Elsevier

Tribology International

Volume 119, March 2018, Pages 250-261
Tribology International

Experimental comparison of the nonlinear dynamic behavior of a rigid rotor interacting with two types of different radial backup bearings: Ball & pinned

https://doi.org/10.1016/j.triboint.2017.07.018Get rights and content

Highlights

  • Non-linear patterns of a rotor with a ball bearing and a pinned bearing as safety bearings.

  • Characterization of friction coefficient.

  • Measured impacts between rotor and safety bearings and its inuence on the orbits.

  • Experimental comparison of two types of mechanical bearings.

  • Double-sided spectra that shows the predominance of forwards whirl.

Abstract

Rotors on magnetic bearings rely on external controls to guarantee stability and are designed in case of partial or total failures, when impacts happen and potentially lead to a breakdown. Therefore backup bearings are indispensable. In such rotor-stator interactions the main undesired phenomenon is the backward whirl. The current work investigates the experimental behavior of a horizontal rigid rotor interacting laterally with two types of backup bearings during run up testing. The experimental data is analyzed by orbit analysis, spectrum analyzers, and force magnitudes collected by sensors installed. It is shown experimentally the nonlinear behavior of the rotor-bearing system and the elimination of backward whirl. The advantages and drawbacks of each type of backup bearing are given.

Introduction

Developments in the field of rotordynamics have increased the important role of mechanical devices required by safety measures to protect the rotating machines, thanks mainly to the recent advances in magnetic bearings. These machines have still not been used in many industrial applications due to safety concerns among others. Therefore a lot of effort and research has been done to understand the consequences of the interaction between the rotor and the backup bearing for improving the quality and thus the safety properties of such elements. The safety bearing consists usually of a bearing with a slightly smaller clearance than that of the magnetic bearing, thus avoiding contact on the final one.

Johnson [1] was one of the first to publish a study on rotors with clearance. His model describes two cases, one undamped and another damped, with the rotor impacting on a circular surface, but he did not include the friction force itself. His investigation was more related to equilibria stability and whether the solutions of the synchronous whirl are positive. The friction force was added in the work of Black [2], whose 2D model presented a whirling and whipping effect caused by the friction coefficient when the rotor is in contact with the surface. Szcygielski [3] performed an analytical and experimental comparison of a gyro pendulum. His results showed good agreement with his piecewise linear model for impacts on the mechanical model. Lingener [4] and Crandall [5] published their findings confirming Black's theoretical results that the rotor may whirl with a slightly lower coupled eigenfrequency. However in 2000, Bartha [6] contested their results using an extended model. He proposed that the system should be modeled as a rotor inside nested rings.

Since the rotor with clearance is subjected to non-smooth impact and friction forces, other nonlinear phenomena may appear such as chaotic motion. Ehrich [7] indicated that when the rotor is performing a rubbing it can develop into chaotic behavior. This was confirmed by Goldman and Muszynska [8] as long as a proper impact model is employed. Muszynska [9], and Jacquet-Richardet [10], have also published an extensive review on the contact of a rotor and stator mentioning some of its most common problems in the academia and industries and how to deal with it.

The backup bearing is an essential element for the feasibility of magnetic rotors according to Schweitzer [11]. These machines are designed to be levitated rotors in vacuum and to operate at very high speeds. Therefore the control of the magnetic field has to be reliable. Nevertheless, failures and external factors can lead to malfunctioning and shutdown that eventually will cause the rotor to execute bigger amplitudes. The safety bearings work as the final mechanical threshold, in order to save the rest of the machine from further damages. The several contacts between the shaft and the backup bearing introduce nonlinear features in the dynamics of the system. In the thesis of Isaksson [12] the contact between a disk with a moving wall showed clearly nonlinear phenomena such as bifurcation diagrams and hysteresis when accelerating and decelerating. Fumagalli [13] developed an investigation of the contact with different impact models previously done by Hertz [14] and Hunt and Crossley [15]. The impact parameters were determined and how they influence the dynamics of the system when the rotor slides and tumbles on the backup bearing. Pradetto and Schmied [16] presented an experimental investigation with a one-ton rotor drop, which provided valuable results on a real rotating machine drop test on its auxiliary bearing. In 1998, Piccoli and Weber [17] observed experimentally chaotic motion in rotors and confirmed it using Lyapunov exponents. Polygonal shapes of backup bearings were tested analytically and experimentally by Simon [18]. The bearing wall was geometrically varied from a simple circular wall, to a triangle and a square and could be extended to any polygon. In any of these cases the numerical simulations showed that the disk described a quasi periodic trajectory while hitting all edges of the bearing, although the circular one induced a backward whirl motion. Ginzinger et al. [19] presented an active auxiliary bearing with linear actuators, which showed a significant reduction of the contact forces. Then Zü low and Liebich [20] designed a flexible pin with roller on the tip, which was meant to reduce the friction forces during contact.

More recent published works by Said et al. [21], [22] determined through a pin-on-disk experiment the coefficient of friction of a body probe and later tested it on a horizontal rotor. Later in 2012 the Said and Santos [23] tested the idea of using pins instead of a circular guide as a backup bearing. Both papers give a good overview of the advantages of employing pins instead of circular wall, especially when avoiding the backward whirl scenario. A further study from Fonseca et al. [24] used length varying pins on a vertical rotor bench. The setup helped the rotor to surpass the known resonance while accelerating. Hui Ma et al. [25] also investigated theoretically the dynamical response of a pinned backup bearing using the Finite Elements Method to characterize the impact phenomenon. The authors also showed the difference between three to four pins in the orbit patterns and performed a frequency analysis where multiple frequencies were excited. In his Phd Thesis, van Rensburg [26] let an active magnetic bearing rotor to drop on backup bearings and defined delevitation levels for several angular velocities. Similarly, in Fonseca et al. [27], chaotic orbits were observed depending on the unbalance mass the rotor has. Both works conducted an experimental and theoretical approach to the topic. In Ref. [28] the authors used a Stribeck-model of friction model for a thermal analysis of a drop test on a sleeve backup bearing. Halminen et al. [29] published a rotor drop test model of misaligned backup bearings, where a ball bearing isconsidered as backup bearing. They mentioned that in case of large misalignment, it may lead to significant damage to the rotor and the bearing. In Ref. [30], the authors proposed a technique to acquire experimentally the forces of an active magnetic bearing during contact with backup bearing. Cole and Hawkins [31] developed a model to predict possible subsynchronous whirl behaviors found in rotor drops.

The current work aims mainly to compare two types of backup bearings for magnetic bearings rotors through experiments. The first one will be an ordinary ball bearing, widely used in the industry, and the second one a pinned bearing designed to withstand the impact forces. Meanwhile, this pin is intentionally made of a polymer instead of metal from past tests. Its friction properties will be assessed with a pin-on-disk device in order to present the pinned bearing a solution to the safety issue. The magnets at the magnetic bearing of the test rig are, in fact, not capable of limiting the orbit of the shaft as it crosses through its own natural frequency. Therefore the test rig is ideal for representing the cases of real active magnetic bearings, whose control is faulty or weak. In this work, the shaft is run at different speeds and its position is constantly being tracked and the forces measured by force transducers inside the backup bearing housing. The different ways that the rotor crosses its own resonance will now be presented and dynamical nonlinear features explored for each type of backup bearing.

Section snippets

Rotor-bearing-system

Fig. 1 is a photo of the test rig at the facilities at DTU. This test bench rotor with a passive magnetic bearing in one end of the shaft is simply supported at the other end and also connected through a coupling to an embarked control AC-Motor. The shaft is made of aluminum and contains a disk which can hold an unbalance mass, (see Fig. 2a). This setup has been widely tested in previous works [22]- [23] and the design and construction of the parts in Ref. [32] with the main specifications

Characterization of the pins

If one is interested in the determination of the efficiency of a new mechanical design, its parameters and physical properties should be analyzed. The pinned bearing will have to support strong impacts and the shaft would certainly not settle down or stay at a permanent contact state if there is any kind of failure. Since the interaction is between polymer (POM) and aluminum, two parameters become the subject of investigation, i.e. the friction coefficient and wear rate. The test rig available

The ball bearing experimental results

The main reason that there is a backup bearing is to limit the orbits of a rotor and to protect the rest of the machine. The gap between the shaft and backup bearing is smaller than the one where the magnets are, and thus the magnetic bearing is spared. Here the rotor is accelerated by a Danfoss 4 HP AC motor that is capable of keeping its angular velocity constant, thanks to an embedded controller. The desired angular velocity is given by a signal from a computer. Also an encoder is connected

A pinned bearing solution

The test rig is designed in a way that it is easy to change the type of backup bearing. In past works [22],- [23], a pinned bearing was proposed and its efficiency tested in many cases. The back up bearing has slightly more space for the shaft to move, but this is determined by the length of the pins. The tighter and smaller the inner space is, the more the pinned backup bearing would look like a simple circular wall. The current set up provides the maximum space of the shaft to move around

Force comparison

As mentioned previously, section 2, the test rig contains four force transducers between two housings. Hence, it is possible to measure the horizontal and vertical impact force components. During acceleration the rotor's impacts are detected when it spins closer to the resonance. The closer it reaches the resonance the bigger the magnitude of the impact is. The changes in magnitude for each angular velocity are shown in Fig. 17, where the black line represents the ball bearing case and the gray

Conclusions

The test performed helped to understand the different advantages and drawbacks between two types of backup bearings designed for rotors such as magnetic levitated rotors. The rolling bearing and the pinned one as backup bearings showed efficiently that the rotor could surpass its critical speed step-by-step in the test scenarios of a faulty magnetic bearing. The case of the rotor with an unbalance mass was revealed as troublesome, because it remained in the contact state after crossing the

Acknowledgement

The authors express their acknowledgement to CNPq through the Science Without Borders Program with the process number: 249728/2013–3, which partially sponsored the elaboration of this paper.

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