The stable operation of a high-speed rotating rotor-bearing system is dependent on the internal damping of its materials. In this study, the dynamic behaviours of a rotor-shaft system with internal damping composite materials under the action of a temperature field are analysed. The temperature field will increase the tangential force generated by the internal damping of the composite material. The tangential force will also increase with the rotor speed, which can destabilise the rotor-shaft system. To better understand the dynamic behaviours of the system, we introduced a finite element calculation model of a rotor-shaft system based on a 3D high-order element (Solid186) to study the turbocharger rotor-bearing system in a temperature field. The analysis was done according to the modal damping coefficient, stability limit speed, and unbalance response. The results show that accurate prediction of internal damping energy dissipation in a temperature field is crucial for accurate prediction of rotor dynamic performance. This is an important step to understand dynamic rotor stress and rotor dynamic design.
Turbochargers are mechanical devices that can improve fuel efficiency and reduce greenhouse gas emissions. The core component of a turbocharger is a rotor composed mainly of a turbine and a compressor. The turbine is crucial because it can recover energy from the exhaust gas and increase the intake air volume by driving the compressor [
Many researchers have studied the effect of material damping on rotor dynamics and stability behaviour. Sin [
The effect of the surrounding temperature on material damping of a turbocharger rotor cannot be disregarded in high-temperature environments. It is very important to understand the dynamic behaviours of the structure in various temperatures when designing a rotor to operate in thermal extremes. San [
Therefore, this research studied the dynamic characteristics of internal material damping and an oil film force turbocharger rotor-bearing system under thermal environments (temperature fields). We used the conjugate heat transfer (CHT) method to simulate the temperature field of the solid part of a rotor-shaft system. The temperature field was coupled with the finite element model of the rotor, compared with the instance without considering the temperature field. The rotor finite element is verified by experiment.
Before the thermal modal analysis, the aerodynamic thermal analysis was performed. The current industry standard modelling approaches assume the turbine and compressor operate under adiabatic conditions [
The turbocharger had an impeller with 10 blades, and the compressor had an impeller with 6 blades and 6 splitters. The turbocharger and compressor parameters are shown in Table
Turbocharger and compressor parameters.
Turbine side | Compressor side | ||
---|---|---|---|
Parameters | Value and units | Parameters | Value and units |
Blades number | 10 | Blades number | 6 + 6 (−) |
Impeller inlet diameter | 55.05 mm | Impeller outlet diameter | 56.5 mm |
Tip clearance | 0.41 mm | Tip clearance | 0.26 mm |
Centrifugal turbocharger and compressor with a solid casing.
CHT involves the direct coupling of fluids and solids. ICEM grid discretisation software (Ansys, Inc., USA) uses the same numerical principles and grid discretisation for both regions. This allows the noninterpolated exchange of heat flux between adjacent grids [
Global grid for conjugate heat transfer calculation.
Computational grids for conjugate heat transfer calculation.
We determined the boundary conditions for aerodynamic thermal analysis using experimental data provided by the turbocharger company; the boundary conditions are shown in Table
The boundary conditions for aerothermal analysis.
Turbine side | Compressor side | ||
---|---|---|---|
Medium (intensity = 5%) | Medium (intensity = 5%) | ||
Inlet mass flow | 0.074 kg/s | Inlet total pressure | 99935.9 Pa |
Inlet total temperature | 872.97 K | Inlet total temperature | 297.201 K |
Outlet static pressure | 96892.7 Pa | Outlet static pressure | 127578 Pa |
The heat transfer of the surrounding air was disregarded, and the out-wall of the turbocharger was assumed to be adiabatic. We applied “no-slip” boundary conditions to all inner walls. An interface was added between the rotating domain and the fixed domain, and the interface was connected by a “frozen rotor” [
CHT refers to a coupled heat transfer phenomenon in which the thermal properties of two materials occur through a medium or in direct contact. The CHT method can calculate the heat transfer between fluid and solid and calculate the temperatures of fluids and solids at the same time. In this study, we used the commercial software Ansys CFX for numerical simulation. CFX is a computational fluid dynamics software package based on the control volume method to solve Navier–Stokes equations. In the fluid domain, the mass conservation, momentum, and energy transport equations are described as
In a solid domain, the conservation of energy equation can explain the heat transfer caused by solid motion, conduction, and a volume heat source. The energy equation is
This study did not directly solve (
The model of the rotor-shaft system was provided by the turbocharger company and agreed with the real one. The rotor-shaft system comprised a turbine wheel, a compressor wheel, a rotating shaft, a floating ring bearing, a thrust bearing, a seal sleeve, and a nut, as Figure
Composition of the rotor-shaft system.
The materials of the main parts of the rotor-shaft system are shown in Table
Material of the main part of the rotor-shaft system.
Part name | Material name |
---|---|
Turbo impeller | K418 |
Compressor impeller and nut | ZL105 |
Shaft | 42CrMo |
Thrust bearing and seal sleeve | 316 stainless steel |
This study investigated the effect of temperature and found that the material properties changed as the temperature changed. The function curves of the material properties of each part as a function of temperature are shown in Figure
Material properties of rotor-shaft system as a function of temperature (Young’s modulus, Poisson ratio, specific heat capacity, and thermal conductivity). (a) K418. (b) ZL105. (c) 42CrMo. (d) 316 stainless steel [
Publication [
Table
Damping coefficient of each part.
Part name | Damping coefficient |
Turbo impeller | 0.002 |
Compressor impeller and nut | 0.001 |
Shaft | 0.005 |
Thrust bearing and seal sleeve | 0.005 |
The rotor shaft was supported by a floating ring bearing whose detailed parameters are shown in Table
Parameters of floating ring bearing that supported the rotor shaft.
Parameter name | Parameter value |
Floating ring mass | 5.17 g |
Inner length | 5.14 mm |
Outer length | 7.96 mm |
Inner diameter | 7.50 mm |
Outer diameter | 12.9 mm |
To aid the simulation, we combined the stiffness and damping coefficients of the inner and outer oil film into a total impedance (equivalent stiffness and damping coefficients) according to [
Total impedance of floating ring bearing (equivalent stiffness and damping coefficients). (a) Turbine side. (b) Compressor side.
This study used a large-scale general software Ansys Workbench for simulation. To obtain the motion trace on the axis, the rotor shaft was equally divided into four parts along the axis direction, as shown in Figure
Rotor shaft divided into four parts and 1/4 cylinder.
The solid model was discretised, and an Ansys Solid186 element was used. The Solid186 element is a high-order, 3D 20-node element with quadratic displacement characteristics. The element is defined by 20 nodes, each node with three degrees of freedom (translation of each node in the
Solid186 element generated by the sweep method.
We transformed (deformed) the original hexahedron element to an approximately one-quarter cylinder element. In Figure
To adapt to the more complicated outer contour of the blade, tetrahedral, pyramid, and prism methods were used to generate the unit in the blade and the remaining part. Figure
Solid186 elements generated by tetrahedral, pyramid, and prism methods.
The effects of rotational inertia, translational inertia, gyro moment, support stiffness, support damping, material damping, rotational damping, and thermal stress stiffness were considered in the model to establish the equation of motion. The rotor model was discretised into
After combining the governing equations of all elements and combining the boundary conditions, the equation of motion of the rotor-bearing system is
Here,
The total displacement and global force vectors
Writing (
Figure
Finite element model of rotor-shaft system.
Figure
Global grid of rotor-shaft system.
To aid the comparison, we considered two cases in this study: case 1, the rotor-shaft system without the influence of temperature, and case 2, the rotor-shaft system affected by temperature. In the following sections,
After the calculation, we verified the numerical results of the mass flow and the supercharger ratio (expansion ratio). The numerical results agreed with the experimental data, and the error control was approximately 7%, as Figure
Numerical simulation verified by experiments. (a) Turbine side. (b) Compressor side.
The temperature distribution of the rotor was obtained through postprocessing, as Figure
Postprocessing rotor temperature distribution.
Rotor temperature distribution of Bohn [
Figures
Figure
Campbell diagram showing whirl frequency and rotor-spin speed for the first four modes.
When the speed was in the critical speed range between
Figure
Stability diagram of rotor-shaft system without considering temperature.
Figure
Mode shapes at 55,000 rpm (SLS 1). (a) Mode 1F. (b) Mode 2F. (c) Mode 3B. (d) Mode 4B.
Figure
Mode shapes at 97,000 rpm (SLS 2). (a) Mode 1F. (b) Mode 2F. (c) Mode 3B. (d) Mode 4B.
We exported the temperature data of each node in Figure
Figure
Effect of temperature on the Campbell diagram.
Figure
Effect of temperature on stability diagram.
We applied a dummy unbalance mass of 0.01
Response comparison between case 1 and case 2 of the turbine side floating ring bearing center position (node 5).
Partial enlargement of Campbell diagram (case 1).
Partial enlargement of Campbell diagram (case 2).
Natural frequency analysis is very important as the basis of a dynamic analysis. We obtained the first two natural frequencies of the rotor by hammering experiments and verified them by numerical simulation. Figure
Hammering experiment for a rotor.
Experimental and calculated values of natural frequencies.
Order number | Experimental value | Simulated value | Error rate |
---|---|---|---|
1 | 1386 Hz | 1453 Hz | 0.046 |
2 | 4100 Hz | 4383 Hz | 0.064 |
A more favorable verification was the oil film data shown in Figure
This study used the CHT numerical simulation method to obtain the temperature of a rotor-shaft system and found that there was a large temperature gradient when the system was in use.
Splitting the rotation shaft solved the problem that a solid model cannot obtain an axis orbit on the Ansys Workbench software platform.
Analysing the Campbell diagram shows that the temperature reduced the stiffness of the rotor structure, causing the intrinsic frequency to decrease, especially for higher-order frequencies. The decrease in stiffness was greater and the critical speed (
For the analysis of an unbalanced response, the response corresponding to the critical speed in the 1F and 2F modes does not appear in Figure
Conjugate heat transfer
Synchronous whirl line
Stable limit speed
Turbocharger
Mass damping coefficient
Stiffness damping coefficient
Natural base
Stress
Damping ratio coefficient
Dimensionless wall thickness.
Bearing
Critical
Constant
Element
Energy
Fluid
Harmonic
Solid
Shaft
Translation
Rotation
Temperature
Total.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the Key Research & Developmental Program of Shandong Province (Grant no. 2019GGX104104). The authors are grateful for technical support and the experimental data from Kangyue Technology Co., Ltd.