附录
MINIMIZING DYNAMIC RESPONSE OF COUNTER-ROTATING ENGINES THROUGH OPTIMIZED NODE PLACEMENT
Peter D. Hylton
Purdue School of Engineering & Technology
Indiana University Purdue University Indianapolis ABSTRACT
It has been previously proposed that a low-speed rotor balancing procedure can be suitable for supercritical shafting (GT2008-50077). That paper documented the necessity of taking into account nodal locations in the bending mode shapes of a supercritical rotor when designing an optimum balance process for such a rotor. This is due to the fact that balance correction forces (or for that matter, any forces) have the least impact when applied near the nodes of a particular mode.
This result led to consideration that node location optimization could help with another issue, i.e. the excitation of backward excited whirl modes in a
counter-rotating system. When designing a two rotor gas turbine, there are distinct advantages to having the two rotors turn in opposite directions. Among these are the ability to shorten and lighten the engine by reducing the length of the engine since a row of static turning vanes can be eliminated. The engine can be further lightened by inclusion of an inter-shaft bearing which eliminates static bearing support structure. Additional reduction in gyroscopic maneuver loads and deflections can also be achieved, thus resulting in multiple benefits to a counter-rotating system with an
inter-shaft bearing.
Unfortunately, the excitation of backward whirl modes of one rotor, which would normally not be a major concern in a co-rotating engine, can be a significant issue when excited in such a counter-rotating engine through the inter-shaft bearing, which serves as a conduit for forces from the other rotor. However, the logic of the earlier statement regarding the effectiveness of forces applied at, or near, a nodal point led to the hypothesis that optimizing the nodal locations relative to the interface points between the rotors could minimize the responsiveness of the system. This led to the hypothesis that by optimizing the node placement relative to the inter-shaft bearing, it should be possible to minimize the excitation of the backward modes. This paper examines that proposition and demonstrates that considering this aspect during the design of such an engine could lead to significant
benefit in terms of minimized dynamic responses.
Keywords: Balancing, Counter-Rotating, Backward Whirl INTRODUCTIONdocumented翻译
In an effort to design and build smaller, lightweight engines, that are still capable of
significant power output, gas turbine designers have made attempts to eliminate static structures through development of innovative two-spool engine configurations. A number of such research activities have been funded through advanced technology
pr ograms such as the Air Force’s Integrated High Performance Turbine Engine Technology (IHPTET) [1,2] and the National Aeronautics and Space Administration’s (NASA) High Speed Rotor Craft (HSRC) [3] programs. Counter-rotation systems have been evaluated in both programs [4,5] and found to offer advantages. If two rotors are designed to rotate in opposite directions, then it is possible to eliminate the row of turning vanes between the last row of turbine blades going in one direction and the following row of turbine blades turning in the opposite direction [6,7]. Elimination of these vanes allows the engine to be shorter and therefore lighter. Freedman [8] has pointed out that, in addition to the savings in length, and thus weight, there is also a savings in required cooling air that would have been used for the removed vanes and additionally there is a gain in efficiency due to improved swirl of the air travelin
g through the stages. As summarized by Zhao and Wang, “The vaneless
counter-rotating turbine, which is composed of a highly loaded single stage high pressure turbine coupled with a vaneless counter-rotating low pressure turbine, is used to significantly increase the thrust-to-weight ratio of the propulsion system.” [9] The second way to eliminate static structure, and thus length and weight, is to move from two separate bearings supporting the two rotors through two bearing support structures, as shown in Figure 1, and go to an inter-shaft bearing and a single bearing support structure, as shown in Figur e 2. As Gamble explains, “Advanced engine configuration studies have shown large life cycle cost advantages for an engine with counter-rotating spools and a rotor support system in which the high-speed rotor is straddle mounted (bearings on each end) with an inter-shaft bearing support at the high pressure turbine.” [10]
Figure 1. Sample turbine configuration showing two separate bearing support structures for the two engine rotors.
Figure 2. Sample turbine configuration showing an inter-shaft bearing and a single bearing support structure.
Additional advantages to counter-rotating the spools of the engine occur when maneuver conditions of
the aircraft are considered. As explained by Cohen, [11] “during the normal maneuvering of airplanes and missiles, gyroscopic loads are applied to the rotating parts.” He goes on to explain that this problem is of concern to engine designers because of the induced vibratory bending stresses between the rotating and stationary parts. Under maneuver conditions, the gyroscopic forces applied by the rotors to the static structures, and thus to the airframe mounts, can be the primary loads for the engine, exceeding the rotational loads. [12] However these loads can be reduced by utilizing counter-rotating designs. This allows weight to be strategically removed from both the engine case and the nacelle structure. The source of this load reduction is that gyroscopic loads occur orthogonal to both the rotational vector associated with the turning axis of the airplane and the rotational vector associated with the rotation of the engine rotor. Since the counter-rotating spools have opposite rotational vectors, the resulting loads from the two spools, when combined through the inter-shaft bearing, tend to cancel each other at the engine case and mounts. It should be noted, however, that this does not reduce the load at the individual bearings, so these must still be accommodated in bearing selection and design.
This can be shown mathematically as follows. Consider a rotating inertia, with an angular velocity about the x axis of the engine, x. This corresponds to the rotational speed of the engine. Now apply to t
his same inertia, an angular rotation about the y axis of y, corresponding to the effect created when the vehicle in which the engine resides experiences a turning maneuver about the y axis (i.e. a yaw motion if the y axis is in the vertical direction relative to the vehicle’s center of gravity consistent with the standard orientation of aircraft axes). Using standard gyroscopic theory, a
couple (i.e. torque) will be created, which is given by Tz = IP x y. Where IP is the polar moment of inertia of the rotating mass and the direction of application of this resulting torque is shown in Figure 3. The forces necessary to react this torque on the rotor system must be supplied to the rotor by the engine case at the bearings and must ultimately be reacted by the airframe structure which supports the engine case.
Figure 3. Application of gyroscopic torque caused by maneuver loads.
If a second rotor exists in the engine, rotating in the same direction, on separate supports, additional forces from the second rotor will have to be reacted by the engine case and mounts. Now suppose the second rotor is instead supported by the first rotor, and is rotating in the same direction as the first rotor, but with an angular velocity of x’. A second gyroscopic torque would be applied to this rotor, given by Tz’ = IP x’ y, as represented in Figure 4. The forces necessary to react this moment would have to be supplied by the first rotor and therefore ultimately by the aforementioned bearings and case. However, if the second rotor is counter-rotating relative to the first rotor, then x’ has the opposite sign as x, and Tz’ is in an opposite direction to Tz (opposite this time to what is shown in Figure 4). If this is the case, then it can be easily seen that the forces which must be reacted by the engine case and mounts, are based on the resultant torque Tz –Tz’, and are therefore less than would hav e to be reacted in either of the previous scenarios.
Figure 4. Application of gyroscopic torque to a co-rotating dual rotor system caused by maneuver load
s.
There are down-side effects to such a design. With a normal, single spool gas turbine, the static natural frequency of the rotor increases due to the gyroscopic stiffening effects that occur as the rotor turns faster, as shown in Figure 5. However, when there are two counter-rotating rotors, which can potentially excite each other through the inter-shaft bearing, the gyroscopic effects create both an increasing and decreasing natural frequency, [13] such that there are both forward excited and backward excited critical speeds, as shown in Figure 6.
This can be shown mathematically as follows. The dynamic equation of motion for a disk rotating on shaft is usually written as follows:
Representing the resultant harmonic motion as a function of the form ei t and rearranging as an eigenvalue problem, we get the following determinant form:

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