedures were developed. First, the fillet
bending stress analysis uses an FE model of a single throw to calculate stress/moment ratios for
two locations (pin and main fillets) for two major load cases (firing and inertia load). The entire
crankshaft is considered as a quasi-static beam model on non-linear supports (main bearings).
This allows fast calculation of the bending moments at the web center in the plane of the throw
as a function of the crank angle Mb( ). Depending on the sign of the moment, it is multiplied by
one of the stress/moment ratios for each main and pin fillet. This produces stresses in the main
m( ) and the pin p( ) fillets as a function of crank angle. Knowing stress over the entire
engine cycle, one can calculate mean and amplitude of the bending stress and then, the effective
fully reversed stress (EFR stress) to compare it against the endurance limit in the deterministic
sense (fatigue margin) or in the probabilistic sense (unreliability %). Second, a pin nominal
torsional stress analysis is performed. The crankshaft is considered as a discrete linear dynamic
torsional model. Calibration of the mass elastic model is performed by tuning the model to
match experimental data. Calculation of the torque acting in the connections between the mass
stations of the model is performed with the calibrated torsional mass-elastic model. The analysis
is done in the frequency domain but time domain data can easily be generated as a synthesis of
the major orders. The amplitude of the nominal stress in each pin (with no regard to stress
concentration factor) is calculated. The mean nominal shear stress is calculated based on the
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engine brake power. The amplitude and the mean stresses are combined together in the shear
EFR stress, which compared against the crank nominal torsional endurance limit, again, in the
deterministic and/or probabilistic sense.
Although consideration of bending and torsional loads based on different crank models
(one static and the other dynamic) may be viewed as an inconsistency, this approach was
confirmed in many experimental studies carried out in the 60s and 70s. Figure 2 demonstrates
the comparison between bearing reaction forces calculated with the quasi-static and dynamic
models. The character and the amplitude of the forces are very similar. On the other hand, static
torque may vary significantly from the dynamic torque, even away from resonance, Figure 3a.
The dynamic model may be tuned easily to match experimental data, Figure 3b.
Figure 2: Main Bearing Reactions calculated with (a) dynamic and (b) quasi-static models at
1000 rpm
Figure 3: (a) Static vs. Dynamic Torque. (b) Calibrated vs. uncalibrated cranknose torsional
displacement
(a)
(b)
(a) (b)
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2.2. Modern Approaches to Crankshaft Combined Stress Analysis
There are two major approaches for stress calculation: (a) based on entire crank, and (b)
based on single throw.
The first procedure can be described as follows:
- Run full crank reduced model (dynamic) to calculate main bearing reactions and
torques.
- Model entire crankshaft with FEM .
- Constrain the model at the flywheel end, as shown in Figure 4.
- Run analysis applying all possible loads (at the pin and main bearing locations) as
unit factors (pressure distributed over bearing area) one at a time. Since direction of
the bearing load is unknown, the load is applied at each of four 90-degree arc.
- Scale and sum up the FE results for each crank angle according to the loads found in
the first step.
Figure 4: Whole crank model
Number of load cases: Pin bearing load (4 # throws) + Main bearing load (4 (#
throws +1)) + Vibratory torque (1 (# throws +1)) + Crank inertia 1 case. Total number of
load cases: 9 # throws + 5 + 1 load cases for the entire crank - 60 for a 6 in-line engine.
FEV employs a variation on this method [6]. In this case the actual loads are applied to
the crank instead of unit load factors. This requires that the FE solution be performed for every
crank angle and multiple engine conditions.
Yet another method used by GM/LMS [8] and MDI [9] is to perform a crankshaft
dynamic analysis to obtain modal participation factors at each point in time. Stress shapes are
obtained from an FE analysis. These are multiplied by the modal participation factors and
summed up to obtain total stress.
According to these approaches, all the features in the entire crankshaft should be modeled
sufficiently accurately at the same time. Alternatively, individual portions of the crankshaft may
be modeled in detail, but this requires that the process be repeated multiple times. Therefore,
great computational power is required.
Another approach is published by AVL [10] and can be described as follows:
- Run dynamic analysis on a reduced model.
- Cut out one throw of the crank through the main journal middle cross-sections (detailed
FE).
- Constrain one cross-section and apply unit kinematic boundary conditions, x1, y1, z1
translational and 1, 1, 1 angular displacements, one at a time and obtain
corresponding stress states.
- Scale stress tensors based on the displacements found in the dynamic analysis (x, y, z,
, , ) and sum them up to produce the combined stress tensor.
Number of load cases: 6 # different throws.
The underling assumption is that the way the crankshaft load is applied does not affect
the stress in the throw as long as the load results in a certain average displacement of the main
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journal middle cross-section. Our experience says that, at least for fillets in bending, the stress
may vary by 20% depending on how the load is applied (on the top portion of the pin firing
load, or on the bottom portion inertia load). Also, it was found that stress in the crank web
pockets and in the end couterbore is very sensitive to the way the load is applied.