CN111123705A - Design method for active vibration control of propeller and transmission shaft system - Google Patents
Design method for active vibration control of propeller and transmission shaft system Download PDFInfo
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
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Abstract
The invention discloses a design method for active vibration control of a propeller and transmission shaft system, which comprises the steps of firstly establishing a model of the propeller and transmission shaft system, designing an active vibration controller meeting the optimal vibration reduction performance according to the model, then realizing the controller by using a proposed active vibration control algorithm, finally confirming whether the optimal design meets the performance requirements of the propeller and transmission shaft system by simulation, if not, returning to reselect an optimal parameter value, confirming the optimal performance of the propeller and transmission shaft system and the compromise condition of the performance of the propeller and transmission shaft system; if the requirements are still not met, the performance index requirements are over high, the index requirements must be reduced, or the system structure parameters must be redesigned. The invention provides an optimal design method for realizing simultaneous vibration reduction of a propeller and a transmission shaft by only implementing control at the transmission shaft, so that the designed propeller/transmission shaft has optimal performance.
Description
Technical Field
The invention relates to a design method for active vibration control of a propeller and transmission shaft system, in particular to an optimal design method for optimal performance of the propeller and the shaft system and compromise condition of the performance of the propeller and the shaft system.
Background
Propellers are widely used in the fields of aviation and navigation, for example, in the field of aviation, the propeller blades rotate in the air to convert the engine rotation power into propulsive force or lift force, thereby propelling an aircraft powered by piston and turboprop engines; or providing lift and torque balance forces to the helicopter in the form of rotors and tail rotors; in the field of seagoing, propellers are used as a propulsion tool of a submersible and become almost the only power transmission source of submarines and ships. However, vibration problems of the propeller and drive shaft system, which is the power transmission source, are also important factors affecting aircraft and marine craft performance and noise. The design of vibration and noise reduction is carried out on the propeller and the transmission shaft, and the design has important significance for military use (reduction of sonar detection risk) and civil use (comfort and environmental protection).
Generally, the vibration control of the propeller and the transmission shaft adopts a separate control method, namely, the propeller and the transmission shaft are separately controlled. For example, in the papers of s.b.chun and c.w.lee, and a.bas, j.gilheany and p.steel, the method of individually controlling the transmission shaft is adopted to control the overall vibration of the system, and in the patent CN201910040569.3 applied by the research institute of ocean development in zhejiang, the objective of overall vibration reduction is also achieved by adopting an optimized transmission structure; and Y.Chen, V.Wickramainghe and D.Zimci adopt a method for controlling a propeller independently so as to achieve the control of the integral vibration of the system. This "single control" strategy, while available with existing control design methods, often requires repeated verification to confirm that the system is being damped. However, in practical engineering, after the vibration of the propeller is optimized, the vibration at the transmission shaft is obviously enhanced; or conversely, after the vibration at the transmission shaft is effectively inhibited, the vibration at the propeller reaches an unacceptable degree again. To achieve global optimization, with the Development of smart materials, the embedding of smart sensing and actuating mechanisms into propellers has also been introduced (e.g., the paper "Wind tunnel testing of a smart rotor blade control"; f.k.straub.h.t.ngo, v.anand, and d.b.domzalski "Development of a piezoelectric actuator for a trailing blade control of a fuel rotor blades") to achieve separate optimization of propellers and drive shafts. However, this method requires the conversion of the sensing and execution signals of the rotating system, and the system is very difficult to implement; meanwhile, the sensing and actuating mode of the embedded blade is unreliable at present, and is only verified in a laboratory environment, and no relevant report is found in industrial practical application.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the design method for the active vibration control of the propeller and the transmission shaft system is provided, the control is only implemented at the transmission shaft, the aim of simultaneously damping the propeller and the transmission shaft is achieved, and the designed propeller/transmission shaft has the optimal performance.
The invention adopts the following technical scheme for solving the technical problems:
a design method for active vibration control of a propeller and drive shaft system comprises the following steps:
S(jω)＝(1-G00(jω)K(jω))-1
wi(jω)＝Cid(jω)
wherein, TydRepresenting the performance response, T, of the drive shaft y to external vibrations dzidIndicating propeller blades ziPerformance response to external vibration d, S (j ω) represents the system sensitivity function, K (j ω) represents the controller to be designed, wi(j ω) represents the i-th vibration signal to be attenuated at the propeller blades, CiIs a complex number representing amplitude and phase shift relative to the external vibration signal, d (j ω) represents the external vibration, Ri(j ω) represents the auxiliary sensitivity function, G00(jω)、Gi0(jω)、G0k(jω)、Gik(j ω) each represents a transfer function, i ═ 1, …, n, n represents the number of performance variables requiring damping;
and draw | Tyd| is less than or equal to 1 and
the geometric representations of (a) are denoted as S-circle and iR-circle, respectively;
step 3, judging whether common intersection exists between all iR-circles and S-circles or not, and if yes, judging that an optimal controller exists so that y (j omega) and z (z omega) can be obtainedi(j ω) simultaneous damping, y (j ω) representing a transmission shaft performance variable, zi(j ω) represents the propeller blade performance variable and proceeds to step 4, otherwise the design method ends;
step 4, reducing the S-circle and the 1R-circle according to the same proportion until the reduced S-circle is tangent to the reduced 1R-circle, wherein the tangent point meets the requirements of y (j omega) and z1(j ω) optimum Performance Point for Simultaneous damping, denoted A1(ii) a The above operation is repeated for each iR-circle with S-circle, i 2, …, n, and the tangent points found are sequentially denoted as a2,…,AnFrom A1,…,AnFind a point satisfying y (j ω) and all zi(j ω) optimal performance point for simultaneous damping;
wherein S (j ω) represents that y (j ω) and all z are satisfiedi(j ω) optimum Performance Point for Simultaneous damping, G00(j ω) represents a transfer function;
step 6, converting the controller K (j omega) under the frequency domain into the controller K(s) under the complex domain by using an active vibration control algorithm;
and 7, simulating according to the controller K(s) obtained in the step 6, verifying whether the optimal performance requirements of the propeller and the transmission shaft system are met, and returning to the step 2 for redesigning if the optimal performance requirements of the propeller and the transmission shaft system are not met.
As a preferred scheme of the present invention, the model of the propeller and transmission shaft system in step 1 is:
wherein the content of the first and second substances,
g denotes a transfer function matrix, G00(jω)、G0i(jω)、Gi0(jω)、Gii(j ω) each represents a transfer function, j ω represents a frequency domain, u (j ω) represents a control input at the drive shaft, w (j ω) represents a control input at the drive shafti(j ω) represents the i-th vibration signal to be damped at the propeller blades, y (j ω) represents the transmission shaft performance variable, zi(j ω) represents the propeller blade performance variable, i ═ 1, …, n, n represents the number of performance variables that require damping;
as a preferred embodiment of the present invention, the slave A in step 41,…,AnFind a point satisfying y (j ω) and all zi(j ω) the optimum performance point of simultaneous damping, the specific process is:
memory satisfying y (j omega) and zi(j ω) the optimal damping performance corresponding to the optimal performance point for simultaneous damping is TiFrom all points of tangency A1,…,AnIn which a point A is selectedk，k＝1,…,n，AkTo satisfy y (j ω) and zk(j ω) optimum Performance Point for Simultaneous damping, while selecting AkAs satisfying y (j ω) and zi≠k(j ω) optimum point of damping, the damping performance lost is less than T i≠k5% of the total.
As a preferred embodiment of the present invention, the specific process of step 6 is:
defining S (j ω) in the optimal controller K (j ω) as a complex number: s (j ω) ═ a + jb, where a and b have the same sign;
when a and b are positive numbers, the controller is as follows:
wherein, A is cd-b omega, c + bd/omega is 1, A is more than 0, d is more than 0; a. b, c, d are real numbers, ω represents the harmonic frequency, G00(s) represents a transfer function, s represents a complex domain;
when a and b are negative numbers, the controller is as follows:
wherein the content of the first and second substances,
a is more than 0, c is more than 0, d is more than 0, and sigma is a positive number.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the invention provides an optimal design method for achieving simultaneous vibration reduction of a propeller and a transmission shaft by only implementing control at the transmission shaft aiming at the problem that the propeller and the transmission shaft system are difficult to control simultaneously so as to achieve overall vibration reduction, so that the designed propeller/transmission shaft has optimal performance.
2. The design method is universal and is suitable for vibration control of aviation and marine propeller and transmission shaft systems.
Drawings
FIG. 1 is a flow chart of the design of active vibration control for a propeller and drive shaft system of the present invention.
FIG. 2 is a diagram of the performance of a military rotor and driveshaft system optimization design according to an embodiment of the present invention.
Fig. 3 shows the performance of the optimal controller according to the embodiment of the present invention at the selected point B, wherein (a) shows the performance of the propeller blades and (B) shows the performance of the propeller shaft base.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As shown in fig. 1, the present invention relates to a design method for active vibration control of a propeller and transmission shaft system, which comprises the following steps:
step 1: establishing a model of a propeller and transmission shaft system;
in the above formula, u (j ω) represents the control input at the propeller shaft, wi(j ω) represents the i-th vibration signal to be attenuated at the propeller blades; y (j ω) is the feedback signal available at the drive shaft, and zi(j ω) is a propeller controllability variable but cannot be used for feedback. Therefore, the design goal is to control the entire structural system using only the feedback u (j ω) ═ K (j ω) y (j ω), i.e., to achieve control over all performance variables y (j ω) and zi(j ω) (i ═ 1 … n). Therefore, the model is a general model, and the corresponding control design is suitable for vibration control of the aviation and navigation propellers and the transmission shaft system.
In the following examples, only two performance variables are considered for the test propeller rotor blade system. The system is represented in (1), and the applicable scenario is that only y is available for feedback control u-Ky, while the vibrations of y and z need to meet the performance requirements simultaneously. Where u represents the force applied to the base of the rotor shaft, y is the acceleration of the shaft base, and z is the acceleration on the rotor blade.
Testing on a tester shows that the measured frequency response of blade acceleration to blade excitation clearly results in a peak transmitted along the shaft at the first resonance in the region of 244 Hz. The objective of the optimal design is to design the active vibration controller such that the rotor and the blades of the propeller vibrate while obtaining optimal vibration damping performance.
Step 2: performing optimal design of an active vibration controller;
first, according to the above model parameters, the following variables are defined:
S＝(1-G00K)-1(2)
wherein: t isydAnd TzidRespectively representing the performance response of y to external vibration d and ziPerformance response to d.
Next, drawing | Tyd| is less than or equal to 1 and
are referred to as S-circle and iR-circle, respectively, and the following is concluded:
concluding that 1: if and only if all iR-circles and the unit S-circle have a common intersection, there is a controller u-Ky such that y (j ω) and zi(jω)
And simultaneously, vibration is reduced.
Concluding that 2: are y (j ω) and zi(j ω) the controller providing optimal damping performance is given by the tangent point of the proportional circles in units of S-circle and iR-circle.
Note that since each S-circle and iR-circle can be scaled differently, there are y (j ω) and zi(j ω) performance trade-off between. This has a profound effect on the actual engineering, for example: there are performance indicators for different performance variables and the best solution must be selected by balancing considerations between the performance variables.
Finally, once selected as y (j ω) and zi(j ω) optimum Performance Point of the designThe corresponding optimal controller can be determined from the definition of the sensitivity.
As shown in FIG. 2, the horizontal axis REAL represents the REAL part, the vertical axis IMAGIANRY represents the imaginary part, ComplexS-Plane represents the complex s-Plane, and | T is plottedydLess than or equal to 1 and TzdThe geometric representation of | ≦ 1, referred to as S-circle and R-circle, respectively, and the following predicate:
as can be seen from the figure, there is a distinct crossover region between S-circle and R-circle. It follows that simultaneous damping is possible for ω 244Hz, y (j ω) and z (j ω).
The 3 points labeled a, B and C in fig. 2 were selected and the corresponding controllers were constructed, respectively. Since point A is located at the S-circle boundary and within the 6dB R-circle boundary, the resulting optimal controller will keep y (j ω) constant while reducing z (j ω) by more than 11 dB; conversely, an optimal controller to select point C will decrease y (j ω) by less than 6dB without increasing z (j ω); finally, point B is located at the midpoint of the intersection point, the location of which indicates that the final optimal controller reduces y (j ω) and z (j ω) by about 3 dB. The optimal controller for these three cases can be given by the formula of predicate 3.
3, concluding that: provided as y (j ω) and zi(j ω) the optimum controller K (j ω) for the optimum vibration damping performance specified by (j ω) is given by:
and step 3: the controller is realized by using the proposed active vibration control algorithm;
defining S (j ω) in the optimal controller as a complex number: s (j ω) ═ a + jb, where a and b have the same sign, the corresponding controller is constructed using the following algorithm:
concluding that 4: if a and b are positive numbers, the controller is implemented as:
wherein: a cd-b ω, c + bd/ω 1, a > 0, d > 0; when the values of a and b are determined by S (j omega) ═ a + jb, c and d are selected from A ═ cd-b omega, and c + bd/omega is determined by 1;
concluding that 5: if a and b are negative numbers, the controller is implemented as:
wherein:
a > 0, c > 0, d > 0. And σ is a small positive number that moves the extreme value of the controller to the left half-plane. Studies have shown that the smaller σ the better, and that K(s) approximates the optimal controller K (j ω) at the harmonic frequency ω, the degradation of the stability margin can lead to a slow transient response. Therefore, a compromise needs to be made for any particular design. The controller is designed according to the above assertion 5, which results in the three cases for the above embodiment that a and b are negative numbers.
And 4, step 4: simulating to confirm that the optimal design meets the performance requirements;
if the design requirements are met, implementing the design; otherwise, returning to the steps 2 and 3, reselecting the optimized parameter values, confirming the optimal performance of the propeller and the shafting system and the compromise condition of the performance of the propeller and the shafting system, and if the performance does not meet the requirements, indicating that the performance index requirement is too high, reducing the index requirement or redesigning the system structure parameters. For the above embodiment, if the design criteria were that both the vibration at the propeller blades and the vibration at the propeller drive shaft were less than 3dB, then it was seen from the above analysis that selecting point B as the optimal point would cause the optimal controller to reduce both y (j ω) and z (j ω) by approximately 3 dB. Now, the controller is implemented according to step 3, and the performance is obtained as shown in (a) and (b) of fig. 3, the vertical axis represents Acceleration, and it can be seen that the performance achieved by the controller conforms to the theoretical predicted value, and the optimal design can be confirmed.
In short, the vibration reduction design of the propeller and the transmission shaft system can only implement control at the transmission shaft, so that the propeller and the transmission shaft simultaneously reduce vibration, and the designed propeller/transmission shaft has optimal performance. The design method is universal and is suitable for vibration control of aviation and marine propeller and transmission shaft systems.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.
Claims (4)
1. A design method for active vibration control of a propeller and drive shaft system is characterized by comprising the following steps:
step 1, establishing a model of a propeller and transmission shaft system;
step 2, according to the parameters of the model established in the step 1, defining the following variables:
S(jω)＝(1-G00(jω)K(jω))-1
wi(jω)＝Cid(jω)
wherein, TydRepresenting the performance response of the propeller shaft y to external vibrations d,
indicating propeller blades ziPerformance response to external vibration d, S (j ω) represents the system sensitivity function, K (j ω) represents the controller to be designed, wi(j ω) represents the i-th vibration signal to be attenuated at the propeller blades, CiIs a complex number representing amplitude and phase shift relative to the external vibration signal, d (j ω) represents the external vibration, Ri(j ω) represents an auxiliary agentSensitivity function, G00(jω)、Gi0(jω)、G0k(jω)、Gik(j ω) each represents a transfer function, i ═ 1, …, n, n represents the number of performance variables requiring damping;
and draw | Tyd| is less than or equal to 1 and
the geometric representations of (a) are denoted as S-circle and iR-circle, respectively;
step 3, judging whether common intersection exists between all iR-circles and S-circles or not, and if yes, judging that an optimal controller exists so that y (j omega) and z (z omega) can be obtainedi(j ω) simultaneous damping, y (j ω) representing a transmission shaft performance variable, zi(j ω) represents the propeller blade performance variable and proceeds to step 4, otherwise the design method ends;
step 4, reducing the S-circle and the 1R-circle according to the same proportion until the reduced S-circle is tangent to the reduced 1R-circle, wherein the tangent point meets the requirements of y (j omega) and z1(j ω) optimum Performance Point for Simultaneous damping, denoted A1(ii) a The above operation is repeated for each iR-circle with S-circle, i 2, …, n, and the tangent points found are sequentially denoted as a2,…,AnFrom A1,…,AnFind a point satisfying y (j ω) and all zi(j ω) optimal performance point for simultaneous damping;
step 5, selecting the product satisfying y (j omega) and all z according to the step 4iThe optimal performance point for damping vibration simultaneously is constructed as y (j omega) and all zi(j ω) an optimal controller K (j ω) providing optimal damping performance, with the formula:
wherein S (j ω) represents that y (j ω) and all z are satisfiedi(j ω) optimum Performance Point for Simultaneous damping, G00(j ω) represents a transfer function;
step 6, converting the controller K (j omega) under the frequency domain into the controller K(s) under the complex domain by using an active vibration control algorithm;
and 7, simulating according to the controller K(s) obtained in the step 6, verifying whether the optimal performance requirements of the propeller and the transmission shaft system are met, and returning to the step 2 for redesigning if the optimal performance requirements of the propeller and the transmission shaft system are not met.
2. The method of designing active vibration control for a propeller and drive shaft system of claim 1 wherein the model for the propeller and drive shaft system of step 1 is:
wherein the content of the first and second substances,
g denotes a transfer function matrix, G00(jω)、G0i(jω)、Gi0(jω)、Gii(j ω) each represents a transfer function, j ω represents a frequency domain, u (j ω) represents a control input at the drive shaft, w (j ω) represents a control input at the drive shafti(j ω) represents the i-th vibration signal to be damped at the propeller blades, y (j ω) represents the transmission shaft performance variable, zi(j ω) represents the propeller blade performance variable, i ═ 1, …, and n represents the number of performance variables that require damping.
3. The method of claim 1 wherein step 4 is a design method for active vibration control of a propeller and drive shaft system1,…,AnFind a point satisfying y (j ω) and all zi(j ω) the optimum performance point of simultaneous damping, the specific process is:
memory satisfying y (j omega) and zi(j ω) the optimal damping performance corresponding to the optimal performance point for simultaneous damping is TiFrom all points of tangency A1,…,AnIn which a point A is selectedk，k＝1,…,n，AkTo satisfy y (j ω) and zk(j ω) optimum Performance Point for Simultaneous damping, while selecting AkAs satisfying y (j ω) and zi≠k(j ω) optimum point of performance for simultaneous dampingDamping performance less than Ti≠k5% of the total.
4. The design method for active vibration control of a propeller and drive shaft system of claim 1, wherein the specific process of step 6 is as follows:
defining S (j ω) in the optimal controller K (j ω) as a complex number: s (j ω) ═ a + jb, where a and b have the same sign;
when a and b are positive numbers, the controller is as follows:
wherein, A is cd-b omega, c + bd/omega is 1, A is more than 0, d is more than 0; a. b, c, d are real numbers, ω represents the harmonic frequency, G00(s) represents a transfer function, s represents a complex domain;
when a and b are negative numbers, the controller is as follows:
wherein the content of the first and second substances,
a is more than 0, c is more than 0, d is more than 0, and sigma is a positive number.
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| CN111881530A (en) * | 2020-07-27 | 2020-11-03 | 南京航空航天大学 | Vibration reduction optimization design method for aircraft engine |
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