Method for reducing dynamic loads of cranes

Abstract

A method and related device for reducing resonant vibrations and dynamic loads of cranes, where vertical motion of a pay load is controlled by a boom winch and a hoist winch. In an embodiment, the method includes determining resonance frequencies of the crane boom and pay load from inertia data of the boom and stiffness on at least the boom and hoist ropes, the resonance frequencies including a first frequency and a lower second frequency. In addition, the method includes automatically modifying the motion of the boom winch or the hoist winch to induce a damping inducing winch motion in the boom or hoist winch, by tuning a proportional integral (PI)-type boom winch speed controller or a PI-type hoist winch speed controller. The boom winch speed controller is tuned to absorb energy at the second frequency, the hoist winch speed controller is tuned to absorb energy at the first frequency.

Claims

1. A device for reducing resonant vibrations and dynamic loads of cranes, the device comprising: a boom winch configured to control a luffing motion of a pivoting boom; and a hoist winch configured to control a vertical distance between a boom tip and a pay load of the crane; a boom winch speed controller coupled to the boom winch; and a hoist winch speed controller coupled to the hoist winch; wherein the device is configured to acquire resonance frequencies of a coupling of the pivoting boom and the pay load from at least inertia data of the pivoting boom and stiffness data on at least a boom rope coupled to the boom winch and a hoist rope coupled to the hoist winch, the resonance frequencies including a first resonance frequency and a second resonance frequency, the second resonance frequency being lower than the first resonance frequency; wherein the boom winch speed controller or the hoist winch speed controller is configured to automatically modify a motion of the boom winch or a motion of the hoist winch, respectively, to induce a damping inducing winch motion; wherein the boom winch speed controller comprises a proportional integral (PI)-type speed controller that is tuned to absorb vibration energy at the second resonance frequency; and wherein the hoist winch speed controller comprises a PI-type speed controller that is tuned to absorb vibration energy at the first resonance frequency.

2. The device of claim 1, wherein the boom winch speed controller includes an integral factor and a proportional factor, and wherein the hoist winch speed controller includes an integral factor and a proportional factor; wherein the integral factor of the boom winch speed controller is substantially equal to a product of an effective inertia of the boom winch and a squared angular boom resonance frequency; wherein the integral factor of the hoist winch speed controller is substantially equal to a product of an effective inertia of the hoist winch and the squared angular boom resonance frequency; and wherein the proportional factor of the boom winch and the proportional factor of the hoist winch each comprise linear combinations of an inverse of the resonance frequencies squared.

3. The device of claim 2, wherein the proportional factor of the boom winch speed controller is proportional to the square of an effective stiffness of a crane pedestal and the boom rope and inversely proportional to a boom inertia and a square of the angular boom resonance frequency squared; and wherein the proportional factor of the hoist winch speed controller is proportional to the square of an effective stiffness of the hoist rope and inversely proportional to an inertia of the pay load and a square of an angular load resonance frequency.

4. The device of claim 3, wherein at least one of the boom winch speed controller and the hoist winch speed controller includes an inertia-compensating term, wherein the inertia-compensating term comprises a product of a time derivative of a measured speed of the corresponding one of the boom winch or hoist winch, and a fraction of a mechanical winch inertia of the corresponding one of the boom winch or hoist winch.

5. A method for reducing resonant vibrations and dynamic loads of cranes, wherein a vertical motion of a pay load is controlled by a boom winch controlling a luffing motion of a pivoting boom and a hoist winch controlling a vertical distance between a boom tip and the pay load, the method comprising: determining resonance frequencies of a coupling of the pivoting boom and the pay load from at least from inertia data of the pivoting boom and stiffness data on at least a boom rope coupled to the boom winch and a hoist rope coupled to the hoist winch, the resonance frequencies including a first resonance frequency and a second resonance frequency, the second resonance frequency being lower than the first resonance frequency; and automatically modifying a motion of the boom winch or a motion of the hoist winch to induce a damping inducing winch motion in the boom winch or hoist winch, respectively, by tuning a proportional integral (PI)-type boom winch speed controller coupled the boom winch or a PI-type hoist winch speed controller coupled to the hoist winch; wherein the boom winch speed controller is tuned to absorb vibration energy at the second resonance frequency; and wherein the hoist winch speed controller is tuned to absorb vibration energy at the first resonance frequency.

6. The method of claim 5, wherein tuning the PI-type boom winch speed controller further comprises: choosing an integral factor of the boom winch speed controller that is substantially equal to a product of an effective inertia of the boom winch and a squared angular boom resonance frequency; and choosing a proportional factor of the boom winch speed controller that comprises a linear combination of an inverse of the resonance frequencies squared.

7. The method of claim 6, wherein the proportional factor of the boom winch speed controller is proportional to a square of an effective stiffness of a crane pedestal and the boom rope and inversely proportional to a boom inertia and a square of the angular boom resonance frequency squared.

8. The method of claim 5, wherein tuning the PI-type hoist winch speed controller further comprises: choosing an integral factor of the hoist winch speed controller that is substantially equal to a product of an effective inertia of the hoist winch and a squared angular boom resonance frequency; and choosing a proportional factor of the hoist winch speed controller to comprise a linear combination of an inverse of the resonance frequencies squared.

9. The method of claim 8, wherein the proportional factor of the hoist winch speed controller is proportional to the square of an effective stiffness of the hoist rope and inversely proportional to an inertia of the pay load and a square of an angular load resonance frequency.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Below, an example of a preferred method and device is explained under reference to the enclosed drawings, where:

(2) FIG. 1 shows schematic view of a crane that is equipped to perform the method according to the principles described herein;

(3) FIG. 2 shows a graph of natural oscillating periods of crane modes;

(4) FIG. 3 shows in a graph a simulation of coupled crane and load oscillations;

(5) FIG. 4 shows in a graph a simulation of crane oscillations with unlocked and stiffly controlled winches;

(6) FIG. 5 shows in a graph a simulation of crane oscillations using force feed-back; and

(7) FIG. 6 shows in a graph a simulation of crane oscillations using tuned speed controllers.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(8) In the present document an offshore crane is utilized for explaining the invention. This does not in any way limit the scope of the document as the principles disclosed here are applicable for similar cranes wherever they are used.

(9) In the present document electrical driven winches are utilized for explaining the invention. This does not in any way limit the scope of the document as the principles disclosed here are applicable also for hydraulically driven winches.

(10) It is to be emphasized that the present invention is focusing on vertical load and boom oscillations, not on the of pendulum oscillations of the load. The latter problem is solved by a number of different techniques, see EP 1886965, U.S. Pat. No. 5,823,369 or U.S. Pat. No. 7,289,875

(11) On the drawings the reference number 1 denotes a pedestal crane that includes a slewing platform 2 that is turnable about a vertical axis 4 of a pedestal 6. The pedestal 6 is fixed to a structure not shown.

(12) An A-frame 10 extends upwardly from the platform 2, while a hinge 12 having a horizontal axis 14 connects a boom 16 of the platform 2. The boom 16 has a centre of gravity 16a.

(13) A boom rope 18 having a number of falls extends between a rope sheave 20 located at the top of the A-frame 10 and a rope sheave 22 on the boom 16. The boom rope (18) is connected to a boom winch 24 that is fixed to the A-frame 10. The boom winch 24 is controlling the luffing motion of the boom 16, thus regulating an angle between the boom 16 and a horizontal plane.

(14) A hoist rope 26 having a number of falls extends between a rope sheave 28 near the tip 30 of the boom 16 and a rope sheave 32 at a hook 34. The hoist rope (26) is connected to a hoist winch 36. The hoist winch 36 is located at the boom 16 and controls the lifting motion of the hook 34. A load 38 is connected to the hook 34.

(15) The boom winch 24 and the hoist winch (36) are electrically connected to a boom speed controller 40 and a hoist speed controller 42. The speed controllers 40, 42 are of a type commonly used for cranes and well known to a skilled person and may be controlled by a Programmable Logic Controller (PLC) 44.

(16) The speed controllers 40, 42 are often included in respective drives (not shown) having power electronics controlling motors (not shown) for the winches 24, 36.

(17) The speed signal from the winches 24, 36 necessary for winch speed control can be analogue or digital tachometers attached to either a motor axis or a drum axis (not shown) of each winch 24, 36. The signal is routed to the respective speed controller 40, 42 being a normal part of the drive electronics. Optional tension sensors can be specially instrumented center bolts (not shown) of the sheaves 20, 22 and 28, or they can be strain gauges sensors (not shown) picking up the force moments in the A-frame 10 and in the boom tip 30. These tension signals are routed to a central computer or a PLC 44 for processing, to give the desired modification of the operator reference speed routed to the drive speed controllers 40, 42. It is also a possibility that the torque signals are routed directly to the drive, provided that the drive is digital with sufficient processing capacity to transform the force signals into a modified speed reference signal.

(18) In FIG. 1 the load radius, that is the horizontal distance from the hinge axis 14 to the hook 34, is denoted R.sub.l, the moment radius to the boom rope 20 from the hinge axis 14 is denoted R.sub.a while the boom weight radius that is the horizontal distance from the hinge axis 14 to the centre of gravity 16a of the boom 16 is denoted R.sub.b.

(19) FIG. 2 shows how the natural periods (related to the angular frequency through T=2/) of a typical offshore crane vary with the load radius R.sub.l. The calculations are carried out with a constant position of the load 38 at 25 m below the boom hinge 12 so that the hoist rope 26 length also vary with the boom angle and load radius R.sub.l. The load is taken from a load chart and represents the largest safe working load for sea lifts with a significant heave height of 2 m. Key crane and wire rope parameters are: M.sub.l=10 000 kg Load mass L.sub.b=59.1 m Boom length J.sub.b=41e6 kgm.sup.2 Boom inertia d=32 mm Rope diameter (both winches) E=60 GPa Effective modulus of rope elasticity n.sub.t=8 Number of falls for the top winch n.sub.l=3 Number of falls for the hoist winch

(20) In FIG. 2 the curve I shows the boom mode period T.sub.1=2/.sub.l, curve II shows the empty boom mode period T.sub.t=2/.sub.t, the curve III shows the load mode period T.sub.l=2/.sub.l with fixed boom and the curve IV shows the load mode period T.sub.2=2/.sub.2.

(21) The two modes, represented by their periods T.sub.1 and T.sub.2, have a higher separation than the uncoupled boom and load modes, represented by the periods T.sub.t and T.sub.l, respectively. However, the coupling effect varies with load radius R.sub.l. With a short load radius R.sub.l, i.e. a highly erected boom 16, the coupling is small, implying that the boom 16 and the load 38 oscillate nearly independent of each other.

(22) FIG. 3 shows the simulated transient motion of a crane 1 for an idealized case when a support (not shown) of the load 38 is suddenly removed while the winches 24, 36 are locked. This case is calculated for the same crane 1 as above and with maximum permissible load at a radius of 43 m (boom angle of 38.6).

(23) In FIG. 3 the curve V shows the vertical speed of the boom tip 30, the curve VI shows the vertical speed of the load 38, while the curve VII shows the difference between the two. The curve VIII shows the effective top force, which equals the sum of tension forces of all falls in the boom rope 20 multiplied by the radius ratio R.sub.l/R.sub.a, the curve IX shows the sum of the tension forces in all falls of the hoist rope 26. The static weight (gravitation force) of the load 38 is included as curve X, for comparison.

(24) The low frequency (boom) mode has a period of 1.6 s while the high frequency (load) mode has a period of approximately 0.4 s, in accordance with FIG. 2.

(25) An embodiment of the invention includes damping by feedback induced winch motion.

(26) It is assumed that the winches 24, 36 are not locked but may be perfectly controlled so that they are linear functions of the accelerations of the vertical boom tip 30 and load 38. It is convenient to write the winch motion as:
w=S.sup.1.sup.1MDiv(16)
where D is a real damping (decay rate) matrix, to be determined. With this winch motion the equations of motion (10) becomes:
(.sup.2I+iD+A)v=0(17)

(27) This is a quadratic eigenvalue problem that can be solved to give complex eigenfrequencies and eigenvectors. The latter represent column vectors in the so-called eigenmatrix, often called X=[x.sub.1 x.sub.2] in text books of linear theory. This theory also predicts that the two modes can be independently damped if the damping matrix can be written as D=XX.sup.1 where is a diagonal matrix representing the decay rates .sub.1 and .sub.2 for the two modes.

(28) The boom tip 30 and load 38 accelerations are normally not measured directly. They can, however, be estimated from the tension forces, because the equation of motion may be written in the following form Miv=f. The winch motions required to achieve a controlled and independent damping of the two modes are therefore given by the vector
w=S.sup.1.sup.1MXX.sup.1M.sup.1f(18)

(29) If the two decay parameters are equal so that =I, then this expression simplifies greatly to w=S.sup.1f. More explicitly the optimal top winch 24 speed is w.sub.t=.Math.f.sub.t/S.sub.t while the optimal hoist winch 36 speed is w.sub.h=.Math.f.sub.h/S.sub.h. Although these formulas describe complex Fourier amplitudes of speeds and forces, they also apply in the time domain. However, it is necessary to apply a kind of high pass or band pass filter in the feedback loop, in order to avoid load dependent slip of the winch speeds. The lower angular cut-off frequency should be well below the lowest crane resonance frequency, .sub.1, and the upper should be well above the highest one, .sub.2, to avoid serious phase distortion at the resonance frequencies. An alternative to using a common wide band pass filter is to apply individual filters for each winch. The top winch feedback signal should then have a filter that is centred around the lowest resonance frequency while the winch feedback signal should have a filter centred around the highest resonance frequency. A suitable filter could be a second order band pass filter represented by:

(30) $\begin{array}{cc}{H}_m=\frac{2i{}_m}{{\left(+i{}_m\right)}^2}& \left(19\right)\end{array}$
and where the subscript .sub.m denotes the mode number 1 or 2. It should be noticed that filtering introduce a weak coupling between the modes so that the resonance frequencies and the damping are slightly shifted from the uncoupled and non-filtered values.

(31) In FIG. 4 that shows crane oscillations with unlocked and stiffly controlled winches, the curve XI shows vertical speed of the boom tip 30, the curve XII shows the vertical speed of the load 38, the curves XIII and XIV shows the vertical speed of the boom winch 24 and the hoist winch 36, but they are so close to zero that they are virtually indistinguishable with the chosen scale of the y-axis. The curve XV shows force in the boom rope 20, the curve XVI shows the force in the hoist rope 26 while the curve XVII shows the force from the load 38.

(32) In FIG. 5 that shows simulated crane oscillations from a similar drop of the load, but now with force feedback induced damping motion of the two winches. The curve XVIII shows the vertical speed of the boom tip 30, the curve XIX shows the vertical speed of the load 38, the curve XX shows the speed of the boom winch 24, the curve XXI shows the speed of the hoist winch 36, the curve XXII shows force in the boom rope 20, the curve XXIII shows the force in the hoist rope 26 while the curve XXIV shows the force from the load 38.

(33) As shown in the FIGS. 4 and 5, damping may be achieved by either acceleration or force feedback for modifying the winch speeds. This kind of winch control is called cascade regulation, because the feedback is an outer control loop using the existing speed controller. The speed controller should be rather stiff to give minimal speed error, which is the difference between demanded and actual speed.

(34) An alternative embodiment of the invention includes damping by tuned winch speed control.

(35) Damping may be achieved by tuning of the winch speed controllers 40, 42, without feedback from measured accelerations or forces. This is justified below.

(36) Details of the derivation of the equation of motion for the winch motion is not explained, but it may be shown that the basic moment balance for the two winches can be transformed into the following matrix equation:
iJ.sub.m.sub.m=Z.sub.m(.sub.set.sub.m)Rf(20)
where J.sub.m is a motor inertia matrix, .sub.set is the vector of operator set motor speeds, .sub.m is the vector of the actual angular motor speeds, Z.sub.m is a speed controller impedance matrix, and R is a coupling radius matrix. All matrices are diagonal where the upper left elements represent the top winch. The two elements of the coupling radius matrix are R.sub.11=R.sub.tR.sub.l/(n.sub.gn.sub.tR.sub.a) and R.sub.22=R.sub.h/(n.sub.gn.sub.l) where R.sub.t is drum radius of top winch, R.sub.h is drum radius of hoist winch and n.sub.g is the gear ratio (motor speed/drum speed, assumed to be equal for the two winches).

(37) The above equation may be transformed to a corresponding equation for vertical winch motions by pre-multiplying R.sup.1 by and inserting the identity R.sup.1R in front of the winch motion vectors:
iM.sub.ww=Z.sub.w(w.sub.setw)f(21)

(38) Here M.sub.w=R.sup.2J.sub.m is effective winch mass matrix, w=R.sub.m is the vertical winch speed vector and Z.sub.w=R.sup.2Z.sub.m is the impedance matrix for vertical speed control. If the speed controllers are standard and independent PI controllers, then this matrix may be represented by Z.sub.w=P.sub.w+I.sub.w/i where P.sub.w and I.sub.w are diagonal matrixes representing the proportional and integral terms, respectively. (The latter should not be confused with the identity matrix which has no subscript.) Using equation (8) for the rope force vector f and assuming constant operator set speed (w.sub.set=0) the above equation may be rewritten as:
(.sup.2M.sub.w+iP.sub.w+I.sub.w+S)w=S.sub.vv(22)

(39) Combining this matrix equation with equation (10) lead to:
{(.sup.2M.sub.w+iP.sub.w+I.sub.w+S)(.sup.2.sup.1M+S.sub.v)SS.sub.v}v=0(23)

(40) Here the fact is used that diagonal matrices commutate, that is, they may change order. This equation may alternatively be written as:
{.sup.4M.sub.w.sup.1Mi.sup.3P.sub.w.sup.1M.sup.2((I.sub.w+S).sup.1M+M.sub.wS.sub.v)+iP.sub.wS.sub.v+I.sub.wS.sub.v}v=0(24)

(41) This 4.sup.th order matrix equation has 8 roots or complex eigenfrequencies that make the matrix within the curly brackets singular. These roots must be found numerically since no analytical solutions exist. It is also possible, by iterations, to solve the inverse problem, which is to find speed controller parameters (the four diagonal terms of P.sub.w and I.sub.w) that represent specified damping rates. Numerical examples have shown that if the integral constant matrix is chosen to be:
I.sub.w=.sup.2M.sub.w(25)
and the proportional matrix is:
P.sub.w=.sup.1M.sup.1S.sup.2.sup.2(26)
where =diag(.sub.1,.sub.2), then the two modes have approximately the same real frequencies as with locked winches and they are dampened with decay rates close to the specified diagonal terms . The above choice for I.sub.w can be regarded as a frequency tuning of the speed controllers, causing the top winch and hoist winch mobility to have maxima at .sub.1 and .sub.2, respectively. The above choice for P.sub.w can regarded as a softening of the speed controllers so that the winches respond to the load variations and absorb vibration energy more efficiently than stiff controllers do.

(42) The winch inertia, represented by M.sub.w or J.sub.w, strongly affect the absorption band width of the tuned speed controllers 40, 42. A high inertia makes the absorption band width narrow while a low inertia improves the band width is improved. A low inertia is favourable because it causes the winch to dampen crane oscillations effectively even if the real resonance frequency deviates substantially from the tuned frequency of the speed controller 40, 42.

(43) The mechanical winch inertia M.sub.w is mainly controlled by the motor inertia, the drum inertia, the gear ratio and the number of falls. In practice, the possibility to select a low inertia is limited because a higher gear (or a lower number of falls) is in conflict with a high pull capacity.

(44) However, the effective inertia can be reduced by applying an extra inertia compensating term in the speed controller. This new term is proportional to the measured motor acceleration and can be written as iJ.sub.c.sub.m, where J.sub.c is a diagonal matrix, typically chosen as some fraction, typically 50%, of the mechanical inertia. If this torque term is added to the right hand side of equation (20), it is realized that it cancels part on the mechanical inertia term on the left hand side. An easy way to include such an inertia term is to redefine the effective motor inertia so that it represents the difference between the mechanical and the compensated inertia, that is J.sub.m=J.sub.mmJ.sub.c where J.sub.mm now represents the mechanical inertia of the winch motors. With this redefinition analysis above applies also when an inertia compensation term is included.

(45) It is not recommended to compensate for the entire mechanical inertia, only up to a maximum of 75%, say. This is because the optimal I-term of the speed controller 40, 42 is proportional to the effective inertia, as shown explicitly in equation (25), and it is desirable to retain some integral action to avoid low frequency speed errors or slip speeds. A practical implementation of inertia compensation should also include some kind of low pass filter of the speed based acceleration signal. This is because time differentiation is a noise driving process that can give high noise levels if the speed signal is not perfectly smooth. The cut-off frequency of such a low pass filter must be well above the tuning frequency in order to avoid large phase distortion of the filtered acceleration signal.

(46) A practical way to implement the desired damping by tuned speed control is to predetermine P- and I factors and store them in 2D look-up tables in the memory of the Programmable Logic Controller (PLC) used for controlling the winches. When a new combination of the pay load and the load radius is detected, the correct speed controller values are picked from these look-up tables for updating the speed controllers.

(47) The dynamically tuneable speed controllers can either be implemented in the drives, that is, in the power electronics controlling the winch motors, or in the PLC controlling the drives. In the latter case the drives must be run in torque mode, which means that the speed controller is bypassed and the output torque is controlled directly by the PLC.

(48) If the pick-up load is known a priori, that is before a lift starts, the resonance frequencies and the speed controller parameters should be adjusted according to this load. If the load is not known a priory, a load estimator should quickly find an approximation of the load based on measured rope tension forces. Alternatively, the load can be roughly estimated from the hoist winch torque, after correcting for friction and inertia effects.

(49) Simulation results with tuned speed controllers are shown in FIG. 6. In FIG. 6 the curve XXV shows vertical speed of the boom tip 30, the curve XXVI shows the vertical speed of the load 38, the curve XXVII shows the speed of the boom winch 24, the curve XXVIII shows the speed of the hoist winch 36, the curve XXIX shows force in the boom rope 20, the curve XXX shows the force in the hoist rope 26 while the curve XXXI shows the force from the load 38.

(50) Even though the condition of a suddenly removed load support is not very realistic, it illustrates the effect of damping of the transient crane oscillations. The damping for the two modes are not identical but quite similar to the feedback induced damping.

(51) The above formalism, where the crane and winch dynamics are described by matrices and vectors, may be generalized and applied also to more complex crane structures with higher degrees of freedom. As an example, if the inertia of the pedestal and A-frame is not neglected, the crane dynamics with locked winches can be described by a similar matrix equation as equations (10) and (11) but now representing a 33 matrix equations. The new system matrix has three eigenfrequencies where the two lowest ones are close to the frequencies found above, and where the highest one represents the resonance frequency of the pedestal/A-frame system.

(52) A similar expansion of the degrees of freedom is needed if the boom is treated as a flexible element rather than a completely fixed structure. In the case of complex crane structures modelled with three or more degrees of freedom the top winch and the hoist winch are no longer capable of damping all crane modes independently. Although active winch control will affect all crane modes, the most pronounced damping effect is expected on the modes for which the feedback or speed control is tuned.