CN109388907B - Design method of shafting with preset longitudinal vibration dynamic flexibility - Google Patents
Design method of shafting with preset longitudinal vibration dynamic flexibility Download PDFInfo
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- CN109388907B CN109388907B CN201811286964.1A CN201811286964A CN109388907B CN 109388907 B CN109388907 B CN 109388907B CN 201811286964 A CN201811286964 A CN 201811286964A CN 109388907 B CN109388907 B CN 109388907B
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Abstract
The invention relates to the field of vibration, in particular to a method for designing a shaft system with preset longitudinal vibration dynamic flexibility, which comprises the following steps: (a) Carrying out dynamic flexibility test on the original shafting to obtain dynamic flexibility data of the original shafting at a joint point with the additional shafting; (b) Designing an additional shafting, and modeling a longitudinal structure model of the additional shafting; (c) Calculating to obtain a dynamic flexibility matrix capable of representing the dynamic characteristics of the additional shafting; (d) Combining the dynamic compliance data and the dynamic compliance matrix to obtain a dynamic compliance equation of the combined shafting; (e) Calculating a dynamic compliance equation of the combined shafting to obtain the dynamic compliance of the combined shafting; (f) And (3) comparing the dynamic flexibility of the combined shafting with the design requirement, if so, finishing the design, and if not, repeating the step (b) and the following steps until the requirement is met. The method directly utilizes the test data of the original shafting, does not need to build a dynamic model of the original shafting structure, and can accurately estimate the longitudinal vibration characteristic after shafting correction.
Description
Technical Field
The invention relates to the technical field of mechanics and vibration, in particular to a design method of a shafting with preset longitudinal vibration dynamic flexibility.
Background
Although finite element methods have been widely used in various fields such as ships, aerospace, automobiles, civil engineering, etc., a large number of numerical models for different problems have been established to predict structural response in the presence of disturbances or excitations to guide optimization of design structure dynamics. However, the theoretical analysis process is greatly simplified, and errors of theoretical assumption, approximation of boundary conditions and damping all cause deviation of a simulation analysis model from an actual structure to a certain extent, so that the actual problem cannot be directly solved based on the simulation analysis model. For a complex structure, although the model accuracy can be improved to a certain extent through model correction, the unavoidable deviation between the numerical model and the actual structure will result in the reduction of the reference value of the numerical model.
In practical engineering application, aiming at a ship shafting structure, on one hand, a larger alternating longitudinal exciting force acts on a propeller working in a stern uneven wake field, on the other hand, along with the upsizing of a ship, the power of a main engine is increased, particularly the long shafting of a multi-cylinder diesel engine is arranged, and as the diesel engine and the harmful longitudinal vibration critical rotating speed of the diesel engine possibly fall into the range of the operating rotating speed, faults are caused by the longitudinal vibration of a rotating shaft, and even shafting parts are damaged. In the design process, a common means is to establish numerical models of the original shafting and the additional shafting through simulation analysis to carry out longitudinal vibration optimization design of the shafting, but the numerical model of the original shafting and the additional shafting is difficult to accurately establish, so that the longitudinal vibration dynamic flexibility of the redesigned shafting cannot be well estimated, and certain difficulty is brought to the optimization design of the shafting.
Therefore, a design method of a shafting with a predetermined longitudinal vibration compliance is needed to solve the above technical problems.
Disclosure of Invention
The invention aims to provide a method for designing a shafting with preset longitudinal vibration dynamic flexibility, which can accurately design the shafting with the longitudinal vibration characteristics meeting the preset requirements without building a dynamic model of an original shafting structure.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for designing a shafting with preset longitudinal vibration dynamic compliance comprises the following steps:
(a) Carrying out dynamic flexibility test on the original shafting to obtain dynamic flexibility data of the original shafting at a joint point with the additional shafting;
(b) Designing the additional shafting, and modeling a longitudinal structure model of the additional shafting;
(c) Calculating to obtain a dynamic compliance matrix capable of representing the dynamic characteristics of the additional shafting;
(d) Combining the dynamic compliance data with the dynamic compliance matrix to obtain a dynamic compliance equation of the combined shafting;
(e) Calculating a dynamic compliance equation of the combined shafting to obtain the dynamic compliance of the combined shafting;
(f) And (c) comparing the dynamic flexibility of the combined shafting, if the dynamic flexibility is met, finishing the design, and if the dynamic flexibility is not met, repeating the steps (b) and the steps below (b) until the requirements are met.
Preferably, the step (b) requires designing the additional shafting according to the space position and weight limitation conditions.
Preferably, said combining point in said step (a) is located at a position where said original axis system can be connected to said additional axis system.
Preferably, the positions where the original axis system can be connected with the additional axis system are end positions on two sides of the original axis system or other middle positions.
Preferably, before performing the step (a), collecting and sorting excitation characteristics of the original shafting.
Preferably, in the step (b), the dynamic compliance equation for modeling the longitudinal structure model of the additional shafting is,
wherein x is D (ω) represents the displacement of the binding site D, x 2 (ω) is the displacement of any point on said additional axis,
for the original dynamic compliance of the additional axis at the coupling point D,
the cross point motion flexibility of the combination point D of the additional axis system relative to any point on the additional axis system,
the cross-point motion flexibility of any point on the additional shaft system relative to the combination point D is ensured,
the original point dynamic flexibility f of any point on the additional shafting is taken as the additional shafting 2 (ω) is the dynamic force loading on the additional shafting,
is the internal force of the influence of the original shafting on the additional shafting.
Preferably, the dynamic compliance equation of the combined shafting in the step (d) is
Wherein
And the original axial system structure is the original point dynamic flexibility of the combination point D.
Preferably, the dynamic compliance equation of the combined shafting in the step (e) is
Wherein
The dynamic flexibility of any point of the additional shafting on the combined shafting.
The invention has the beneficial effects that:
the invention avoids the errors caused by the correction of the longitudinal vibration model of the original shafting and the inaccurate constraint of the corresponding model simplification, boundary conditions and the like, directly utilizes the dynamic compliance test data of the original shafting at the joint point with the additional shafting, does not need to build a dynamic model of the original shafting structure, only relates to the accuracy of the estimated result of the dynamic compliance test result of the original shafting and the accuracy of the dynamic model of the additional shafting, and can accurately and quickly correct the original shafting into the combined shafting which meets the preset requirement and has the longitudinal vibration characteristic after calculation and correction.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic structural diagram of the combined shafting system of the present invention;
FIG. 3 is a schematic diagram of a discrete numerical model of a combined shafting in an embodiment of the present invention;
FIG. 4 is a comparison graph of dynamic compliance amplitude of a discrete numerical model based on a combined axis system using the calculation results of the present invention and the calculation results of the numerical model;
FIG. 5 is a comparison graph of dynamic compliance phase of a discrete numerical model based on a combined axis system, using the calculation result of the present invention and the calculation result of the numerical model.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings and the embodiment. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some but not all of the features relevant to the present invention are shown in the drawings.
As shown in fig. 1, the present invention provides a method for designing a shaft system with a preset longitudinal vibration dynamic compliance, comprising the following steps:
(a) Carrying out dynamic flexibility test on the original shafting to obtain dynamic flexibility data of the original shafting at a joint point with the additional shafting;
(b) Designing an additional shafting, and modeling a longitudinal structure model of the additional shafting;
(c) Calculating to obtain a dynamic flexibility matrix capable of representing the dynamic characteristics of the additional shafting;
(d) Combining the dynamic compliance data with the dynamic compliance matrix to obtain a dynamic compliance equation of the combined shafting;
(e) Calculating a dynamic compliance equation of the combined shafting to obtain the dynamic compliance of the combined shafting;
(f) And (c) comparing the dynamic flexibility of the combined shafting with the design requirement, if so, finishing the design, and if not, repeating the steps (b) and (b) until the requirement is met. According to the dynamic flexibility estimation method, dynamic flexibility data of the original shafting and the additional shafting are directly utilized, a dynamic model of the original shafting structure is not required to be built, the accuracy of the estimation result is only related to the accuracy of the dynamic model of the additional shafting, the dynamic flexibility of the combined shafting can be accurately estimated after calculation and correction, great convenience is brought to subsequent optimization design, and meanwhile, the shafting modification cost can be effectively reduced.
Specifically, before the step (a), collecting and sorting excitation characteristics of an original shafting, so as to determine boundary conditions of the design of the longitudinal vibration dynamic compliance of the combined shafting, wherein the excitation characteristics mainly include frequencies to be avoided by longitudinal vibration of the shafting, vibration response amplitudes under action of different frequency action forces, and the like. Then, the dynamic compliance test is performed on the original axis system to obtain dynamic compliance data of the original axis system at the joint point with the additional axis system, as shown in fig. 2, where the position of the joint point, that is, the position where the original axis system can be connected to the additional axis system, may be the end point positions on both sides of the original axis system or other middle positions, and no limitation is made herein.
Specifically, based on the limited conditions including spatial position, arrangement, weight and the like on site, the spatial position and the basic geometric dimension of the additional shafting structure are preliminarily determined, and the additional shafting is designed. Then, a model of the longitudinal structure of the additional shafting is modeled. The influence of the original shafting on the additional shafting is described as the form of the internal force, which is assumed here to be
The structure is expressed by adopting a dynamic flexibility matrix, and only a single dynamic force f is loaded on an additional shafting structure 2 Then the dynamic compliance equation can be written as follows:
wherein x is D (ω) represents the displacement of the binding site D, x 2 (ω) is the displacement of any point on said additional axis,
for the original dynamic flexibility of the additional axis system at the combining point D,
for the cross-point motion flexibility of the additional shafting at the combination point D relative to any point on the additional shafting,
the cross point motion flexibility of any point of the additional shaft system relative to the combination point D is realized,
the dynamic flexibility of any point of the additional shafting on the combined shafting.
And (3) calculating to obtain a dynamic compliance matrix of the additional shafting through a dynamic compliance equation (1).
Specifically, the original structure shafting is subjected to stress analysis independently, and then the motion equation of the original shafting structure at the combination point D can be written into the following form:
in the case of the equation (2),
for the original point of dynamic compliance of the original shafting structure at the junction point D, it should be noted that the negative sign is caused by the equal magnitude but opposite direction of the internal forces at the junction point.
Namely, the method can be directly obtained by carrying out modal measurement on the original shaft system, namely, the method is
And (2) calculating to obtain a dynamic compliance matrix of the additional shafting through a dynamic compliance equation (1), and further calculating the dynamic compliance of the combined shafting structure by combining the dynamic compliance matrix of the original shafting structure obtained by measurement as follows: in equation (1), let the internal force
A simple harmonic force of one unit magnitude, and substituting equation (2) into equation (1), equation (1) can be written as follows:
the equation (3) is simplified, and the original point dynamic compliance, namely the original point dynamic compliance at any point of the additional shafting on the modified combined shafting structure can be further obtained
Can be calculated as shown in equation (4):
and finally, performing step (f), if so, finishing the design, and if not, repeating the steps (b) and (b) below until the requirements are met.
The method is verified by building a discrete numerical model of the combined shafting as shown in fig. 3, and it should be noted that the present invention is not limited to an additional shafting structure which can be simplified into a discrete model. As shown in fig. 3, the original axis system is simplified into a 7-mass model, and the masses corresponding to serial numbers 1 to 7 are 395, 50, 45, 33, 35, 52 and 72, respectively, and the unit is kg; the corresponding stiffness of 7 springs with serial numbers 1 to 7 is 8000, 10000, 50000, 70000, 32000, 3200, 1300 respectively, and the unit is MN/m. The additional shafting is simplified into a 3-mass model, the corresponding masses are respectively 36, 72 and 81, and the unit is kg; the stiffness was 1300, 1300 respectively, in MN/m. By utilizing the method provided by the invention, the dynamic compliance of the combined shafting at the joint position after the additional shafting is added is calculated, and the result is shown in fig. 4 and 5, and compared with the numerical model calculation result of the combined shafting structure, the amplitude and the phase are completely consistent on the basis of the calculation result of the invention: the feasibility of the method is proved.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (5)
1. A method for designing a shafting with preset longitudinal vibration dynamic compliance is characterized by comprising the following steps:
(a) Carrying out dynamic flexibility test on the original shafting to obtain dynamic flexibility data of the original shafting at a joint point with the additional shafting;
(b) Designing the additional shafting, modeling a longitudinal structure model of the additional shafting, and setting a dynamic compliance equation for modeling the longitudinal structure model of the additional shafting as
Wherein x is D (ω) represents the displacement of the binding site D, x 2 (ω) is the displacement of any point on said additional axis,
for the original dynamic compliance of the additional axis at the coupling point D,
the cross-point motion flexibility of the additional axis system relative to the any point on the additional axis system at the combination point D,
the cross point motion flexibility of any point on the additional axis system relative to the combination point D is determined,
the original point dynamic flexibility f of any point on the additional shafting is taken as the additional shafting 2 (ω) is the dynamic force loading on the additional shafting,
an internal force being the influence of the original shafting on the additional shafting;
(c) Calculating to obtain a dynamic flexibility matrix capable of representing the dynamic characteristics of the additional shafting;
(d) Combining the dynamic compliance data and the dynamic compliance matrix to obtain a dynamic compliance equation of the combined shafting, wherein the dynamic compliance equation of the combined shafting is
Wherein
The original point dynamic flexibility of the original shafting structure at the combination point D is obtained;
(e) Calculating a dynamic compliance equation of the combined shaft system to obtain the dynamic compliance of the combined shaft system, wherein the dynamic compliance equation of the combined shaft system is
Wherein
The dynamic flexibility of any point of the additional shafting on the combined shafting;
(f) And (c) comparing the dynamic flexibility of the combined shafting with the preset longitudinal vibration dynamic flexibility of the design requirement, if the design requirement is met, finishing the design, and if the design requirement is not met, repeating the steps (b) and (b) until the design requirement is met.
2. The method as claimed in claim 1, wherein step (b) requires designing the additional shafting according to space and weight constraints.
3. The method as claimed in claim 1, wherein the joint in step (a) is located at a position where the original shafting can be connected to the additional shafting.
4. The method as claimed in claim 3, wherein the positions where the original shafting can be connected to the additional shafting are end positions on two sides of the original shafting or other middle positions.
5. The method of claim 1, wherein before step (a), the excitation characteristics of the original shafting are collected and sorted.
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| CN110298140B (en) * | 2019-07-16 | 2022-11-11 | 中船动力研究院有限公司 | Method, device, equipment and storage medium for estimating dynamic characteristics |
| CN112395709B (en) * | 2020-11-30 | 2024-03-29 | 中船动力研究院有限公司 | Modification method, device, equipment and medium for indirect shafting torsional vibration dynamic characteristics |
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| CN105808847A (en) * | 2016-03-08 | 2016-07-27 | 哈尔滨工程大学 | Camshaft-containing shafting complex vibration and regulation coupling modeling analysis system for diesel engine and analysis method thereof |
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- 2018-10-31 CN CN201811286964.1A patent/CN109388907B/en active Active
Patent Citations (6)
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| JP2010286377A (en) * | 2009-06-12 | 2010-12-24 | Toyota Motor Corp | Model generation method |
| CN102353506A (en) * | 2011-06-16 | 2012-02-15 | 中国海洋大学 | Method for analyzing vertical vibration of deepwater top-tensioned type vertical pipe |
| CN102540398A (en) * | 2012-02-23 | 2012-07-04 | 西安电子科技大学 | Full-compliant two-spindle rotating and reflecting mirror with low cross coupling |
| CN103592125A (en) * | 2013-10-08 | 2014-02-19 | 东北大学 | Method for measuring radial dynamic flexibility of rolling bearing |
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