CN115470548A - Linear design optimization method for vacuum tube magnetic suspension traffic line - Google Patents
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Abstract
The invention relates to a linear design optimization method for a vacuum tube magnetic levitation traffic line. The existing design system can not meet the design requirements of the magnetic suspension traffic line of the ultra-high-speed vacuum tube. The method establishes a vehicle motion stress analysis model to obtain a calculation formula of the guiding force and the suspension force in any line shape; calculating the guiding force and the suspension force of different linear shapes according to the vehicle parameters and the linear characteristic parameters of different linear shapes; selecting linear combinations with relatively gentle changes, and optimizing linear characteristic parameters of different linear shapes; establishing a dynamic interaction model of the vehicle and the guide rail beam, and calculating dynamic response indexes of all linear combinations; and comparing the dynamic response indexes and the statistical distribution characteristics of all linear combinations to obtain the optimal linear combination. The method can accurately consider the change rule of comfort and safety under the condition of ultrahigh-speed operation, realizes the parameter determination and design scheme optimization of the vacuum tube magnetic suspension traffic line, and provides guarantee for the engineering application of ultrahigh-speed vacuum tube magnetic suspension traffic.
Description
Technical Field
The invention relates to the technical field of railway engineering, in particular to a linear design optimization method for a vacuum tube magnetic suspension traffic line.
Background
The vacuum tube superspeed magnetic levitation traffic system reduces air resistance by utilizing a vacuum environment and a supersonic speed appearance, reduces friction resistance through magnetic levitation, and can theoretically realize supersonic speed running. The ultra-high speed vacuum magnetic suspension traffic system has the characteristics of ultra-high speed, high safety, low energy consumption, low noise, low pollution and the like, is a hot spot and trend of current domestic and foreign research, and has wide development prospect in the future. At present, from the technical scheme of vacuum pipeline transportation at home and abroad, a Swiss SMETRO scheme adopting electromagnetic suspension, an American Hyperloop system adopting permanent magnetic suspension and a southwest transportation university scheme adopting a high-temperature superconducting magnetic suspension technology are mainly adopted. It is worth pointing out that the current research on pipeline engineering technology mainly focuses on the aspect of load bearing structure, and the system analysis for the aspect of line arrangement and line optimization is still lacked.
At present, a design system of a high-speed normally-conductive magnetic suspension traffic line with the speed of 600 kilometers per hour or less is established, corresponding magnetic suspension traffic design specifications and technical specifications are formulated, a line design method and parameter values are determined according to the comfort and the normally-conductive suspension guide characteristics, and a design scheme is optimized by comprehensively considering the comfort and the safety. For vacuum tube magnetic suspension traffic with the running speed of up to 1000km/h, the requirements on the aspects of running safety, running comfort and the like are obviously different, the existing line design method and parameter value cannot meet the requirements of an ultrahigh-speed vacuum tube magnetic suspension traffic system, and the aspect is blank.
Disclosure of Invention
The invention aims to provide a linear design optimization method for a vacuum tube magnetic levitation traffic route, which aims to solve the problem that the prior art cannot meet the design requirements of an ultrahigh-speed vacuum tube magnetic levitation traffic route.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the linear design optimization method of the vacuum tube magnetic suspension traffic line comprises a straight line, a circular curve and a relaxation curve, and a plurality of linear combinations are drawn up as a design scheme, wherein the linear combinations comprise different continuous linear shapes;
the method comprises the following steps:
establishing a vehicle motion stress analysis model to obtain a calculation formula of any linear guide force and suspension force;
calculating the guiding force and the suspension force of different linear shapes according to the vehicle parameters and the linear characteristic parameters of different linear shapes;
selecting linear combinations with relatively gentle changes according to the calculation results of the guiding force and the suspending force, and optimizing linear characteristic parameters of different linear shapes;
establishing a dynamic interaction model of the vehicle and the guide rail beam, and calculating dynamic response indexes of all linear combinations;
and comparing the dynamic response indexes and the statistical distribution characteristics of all linear combinations to obtain the optimal linear combination.
Further, a vehicle motion stress analysis model is established, and a calculation formula of the guiding force and the suspension force in any linear shape is obtained, wherein the calculation formula comprises the following steps:
the vehicle is simplified into a rigid body rotating around a longitudinal axis in the advancing direction, a vehicle motion stress analysis model can be obtained according to the centroid motion theorem and the momentum moment theorem on the centroid, and a guiding force and suspension force calculation formula is derived according to the vehicle motion stress analysis model.
Further, the guiding force calculation formula is:
the suspension force calculation formula is as follows:
in the formula:
F D the lateral guiding force of the wheel set along the top surface of the rail is provided;
m is the mass of the whole vehicle;
d is the distance from the mass center to the top surface of the rail;
h is an actual ultrahigh value;
R S is the radius of the vertical curve;
k S is the curvature of a vertical curve;
g is gravity acceleration;
s is a track gauge;
k p is a plane curve curvature;
v is the vehicle speed;
F C1 、F C2 the inner and outer wheels are subjected to suspension force vertical to the top surface of the rail;
ρ 0 is the inertia radius of the whole vehicle to the mass center。
Further, according to the calculation results of the guiding force and the suspending force, selecting a linear combination with a relatively gentle change, and optimizing linear characteristic parameters of different linear shapes, wherein the linear characteristic parameters comprise:
selecting linear combinations with more gradual changes;
and reversely calculating by using fixed thresholds of the guiding force and the suspending force to obtain values of the radius of the circular curve and the length of the easement curve, thereby realizing optimization of linear characteristic parameters.
Further, the vehicle and guide rail beam dynamic interaction model comprises a vehicle dynamic model and a guide rail beam dynamic model;
the method comprises the following steps that a vehicle body, a bogie and a magnet device are all considered to be rigid bodies, a suspension system is similar to a spring damping element, sinking and floating, nodding, traversing, shaking and rolling motions are considered to be carried out on each rigid body, a vehicle motion equation is established based on a multi-rigid-body dynamics theory, and an additional force action generated by line shapes and track irregularity is considered to obtain a vehicle dynamics model;
establishing a beam vibration equation by adopting a modal method or a finite element method on the basis of considering the influence of structural vibration participation to obtain a guide rail beam dynamic model;
and establishing mathematical relations between the suspension gap and the suspension force and between the guide gap and the guide force based on tests and magnetic field analysis, connecting the vehicle dynamic model with the guide rail beam dynamic model, and solving a motion equation of the vehicle and guide rail dynamic interaction system by adopting cross iterative numerical integration so as to obtain the vehicle and guide rail beam dynamic interaction model.
Further, calculating the dynamic response index of each linear combination comprises:
and calculating dynamic response indexes of each linear combination by using a vehicle and guide rail beam dynamic interaction model, wherein the dynamic response indexes comprise vehicle body vibration acceleration, suspension force, guide force, suspension gap, guide rail beam deformation and guide rail beam vibration acceleration.
Further, comparing the dynamic response index and the statistical distribution characteristic of each linear combination to obtain an optimal linear combination, wherein the method comprises the following steps:
the dynamic response index time history results of each linear combination are statistically analyzed to obtain statistical distribution characteristics of each index in different sections in the combination, wherein the statistical distribution characteristics comprise the maximum value, the average value, the standard deviation, the 99% probability value and the 95% probability value;
and comparing the dynamic response indexes and the statistical distribution characteristics of all linear combinations, and taking the linear combination with the minimum statistical distribution characteristic value and the best dynamic performance as the optimal linear combination.
Compared with the prior art, the invention has the following beneficial effects:
the design scheme of the ultrahigh-speed vacuum tube magnetic suspension traffic line determined by the method can accurately consider the change rule of comfort and safety under the ultrahigh-speed running condition, realize the parameter determination and the design scheme optimization of the vacuum tube magnetic suspension traffic line, and provide guarantee for the engineering application of the ultrahigh-speed vacuum tube magnetic suspension traffic.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings of the embodiments can be obtained according to the drawings without creative efforts.
FIG. 1 is a graph of vehicle stress analysis in a curved section.
FIG. 2 is a side view of a model of the dynamic interaction of a vehicle with a guideway beam.
FIG. 3 is a cross-sectional view of a model of the dynamic interaction of a vehicle with a guideway beam.
FIG. 4 is a flow chart of the method of the present invention.
FIG. 5 is a plan view of a circuit section in example 2.
FIG. 6 is a vertical sectional view showing the layout of the structure of example 2.
FIG. 7 is a time course graph of example 2, scheme 1.
Fig. 8 is a time course graph of example 2, scheme 2.
Fig. 9 is a time course graph of embodiment 2, scheme 3.
FIG. 10 is a graph comparing the statistical data for the three protocols.
Detailed Description
To facilitate an understanding of the invention, the invention will now be described more fully with reference to the accompanying drawings. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
It should be noted that like reference numerals and letters refer to like items and, thus, once an item is defined in one embodiment, it need not be further defined and explained in subsequent embodiments. Also, the terms "comprises," "comprising," or the like, as well as any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The vacuum pipeline line engineering must possess very high security, leakproofness, reliability, and the linear setting of circuit is closely related with vacuum pipeline magnetic levitation traffic system's bearing structure form, and generally, the linear shape of circuit has following characteristics: (1) The vacuum tube ultra-high speed maglev line structure needs to meet the running requirement of a 1000km/h speed level train, the line bearing structure needs to reach high precision in the manufacturing, installation and maintenance processes, and the smoothness and structural deformation of the line must be strictly controlled. (2) The train directly acts on the line bearing beam through the levitation force and the guiding force, the linear change can be more clearly reflected on the bearing structure, and the acceleration and the impact caused by the linear change are more and more obvious. (3) High precision manufacturing and positioning techniques enable the implementation and operational maintenance of complex line shapes on load bearing structures.
The key parameters of the linear design of the vacuum tube magnetic suspension traffic line comprise a transition curve type, a minimum curve radius, a minimum length of the transition curve and the like. For vacuum tube magnetic suspension traffic with the running speed of 1000km/h, the requirements on the aspects of running safety, running comfort and the like are obviously improved, the existing wheel rail railway line design method and parameter values cannot meet the requirements of an ultrahigh-speed vacuum tube magnetic suspension traffic system, and the aspect is blank.
Example 1:
the embodiment provides a linear design optimization method for a vacuum tube magnetic levitation transportation line, wherein the linear shape comprises a straight line, a circular curve and a gentle curve, a plurality of linear combinations are drawn up as a design scheme, and the linear combinations comprise continuous different linear shapes. When designing a line, the aim of setting a longer straight line segment is to shorten the length of the line and improve the running condition on the premise of straightening the line. However, in order to adapt to the terrain and avoid the ground objects to reduce the number of projects and the project investment, a circular curve and a gentle curve with a certain length must be arranged. The straight line has the characteristics of good visibility condition, simple driving stress, definite direction, convenience in measurement and setting and the like, and the characteristic parameters of the straight line comprise the minimum length of the included straight line and the like. The circular curve has the characteristics of easy adaptation to terrain, beautiful line shape, easy measurement and setting and the like, and the characteristic parameters of the circular curve comprise minimum curve radius, curve length and the like. The gentle curve has the characteristics of continuous curvature change, gradual centrifugal acceleration change, ultrahigh height, gradual widening change and the like, and the characteristic parameters of the gentle curve comprise the minimum length of the gentle curve, the type of the gentle curve and the like.
The method specifically comprises the following steps:
s1: and establishing a vehicle motion stress analysis model to obtain a calculation formula of the guide force and the suspension force in any line shape.
After the vehicle enters the relaxation curve, the vehicle presents various motion postures of side rolling, nodding, shaking and the like. The research shows that the total angular displacement of the nodding head of the vehicle in the section of the gentle curve is smaller in magnitude compared with the total angular displacement of the rolling head and the rolling side, and the wheel-track force related to the shaking head motion of the vehicle is smaller than the wheel-track force causing the rolling side motion by 3 magnitudes, so that the nodding head and shaking head motion of the vehicle can be ignored, and the vehicle is simplified into a rigid body rotating around a longitudinal axis in the advancing direction. The force analysis of any ultra-high speed vehicle is shown in fig. 1, and the side close to the curvature center is defined as the inner side.
The vehicle is simplified into a rigid body rotating around a longitudinal axis in the advancing direction, a vehicle motion stress analysis model can be obtained according to the centroid motion theorem and the momentum moment theorem on the centroid, and a guiding force and suspension force calculation formula is derived according to the vehicle motion stress analysis model.
The vehicle motion stress analysis model is as follows:
mgsinα+F D ＝m(k p v 2 cosα+Lα”cosθ+L(α') 2 sinθ)
mgcosα-F C1 -F C2 ＝m(-k p v 2 sinα-Lα”sinθ+L(α') 2 cosθ)
in the formula:
sinα≈α＝HR s k s /S
cosα≈1
sinθ＝S/(2L)
cosθ＝D/L
α'＝HR s k′ s /S
α”＝HR s k″ s /S
the vehicle parameters and the linear characteristic parameters in the formula comprise:
m is the mass of the whole vehicle;
g is the acceleration of gravity;
alpha is a transverse slope angle;
F D the lateral guiding force of the wheel set along the top surface of the rail is provided;
k p is a plane curve curvature;
v is the vehicle speed;
l is the distance from the centroid O of the vehicle to the connecting line of the contact points of the inner side wheel rails;
theta is an included angle between a connecting line from the center of mass of the vehicle to the contact point of the inner side wheel rail and the y axis;
F C1 、F C2 the inner and outer wheels are subjected to suspension force vertical to the top surface of the rail;
s is a track gauge;
d is the distance from the center of mass to the top surface of the rail;
ρ 0 the inertia radius of the mass center of the whole vehicle pair is obtained;
h is an actual ultrahigh value;
R S is the radius of the vertical curve;
k S is the vertical curve curvature.
And (3) deforming and deducing the model to obtain:
the guiding force calculation formula is as follows:
suspension force calculation formula:
s2: and calculating the guiding force and the suspension force of different linear shapes according to the vehicle parameters and the linear characteristic parameters of different linear shapes.
And (4) if the vehicle parameters and the linear characteristic parameters of different linear shapes are known, substituting the known vehicle parameters and the linear characteristic parameters into the related formula in the step S1, and calculating the guiding force and the suspending force.
S3: and selecting linear combinations with relatively gentle changes according to the calculation results of the guiding force and the suspending force, and optimizing linear characteristic parameters of different linear shapes.
According to the change rule of force along with mileage, a linear combination with gentle change is selected, the curve curvature change is continuous, and no obvious mutation exists.
And reversely calculating by using fixed thresholds of the guiding force and the suspending force to obtain values of the radius of the circular curve and the length of the easement curve, thereby realizing optimization of linear characteristic parameters.
S4: and establishing a dynamic interaction model of the vehicle and the guide rail beam, and calculating the dynamic response index of each linear combination.
S401: and establishing a dynamic interaction model of the vehicle and the guide rail beam, wherein the dynamic interaction model of the vehicle and the guide rail beam comprises a vehicle dynamic model and a guide rail beam dynamic model.
As shown in fig. 2 and 3, the vehicle body, the bogie and the magnet device are all considered as rigid bodies, the suspension system is approximate to a spring damping element, each rigid body considers the motions of sinking and floating, nodding, traversing, shaking and rolling, a vehicle motion equation is established based on a multi-rigid body dynamics theory, and the action of additional force generated by linear shape and rail irregularity is considered, so that a vehicle dynamics model is obtained. And establishing a beam vibration equation by adopting a modal method or a finite element method on the basis of considering the influence of the structure vibration, so as to obtain a guide rail beam dynamic model. And establishing mathematical relations between the suspension clearance and the suspension force and between the guide clearance and the guide force based on tests and magnetic field analysis, linking the vehicle model with the guide rail beam model, and solving a motion equation of the vehicle and guide rail dynamic interaction system by adopting cross iterative numerical integration so as to obtain a vehicle and guide rail beam dynamic interaction model.
S402: calculating the dynamic response index of each linear combination, including:
and calculating dynamic response indexes of each linear combination by using a vehicle and guide rail beam dynamic interaction model, wherein the dynamic response indexes comprise vehicle body vibration acceleration, suspension force, guide force, suspension gap, guide rail beam deformation and guide rail beam vibration acceleration.
S5: and comparing the dynamic response indexes and the statistical distribution characteristics of all linear combinations to obtain the optimal linear combination.
Statistically analyzing the time course results of the dynamic response indexes of each linear combination to obtain statistical distribution characteristics of each index in different sections in the combination, wherein the statistical distribution characteristics comprise a maximum value, an average value, a standard deviation, a 99% probability value and a 95% probability value;
and comparing the dynamic response indexes and the statistical distribution characteristics of all linear combinations, and taking the linear combination with the minimum statistical distribution characteristic value and the best dynamic performance as the optimal linear combination.
After obtaining the dynamic response indexes and the statistical distribution characteristics of each linear combination, aiming at improving the comfort and reducing the dynamic response frequency distribution with larger amplitude, a section with poorer dynamic performance in the linear combination can be selected, sensitive linear parameters influencing the dynamic response are determined, the sensitive linear parameters are adjusted to form a new linear combination, then the dynamic response indexes and the statistical distribution characteristics of each linear combination are compared again, and the dynamic response indexes and the statistical distribution characteristics of each linear combination are repeatedly adjusted and compared in this way, so that a satisfactory optimization scheme is obtained.
The steps of the present embodiment may be performed in a computer system such as a set of computer-executable instructions and, although a logical order is shown in the flow diagrams, in some cases, may be performed in an order different than here.
Example 2:
three different line design schemes exist, the line plan and vertical section design diagrams are shown in fig. 5 and fig. 6, the parameter design of the different schemes is shown in table 1, wherein l 1 Is the first easement curve length, R 1 Is the radius of the first circular curve,/ 0 To clamp the length of the line, /) 2 Is the length of the second easement curve, R 2 Is the radius of the second circular curve,/ 3 Is the length of the straight line, i is the slope, and L is the length of the slope section. According to different design schemes, specific parameter values such as linear length, relaxation curve length, circular curve length, radius, gradient and slope section length are input into a built vehicle and guide rail beam dynamic interaction model, six dynamic response indexes including vertical acceleration of a vehicle body, transverse acceleration of the vehicle body, suspension clearance, guide clearance, suspension force and guide force are obtained, dynamic response time course results of the three schemes are counted, time course curves are shown in figures 7-9, and the maximum value, the average value, the standard deviation, the 99% probability value and the 95% probability value of each index in different schemes are compared, and are shown in figure 10. Compared with the schemes 1 and 2, the scheme 3 has the advantages that the statistical distribution characteristic value of the dynamic response indexes is minimum, and the dynamic performance is better. Thus, scheme 3 is more preferred.
| l 1 /m | R 1 /m | l 0 /m | l 2 /m | R 2 /m | l 3 /m | i 1 /‰ | i 2 /‰ | i 3 /‰ | |
| Scheme 1 | 500 | 10000 | 1000 | 500 | 10000 | 1000 | 1 | 2 | 3 |
| |
500 | 10000 | 1000 | 1120 | 23000 | 1000 | 1 | 2 | 3 |
| Scheme 3 | 1120 | 23000 | 1000 | 1120 | 23000 | 1000 | 1 | 2 | 3 |
The length of the circular curve is equal to that of the gentle curve, and the slope changing points of the longitudinal section are all at the middle point of the circular curve.
The invention provides a vacuum tube magnetic suspension traffic line design method based on dynamic analysis on the basis of more objectively considering riding comfort and safety under different line conditions, and has important theoretical significance and engineering practical value.
The present invention has been described in terms of specific examples, which are provided to aid understanding of the invention and are not intended to be limiting. For a person skilled in the art to which the invention pertains, several simple deductions, modifications or substitutions may be made according to the idea of the invention.
Claims (7)
1. The linear design optimization method of the vacuum tube magnetic suspension traffic line is characterized by comprising the following steps:
the linear shapes comprise straight lines, circular curves and relaxation curves, and a plurality of linear shape combinations are drawn up as a design scheme, wherein the linear shape combinations comprise continuous different linear shapes;
the method comprises the following steps:
establishing a vehicle motion stress analysis model to obtain a calculation formula of any linear guide force and suspension force;
calculating the guiding force and the suspension force of different linear shapes according to the vehicle parameters and the linear characteristic parameters of different linear shapes;
selecting linear combinations with relatively gentle changes according to the calculation results of the guiding force and the suspending force, and optimizing linear characteristic parameters of different linear shapes;
establishing a dynamic interaction model of the vehicle and the guide rail beam, and calculating dynamic response indexes of all linear combinations;
and comparing the dynamic response indexes and the statistical distribution characteristics of all linear combinations to obtain the optimal linear combination.
2. The method of claim 1, wherein:
establishing a vehicle motion stress analysis model to obtain a calculation formula of the guiding force and the suspending force in any line shape, wherein the calculation formula comprises the following steps:
the vehicle is simplified into a rigid body rotating around a longitudinal axis in the advancing direction, a vehicle motion stress analysis model can be obtained according to the centroid motion theorem and the momentum moment theorem on the centroid, and a guiding force and suspension force calculation formula is derived according to the vehicle motion stress analysis model.
3. The method of claim 2, wherein:
the guiding force calculation formula is as follows:
the suspension force calculation formula is as follows:
in the formula:
F D the lateral guiding force of the wheel set along the top surface of the rail is provided;
m is the mass of the whole vehicle;
d is the distance from the mass center to the top surface of the rail;
h is an actual ultrahigh value;
R S is the radius of the vertical curve;
k S is a vertical curve curvature;
g is the acceleration of gravity;
s is a track gauge;
k p is a plane curve curvature;
v is the vehicle speed;
F C1 、F C2 the inner and outer wheels are subjected to suspension force vertical to the top surface of the rail;
ρ 0 the inertia radius of the whole vehicle to the mass center.
4. The method of claim 3, wherein:
according to the calculation results of the guiding force and the suspending force, selecting linear combination with more gentle change, and optimizing linear characteristic parameters of different linear shapes, wherein the method comprises the following steps:
selecting linear combinations with more gradual changes;
and reversely calculating by using fixed thresholds of the guiding force and the suspending force to obtain values of the radius of the circular curve and the length of the easement curve, thereby realizing optimization of linear characteristic parameters.
5. The method of claim 4, wherein:
the vehicle and guide rail beam dynamic interaction model comprises a vehicle dynamic model and a guide rail beam dynamic model;
the method comprises the following steps that a vehicle body, a bogie and a magnet device are all considered to be rigid bodies, a suspension system is similar to a spring damping element, sinking and floating, nodding, traversing, shaking and rolling motions are considered to be carried out on each rigid body, a vehicle motion equation is established based on a multi-rigid-body dynamics theory, and an additional force action generated by line shapes and track irregularity is considered to obtain a vehicle dynamics model;
establishing a beam vibration equation by adopting a modal method or a finite element method on the basis of considering the influence of structural vibration, and obtaining a guide rail beam dynamic model;
and establishing mathematical relations between the suspension gap and the suspension force and between the guide gap and the guide force based on tests and magnetic field analysis, connecting the vehicle dynamic model with the guide rail beam dynamic model, and solving a motion equation of the vehicle and guide rail dynamic interaction system by adopting cross iterative numerical integration so as to obtain the vehicle and guide rail beam dynamic interaction model.
6. The method of claim 5, wherein:
calculating a dynamic response index for each linear combination, comprising:
and calculating dynamic response indexes of each linear combination by using a vehicle and guide rail beam dynamic interaction model, wherein the dynamic response indexes comprise vehicle body vibration acceleration, suspension force, guide force, suspension gap, guide rail beam deformation and guide rail beam vibration acceleration.
7. The method of claim 6, wherein:
comparing the dynamic response indexes and the statistical distribution characteristics of all linear combinations to obtain the optimal linear combination, wherein the method comprises the following steps:
the dynamic response index time history results of each linear combination are statistically analyzed to obtain statistical distribution characteristics of each index in different sections in the combination, wherein the statistical distribution characteristics comprise the maximum value, the average value, the standard deviation, the 99% probability value and the 95% probability value;
and comparing the dynamic response indexes and the statistical distribution characteristics of all linear combinations, and taking the linear combination with the minimum statistical distribution characteristic value and the best dynamic performance as the optimal linear combination.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116002521A (en) * | 2023-03-27 | 2023-04-25 | 山东拓新电气有限公司 | Adjustable monorail crane and power control system |
| CN116499698A (en) * | 2023-06-29 | 2023-07-28 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Pneumatic and kinematic mechanical coupling analysis method for magnetic levitation flight wind tunnel magnetic levitation platform |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116002521A (en) * | 2023-03-27 | 2023-04-25 | 山东拓新电气有限公司 | Adjustable monorail crane and power control system |
| CN116002521B (en) * | 2023-03-27 | 2023-06-30 | 山东拓新电气有限公司 | Adjustable monorail crane and power control system |
| CN116499698A (en) * | 2023-06-29 | 2023-07-28 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Pneumatic and kinematic mechanical coupling analysis method for magnetic levitation flight wind tunnel magnetic levitation platform |
| CN116499698B (en) * | 2023-06-29 | 2023-08-29 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Pneumatic and kinematic mechanical coupling analysis method for magnetic levitation flight wind tunnel magnetic levitation platform |
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