Mitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
1Reliability and Performance Gain Design Technique ofFluid Machinery Using Lubrication-Mechanism-Structure
Coupled Analysis

TAKAYA FUTAE*1TOSHIGAZU HAYASHI*2

HIROYUKI KANAZAWA*2 KEITARO KAMATA*1TORU SUZUKI*1

It is difficult to make an evaluation with only a single analytical technology to improve thereliability and performance of fluid machinery, and the application of multiphysics analysis thattakes into account the interaction between fluid force and structure is required. Mitsubishi HeavyIndustries, Ltd. (MHI) has developed technology for the reduction of shaft vibration and noise of aturbocharger and the improvement of the efficiency and reliability of a swash plate type hydraulicpiston pump by using lubrication-mechanism-structure coupled analysis. The technology
introduced here is targeted at fluid machinery for which the lubrication state shows a time historychange (self-excited vibration of bearings of a turbocharger and position/attitude change causedby reciprocating motion of swash plate type hydraulic piston pump). This technology enables theanalysis of state changes at any given moment by coupling lubrication, mechanism and structure
analysis. Furthermore, combining this analysis technology with optimization calculation facilitates
the optimum design.

|1. Introduction
In the field of turbochargers for automobiles and hydraulic transmissions for large vehicles,
attractive products that reduce both losses of bearings and transmission devices, the soundness ofbearings and sliding parts and low vibration and noise are in demand to improve performance.
Evaluation in response to this demand using only a single analytical technology is difficult, and theapplication of multiphysics, etc., is required.
Therefore, we applied lubrication-mechanism-structure coupled analysis technology topromote efficiency enhancement through the reduction of vibration and loss of a turbocharger,
which is a high-speed rotating machine, and balancing the mechanical loss and leakage loss of ahydraulic machine. This paper describes the outline and future outlook of such coupled analysis
technology.

|2. Coupled analytical technology for improving reliability andperformance of fluid machinery
2.1

Turbocharger for automobiles

Figure 1 shows the shaft vibration measurement results of a turbocharger for automobiles.
Since the turbocharger is a small high-speed rotating body, in addition to unbalanced vibration
caused by an unbalance of the shaft, self-excited vibration caused by the bearing oil film can occur.
Since the self-excited vibration is generated by the oil film pressure distribution determined by the
relative position between the shaft and the bearing, it is necessary to accurately predict the time
history change of the oil film pressure distribution to reduce the self-excited vibration.
Furthermore, to improve the transient responsiveness of the engine, the reduction of loss in thebearing of the turbocharger is also needed, and a bearing design that attains low vibration and lowloss is required.
*1*2

Machinery Research Department, Research & Innovation Center
Chief Staff Manager, Machinery Research Department, Research & Innovation CenterMitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
2Therefore, we developed coupled analysis technology of the multibody dynamic (MBD)model and bearing lubrication model considering the vibration characteristics of the shaft and therigidity of the structure and now utilize the technology for product development. Such analyticaltechnology is also being studied at university research institutes(1)(2)(3) and automobilemanufacturers. We also couple the thermal deformation of the bearing clearance during operation,
which is considered to be one of the causative factors, with the bearing and shaft vibration analysis
to improve the prediction accuracy.

Figure 1

2.2

Shaft vibration measurement results of turbocharger for automobiles

Swash plate type hydraulic piston pump

Figure 2 shows the structure of the swash plate type hydraulic piston pump. Components ofa swash plate type hydraulic piston pump behave in a complicated manner owing to mutual
influence between multiple sliding parts such as the piston and the cylinder, the shoe and the swash
plate, the valve plate and the cylinder block, etc., occurs, and the components. For this reason,
product development progresses while design and verification are repeated, which leads to a
prolonged development period. Therefore, we combined lubrication-mechanism-coupled analysis
capable of simultaneous evaluation of multiple sliding parts with an optimization algorithm(4) basedon the Kriging response surface method developed by our company to construct an optimum design
method to realize reliability and performance simultaneously to promote the shortening of theproduct development period.

Figure 2

Swash plate type hydraulic piston pump

The next section describes an overview of the lubrication-mechanism-structure coupledanalysis technology developed by our company.

Mitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)3|3. Outline of design technology with coupled analysis
3.1

Low vibration and low loss bearing design technology of turbocharger

To predict self-excited vibration amplitude, the vibration displacement of the shaft and theoil film reaction force that change at any given moment are coupled-analyzed. Figure 3 gives a
calculation flowchart. This calculation can reproduce the occurrence of self-excited vibration bycoupling shaft vibration analysis and bearing analysis as shown in the flow. By using the coupledanalysis method, the behavior of the shaft and the bearing in the case of the occurrence ofself-excited vibration can be estimated, and the creation of a bearing shape plan for reducing
self-excited vibration is possible.

Figure 3 Calculation flow ofturbocharger vibration
characteristics

Figure 4 Conceptual diagram of oil film pressure
distribution of existing bearing and improved
bearing

Figure 4 illustrates a conceptual diagram of the oil film pressure distribution of existing
bearings and improved bearings. In the case of existing bearings, for example, when an externalload acts in the vertical direction, an oil film reaction force is generated in a direction tilted withrespect to the external load due to the oil film pressure distribution, and a destabilizing force whichcauses self-excited vibration occurs. On the other hand, it is known that the oil film pressure
distribution can change when the bearing surface is multilobe, so the destabilizing force can bereduced by changing the direction of the oil film reaction force. Based on this concept, we havedevised an improved bearing for the turbocharger with a multilobe inner peripheral surface. Figure 5
presents the calculation results of the vibration characteristics of the improved bearing. As can beseen in this figure, in the case of the improved bearing, the self-excited vibration amplitude wasreduced. Figure 6 shows the bearing loss measurement results of the improved bearing. Thebearing loss of the improved bearing is equivalent to that of existing bearings, and it was also
confirmed on actual equipment that the bearing loss is equivalent and self-excited vibration can besuppressed. Therefore, the improved bearing is currently being applied to products.

Figure 5 Calculation results of vibration characteristics of multilobe bearingMitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
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Figure 6

Bearing loss measurement results of improved bearing

To further improve the accuracy of the analysis technology, coupled analysis of thermal
deformation of bearing clearance was established. Figure 7 shows a conceptual diagram ofbearing-axis vibration-thermal deformation coupled analysis. As can be seen in this figure, using
the bearing loss (heat generation) obtained by the bearing-shaft vibration coupled analysis, thetemperature increase of the bearing surface was predicted and the thermal deformation around thebearing was estimated. Figure 8 depicts the element test apparatus which was the object ofcalculation. This device has less disturbance such as heat influence from the outside than the actual
turbocharger, drives the rotor with a motor to rotate it at a high speed and measures the shaft
vibration and the ambient temperature around the bearing.

Figure 7

Flow chart of bearing-axis vibration-thermal deformation coupled analysis

Figure 8

Element test apparatus

Mitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
5Self-excited vibration amplitude was calculated using the calculation model where theboundary condition around the bearing was reasonable. It was verified from the calculation resultsthat the calculation accuracy of the amplitude and frequency of asynchronous vibration improved
by approximately 10% due to consideration of thermal deformation.

3.2

Performance and reliability optimum design technology of swash plate typehydraulic piston pump

Figure 9 gives the performance and reliability optimum design flow. Figure 10 depicts an
example of lubrication-mechanism-structure coupled analysis considering multiple sliding parts
simultaneously (oil film pressure distribution). This design method performs optimization
calculation using the leakage loss, friction loss and PV value (product of the contact surfacepressure and slip velocity) as evaluation indices. Each evaluation index was calculated from theleakage flow rate, axial power, contact force, inclination angle and sliding velocity obtained bylubrication-mechanism-structure coupled analysis. From the viewpoint of calculation cost, acalculation mesh with coarse density was used to represent local contacts in the coupled analysis.
Therefore, the contact surface pressure was separately calculated using the contact force andinclination angle obtained by the coupled analysis using three-dimensional elastic contact analysis(detailed analysis of the contact area). Regarding the optimization calculation, the calculation of thenext calculation condition used an optimization algorithm (EGO: Efficient Global Optimization)
combining functions for sequentially updating the response surface, and the creation of theresponse surface used the Kriging method. The response surface was repeatedly updated until theEIF converged to derive the optimal solution.

Figure 9Performance and reliability optimum design flow

Figure 10 Example of lubrication-mechanism-structure
coupled analysis considering multiple sliding parts
simultaneously (oil film pressure distribution)

Mitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
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Figure 11 shows an example of a response surface finally obtained by the optimization
calculation. Optimization calculation was performed using the clearance of each sliding part as aparameter with the constraint condition where the seizure limit value PV* of the components
should not be exceeded, and it was confirmed that the minimum loss point exists outside the design
range so far. It is also expected that this method can improve the efficiency by 4% and the output
density by about 30% in comparison with the conventional design with the condition that thecontact PV value of the sliding parts does not exceed the seizure limit.

Figure 11 Example of response surface finallyobtained by optimization calculation|4. Conclusion
MHI now utilizes the lubrication-mechanism-structure coupled analysis technology toimprove the reliability and performance of fluid machinery. This paper presented the coupledanalysis technology using the optimum design of self-excited vibration of the bearing of aturbocharger and multiple sliding parts of a swash plate type hydraulic piston pump as examples.
Using this method, it is possible to develop products that can achieve both efficiency andreliability. In the future, we will continue to develop highly-efficient products while maintaining
reliability.

References
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Bernhauser, L.et al., The Effect of Non-Circular Bearing Shapes in. Hydrodynamic Journal Bearings onthe Vibration. Behavior of Turbocharger Structures, Lubricants 2017, 5(1), 6Ioannis,C. et al., Experimental and Numerical Investigations of Turbocharger Rotors on Full-floating Ring
Bearings with Circumferential Oil-Groove, Proceedings of ASME Turbo Expo, GT2017-64628
Aror, R. et al., Design Technique for Mechanism Analysis Using Nonlinear Response Surface byApplying High-speed, High-precision Optimisation Method, Mitsubishi Heavy Industries TechnicalReview Vol. 53 No. 4 (2016)