- Original Article
- Open Access
Investigation of Induced Unbalance Magnitude on Dynamic Characteristics of High-speed Turbocharger with Floating Ring Bearings
© The Author(s) 2018
- Received: 14 June 2016
- Accepted: 26 September 2018
- Published: 16 October 2018
Due to operational wear and uneven carbon absorption in compressor and turbine wheels, the unbalance (me) vibration is induced and could lead to sub-synchronous vibration accidents for high-speed turbocharger (TC). There are very few research works that focus on the magnitude effects on such induced unbalance vibration. In this paper, a finite element model (FEM) is developed to characterize a realistic automotive TC rotor with floating ring bearings (FRBs). The nonlinear dynamic responses of the TC rotor system with different levels of induced unbalance magnitude in compressor and turbine wheels are calculated. From the results of waterfall and response spectral intensity plots, the bifurcation and instability phenomena depend on unbalance magnitude during the startup of TC. The sub-synchronous component 0.12× caused rotor unstable is the dominant frequency for small induced unbalance. The nonlinear effects of induced unbalance in the turbine wheel is obvious stronger than the compressor wheel. As the unbalance magnitude increases from 0.05 g·mm to 0.2 g·mm, the vibration component changes from mainly 0.12× to synchronous vibration 1×. When unbalance increases continuously, the rotor vibration response amplitude is rapidly growing and the 1× caused by the large unbalance excitation becomes the dominant frequency. A suitable un-balance magnitude of turbine wheel and compressor wheel for the high-speed TC rotor with FRBs is proposed: the value of induced un-balance magnitude should be kept around 0.2 g·mm.
- High-speed TC with FRBs
- Induced unbalance magnitude
- Nonlinear dynamic response
- Sub-synchronous vibration
High-speed turbochargers (TCs) have gained significant attention in recent years. They already have been widely used in commercial vehicles. The weight of a typical automotive TC is about 1 kg. It has 200 mm in length and 5‒15 mm in diameter and operates above 100000 r/min, which fails in the high-speed and light-weight rotor category. A small TC rotor with small unbalance can produce large vibration when it spins at high speed . It is well known that the first exhaust TC was invented at the beginning of last century. There are many efforts to investigate the rotordynamics of TC rotor-bearing system [2, 3]. The floating ring bearing (FRB) configuration is the simplest bearing design and the most widely used in small TCs. In such FRB design, two fluid films are connected in series in a floating ring, which are capable of providing higher damping and fewer friction losses than a single-film plain journal bearing . However, due to its high speed and high nonlinear feature, the FRB system exhibits high magnitude sub-synchronous vibration for a wide speed range . The bearing fluid-film whirl instability is the main source of the sub-synchronous vibration. The nonlinear reaction forces inside the bearings are usually causing the TC rotor to whirl in a limit cycle but may become large enough to cause permanent damages. Based on classical linear eigenvalue analysis presented by Kirk et al. , both inner and outer films always lead to the instability for high-speed TCs. Li et al.  developed a stability analysis and an identification method for rotor-bearings system. Surprisingly, because of high non-linear characteristics of the inner and outer oil films, it was observed that the loss of instability can induce the onset of stable limit cycles under sub-synchronous frequency via a Hopf bifurcation , which can always ensure the safe operation of a TC . Interestingly, according to the published simulation and experimental results [10, 11], it has been shown that the proved the final occurrence of the above-mentioned possibilities is sensitive to the rotor-FRB system physical parameters of TC, such as bearing structural parameters, oil feeding conditions and imposed unbalance values. The deep sensitivity clearly implies the possibility to optimize the TC rotor dynamic response and reduce the vibration by adjusting the physical structural parameters of a TC.
Rotor unbalance is a classic structural parameter which can induce the vibration for the high-speed TC rotor systems. Zhai et al.  analyzed the shaft dynamic response due to the unbalanced mass using the finite element analysis. Gunter et al.  studied the effects of rotor unbalance in the compressor and turbine wheels. These effects can strongly influence the limit cycle orbits. Alsaeed , presented a method to suppress the sub-synchronous vibrations by inducing the TC rotor unbalance. Sterling et al.  developed a theory to study the effect of induced unbalance on sub-synchronous vibration of an automotive TC. It was shown that an increasing unbalance can cause a reduction in the sub-synchronous vibration. Kirk et al.  also investigated the influence of TC unbalance on sub-synchronous vibration amplitude. Tian et al.  developed the influence of unbalance on the rotordynamic characteristics of a real TC-FRB system over the speed range from 0 Hz to 3500 Hz, and confirmed the unbalance magnitude is a critical parameter for the system response. Yao et al.  developed a method to suppress the multi-frequency rotor vibration using electromagnetic force. Other methods are also developed for rotor machine [19, 20]. In a word, many researchers devoted to investigate the influence of the unbalance level on TC dynamics at a fixed unbalance location. Appropriate unbalance can suppress the sub-synchronous vibration and improve the response behavior of TC as many researchers mentioned, which is determined by the special structure, high speed operation conditions, and nonlinear FRB. However, the nonlinear analysis is also rare at high speed for the small-sized and light-weight TC rotor with FRB. The influence of unbalance magnitude on the rotordynamic characteristics has not performed adequately.
Interestingly, the turbine impeller may exist some uncertain coke deposition in the extreme running condition with high temperature and variational operation speed mode. Thus, the induced unbalance in the turbine and compressor impellers can be formed after running a certain period for the high-speed TC. Furthermore, the unbalance can be grown with the running time, which directly influences the high-efficiency operation of high-speed TC and even causes serious nonlinear vibration accident. Therefore, it is necessary to investigate the effects of induced unbalance magnitude on the dynamic characteristics and reduce the vibration to an acceptable level by controlling the unbalance magnitude for the high-speed TC with FRB.
Major steps are outlined below. First, a FEM is required to characterize the TC rotor dynamics. The logarithmic decrements and modes are used to determine the TC rotor system stability. Second, based on the frequency domain of time transient analysis from the FEM, the nonlinear dynamic responses of the TC rotor system with different levels of induced unbalance magnitude in compressor and turbine wheels are calculated. Finally, the waterfall and response spectral intensity plots are compared to propose a suitable unbalance magnitude of turbine wheel and compressor wheel for the high-speed TC rotor with FRBs. In summary, the unbalance magnitude is an effective way to achieve the small vibration and stable operation for the high-speed TC rotor with FRBs.
The article proceeds as follows. First, the TC rotor and bearing model is described. Then, a realistic automotive TC rotor with FRB is taken as an example and its dynamic finite element model is presented to characterize the dynamic of rotor. Moreover, the rotor stability analysis is discussed. This is followed by simulation and discussion. Conclusions are given in the last section.
2.1 FRB Model
2.2 TC Rotor with Induced Unbalance
The residual mass unbalance of a rotating assembly is usually determined by using the multi-plane balancing machines. However, with the development of dynamic balancing technology, the balancing precision is very high, it is urgent to know how to control the unbalance magnitude for small vibration and stable operation in the design process. It is inevitably that the unbalance existed in the rotation, especially for the high-speed rotating machine. These mass unbalance locates at different locations of two impellers with variable magnitude of me. As expressed in unbalance force Eqs. (7), (8) and the governing Eq. (6), it is obvious seen that the unbalance Fub directly affects the motion of TC rotor and bearing system. The rotor motion may change with the variable magnitude of unbalance in turbine or compressor wheel. Thus, it is necessary to investigate the relationship between unbalance magnitude and dynamic characteristics for the small-sized and high-speed TC rotor with FRB.
3.1 Dynamic Model of FRB
Structural and lubricating parameters of FRB
Ring mass mr (g)
Inner length Li (mm)
Outer length Lo (mm)
Inner diameter Di (mm)
Outer diameter Do (mm)
Shaft diameter Ds (mm)
Bearing diameter Db (mm)
Inner viscosity ηi (cp)
Outer viscosity ηo (cp)
Speed ratio λ
The two rings of FRB were modeled as rigid body, the inner and outer oil film viscosities were assumed to be constant values with the typical 15W-40 supply lubricant, and the ring speed ratio was taken to be 0.24 according to Eq. (4).
Bearing stiffness coefficients
Inner film Ki (N/mm)
8.54 × 102
1.57 × 104
− 2.01 × 104
4.47 × 102
Outer film Ko (N/mm)
1.07 × 102
1.04 × 103
− 1.36 × 103
1.53 × 102
Bearing damping coefficients
Inner film Ci (Ns/mm)
− 6.97 × 10−2
− 6.97 × 10−2
Outer film Co (Ns/mm)
5.18 × 10−1
− 3.64 × 10−2
− 3.64 × 10−2
6.75 × 10−1
Note that the FRB used for time transient numerical analysis is nonlinear, and the rotor system is also highly nonlinear. Thus, it is a very straightforward procedure for the nonlinear time transient analysis by coupling the rotor governing Eq. (5) with bearing Reynolds Eqs. (1) and (2).
3.2 FE Modeling for TC Rotor with FRB
The TC is a typical double overhung rotor with a steel turbine and an attached aluminum compressor impeller. That is, the turbine and compressor impellers are outboard of two bearings. The rotor shaft, FRB, shaft seal, thrust collar, shaft nut and other parts are included in the TC. All rotor components should be taken into account in the rotordynamic computation to investigate the rotor vibration response, such as the stability analysis and the frequency components in the waterfall plot. The compressor and turbine impellers are generally regarded as rigid disk to model. Due to its complex structure, the mass of rotating components, moment of inertia, and the center of gravity position can be obtained by using CAE 3-dimensional software to model and calculate, and then add to the rotor-shaft regarded as a rigid disk.
The bearing modeling methods are different for the analysis of the various applications. For linear analysis, the bearing stiffness and damping coefficients are linearized and import by selecting the appropriate boundary conditions as mentioned before and the two rings of FRBs can be modeled as rigid body. However, for time transient numerical analysis, the vibration response can be got to solve directly the motion governing equation of TC rotor combined with the Reynolds equation including the bearing parameters and lubricating conditions.
3.3 Stability Analysis for TC Rotor with FRB
To obtain further insight into the dynamics of TC, it is useful to know the approximate normal modes and stability of the rotor system. Since the TC rotor is highly nonlinear due to the FRBs, in the strict sense it is hard to estimate the speed region of stability. To get approximate information on the vibration modes, the TC rotor with nonlinear FRBs should be linearized about an equilibrium position.
It can be seen from Figure 4 that there is only one mode of instability nearly at low speeds and two modes of instability at higher speeds. The threshold of instability is about 30000 r/min. In fact, the threshold of instability is only defined in connection with a linearization of the perfectly balanced rotor around a stable equilibrium position and corresponding eigenvalue analysis. For the stability analysis with nonlinear bifurcation analyses of high-speed TC rotor with FRB, bifurcation from a stable equilibrium position (more generally unbalance vibrations around a stable equilibrium position) to the fully developed oil whirl/whip region with bearing eccentricities close to 1 may be rather sophisticated and depends on various system parameters, initial conditions, etc.
Four different magnitudes of induced unbalance
Unbalance U (g·mm)
4.1 Induced Unbalance on Turbine Wheel
When unbalance is small with 0.05 g·mm, there are four sub-synchronous frequency components: 0.5×, 0.12×, 0.3×, and 0.37× from Figure 6(a) and Figure 7(a). Note that the whirl speed with sub 0.5× which mainly caused by inner oil film approximately equals to the half of rotor speed, and the predominated 0.12× response which mainly caused by outer oil film equals to the half of the ring speed. However, the whirl speed with sub 0.3× which mainly caused by inner and outer oil film approximately equals to the half of the whirl speed 0.5× and 0.12×, and sub 0.37× which mainly caused by inner and outer oil film approximately equals to the half of the whirl speed 0.5× and 0.24×.
When unbalance magnitude increases to 0.1 g·mm, the waterfall plot from Figure 6(b) just exist sub 0.5×, 0.12×, and 0.37×. The 1× grows but is very small at the low speed. The onset speed of the sub 0.12× is 94000 r/min for the unbalance 0.1 g·mm and 85000 r/min for the unbalance 0.05 g·mm from Figure 7(a) and (b), respectively. Then the predominated 0.12× response increases rapidly with the rotational speed and turns to a conical forward mode, due to the instability of outer films at both FRBs.
When unbalance magnitude is not big, the TC rotor with FRBs system becomes unstable at the start of simulation, which is confirmed in Figure 6(a) and (b). This instability is originated from the instability of inner films with sub 0.5×, and Figure 5(a) shows that a conical mode is excited. With increasing rotor speed, this instability can be pass through, and the system becomes unstable again which the dominant frequency component jumps from the sub 0.5× to 0.12×. The presence of instability sub 0.5× is bifurcated as two new instability sub 0.3× and 0.37× which their influence is less than sub 0.12×.
Figure 6(c) and (d) show that higher unbalance magnitude values, e.g., 0.2 g·mm and 0.4 g·mm, can suppress sub 0.5× at the very beginning of the run-ups compared with Figure 6(a) and (b). The onset speed of the sub 0.12× delays to approximately 136000 r/min for the induced unbalance 0.2 g·mm and disappears for the 0.4 g·mm from Figure 7(c) and (d), respectively. Obviously, the rotor undergoes purely unbalance induced vibrations for the enough unbalance magnitude. Moreover, the total vibration value of TC rotor decreases with increasing of induced unbalance magnitude, and the sub-synchronous frequency components can be suppressed.
4.2 Induced Unbalance on Compressor Wheel
Compared with the unbalance magnitude on turbine wheel, the synchronous 1× exists even in the condition with small unbalance (0.05 g·mm and 0.1 g·mm) and its amplitude is higher for the corresponding induced unbalance magnitude on compressor wheel. When the induced unbalance magnitude is the smallest, there are three sub-synchronous frequency components: 0.5×, 0.12×, and 0.3× from Figure 8(a) and Figure 9(a). Meantime, the rotor motion is predominated by the sub 0.12×.
When unbalance magnitude increases to 0.1 g·mm, the waterfall plot from Figure 8(b) just exists sub 0.5× and 0.12×. The 0.5× just exists in the beginning of run-up but its amplitude is very small. The onset speed of the predominated 0.12× is about 88000 r/min for the unbalance 0.05 g·mm and 133000 r/min for the unbalance 0.1 g·mm from Figure 9(a) and (b), respectively. Then the sub 0.12× frequency vibration increases rapidly with the rotational speed and also turns to a conical forward mode, due to the instability of outer films at both FRBs.
When unbalance magnitude is not big, the TC rotor with FRBs system becomes unstable at the start of run-up simulation, which is confirmed in Figure 8(a) and (b). This instability is also due to the sub 0.5×, and Figure 5(a) shows is a conical mode. At 88000 r/min, the dominant frequency component jumps from sub 0.5× to sub 0.12× from Figure 9(a). It is very interesting that the presence of instability sub 0.5× is bifurcated as two new instability sub 0.12× and 0.3×. Moreover the sub 0.12× is a conical mode shown in Figure 5(b), and the sub 0.3× is a bending cylindrical mode shown in Figure 5(c).
Figure 8(c) and (d) show that higher unbalance magnitude on the compressor wheel, e.g., 0.2 g·mm and 0.4 g·mm, obviously can suppress sub 0.5× at the beginning of the run-ups and becomes mainly the 1× caused by the large unbalance excitation. Moreover, the total vibration value of TC rotor increases with the increasing of induced unbalance magnitude because the rotor only predominates purely unbalance vibration mode.
The waterfall and response spectral intensity plots are obvious different for the four different unbalance magnitudes. The onset speed of sub-synchronous frequency is not identical and the total vibration amplitude is different with the variable unbalance. Moreover, the sub 0.12× is the dominant frequency for the small induced unbalance magnitude. Large magnitude of low-frequency whirl due to the sub-synchronous frequency may lead to the instability of the high-speed TC rotor. The induced unbalance magnitude should be controlled in the running process for the high speed TC rotor with FRBs.
The bifurcation and instability phenomena occur during the startup strongly depends on the induced unbalance magnitude. For the small unbalance magnitude, the rotor motion is predominated by the sub-synchronous components and the synchronous vibration is small. The bifurcation phenomena are nearly consistent for the induced unbalance on turbine wheel and compressor wheel, but the sub-synchronous responses caused by unbalance inducing the turbine wheel is stronger than the compressor wheel for the same level of unbalance magnitude. The main difference for the biggest unbalance magnitude (0.4 g·mm) is that all sub-synchronous frequencies disappear and just only exist synchronous response 1×, which the high-speed TC rotor with FRBs performs the pure unbalance oscillations around the equilibrium position.
The sub-synchronous frequencies can make the rotor unstable and cause large vibration for the TC rotor with small unbalance magnitude. The main reason for the excessive vibration is caused by the oil film asynchronous vibration. The oil whirl/whip can be suppressed for the high speed range of TC. Meantime, the sub-synchronous frequencies vibration can be suppressed by a suitable unbalance magnitude. However, as unbalance increases from 0.2 g·mm to 0.4 g·mm, the rotor response amplitude increases too and becomes mainly the 1× caused by the large unbalance excitation. Therefore, a suitable unbalance magnitude of turbine wheel and compressor wheel is proposed. To control the induced unbalance magnitude is an effective way to achieve the small vibration and stable operation for the high-speed TC rotor with FRBs.
G-FB and YH was in charge of the whole trial; G-FB and X-JL wrote the manuscript; G-FB and S-PG assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.
Guang-Fu Bin, born in 1981, is currently an associate professor at Health Maintenance for Mechanical Equipment Key Lab of Hunan Province, Hunan University of Science and Technology, China. He acted as an academic visitor in University of Ottawa from 2008 to 2009. He received his PhD degree from Beijing University of Chemical Technology, China, in 2013. His research interests include rotating machinery dynamics and modal analysis, shafting dynamic balance, mechanical dynamic testing.
Yuan Huang, born in 1993, is currently a master candidate at Health Maintenance for Mechanical Equipment Key Lab of Hunan Province, Hunan University of Science and Technology, China. His research interests include rotordynamics, automotive turbochargers and oil film bearing.
Shuai-Ping Guo, born in 1987, is currently a lecturer at Health Maintenance for Mechanical Equipment Key Lab of Hunan Province, Hunan University of Science and Technology, China. He received his PhD degree from Hunan University, China, in 2015. His research interests include mechanical dynamics, buckling analysis, heat conduction, boundary element method.
Xue-Jun Li, born in 1969, is currently a professor at Health Maintenance for Mechanical Equipment Key Lab of Hunan Province, Hunan University of Science and Technology, China. He received his PhD degree from Central South University, China, in 2003. He received post-doctor degree from Tsinghua University, China, in 2009. His main research interests include mechanical dynamics and fault diagnosis, signal analysis and processing.
Gang Wang, born in 1971, is currently an associate professor at Department of Mechanical and Aerospace Engineering, the University of Alabama in Huntsville, Huntsville, USA. He received his PhD degree from University of Maryland at College Park, USA, in 2001. His main research interests include mechanical dynamics and fault diagnosis, signal analysis and processing.
The authors declare that they have no competing interests.
Supported by National Natural Science Foundation of China (Grant Nos. 51575176, 11672106, 51775030, 51875196), and Youth Innovative Talents of Hunan Province of China (Grant No. 2015RS4043).
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