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A new active gyrostabiliser system for ride control of marine vehicles
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Ocean Engineering 34 (2007) 1607–1617 www.elsevier.com/locate/oceaneng
A new active gyrostabiliser system for ride control of marine vehicles N.C. Townsend, A.J. Murphy, R.A. Shenoi School of Engineering Sciences, Ship Science, University of Southampton, UK Received 11 June 2006; accepted 2 November 2006 Available online 7 February 2007
Abstract A new gyroscopic method of active ride control on marine vehicles is presented. Gyroscopic stabilisation is selected because it acts entirely within the hull of the vessel while not requiring sufficient movable weight to generate control moments. The new approach is capable of generating greater stabilising moments than existing gyroscopic systems. Physical experiments, using a modulation theory approach, on a ship model practically demonstrate that the specified system is capable of providing levels of ride control comparable with existing systems. Theoretical estimates of the system on full-scale vessels demonstrate its practical feasibility for application on small and medium sized vessels. r 2007 Published by Elsevier Ltd. Keywords: Gyro stabilisation; Ride control; Motion control; Sea keeping; Ship model experimentation; Modulation theory
1. Introduction Motion control systems are fitted to a variety of marine structures in order to provide a stable platform for mission deployment and/or for human comfort (Burger and Corbet, 1966). As indicated in the examples provided in Table 1, systems that have been developed to control undesirable ship motions can be classified as either external or internal systems. Furthermore, they may be actively forced, or more simply, passively react in order to reduce vessel motions. External systems generate motion-controlling forces and moments outside the hull of the ship and generally rely on hydrodynamic interactions. Internal systems generate moments and forces entirely within the hull. Most commonly, internal systems use moving weights to generate stabilising moments. A common example of this approach is watertank stabilisation systems in which a transfer of water is used to provide righting moments, acting to counter, say, roll motion (Gillmer and Johnson, 1985; Lewis, 1986). Whereas, appropriate, actively controlling the actuation of a system usually improves its performance compared to the passive equivalent (Bennett, 1970). Corresponding author. Tel.: +44 23 8059 2375; fax: +44 23 8059 3299.
E-mail address: [email protected] (A.J. Murphy). 0029-8018/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.oceaneng.2006.11.004
Both internal and external systems, when appropriately applied, can provide adequate solutions to the challenge of reducing undesirable ship motions in a seaway. However, as indicated in Table 1, these two distinctly different approaches also have associated disadvantages. Consequently, lighter external systems are used on weight-critical vessels (e.g. passenger ships), whereas weight based internal systems are used on deadweight carriers (e.g. offshore supply vessels) wherein the stabilisation weight also often provides ballast weight. Alternatively, the use of gyroscopes to stabilise marine vehicles is one method to generate stabilising moments entirely within the hull of the vessel without simply relying on providing sufficient movable weight. Historic and current gyroscopic systems are however limited by the magnitude of stabilising moments they can generate. Recent industrial interest in providing an internal stabilisation system, that does not simply rely on the use of additional weight, has led to the development of an active gyro stabilisation system that uses a new mode of operation to improve the stabilisation performance compared to historic or current systems (Townsend, 2005). In this paper, a theoretical and physical experimental study of this active gyrostabiliser is carried out at model-scale. Furthermore, the viability of the proposed system for use at full-scale is theoretically demonstrated.
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Nomenclature A1, A2 motion or signal amplitude A0 time-varying amplitude A0Max , A0Min maximum and minimum values of timevarying amplitude d linear distance g acceleration due to gravity GM metacentric height I mass moment of inertia Iz mass moment of inertia about z-axis L length Mx, My, Mz moments acting about x, y and z axes
t time w weight df increment of rotation dfMax maximum increment of rotation D displacement _ c spin rate $, o1, o2 cyclic frequencies oe encounter frequency o0 e non-dimensional encounter frequency $x, $y, $z angular velocity or rate about the x, y and z axes _ y, o _ z angular acceleration about the x, y and z _ x, o o axes
Table 1 Overview of marine stabilisation systems Passive reaction
Active actuation
Internal stabilisation systems Moving weight: solid weight
Moving weight: liquid tanks
Suspended cabin Gyroscopic flywheels
External stabilisation systems Bilge keels Fins and foils Jet flaps Rudder control Trim tabs and interceptors
Principal advantages
Principal disadvantages
No hydrodynamic drag and effective at zero forward speed
Weight and volume penalty
Experimental device never fully tested Bessemer (1872)
Potentially light Current systems are limited in stabilisation capability. weight with no hydrodynamic drag and is effective at zero forward speed
Lightweight
2. Background to gyro stabilisation A gyrostabiliser uses the inertial property of a rotating flywheel to apply moments to a vehicle (or other object). These moments alter the amplitude of oscillatory motions that a vehicle suffers when subject to external excitation (e.g. wave excitation of a ship). While the particular method presented in this paper is novel, it is notable that the principle of gyroscopic stabilisation has been successfully used in a number of different applications historically and in recent times. In a non-marine context, the first reference to a gyrostabiliser was for application in automobile stabilisation (Benz, 1888). This was followed by similar patents (Brennan, 1903; Sperry, 1908; Schilovski, 1909); Schilovski, 1914) providing the first full-scale practical application of
Create hydrodynamic drag, are vulnerable to damage and are ineffective at zero forward speed) Lewis (1986) and Lloyd (1998).
automobile gyro stabilisation. In recent times, gyrostabilisers have also been used for a number of different nonmarine applications including, structures operating in outer space (e.g. satellites) using single gimballed control moment gyros (CMGs), and/or variable speed control moment gyros, to provide damping of structural vibrations, and curvature control (Aubrun and Margulies, 1979). In addition, gyro stabilisation has been applied to two-wheeled vehicles (Karnopp, 2002; Beznos et al., 1998) and autonomous underwater vehicles (AUVs) (Woolsey and Leonard, 2002; Schultz and Woolsey, 2003). Gyroscopic stabilisation has also been successfully used to stabilise marine vehicles operating in the free surface. The first record of a gyroscope affecting body motions in a marine context, admittedly accidentally, was experienced with a torpedo that contained a 16 in diameter flywheel
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(rotating at 16 000 rpm) (Sperry, 1910). The earliest proposals for ship gyro stabilisation systems used passive devices. Dr. Otto Schlick proposed such a device for roll reduction in 1904 (Schlick, 1904a, b). In 1903 and 1904, Louis Brennan and Thomas C. Forbes also proposed passive gyrostabilisers for ships (as well as mono rails and automobiles), see Brennan (1903), Forbes (1904) and Tomlinson (1980). Active gyro stabilisation was first demonstrated in the marine context at model-scale by Elmer Sperry in 1908. The first full size active gyrostabiliser, was installed on the USS Worden following shore tests conducted in May of 1912; Hughes provides details of these devices, (Hughes, 1971). Later, in 1915, Elmer Sperry was granted a patent for his active gyrostabiliser, following several installations of the device on military vessels (Sperry, 1915). Following these military applications, active gyrostabilisers were installed in about 40 ships with the majority being installed on yachts (Burger and Corbet, 1966). The largest vessel an active gyrostabiliser was installed on was the Conte Di Savoia (1932–1950), a 41 700 tonnes (41 000 tons) displacement Italian luxury liner. This installation was capable of providing approximately 60% roll reduction (Gillmer, 1984). Since 1950 no further development or use of gyrostabilisers for ship stabilisation has materialised. However, comparatively recently new passive gyro stabilisation systems have been developed. One such system is the anti roll gyro (ARG) developed by Kisaka Marine Co. Ltd. and Mitsubishi Heavy Industries in Japan. The Ferretti custom line yachts, which range from 83 to 128 feet in length, are installed with ARG stabilisation systems (Petrie, 2004). Furthermore, in Australia, Sea Gyro Pty Ltd. have developed a passive gyrostabiliser called the Sea Gyro. The Sea Gyro is a passive gyrostabiliser that stabilises roll motion of marine craft less than 50 m in length (Ayres, 2005). The reason for the historic hiatus in marine gyro stabilisation is not apparent in publicly available literature. However, the past and present examples demonstrate the viability of gyro stabiliser systems for marine application. The re-emergence of commercial passive systems indicates that the technological infrastructure exists to produce marine stabilizing gyroscopes. Furthermore, in the earlier systems improved motion control was possible using active control, see Taylor (1910), Sperry (1910). Therefore, this research examined active gyro stabilisation. As demonstrated in Section 3.5, a novel approach to active gyroscope actuation can further improve modern marine gyrostabilisers systems.
the following sections. This is followed by an explanation of the physical principles associated with current active control for gyro stabilisation before the new mode of operation is presented. 3.1. Principles of weight-based stabilisation systems Weight-based stabilisation systems use the transfer of weight (usually liquid), within the vessel, to generate moments that counteract the targeted (undesirable) motions (e.g. roll motion). Thus, the stabilising moment is a function of the magnitude of the transferred weight and the distance through which it is moved. Considering a weightbased roll stabiliser, for example; the maximum amplitude of ship motion that can be built up, or reduced, df, in a single roll period, occurs if the weight is transported across the width of the vessel instantaneously (Rawson and Tupper, 2001), i.e. wd , (1) DGM in which wd is the moment applied about the roll axis of the ship My (or Mx depending on axis definition) by the movement of the weight, w, through the linear distance, d. Therefore, the maximum motion stabilisation that can provided by a weight-based system is constrained by the linear dimensions of the vessel and the acceptable deadweight penalty associated with carrying the stabilising weight. dfMax ¼
3.2. Principles of gyroscopic-based stabilisation systems The moments acting around each orthogonal axis of a gyroscope, defined in Fig. 1, can be derived from the general equations of motion (Housner and Hudson, 1959). These moments are given by _ _ x oy oz Þ þ I z oy ðoz þ cÞ, M x ¼ Iðo
(2)
_ _ y þ ox oz Þ I z ox ðoz þ cÞ, M y ¼ Iðo
(3)
and _ _ z þ cÞ. M z ¼ I z ðo
(4)
When operating, the flywheel of the gyroscope rotates about an axis, which itself is free to rotate. Therefore, in
3. Principles of operation of internal stabilisation systems In order to demonstrate the advantages provided by a gyroscopic approach to stabilisation as compared to the more common weight-based systems, the principle of operation of each system is explained and compared in
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Fig. 1. Definition of the gyroscopic axis system.
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addition to the usual terms that account for moments when the flywheel is not spinning, Eqs. (2) and (3) indicate the existence of additional gyroscopic moments that act around the x and y axes, namely; M x ¼ I z oy c_
(5)
and _ M y ¼ I z ox c.
(6)
These gyroscopic moments provide an alternative means for generating motion-controlling moments compared to current internal weight-based stabilisation systems. It is notable that the gyroscopic moments act around an axis orthogonal to the axis of rotation. That is, a moment applied to the gyroscope about its x-axis, say, generates a moment about the y-axis (Eq. (5)), and vice versa (Eq. (6)). As illustrated in Fig. 2, when used as a stabilisation device, one of the gyroscopic axes is fixed to the axis of the vessel about which the undesirable (target) motion occurs. The other axis of the gyroscope is permitted to rotate independent of the vessel. In the case of a passive gyrostabiliser system, illustrated in Fig. 2(a), the moment causing the undesirable motion is reacted by the gyroscope and results in a rotation of the gyroscope about its free axis. This free rotation is referred to as precession. Alternatively using an active gyrostabiliser system, as presented in Fig. 2(b), the reverse approach is adopted. That is, the gyroscope is forced to rotate about its free axis, this forced rotation is referred to as nutation. This nutation
results in a motion-controlling moment being generated about the ship-fixed axis of the gyroscope. 3.3. Comparison of weight-based and gyroscopic shipstabilisation systems The explanations provided in the preceding sections demonstrate that the magnitude of the moment that can be generated using a weight-based system is limited by the distance through which the weight can be moved (usually restricted by the dimensions of the vessel) and the amount of weight and/or volume that can economically be accommodated. Alternatively, the motion-controlling moment generated using a gyroscope is dependent on a number of factors, namely; (a) the mass-moment-of-inertia of the flywheel about the spin axis, Iz, which is dependent on both the magnitude and distribution of the weight within the flywheel, _ and (b) the spin rate of the flywheel about the spin axis, c (c) the rate of rotation of the gyroscope about its free axis (ox or oy, depending on axis definition). 3.4. Comparison of passive and active gyroscopic stabilisation The wave excitation moments, causing undesirable motions on a ship, are oscillatory. In a passive gyro stabilisation system this results in oscillatory rotations of
a
b
Fig. 2. Principles of operation of roll gyro stabilisation systems (a) passive and (b) active.
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the gyroscope about its free axis, ox or oy (depending on axis definition). Therefore the magnitude of the motioncontrolling moments is limited to the product of the mass _ as moment of inertia of the flywheel, Iz, and its spin rate, c, demonstrated by Eqs. (5) and (6). Alternatively, to increase the magnitude of the reactive gyroscopic moments, the gyroscope can be forced to oscillate about its free axis. By forcing the free rotation (ox or oy) a greater magnitude of rotation of the flywheel can be achieved for a given excitation frequency. That is, in the case of forced nutation of the gyroscope, the magnitude of the motion-controlling moments are a product of not only the mass moment of inertia of the flywheel, Iz, and its _ but also the oscillatory rotation of the spin rate, c, gyroscope about its free axis, ox or oy (depending on axis definition). This is the principle of operation of an active gyro stabilisation system. 3.5. The principle of operation of the new active gyro stabilisation system While forced nutation of a gyroscope in previous active marine gyro stabilisation systems allows the generation of greater stabilisation moments than the passive equivalent, there still remains a principal limitation to this approach. This is because the motion-controlling moments act about the gyroscopic frame of reference (x, y and z, as defined in Fig. 1) rather than the ship-fixed reference frame (X, Y and Z). Therefore, the gyroscopic moments act solely about the desired ship-fixed axis of rotation only when the plane of the flywheel is horizontal (hence parallel to deckplane of the ship). Thus, the gyroscopic moments act around the desired ship axis of rotation in proportion to the cosine of its angular displacement from horizontal but also about the yaw axis of the ship in proportion to the corresponding sine function. As a consequence, the previous use of forced rotation of gyroscopes for ship stabilisation systems has been limited to small perturbations of the gyroscope about the desired mean position (i.e. flywheels in the horizontal plane). This mode of operation limits the action of undesired moments (acting in yaw). Therefore, although forcing the rotation of the gyroscope can increase the magnitude of the motioncontrolling moments, the amplitude of the forced rotation (and hence motion controlling moments) is necessarily restricted. This problem is mitigated in non-marine applications of CMGs in which pairs of gyroscopes act in tandem. The flywheel in each of the two CMGs spins at the same rate in the opposite direction to the other. To produce the desired moment about a single body-fixed axis, each gyroscope is forced in corresponding oscillatory nutation in opposing directions. This is sometimes referred to as a V-arrangement or scissor arrangement (Aubrun and Margulies, 1979). In the V-arrangement the component of the gyroscopic moment acting about the desired body-fixed axis from each gyroscope are additive, whereas the
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undesired gyroscopic moment components are subtractive and thus have no net effect on the body of interest. This oscillatory operation of a pair of CMGs could achieve ship stabilisation while mitigating the undesired gyroscopic moments. In this method of operation, however, the maximum motion-controlling moments provided by the gyroscopes are still restricted because only oscillatory rotations of the gyroscopes are forced. That is, ox or oy from Eqs. (5) and (6) are, relatively small, oscillatory variables. The new mode of gyroscopic operation permits the generation of greater stabilisation moments than existing modes of operation. In the new mode of operation, the forced gyroscopic rotations are constant rather than oscillatory. That is, rather than oscillate the stabilisation gyroscopes in rotation, the forced rotation of the gyroscopes remains constant so that each gyroscope completes whole revolutions over the duration of one wave period. Nutating the gyroscopic flywheels in a constant direction simplifies their mechanical actuation in comparison to existing oscillatory methods. Furthermore, the moment generated in an active system is dependent on the rate of nutation (for a given flywheel with a given spin rate). Therefore, nutating the flywheel in a constant direction to complete one revolution in a single wave period allows a greater moment to be generated than if it is oscillated through small perturbations for the same duration. That is, the rate of nutation required to perform full revolutions in a given time period is greater than the corresponding maximum nurtation rate required to oscillate the flywheels through only fractions of a revolution. 4. The experimental gyrostabiliser system Fig. 3 provides a sketch of the gyro stabilisation system used for practical experimentation. Consistent with the principles outlined in Section 3.5, the new gyro stabiliser uses a pair of gyroscopes nutating at a constant rate about their free axes. To remove the effects of gyroscopic moments acting about the undesired axis of ship rotation, it is necessary to spin the flywheels in opposite directions while also nutating the gyroscopes in opposing directions. This latter point is well established in CMGs (both theoretically and experimentally) but does require additional mechanical complexity to implement practically. Therefore, to avoid this mechanical complexity while still permitting the demonstration of the principal objective of this proposal (i.e. the use of constantly nutating gyroscopes to provide stabilising moments on a marine vehicle) the practical experiments used gyroscopes that were spinning in the same direction as well as nutating in the same direction as each other. Although it has been indicated that contra-nutating gyroscopes are not required in order to demonstrate the effectiveness of the new uni-directional nutation mode of operation, two gyroscopes were nevertheless provided and used for the experiments. The reason for this approach is;
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Fig. 3. General arrangement of the gyrostabiliser used in the physical experiments.
this added little extra mechanical complexity and minimises manufacturing resources while preparing for future research with the fully controlled system. Furthermore, using two gyroscopes permitted simple comparison between the experimental and theoretical calculations that assume the use of two gyroscopes spinning and nutating in opposing directions. To remove the effects of the undesired gyroscopic moments in the experiments, the model vessel was restrained in the direction of freedom affected by the undesirable gyroscopic moments (yaw in this case). Active gyro stabilisation requires controlling to ensure it operates at a specified frequency and phase compared to wave excitation moments. For the purposes of demonstrating the new mode of operation, a control system was found to be unnecessary. That is, for the purposes of experimental work a novel approach was used that circumvented the need to provide a (complex) control system, while still demonstrating the effects of the new gyrostabiliser system. Details of this method are supplied in Section 5.1.
combined weight of the two rotors of the experimental gyrostabiliser is 11.5% of the total displacement of the model vessel. The combined mass-moment of inertia, about the spin axis (Iz), of the two rotors is 1.02% of the pitch mass-moment of inertial of the model vessel. The model vessel, attached to the towing post, was free to move in pitch and heave whilst being restrained in all other degrees of freedom. In each experiment, pitch was recorded as a function of time. 5.1. Experimental programme Three sets of tests were carried out as indicated in Table 2. The control experiments were carried out with the vessel at zero forward speed. In these experiments, it was observed that nutating the gyroscope with spinning flywheels on the model-ship otherwise at rest in calm water, did induce vessel motion as expected, i.e. oscillatory pitch motion. However, no measurable vessel motions were observed when
5. Experimental investigations The aim of the experimental investigations was to demonstrate the effectiveness of the new device, described in Section 4, as a ride control system for marine vehicles. These experiments were carried out on a ship-model in a towing tank. The ship-fixed axis of rotation about which the undesirable motions are targeted using the gyro stabiliser is arbitrary. For the experiments reported here, the targeted motion was pitch. This readily permitted testing with the model ship at forward speed in a towing tank (where the wave excitation induces pitch). Furthermore, this research attracted industrial support in which the principal concern was controlling pitch motions of fast catamaran ferries. Therefore, experiments with the gyro stabiliser were carried out on a catamaran model with a hull form representative of the specified ferry type. The
(a) the flywheels were spinning within the otherwise static gyroscope structures and (b) gyroscopes were nutated with otherwise static flywheels. Thus, as required, the gyroscope-induced motion is entirely due to the expected gyroscopic moments. It is common practice to determine the effectiveness of ship stabilisation systems from the motions they can induce in calm water (Rawson and Tupper, 2001). Therefore, the effectiveness of the gyrostabilier to induce motions with the vessel advancing in otherwise calm water was investigated. In these experiments, the ship-model was towed while the gyro stabiliser was used to induce pitch motion. The third set of experiments examined the effectiveness of the gyrostabiliser to reduce pitch motion with the model
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Table 2 Summary of experimental investigations Experiment
Description
Control experiments
Verification that motion caused by the gyroscope is entirely due to the expected gyroscopic moments, as defined in Eqs. (5) and (6) rather than: (i) Imbalance in the gyroscopic flywheels or (ii) Inertial accelerations caused by imbalance in the supporting structures during notation
Experiments in calm water Experiments in regular head seas
To determine the effectiveness of the gyro stabiliser to induce pitch motions on a vessel advancing in otherwise calm water To determine the effectiveness of the gyro stabiliser to reduce pitch motions on a vessel advancing in a head sea
Fig. 4. Diagrammatic representation of modulation theory.
vessel advancing at forward speed in regular head-seas. While the gyroscopes were actively actuated (in nutation) it was found unnecessary to provide a complex control system to demonstrate the effectiveness of the stabiliser to reduce ship motion in regular seas. The principles and practical application of the experimental approach adopted in these experiments is provided next. 5.1.1. Modulation theory All mechanical systems employed as ship motion reducers need a definite phase relation between the mechanism and that of the ships motion (Lewis, 1986). In the case of active stabilisers, the required phase relationship is provided by a control system. To circumvent the need to provide this complex control system, a modulation theory approach was adopted. Modulation theory (often applied to the study of radio waves) is concerned with the regular variation in the amplitude of a waveform from the superposition of a number of different waves. Fig. 4 illustrates the signal generated from the linear summation of two regular sinusoidal waves of different frequencies and amplitudes. The complete waveform in Fig. 4 is given by A1 cos o1 t þ A2 cos o2 t qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ A21 þ 2A1 A2 cos ½ðo1 o2 Þt þ A22 A2 sin ðo1 o2 Þt 1 cos o2 t þ tan , A1 þ A2 cos ðo1 o2 Þt
ð7Þ
where the effect of modulation is described by the envelope indicating the time-varying amplitude of the resulting waveform, (Goldman, 1967), i.e. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (8) A0 ¼ A21 þ 2A1 A2 cos ½ðo1 o2 Þt þ A22 . The maximum and minimum amplitude of the modulating signal can therefore be found from qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (9) A0Max ¼ ðA1 þ A2 Þ2 and A0Min ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðA1 A2 Þ2 ,
(10)
respectively. 5.1.2. Experimental application of modulation theory Fig. 5(a) and (b) presents the experimentally determined pitch response of the model ship, advancing with forward speed, subject to gyroscopic and wave excitation, respectively. The pitch response has been non-dimensionalised using the amplitude of the model vessel response in waves. In Fig. 5(a) and (b) the frequency of excitation is slightly different. Fig. 5(c) provides the ship-model pitch response when subject to both the wave and gyroscopic excitations of Fig. 5(a) and (b) simultaneously. The envelope indicated in Fig. 5(c) describing the modulated amplitude of the ship model response, has been determined by fitting the indicated maxima and minima, based on least-squared
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Fig. 5. Pitch responses for the model-ship advancing with forward speed subject to, (a) gyrostabiliser pitch excitation (gyroscopic nutation rate ¼ 51 rpm and spin rate ¼ 6200 rpm), (b) head-sea wave excitation (wave amplitude ¼ 0.02 m) and (c) simultaneous gyrostabiliser pitch excitation and head-sea wave excitation (gyroscope operation and head waves as specified in (a) and (b)).
errors, using Eq. (8). This envelope is clearly consistent with the theoretical envelope provided in Fig. 4 and demonstrates that the practical application of the proposed modulation theory is an effective method to determine the performance of the gyroscopic stabiliser in the absence of a sophisticated control system. The maximum amplitude of the model ship response is due to the in-phase summation of the wave and gyroscopic excitation moments (Eq. (9)), whereas the minimum amplitude of the model ship response results when the gyroscopic moment acts in opposition to the wave excitation moment (Eq. (10)). The latter case provides a measure of the performance of the gyroscopic stabiliser if it were appropriately controlled. All data resulting from simultaneous wave and gyroscopic excitation were analysed following this reasoning. 6. Presentation of results The experimental apparatus readily permitted the operation of the gyro stabiliser at two spin and two nutation rates. The two spin rates were 4000 and 6200 rpm and the two rates of nutation were 61 and 85 rpm. The heights of the regular head waves used were approximately 29% of the model ship draught. Fig. 6 provides the relative amplitude of the induced bow motion when the gyroscope was operated, at the different specified spin and nutation rates, on the vessel advancing in
otherwise calm water. In this figure gyroscopic excitation frequency is presented in terms of non-dimensional encounter frequency, consistent with later presentations with the vessel also subject to head-sea excitation. Fig. 7 presents the pitch response of the model-vessel with and without gyroscopic stabilisation while subject to head seas. In this figure estimations of the vessel response in waves are presented for both experimental and theoretical methods. The experimental estimates of the stabilised response are made by subtracting the reduction in pitch, determined using the modulation approach, from the experimentally determined unstabilised pitch response in head seas. The theoretical estimates of the pitch response are based on the research of Hudson (Hudson, 1999), for the type of vessel under consideration. The theoretical reduction in response due to gyroscopic stabilisation assumes the magnitude of the gyroscopic moment to be the same as that applied by the experimental device. These gyroscopic moments are calculated using Eq. (6) with the measured physical quantities of the as-built gyrostabiliser (linear dimensions, weights, rotation rates, etc.). High levels of accuracy are not required from the selected theoretical method for the prediction of model vessel’s unstabilised pitch response. These predictions simply serve as an approximate datum from which to provide a theoretical indication of the effectiveness of the gyroscopic stabilisation system. While Fig. 7 indicates that
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Amplitude of bow vertical displacement / draught
0.18 Spin rate 6200rpm and nutation rate 85rpm
0.16
Spin rate 4000rpm and nutation rate 85rpm 0.14
Spin rate 6200rpm and nutation rate 51rpm
0.12
Spin rate 4000rpm and nutation rate 51rpm
0.1 0.08 0.06 0.04 0.02 0 2
2.5
3
3.5
4
Non dimensional encounter frequency,
Fig. 6. Induced motions with the model vessel advancing in calm water.
Predicted unstablised Experiment unstabilised Predicted stabilised
1.6
Experiment stabilised
Non dimensional pitch response
1.4 1.2 1 0.8 0.6 0.4 0.2 0 2
2.5
3
3.5
4
4.5
5
5.5
6
Non dimensional encounter frequency,
Fig. 7. Performance of the gyro stabiliser determined experimentally and theoretically.
the selected prediction method over-estimates the vessel response, it nevertheless provides a reasonable indication of the behaviour, in pitch, of the type of vessel used in the experiments. Furthermore, the theoretical predictions of the effectiveness of the gyro stabiliser, presented in Fig. 7, are reasonably consistent with those found experimentally.
7. Discussion The maximum amplitude of the bow motion induced by the operation of the gyroscope on the model vessel advancing in otherwise calm water were observed to be of the order of magnitude of the wave heights selected for
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head sea experiments. This provided confirmation that the gyroscopic parameters had been sufficiently well specified for the intended head sea experiments. Furthermore, in Fig. 6, for the vessel advancing in otherwise calm water, it is notable that the variation in experimentally induced pitch response is consistent with theoretical expectations (Eq. (6)). That is, for each of the two nutation (excitation) frequencies used, there is an approximately linear variation in the response of the vessel with gyroscopic spin rate. The demonstration of the effectiveness of the new gyroscopic stabilisation system in Fig. 7, indicates that the motion reduction achievable using the specified experimental system is in the range from 30% to 70%. The work of Sclavounos and Borgen (2004), Ryle (1998), amongst others, examines current pitch ride control systems for catamarans, including controlled bow foil and stern flaps. Their research has demonstrated that pitch reductions of 50% compared to the vessel without these control appendages is usual. Therefore, the proposed new internal system is comparable to current external systems. Based on the reasonable correlation between experimental results and theoretical calculations at model scale Fig. 8 provides an indication of the effectiveness of the new stabilisation system for a hypothetical full-scale application. Consistent with the industrial interest in this research, the hypothetical full-scale application assumes the experimental device is simply scaled in terms of linear dimensions from the model scale to an equivalent 45 m fast catamaran ferry. The hypothetical study set out to determine the feasability of the full-scale application of the new apprach to gyrostabilisation, therefore no particular attention was paid to optimising the gyroscopic rotors in terms of their geometric or material properties. Thus, consistent with the experimental device, the full-scale device is assumed to use
solid steel discs. The resulting hypothetical full-scale device therefore uses two 3.23 m diameter steel rotors with a combined weight of approximately 52,000 kg. This corresponds to approximately 17.4% of the displacement of the selected vessel. The combined mass moment of inertia of the two gyroscopic flywheels is 0.94% of the pitch mass moment of inertia of the vessel. In Fig. 8, the contours indicate the gyroscopic spin rates required to counter different fractions of the total head sea pitch excitation moments. These spin rates are well within practical limits, and are readily achievable as demonstrated from current flywheel and CMG systems, see Lazarewicz et al. (2000), (Richie and Tsiotras (2001) among others. For full-scale applications of the gyroscopic stabilisation method presented in this paper, a refinement of the gyroscopic rotors is required as well as the application of an appropriate control strategy. For example, in Fig. 8, simple linear scaling of solid steel rotors was used to verify that the proposed system is readily achievable at full scale; the mass of the stabilisation system could be reduced through a judicious selection of spin rate and flywheel mass-moment of inertia. The existing technological infrastructure for the recently developed passive systems indicates this is readily achievable. In addition to the specific case study in this paper, other hypothetical cases have been studied comparing pitch and roll stabilisation for a range of vessels. These studies revealed that gyroscopic stabilisation in this new mode of operation would be effective on small to medium sized vessels and that the practical limit of performance is essentially controlled, not by limits on the operation of the gyroscopic flywheel, but rather by the magnitude of the excitation moments which must be supplied to actively nutate the gyroscopic flywheels.
1600 100% 1400 1200 Spin rate in rpm
75% 1000 800
50%
600 400 200 0 1
2
3
4
5
6
7
Non dimensional encounter frequency,
Fig. 8. Gyroscopic spin rates required to counter head-sea pitch excitation moments on a 45 m fast catamaran ferry. Contours indicate different levels of effectiveness.
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8. Conclusions The initial motivation for this research was to examine alternative ride control systems that are capable of providing levels of motion reduction, on ships, comparable to existing external systems, while also overcoming the associated hydrodynamic disadvantages. Furthermore, the new system was required to exploit alternative approaches to generating moments within the hull in order to circumvent the weight penalties incurred by simply providing sufficient movable mass to generate stabilising moments. In this research, the emergence of modern passive marine gyro stabilisation and the fact that active control of historic systems improved ride control performance, led to an investigation of alternative strategies for active gyro stabilisation. The new mode of operation uses two gyroscopic flywheels, spinning in opposing directions while being forced to nutate at constant rates, also in opposition was proposed. The experimental investigation used a novel application of the theory of wave modulation to assess the ride control capabilities of the device. These investigations demonstrate that the new mode of gyroscopic stabilisation, when applied on marine vehicles, is capable of providing levels of ride control consistent with contemporary external systems. Theoretical estimates of the system at full-scale indicate that the proposed method is readily achievable in practice and that it is suitable for ride control in pitch and roll for small and medium size vessels. The principal practical limitation of the method is the levels of torque required to nutate the gyroscopic flywheels, rather than operating the gyroscopic flywheels themselves. Further research is required to provide an appropriate control strategy. Furthermore, exploiting the versatility afforded by a judicious combination of the gyroscopic parameters (spin rate and mass distribution within the rotor) will permit appropriate specification of the weight and volume of the system for application on a variety of vessels. Acknowledgements This research was funded by FBM Babcock Ltd. and the Engineering and Physical Science Research Council, EPSRC. We are grateful to Mr. N. Warren for helpful discussions on this subject. References Aubrun, J.N. and Margulies, G., 1979. Gyrodampers for large scale space structures. Technical Report, NASA CR-159 171. Ayres, C., 2005. Sea gyro email correspondence. Bennett, D.A., 1970. Comparison of ship roll stabilisation methods. Shipping World Shipbuilder, v163, n3847, July 1970, pp. 989–90, 993–4. Benz, C., 1888. Self-propelling vehicle. Patent US 385,087.
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Beznos, A.V., Formal’sky, A.M., Gurfinkel, E.V., Jicharev, D.N., Lensky, A.V., Savitsky, K.V., Tchesalin, L.S., 1998. Control of autonomous motion of twowheel bicycle with gyroscopic stabilization. Proceedings—IEEE International Conference on Robotics and Automation 3, 2670–2675. Brennan, L., 1903. Improvements in and relating to the imparting of stability to otherwise unstable bodies, structures or vehicles, Patent GB 27, 212. Burger, W., Corbet, A.G., 1966. Ship Stabilizers. Pergamon Press Ltd. Forbes, T.C., 1904. Device for steadying ships. Patent US 769, 693. Gillmer, R., 1984. Modern Ship Design. United States Naval Institute. Gillmer, R., Johnson, B., 1985. Introduction to Naval Architecture. United States Naval Institute. Goldman, S., 1967. Frequency Analysis, Modulation and Noise. Dover Publications Inc., New York. Hudson, D., 1999. A validation study on mathematical models of speed and frequency dependence in seakeeping of high speed craft. Ph.D. Thesis, The University of Southampton. Hughes, T.P., 1971. Elmer Sperry Inventor and Engineer. Johns Hopkins Press. Housner, G.W., Hudson, D.E., 1959. Applied Mechanics Dynamics, second ed. D. Van Nostrand Company, Inc. Karnopp, D., 2002. Tilt control for gyro-stabilized two-wheeled vehicles. Vehicle System Dynamics 37 (2), 145–156. Lazarewicz, M.L, Hockney, R.L.; Jesi, J., 2000. Reliable power for telecommunications using flywheels. In: Proceedings of International IEEE Telecommunications Energy Conference, 10–14 September 2000. Lewis, V.E., 1986. Principles of Naval Architecture. The Society of Naval Architects and Marine Engineers. Chapter IX. Lloyd, A.R.J.M., 1998. Seakeeping Ship Behaviour in Rough Weather. Ellis Horwood Ltd. Petrie, L.G., 2004. On the level. Power and motoryacht. Available: /http://powerandmotoryacht.com/features/0704stabilizers/index1. htmlS, Accessed August 2005. Rawson, K.J., Tupper, E.C., 2001. Basic Ship Behaviour. Butterworth Heinemann. Richie, D.J., Tsiotras, P., 2001. Simultaneous attitude control and energy storage using VSCMGs: theory and simulation. In: Proceedings of the American Control Conference, Arlington, June 25–27, 2001. Ryle, M., 1998. Smoothing out the ride. The Motor Ship, pp. 23–26, January. Schlick, E.O., 1904a. Device for minimising the oscillatory movements of ships, Patent US769, 493. Schlick, E.O., 1904b. The gyroscopic effect of flywheels on board ship. Transactions of the Institute of Naval Architects 23, 117–134. Schilovski, P.P., 1909. Gyrocar. Patent GB 12,021. Schilovski, P.P., 1914. Gyrocar. Patent GB 12,940. Schultz, C. and Woolsey, C.A., 2003. An experimental platform for validating internal actuator control strategies. In: IFAC Workshop on Guidance and Control of Underwater Vehicles, April 2003, Newport, South Wales, UK, pp. 209–214. Sclavounos, P.D., Borgen, H., 2004. Seakeeping Analysis of a high-speed monohull with a motion—control bow hydrofoil. Journal of Ship Research 48 (2), 77–117. Sperry, E.A., 1908. Steadying device for vehicles. Patent US 907,907. Sperry, E.A., 1910. The gyroscope for marine purposes. Transactions of the Society of Naval Architects and Marine Engineers XVIII, 143–154. Sperry, E.A., 1915. Ships’ gyroscopes, Patent US 1,150,311. Taylor, D.W., 1910. Report from Captain David W. Taylor to chief constructor. Bureau Construction and Repair, Navy Deparment, Washington,DC., July 15. Tomlinson, N., 1980. Louis Brennan—Inventor Extraordinaire. Published by John Halliwell. Townsend, N.C., 2005. Development of an innovative ride control system for marine vehicles. Engineering Doctorate Interim Thesis, University of Southampton and FBM Babcock Ltd. Woolsey, C.A., Leonard, N.E., 2002. Stabilizing underwater vehicle motion using internal rotors. Automatica 38 (12), 2053–2062.
Ocean Engineering 34 (2007) 1607–1617 www.elsevier.com/locate/oceaneng
A new active gyrostabiliser system for ride control of marine vehicles N.C. Townsend, A.J. Murphy, R.A. Shenoi School of Engineering Sciences, Ship Science, University of Southampton, UK Received 11 June 2006; accepted 2 November 2006 Available online 7 February 2007
Abstract A new gyroscopic method of active ride control on marine vehicles is presented. Gyroscopic stabilisation is selected because it acts entirely within the hull of the vessel while not requiring sufficient movable weight to generate control moments. The new approach is capable of generating greater stabilising moments than existing gyroscopic systems. Physical experiments, using a modulation theory approach, on a ship model practically demonstrate that the specified system is capable of providing levels of ride control comparable with existing systems. Theoretical estimates of the system on full-scale vessels demonstrate its practical feasibility for application on small and medium sized vessels. r 2007 Published by Elsevier Ltd. Keywords: Gyro stabilisation; Ride control; Motion control; Sea keeping; Ship model experimentation; Modulation theory
1. Introduction Motion control systems are fitted to a variety of marine structures in order to provide a stable platform for mission deployment and/or for human comfort (Burger and Corbet, 1966). As indicated in the examples provided in Table 1, systems that have been developed to control undesirable ship motions can be classified as either external or internal systems. Furthermore, they may be actively forced, or more simply, passively react in order to reduce vessel motions. External systems generate motion-controlling forces and moments outside the hull of the ship and generally rely on hydrodynamic interactions. Internal systems generate moments and forces entirely within the hull. Most commonly, internal systems use moving weights to generate stabilising moments. A common example of this approach is watertank stabilisation systems in which a transfer of water is used to provide righting moments, acting to counter, say, roll motion (Gillmer and Johnson, 1985; Lewis, 1986). Whereas, appropriate, actively controlling the actuation of a system usually improves its performance compared to the passive equivalent (Bennett, 1970). Corresponding author. Tel.: +44 23 8059 2375; fax: +44 23 8059 3299.
E-mail address: [email protected] (A.J. Murphy). 0029-8018/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.oceaneng.2006.11.004
Both internal and external systems, when appropriately applied, can provide adequate solutions to the challenge of reducing undesirable ship motions in a seaway. However, as indicated in Table 1, these two distinctly different approaches also have associated disadvantages. Consequently, lighter external systems are used on weight-critical vessels (e.g. passenger ships), whereas weight based internal systems are used on deadweight carriers (e.g. offshore supply vessels) wherein the stabilisation weight also often provides ballast weight. Alternatively, the use of gyroscopes to stabilise marine vehicles is one method to generate stabilising moments entirely within the hull of the vessel without simply relying on providing sufficient movable weight. Historic and current gyroscopic systems are however limited by the magnitude of stabilising moments they can generate. Recent industrial interest in providing an internal stabilisation system, that does not simply rely on the use of additional weight, has led to the development of an active gyro stabilisation system that uses a new mode of operation to improve the stabilisation performance compared to historic or current systems (Townsend, 2005). In this paper, a theoretical and physical experimental study of this active gyrostabiliser is carried out at model-scale. Furthermore, the viability of the proposed system for use at full-scale is theoretically demonstrated.
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Nomenclature A1, A2 motion or signal amplitude A0 time-varying amplitude A0Max , A0Min maximum and minimum values of timevarying amplitude d linear distance g acceleration due to gravity GM metacentric height I mass moment of inertia Iz mass moment of inertia about z-axis L length Mx, My, Mz moments acting about x, y and z axes
t time w weight df increment of rotation dfMax maximum increment of rotation D displacement _ c spin rate $, o1, o2 cyclic frequencies oe encounter frequency o0 e non-dimensional encounter frequency $x, $y, $z angular velocity or rate about the x, y and z axes _ y, o _ z angular acceleration about the x, y and z _ x, o o axes
Table 1 Overview of marine stabilisation systems Passive reaction
Active actuation
Internal stabilisation systems Moving weight: solid weight
Moving weight: liquid tanks
Suspended cabin Gyroscopic flywheels
External stabilisation systems Bilge keels Fins and foils Jet flaps Rudder control Trim tabs and interceptors
Principal advantages
Principal disadvantages
No hydrodynamic drag and effective at zero forward speed
Weight and volume penalty
Experimental device never fully tested Bessemer (1872)
Potentially light Current systems are limited in stabilisation capability. weight with no hydrodynamic drag and is effective at zero forward speed
Lightweight
2. Background to gyro stabilisation A gyrostabiliser uses the inertial property of a rotating flywheel to apply moments to a vehicle (or other object). These moments alter the amplitude of oscillatory motions that a vehicle suffers when subject to external excitation (e.g. wave excitation of a ship). While the particular method presented in this paper is novel, it is notable that the principle of gyroscopic stabilisation has been successfully used in a number of different applications historically and in recent times. In a non-marine context, the first reference to a gyrostabiliser was for application in automobile stabilisation (Benz, 1888). This was followed by similar patents (Brennan, 1903; Sperry, 1908; Schilovski, 1909); Schilovski, 1914) providing the first full-scale practical application of
Create hydrodynamic drag, are vulnerable to damage and are ineffective at zero forward speed) Lewis (1986) and Lloyd (1998).
automobile gyro stabilisation. In recent times, gyrostabilisers have also been used for a number of different nonmarine applications including, structures operating in outer space (e.g. satellites) using single gimballed control moment gyros (CMGs), and/or variable speed control moment gyros, to provide damping of structural vibrations, and curvature control (Aubrun and Margulies, 1979). In addition, gyro stabilisation has been applied to two-wheeled vehicles (Karnopp, 2002; Beznos et al., 1998) and autonomous underwater vehicles (AUVs) (Woolsey and Leonard, 2002; Schultz and Woolsey, 2003). Gyroscopic stabilisation has also been successfully used to stabilise marine vehicles operating in the free surface. The first record of a gyroscope affecting body motions in a marine context, admittedly accidentally, was experienced with a torpedo that contained a 16 in diameter flywheel
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(rotating at 16 000 rpm) (Sperry, 1910). The earliest proposals for ship gyro stabilisation systems used passive devices. Dr. Otto Schlick proposed such a device for roll reduction in 1904 (Schlick, 1904a, b). In 1903 and 1904, Louis Brennan and Thomas C. Forbes also proposed passive gyrostabilisers for ships (as well as mono rails and automobiles), see Brennan (1903), Forbes (1904) and Tomlinson (1980). Active gyro stabilisation was first demonstrated in the marine context at model-scale by Elmer Sperry in 1908. The first full size active gyrostabiliser, was installed on the USS Worden following shore tests conducted in May of 1912; Hughes provides details of these devices, (Hughes, 1971). Later, in 1915, Elmer Sperry was granted a patent for his active gyrostabiliser, following several installations of the device on military vessels (Sperry, 1915). Following these military applications, active gyrostabilisers were installed in about 40 ships with the majority being installed on yachts (Burger and Corbet, 1966). The largest vessel an active gyrostabiliser was installed on was the Conte Di Savoia (1932–1950), a 41 700 tonnes (41 000 tons) displacement Italian luxury liner. This installation was capable of providing approximately 60% roll reduction (Gillmer, 1984). Since 1950 no further development or use of gyrostabilisers for ship stabilisation has materialised. However, comparatively recently new passive gyro stabilisation systems have been developed. One such system is the anti roll gyro (ARG) developed by Kisaka Marine Co. Ltd. and Mitsubishi Heavy Industries in Japan. The Ferretti custom line yachts, which range from 83 to 128 feet in length, are installed with ARG stabilisation systems (Petrie, 2004). Furthermore, in Australia, Sea Gyro Pty Ltd. have developed a passive gyrostabiliser called the Sea Gyro. The Sea Gyro is a passive gyrostabiliser that stabilises roll motion of marine craft less than 50 m in length (Ayres, 2005). The reason for the historic hiatus in marine gyro stabilisation is not apparent in publicly available literature. However, the past and present examples demonstrate the viability of gyro stabiliser systems for marine application. The re-emergence of commercial passive systems indicates that the technological infrastructure exists to produce marine stabilizing gyroscopes. Furthermore, in the earlier systems improved motion control was possible using active control, see Taylor (1910), Sperry (1910). Therefore, this research examined active gyro stabilisation. As demonstrated in Section 3.5, a novel approach to active gyroscope actuation can further improve modern marine gyrostabilisers systems.
the following sections. This is followed by an explanation of the physical principles associated with current active control for gyro stabilisation before the new mode of operation is presented. 3.1. Principles of weight-based stabilisation systems Weight-based stabilisation systems use the transfer of weight (usually liquid), within the vessel, to generate moments that counteract the targeted (undesirable) motions (e.g. roll motion). Thus, the stabilising moment is a function of the magnitude of the transferred weight and the distance through which it is moved. Considering a weightbased roll stabiliser, for example; the maximum amplitude of ship motion that can be built up, or reduced, df, in a single roll period, occurs if the weight is transported across the width of the vessel instantaneously (Rawson and Tupper, 2001), i.e. wd , (1) DGM in which wd is the moment applied about the roll axis of the ship My (or Mx depending on axis definition) by the movement of the weight, w, through the linear distance, d. Therefore, the maximum motion stabilisation that can provided by a weight-based system is constrained by the linear dimensions of the vessel and the acceptable deadweight penalty associated with carrying the stabilising weight. dfMax ¼
3.2. Principles of gyroscopic-based stabilisation systems The moments acting around each orthogonal axis of a gyroscope, defined in Fig. 1, can be derived from the general equations of motion (Housner and Hudson, 1959). These moments are given by _ _ x oy oz Þ þ I z oy ðoz þ cÞ, M x ¼ Iðo
(2)
_ _ y þ ox oz Þ I z ox ðoz þ cÞ, M y ¼ Iðo
(3)
and _ _ z þ cÞ. M z ¼ I z ðo
(4)
When operating, the flywheel of the gyroscope rotates about an axis, which itself is free to rotate. Therefore, in
3. Principles of operation of internal stabilisation systems In order to demonstrate the advantages provided by a gyroscopic approach to stabilisation as compared to the more common weight-based systems, the principle of operation of each system is explained and compared in
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Fig. 1. Definition of the gyroscopic axis system.
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addition to the usual terms that account for moments when the flywheel is not spinning, Eqs. (2) and (3) indicate the existence of additional gyroscopic moments that act around the x and y axes, namely; M x ¼ I z oy c_
(5)
and _ M y ¼ I z ox c.
(6)
These gyroscopic moments provide an alternative means for generating motion-controlling moments compared to current internal weight-based stabilisation systems. It is notable that the gyroscopic moments act around an axis orthogonal to the axis of rotation. That is, a moment applied to the gyroscope about its x-axis, say, generates a moment about the y-axis (Eq. (5)), and vice versa (Eq. (6)). As illustrated in Fig. 2, when used as a stabilisation device, one of the gyroscopic axes is fixed to the axis of the vessel about which the undesirable (target) motion occurs. The other axis of the gyroscope is permitted to rotate independent of the vessel. In the case of a passive gyrostabiliser system, illustrated in Fig. 2(a), the moment causing the undesirable motion is reacted by the gyroscope and results in a rotation of the gyroscope about its free axis. This free rotation is referred to as precession. Alternatively using an active gyrostabiliser system, as presented in Fig. 2(b), the reverse approach is adopted. That is, the gyroscope is forced to rotate about its free axis, this forced rotation is referred to as nutation. This nutation
results in a motion-controlling moment being generated about the ship-fixed axis of the gyroscope. 3.3. Comparison of weight-based and gyroscopic shipstabilisation systems The explanations provided in the preceding sections demonstrate that the magnitude of the moment that can be generated using a weight-based system is limited by the distance through which the weight can be moved (usually restricted by the dimensions of the vessel) and the amount of weight and/or volume that can economically be accommodated. Alternatively, the motion-controlling moment generated using a gyroscope is dependent on a number of factors, namely; (a) the mass-moment-of-inertia of the flywheel about the spin axis, Iz, which is dependent on both the magnitude and distribution of the weight within the flywheel, _ and (b) the spin rate of the flywheel about the spin axis, c (c) the rate of rotation of the gyroscope about its free axis (ox or oy, depending on axis definition). 3.4. Comparison of passive and active gyroscopic stabilisation The wave excitation moments, causing undesirable motions on a ship, are oscillatory. In a passive gyro stabilisation system this results in oscillatory rotations of
a
b
Fig. 2. Principles of operation of roll gyro stabilisation systems (a) passive and (b) active.
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the gyroscope about its free axis, ox or oy (depending on axis definition). Therefore the magnitude of the motioncontrolling moments is limited to the product of the mass _ as moment of inertia of the flywheel, Iz, and its spin rate, c, demonstrated by Eqs. (5) and (6). Alternatively, to increase the magnitude of the reactive gyroscopic moments, the gyroscope can be forced to oscillate about its free axis. By forcing the free rotation (ox or oy) a greater magnitude of rotation of the flywheel can be achieved for a given excitation frequency. That is, in the case of forced nutation of the gyroscope, the magnitude of the motion-controlling moments are a product of not only the mass moment of inertia of the flywheel, Iz, and its _ but also the oscillatory rotation of the spin rate, c, gyroscope about its free axis, ox or oy (depending on axis definition). This is the principle of operation of an active gyro stabilisation system. 3.5. The principle of operation of the new active gyro stabilisation system While forced nutation of a gyroscope in previous active marine gyro stabilisation systems allows the generation of greater stabilisation moments than the passive equivalent, there still remains a principal limitation to this approach. This is because the motion-controlling moments act about the gyroscopic frame of reference (x, y and z, as defined in Fig. 1) rather than the ship-fixed reference frame (X, Y and Z). Therefore, the gyroscopic moments act solely about the desired ship-fixed axis of rotation only when the plane of the flywheel is horizontal (hence parallel to deckplane of the ship). Thus, the gyroscopic moments act around the desired ship axis of rotation in proportion to the cosine of its angular displacement from horizontal but also about the yaw axis of the ship in proportion to the corresponding sine function. As a consequence, the previous use of forced rotation of gyroscopes for ship stabilisation systems has been limited to small perturbations of the gyroscope about the desired mean position (i.e. flywheels in the horizontal plane). This mode of operation limits the action of undesired moments (acting in yaw). Therefore, although forcing the rotation of the gyroscope can increase the magnitude of the motioncontrolling moments, the amplitude of the forced rotation (and hence motion controlling moments) is necessarily restricted. This problem is mitigated in non-marine applications of CMGs in which pairs of gyroscopes act in tandem. The flywheel in each of the two CMGs spins at the same rate in the opposite direction to the other. To produce the desired moment about a single body-fixed axis, each gyroscope is forced in corresponding oscillatory nutation in opposing directions. This is sometimes referred to as a V-arrangement or scissor arrangement (Aubrun and Margulies, 1979). In the V-arrangement the component of the gyroscopic moment acting about the desired body-fixed axis from each gyroscope are additive, whereas the
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undesired gyroscopic moment components are subtractive and thus have no net effect on the body of interest. This oscillatory operation of a pair of CMGs could achieve ship stabilisation while mitigating the undesired gyroscopic moments. In this method of operation, however, the maximum motion-controlling moments provided by the gyroscopes are still restricted because only oscillatory rotations of the gyroscopes are forced. That is, ox or oy from Eqs. (5) and (6) are, relatively small, oscillatory variables. The new mode of gyroscopic operation permits the generation of greater stabilisation moments than existing modes of operation. In the new mode of operation, the forced gyroscopic rotations are constant rather than oscillatory. That is, rather than oscillate the stabilisation gyroscopes in rotation, the forced rotation of the gyroscopes remains constant so that each gyroscope completes whole revolutions over the duration of one wave period. Nutating the gyroscopic flywheels in a constant direction simplifies their mechanical actuation in comparison to existing oscillatory methods. Furthermore, the moment generated in an active system is dependent on the rate of nutation (for a given flywheel with a given spin rate). Therefore, nutating the flywheel in a constant direction to complete one revolution in a single wave period allows a greater moment to be generated than if it is oscillated through small perturbations for the same duration. That is, the rate of nutation required to perform full revolutions in a given time period is greater than the corresponding maximum nurtation rate required to oscillate the flywheels through only fractions of a revolution. 4. The experimental gyrostabiliser system Fig. 3 provides a sketch of the gyro stabilisation system used for practical experimentation. Consistent with the principles outlined in Section 3.5, the new gyro stabiliser uses a pair of gyroscopes nutating at a constant rate about their free axes. To remove the effects of gyroscopic moments acting about the undesired axis of ship rotation, it is necessary to spin the flywheels in opposite directions while also nutating the gyroscopes in opposing directions. This latter point is well established in CMGs (both theoretically and experimentally) but does require additional mechanical complexity to implement practically. Therefore, to avoid this mechanical complexity while still permitting the demonstration of the principal objective of this proposal (i.e. the use of constantly nutating gyroscopes to provide stabilising moments on a marine vehicle) the practical experiments used gyroscopes that were spinning in the same direction as well as nutating in the same direction as each other. Although it has been indicated that contra-nutating gyroscopes are not required in order to demonstrate the effectiveness of the new uni-directional nutation mode of operation, two gyroscopes were nevertheless provided and used for the experiments. The reason for this approach is;
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Fig. 3. General arrangement of the gyrostabiliser used in the physical experiments.
this added little extra mechanical complexity and minimises manufacturing resources while preparing for future research with the fully controlled system. Furthermore, using two gyroscopes permitted simple comparison between the experimental and theoretical calculations that assume the use of two gyroscopes spinning and nutating in opposing directions. To remove the effects of the undesired gyroscopic moments in the experiments, the model vessel was restrained in the direction of freedom affected by the undesirable gyroscopic moments (yaw in this case). Active gyro stabilisation requires controlling to ensure it operates at a specified frequency and phase compared to wave excitation moments. For the purposes of demonstrating the new mode of operation, a control system was found to be unnecessary. That is, for the purposes of experimental work a novel approach was used that circumvented the need to provide a (complex) control system, while still demonstrating the effects of the new gyrostabiliser system. Details of this method are supplied in Section 5.1.
combined weight of the two rotors of the experimental gyrostabiliser is 11.5% of the total displacement of the model vessel. The combined mass-moment of inertia, about the spin axis (Iz), of the two rotors is 1.02% of the pitch mass-moment of inertial of the model vessel. The model vessel, attached to the towing post, was free to move in pitch and heave whilst being restrained in all other degrees of freedom. In each experiment, pitch was recorded as a function of time. 5.1. Experimental programme Three sets of tests were carried out as indicated in Table 2. The control experiments were carried out with the vessel at zero forward speed. In these experiments, it was observed that nutating the gyroscope with spinning flywheels on the model-ship otherwise at rest in calm water, did induce vessel motion as expected, i.e. oscillatory pitch motion. However, no measurable vessel motions were observed when
5. Experimental investigations The aim of the experimental investigations was to demonstrate the effectiveness of the new device, described in Section 4, as a ride control system for marine vehicles. These experiments were carried out on a ship-model in a towing tank. The ship-fixed axis of rotation about which the undesirable motions are targeted using the gyro stabiliser is arbitrary. For the experiments reported here, the targeted motion was pitch. This readily permitted testing with the model ship at forward speed in a towing tank (where the wave excitation induces pitch). Furthermore, this research attracted industrial support in which the principal concern was controlling pitch motions of fast catamaran ferries. Therefore, experiments with the gyro stabiliser were carried out on a catamaran model with a hull form representative of the specified ferry type. The
(a) the flywheels were spinning within the otherwise static gyroscope structures and (b) gyroscopes were nutated with otherwise static flywheels. Thus, as required, the gyroscope-induced motion is entirely due to the expected gyroscopic moments. It is common practice to determine the effectiveness of ship stabilisation systems from the motions they can induce in calm water (Rawson and Tupper, 2001). Therefore, the effectiveness of the gyrostabilier to induce motions with the vessel advancing in otherwise calm water was investigated. In these experiments, the ship-model was towed while the gyro stabiliser was used to induce pitch motion. The third set of experiments examined the effectiveness of the gyrostabiliser to reduce pitch motion with the model
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Table 2 Summary of experimental investigations Experiment
Description
Control experiments
Verification that motion caused by the gyroscope is entirely due to the expected gyroscopic moments, as defined in Eqs. (5) and (6) rather than: (i) Imbalance in the gyroscopic flywheels or (ii) Inertial accelerations caused by imbalance in the supporting structures during notation
Experiments in calm water Experiments in regular head seas
To determine the effectiveness of the gyro stabiliser to induce pitch motions on a vessel advancing in otherwise calm water To determine the effectiveness of the gyro stabiliser to reduce pitch motions on a vessel advancing in a head sea
Fig. 4. Diagrammatic representation of modulation theory.
vessel advancing at forward speed in regular head-seas. While the gyroscopes were actively actuated (in nutation) it was found unnecessary to provide a complex control system to demonstrate the effectiveness of the stabiliser to reduce ship motion in regular seas. The principles and practical application of the experimental approach adopted in these experiments is provided next. 5.1.1. Modulation theory All mechanical systems employed as ship motion reducers need a definite phase relation between the mechanism and that of the ships motion (Lewis, 1986). In the case of active stabilisers, the required phase relationship is provided by a control system. To circumvent the need to provide this complex control system, a modulation theory approach was adopted. Modulation theory (often applied to the study of radio waves) is concerned with the regular variation in the amplitude of a waveform from the superposition of a number of different waves. Fig. 4 illustrates the signal generated from the linear summation of two regular sinusoidal waves of different frequencies and amplitudes. The complete waveform in Fig. 4 is given by A1 cos o1 t þ A2 cos o2 t qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ A21 þ 2A1 A2 cos ½ðo1 o2 Þt þ A22 A2 sin ðo1 o2 Þt 1 cos o2 t þ tan , A1 þ A2 cos ðo1 o2 Þt
ð7Þ
where the effect of modulation is described by the envelope indicating the time-varying amplitude of the resulting waveform, (Goldman, 1967), i.e. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (8) A0 ¼ A21 þ 2A1 A2 cos ½ðo1 o2 Þt þ A22 . The maximum and minimum amplitude of the modulating signal can therefore be found from qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (9) A0Max ¼ ðA1 þ A2 Þ2 and A0Min ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðA1 A2 Þ2 ,
(10)
respectively. 5.1.2. Experimental application of modulation theory Fig. 5(a) and (b) presents the experimentally determined pitch response of the model ship, advancing with forward speed, subject to gyroscopic and wave excitation, respectively. The pitch response has been non-dimensionalised using the amplitude of the model vessel response in waves. In Fig. 5(a) and (b) the frequency of excitation is slightly different. Fig. 5(c) provides the ship-model pitch response when subject to both the wave and gyroscopic excitations of Fig. 5(a) and (b) simultaneously. The envelope indicated in Fig. 5(c) describing the modulated amplitude of the ship model response, has been determined by fitting the indicated maxima and minima, based on least-squared
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Fig. 5. Pitch responses for the model-ship advancing with forward speed subject to, (a) gyrostabiliser pitch excitation (gyroscopic nutation rate ¼ 51 rpm and spin rate ¼ 6200 rpm), (b) head-sea wave excitation (wave amplitude ¼ 0.02 m) and (c) simultaneous gyrostabiliser pitch excitation and head-sea wave excitation (gyroscope operation and head waves as specified in (a) and (b)).
errors, using Eq. (8). This envelope is clearly consistent with the theoretical envelope provided in Fig. 4 and demonstrates that the practical application of the proposed modulation theory is an effective method to determine the performance of the gyroscopic stabiliser in the absence of a sophisticated control system. The maximum amplitude of the model ship response is due to the in-phase summation of the wave and gyroscopic excitation moments (Eq. (9)), whereas the minimum amplitude of the model ship response results when the gyroscopic moment acts in opposition to the wave excitation moment (Eq. (10)). The latter case provides a measure of the performance of the gyroscopic stabiliser if it were appropriately controlled. All data resulting from simultaneous wave and gyroscopic excitation were analysed following this reasoning. 6. Presentation of results The experimental apparatus readily permitted the operation of the gyro stabiliser at two spin and two nutation rates. The two spin rates were 4000 and 6200 rpm and the two rates of nutation were 61 and 85 rpm. The heights of the regular head waves used were approximately 29% of the model ship draught. Fig. 6 provides the relative amplitude of the induced bow motion when the gyroscope was operated, at the different specified spin and nutation rates, on the vessel advancing in
otherwise calm water. In this figure gyroscopic excitation frequency is presented in terms of non-dimensional encounter frequency, consistent with later presentations with the vessel also subject to head-sea excitation. Fig. 7 presents the pitch response of the model-vessel with and without gyroscopic stabilisation while subject to head seas. In this figure estimations of the vessel response in waves are presented for both experimental and theoretical methods. The experimental estimates of the stabilised response are made by subtracting the reduction in pitch, determined using the modulation approach, from the experimentally determined unstabilised pitch response in head seas. The theoretical estimates of the pitch response are based on the research of Hudson (Hudson, 1999), for the type of vessel under consideration. The theoretical reduction in response due to gyroscopic stabilisation assumes the magnitude of the gyroscopic moment to be the same as that applied by the experimental device. These gyroscopic moments are calculated using Eq. (6) with the measured physical quantities of the as-built gyrostabiliser (linear dimensions, weights, rotation rates, etc.). High levels of accuracy are not required from the selected theoretical method for the prediction of model vessel’s unstabilised pitch response. These predictions simply serve as an approximate datum from which to provide a theoretical indication of the effectiveness of the gyroscopic stabilisation system. While Fig. 7 indicates that
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Amplitude of bow vertical displacement / draught
0.18 Spin rate 6200rpm and nutation rate 85rpm
0.16
Spin rate 4000rpm and nutation rate 85rpm 0.14
Spin rate 6200rpm and nutation rate 51rpm
0.12
Spin rate 4000rpm and nutation rate 51rpm
0.1 0.08 0.06 0.04 0.02 0 2
2.5
3
3.5
4
Non dimensional encounter frequency,
Fig. 6. Induced motions with the model vessel advancing in calm water.
Predicted unstablised Experiment unstabilised Predicted stabilised
1.6
Experiment stabilised
Non dimensional pitch response
1.4 1.2 1 0.8 0.6 0.4 0.2 0 2
2.5
3
3.5
4
4.5
5
5.5
6
Non dimensional encounter frequency,
Fig. 7. Performance of the gyro stabiliser determined experimentally and theoretically.
the selected prediction method over-estimates the vessel response, it nevertheless provides a reasonable indication of the behaviour, in pitch, of the type of vessel used in the experiments. Furthermore, the theoretical predictions of the effectiveness of the gyro stabiliser, presented in Fig. 7, are reasonably consistent with those found experimentally.
7. Discussion The maximum amplitude of the bow motion induced by the operation of the gyroscope on the model vessel advancing in otherwise calm water were observed to be of the order of magnitude of the wave heights selected for
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head sea experiments. This provided confirmation that the gyroscopic parameters had been sufficiently well specified for the intended head sea experiments. Furthermore, in Fig. 6, for the vessel advancing in otherwise calm water, it is notable that the variation in experimentally induced pitch response is consistent with theoretical expectations (Eq. (6)). That is, for each of the two nutation (excitation) frequencies used, there is an approximately linear variation in the response of the vessel with gyroscopic spin rate. The demonstration of the effectiveness of the new gyroscopic stabilisation system in Fig. 7, indicates that the motion reduction achievable using the specified experimental system is in the range from 30% to 70%. The work of Sclavounos and Borgen (2004), Ryle (1998), amongst others, examines current pitch ride control systems for catamarans, including controlled bow foil and stern flaps. Their research has demonstrated that pitch reductions of 50% compared to the vessel without these control appendages is usual. Therefore, the proposed new internal system is comparable to current external systems. Based on the reasonable correlation between experimental results and theoretical calculations at model scale Fig. 8 provides an indication of the effectiveness of the new stabilisation system for a hypothetical full-scale application. Consistent with the industrial interest in this research, the hypothetical full-scale application assumes the experimental device is simply scaled in terms of linear dimensions from the model scale to an equivalent 45 m fast catamaran ferry. The hypothetical study set out to determine the feasability of the full-scale application of the new apprach to gyrostabilisation, therefore no particular attention was paid to optimising the gyroscopic rotors in terms of their geometric or material properties. Thus, consistent with the experimental device, the full-scale device is assumed to use
solid steel discs. The resulting hypothetical full-scale device therefore uses two 3.23 m diameter steel rotors with a combined weight of approximately 52,000 kg. This corresponds to approximately 17.4% of the displacement of the selected vessel. The combined mass moment of inertia of the two gyroscopic flywheels is 0.94% of the pitch mass moment of inertia of the vessel. In Fig. 8, the contours indicate the gyroscopic spin rates required to counter different fractions of the total head sea pitch excitation moments. These spin rates are well within practical limits, and are readily achievable as demonstrated from current flywheel and CMG systems, see Lazarewicz et al. (2000), (Richie and Tsiotras (2001) among others. For full-scale applications of the gyroscopic stabilisation method presented in this paper, a refinement of the gyroscopic rotors is required as well as the application of an appropriate control strategy. For example, in Fig. 8, simple linear scaling of solid steel rotors was used to verify that the proposed system is readily achievable at full scale; the mass of the stabilisation system could be reduced through a judicious selection of spin rate and flywheel mass-moment of inertia. The existing technological infrastructure for the recently developed passive systems indicates this is readily achievable. In addition to the specific case study in this paper, other hypothetical cases have been studied comparing pitch and roll stabilisation for a range of vessels. These studies revealed that gyroscopic stabilisation in this new mode of operation would be effective on small to medium sized vessels and that the practical limit of performance is essentially controlled, not by limits on the operation of the gyroscopic flywheel, but rather by the magnitude of the excitation moments which must be supplied to actively nutate the gyroscopic flywheels.
1600 100% 1400 1200 Spin rate in rpm
75% 1000 800
50%
600 400 200 0 1
2
3
4
5
6
7
Non dimensional encounter frequency,
Fig. 8. Gyroscopic spin rates required to counter head-sea pitch excitation moments on a 45 m fast catamaran ferry. Contours indicate different levels of effectiveness.
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8. Conclusions The initial motivation for this research was to examine alternative ride control systems that are capable of providing levels of motion reduction, on ships, comparable to existing external systems, while also overcoming the associated hydrodynamic disadvantages. Furthermore, the new system was required to exploit alternative approaches to generating moments within the hull in order to circumvent the weight penalties incurred by simply providing sufficient movable mass to generate stabilising moments. In this research, the emergence of modern passive marine gyro stabilisation and the fact that active control of historic systems improved ride control performance, led to an investigation of alternative strategies for active gyro stabilisation. The new mode of operation uses two gyroscopic flywheels, spinning in opposing directions while being forced to nutate at constant rates, also in opposition was proposed. The experimental investigation used a novel application of the theory of wave modulation to assess the ride control capabilities of the device. These investigations demonstrate that the new mode of gyroscopic stabilisation, when applied on marine vehicles, is capable of providing levels of ride control consistent with contemporary external systems. Theoretical estimates of the system at full-scale indicate that the proposed method is readily achievable in practice and that it is suitable for ride control in pitch and roll for small and medium size vessels. The principal practical limitation of the method is the levels of torque required to nutate the gyroscopic flywheels, rather than operating the gyroscopic flywheels themselves. Further research is required to provide an appropriate control strategy. Furthermore, exploiting the versatility afforded by a judicious combination of the gyroscopic parameters (spin rate and mass distribution within the rotor) will permit appropriate specification of the weight and volume of the system for application on a variety of vessels. Acknowledgements This research was funded by FBM Babcock Ltd. and the Engineering and Physical Science Research Council, EPSRC. We are grateful to Mr. N. Warren for helpful discussions on this subject. References Aubrun, J.N. and Margulies, G., 1979. Gyrodampers for large scale space structures. Technical Report, NASA CR-159 171. Ayres, C., 2005. Sea gyro email correspondence. Bennett, D.A., 1970. Comparison of ship roll stabilisation methods. Shipping World Shipbuilder, v163, n3847, July 1970, pp. 989–90, 993–4. Benz, C., 1888. Self-propelling vehicle. Patent US 385,087.
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