CN111008354B - Radial gate gravity center calculation method and gravity moment calculation method - Google Patents
Radial gate gravity center calculation method and gravity moment calculation method Download PDFInfo
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- CN111008354B CN111008354B CN201911283016.7A CN201911283016A CN111008354B CN 111008354 B CN111008354 B CN 111008354B CN 201911283016 A CN201911283016 A CN 201911283016A CN 111008354 B CN111008354 B CN 111008354B
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
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- E—FIXED CONSTRUCTIONS
- E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
- E02B—HYDRAULIC ENGINEERING
- E02B7/00—Barrages or weirs; Layout, construction, methods of, or devices for, making same
- E02B7/20—Movable barrages; Lock or dry-dock gates
- E02B7/40—Swinging or turning gates
- E02B7/42—Gates of segmental or sector-like shape with horizontal axis
Abstract
The invention discloses a calculation method for the gravity center and a calculation method for the gravity moment of a radial gate, wherein the calculation method for the gravity center of the radial gate comprises the following steps: step 1, calculating the weight m of each component i of the radial gate in the fully closed state i And equivalent gravity force arm r Gi,j (ii) a Step 2, calculating the gravity force arm r of the radial gate in the fully closed state j (ii) a Step 3, calculating the gravity arm r of each component i of the radial gate in the fully closed state Gi,k (ii) a Step 4, calculating the gravity force arm r of the radial gate in the fully open state k (ii) a Step 5, calculating the circumferential coordinate theta of the gravity center of the radial gate in the fully closed state by using the following formula G ：sin(θ G +Δθ)/sinθ G = f, where f is a constant coefficient, and Δ θ is an angle through which the arc gate is rotated from the fully closed state to the fully open state; step 6, using formula r j ＝r G sinθ G Calculating the radial coordinate r of the center of gravity of the radial gate in the fully closed state G . The method can simply and conveniently calculate the gravity center and the gravity moment of the radial gate, and has the outstanding advantages of high efficiency and high precision.
Description
Technical Field
The invention belongs to the technical field of water conservancy and hydropower engineering, and particularly relates to a calculation method of the gravity center and a calculation method of the gravity moment of a radial gate.
Background
The gravity moment of the radial gate is an important factor influencing the opening and closing force. Unlike a plane gate, a radial gate has a complex structure, and the center of gravity of the radial gate is not easy to accurately obtain. The 'design specification SL 74-2013' of the steel gate for hydraulic and hydroelectric engineering and the 'design specification NB 35055-2015' of the steel gate for hydroelectric engineering in China both simply provide an expression for calculating the opening and closing force of the arc door, wherein the gravity moment is expressed by the product of the dead weight and the force arm, but do not provide a calculation formula for the dead weight and the force arm under different opening degrees of the arc door. For a long time, the dead weight of each component of the arc door is simplified into a regular rectangular plate for calculation, the gravity force arm is generally calculated by an empirical formula, namely the gravity center is approximately positioned at a radius which is 0.8 or 0.85 times of the center of a hinge on the action line of the total water pressure when the arc door is completely closed, and the gravity force arm under any opening degree of the arc door is obtained by angle conversion. The empirical formula comprehensively considers the actual external load of the arc door and the reasonable rigidity ratio of the main frame, is obtained according to the design concept of equal safety level and by combining a large amount of engineering experience, has clear concept and simple and convenient calculation, and is generally applied in the engineering field. However, the actual weight distribution during the design of the radial gate is not considered by the formula, and particularly for the radial gate with local weight or special-shaped structure, a large error is inevitably generated.
With the development and the common application of a three-dimensional aided design platform of a computer, a designer can obtain the accurate values of the dead weight and the gravity center of the arc door only by establishing a three-dimensional model of the arc door. Many scholars have directly calculated the internal force and the opening and closing force with higher precision by adopting a numerical simulation method. However, in the existing method, the arc door structure optimization and the hoist arrangement optimization are difficult to realize on the same platform through a program. Designers often need to establish a model of the radial gate designed by adopting a plane system method on a three-dimensional auxiliary design platform, and then perform opening and closing force calculation and arrangement optimization after obtaining the center of gravity, so that the calculation and optimization efficiency is low, and the global optimal result of the arrangement of the radial gate structure and the hoist cannot be obtained. In addition, the three-dimensional aided design platform needs to consume a large amount of computer capacity, and the calculation time is long. In the design, a set of analysis calculation method of the center of gravity and the gravity moment of the arc door is expected, and further the calculation of the arc door structure and the arrangement optimization of the hoist can be combined so as to obtain a global optimal solution.
For the analytical calculation method of the center of gravity of the arc door, a combination method can be adopted at present. Combined method meterThe idea of calculating the center of gravity of the arc door is as follows: calculating the weight m of each component when the gate is in the fully closed state i And center of gravity x to its main axis of inertia 0Ci Further, the center of gravity (x) of each member in a rectangular coordinate system xoy is calculated by coordinate transformation Ci ,y Ci ) Then calculating the center of gravity (x) of the arc door under the rectangular coordinate system C ,y C ) Then, the polar coordinate expression of the center of gravity of the arc door is easily obtained:
θ G ＝arctan(x C /y C ) And the gravity moment under any opening degree of the arc door can be obtained through the angle relation. Compared with an empirical formula and a three-dimensional model, the method has certain advantages, but the gravity center of each component needs to be calculated, coordinate transformation is needed, and the calculation process is still complex.
Disclosure of Invention
The invention aims to provide a simple, high-efficiency and high-precision calculation method for the gravity center and the gravity moment of the radial gate, aiming at the defects of low precision of empirical formulas, complex modeling of three-dimensional models and complex calculation process of a combination method in the prior art.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a method for calculating the gravity center of a radial gate is characterized by comprising the following steps:
step 1, calculating the weight m of each component i of the radial gate in the fully closed state i And equivalent gravity force arm r Gi,j ；
Step 3, calculating the gravity arm r of each component i of the radial gate in the fully closed state Gi,k ；
Step 4, calculating the gravity force arm r of the radial gate in the fully open state k ；
sin(θ G +Δθ)/sinθ G ＝f
Wherein f is a constant coefficient, and delta theta is the rotating angle of the radial gate from the fully closed state to the fully open state;
step 6, utilizing a formula r j ＝r G sinθ G Calculating the radial coordinate r of the center of gravity of the radial gate in the fully closed state G 。
Preferably, in the first step, m is i ＝ρδ i B i A i ，
Wherein rho is the material density of the radial gate, delta i Is the radial height of the member i, B i For the width of the member i in a direction parallel to the hinge of the radial gate, A i Taking the micro-element annular length of the component i, and taking the panel, the longitudinal beam front flange and the longitudinal beam web plate
For other members than panels, stringer front flanges and stringer webs, A i Get the ring to the height and get the ring to the height>
Is the radial mean radius of component i>
Is half a wrap angle of component i, is>
The average value of the angle of the member i in the fully closed state of the radial gate.
Preferably, r is j ＝M j /(mg)＝(∑m i r Gi,j )/(∑m i ) (ii) a Wherein M is j The gravity moment is the gravity moment when the radial gate is in a fully closed state; m is the mass of the radial gate; g is the acceleration of gravity;
r k ＝M k /(mg)＝(∑m i r Gi,k )/(∑m i ) (ii) a Wherein M is k Is the gravity moment when the radial gate is in a full-open state.
Based on the same inventive concept, the invention also provides a radial gate gravity moment calculation method, which is characterized by comprising the following steps:
step 6, using formula r k ＝r G sin(θ G + delta theta) calculating the gravity force arm r of the radial gate in the fully open state k ；
Step 7, using formula M k ＝mgr G sin(θ G + Delta theta) calculation of the gravitational moment M of the radial gate in the fully open state k Wherein m is the mass of the radial gate; g is the acceleration of gravity.
Compared with the prior art, the method can simply and conveniently calculate the gravity center and the gravity moment of the radial gate, and has the outstanding advantages of high efficiency and high precision.
Drawings
FIG. 1 is a simplified diagram of calculation of the gravity center and the gravitational moment of the radial gate of the present invention.
FIG. 2 shows a finite element model of example (1).
FIG. 3 is a finite element model of example (2).
Detailed Description
Fig. 1 is a simplified diagram of the calculation of the center of gravity and the gravitational moment of the radial gate of the present invention. In fig. 1, 1 is a radial gate pivot, 2 is a total water pressure action line when the radial gate is in a fully closed state, 3 is a radial gate lifting lug, 4 is a hoist pivot, and 5 is a hoist rod axis.
The method for calculating the gravity center of the radial gate comprises the following steps of:
step 1, calculating the weight m of each component i of the radial gate in a fully closed state i And an equivalent gravity arm rGi, j ；
Step 3, calculating the gravity force of each component i of the radial gate in the fully closed stateArm r Gi,k ；
Step 4, calculating the gravity force arm r of the radial gate in the fully open state k ；
sin(θ G +Δθ)/sinθ G ＝f
Wherein f is a constant coefficient, and delta theta is an angle rotated by the radial gate clockwise from a fully closed state to a fully open state;
step 6, utilizing a formula r j ＝r G sinθ G Calculating the radial coordinate r of the center of gravity of the radial gate in the fully closed state G 。
In the step one, m i ＝ρδ i B i A i ，
Wherein rho is the material density of the radial gate, delta i Is the radial height of the member i, B i The width of the member i in the direction perpendicular to the plane of the paper in FIG. 1, i.e. parallel to the hinge of the radial gate, A i Taking the micro-element annular length of the component i and taking the value of the length of the panel, the front flange of the longitudinal beam and the web of the longitudinal beam>
For other members than panels, stringer front flanges and stringer webs, A i Get the ring to the height and get the ring to the height>
Is the radial mean radius of component i, i.e.>
Wherein R is i Is the outer radius of member i; />
Is half a wrap angle of member i, i.e.>
In units of radian, θ 1i Is the lower limit value of the angular range of the circumferential enclosure of the component i (such as a panel, a front flange of a main beam and the like), theta 2i Is the upper limit value of the angle range surrounded by the circumferential direction of the component i (such as a panel, a front flange of a main beam and the like), and the room>
The average value of the angle of the component i in the fully closed state of the radial gate.
r j ＝M j /(mg)＝(∑m i r Gi,j )/(∑m i ) (ii) a Wherein M is j The gravity moment is the gravity moment when the radial gate is in a fully closed state; m is the mass of the radial gate; g is the acceleration of gravity;
wherein, M k Is the gravity moment of the radial gate in the full-open state.
In step 5, f = M k /M j 。
The method for calculating the gravity moment of the radial gate comprises the method for calculating the gravity center of the radial gate, and further comprises the following steps:
step 6, utilizing a formula r k ＝r G sin(θ G + delta theta) calculating the gravity force arm r of the radial gate in the fully open state k ；
Step 7, using formula M k ＝mgr G sin(θ G + Delta theta) calculation of the gravitational moment M of the radial gate in the fully open state k Wherein m is the mass of the radial gate; g is the acceleration of gravity.
The method of the invention is referred to as the rotary method for short.
Empirical formulas, combinatorial and rotational calculations and comparisons are shown in table 1 below.
TABLE 1 calculation method and comparison of gravity center and gravity moment of radial gate
The analysis shows that the invention has strong practical value.
Two specific engineering examples are given below.
Example (1): pan Kou spillway open top type arc gate aperture width 20.0m, aperture height 18.327m, downstream water-free, panel curvature radius 23.0m, rotary hinge height 10.327m, gate leaf height 18.8m, gate gravity 3000kN. The force arm of the rotary hinge friction resistance is 0.425m, the force arm of the water seal friction resistance is 23.0m, and the force arm of the water seal uplifting force is 20.55m. The known gate can be lowered by self weight, and the maximum door opening force is calculated by an empirical formula when the water retaining state is realized, wherein the opening and closing force arm 10.946m is realized.
Example (2): pan Kou flood discharge hole down-the-hole radial gate has 8.0m of orifice width, 10.0m of orifice height, 16.0m of panel curvature radius, 13.10m of rotary hinge height, 10.15m of gate leaf height and 2334.5kN of gate gravity. The arm of the rotary hinge frictional resistance force is 0.35m, the arm of the water seal frictional resistance force is 16.0m, and the arms of the top and bottom water seal uplift force are 16.0m and 9.2m respectively. The known gate can be lowered by self weight, the maximum opening force is calculated by an empirical formula when the gate is in a fully open state, and the arm of force of the opening and closing force is 11.05m at the moment.
And (3) related parameters: the density of the steel material is 7850kg/m 3 The Poisson's ratio is 0.31; the sliding friction coefficient of the hinged shaft is 0.1, the compression amount of the side water seal is 4mm, the water seal line pressure is p =58N/cm, and the friction coefficient is 0.5; the length of the bottom water seal is 110mm, the thickness is 15mm, the compression amount of the gate in a water retaining state is 5mm, and the elastic modulus is 6MPa.
And respectively calculating the gravity center of the radial gate in the example by adopting an empirical formula, a three-dimensional model, a combination method and a rotation method. Wherein, the gravity center is obtained by using an APDL program in the three-dimensional finite element model, and the combination method and the rotation method are realized by MATLAB programming. The finite element model of the example (1) is shown in fig. 2, and the finite element model of the example (2) is shown in fig. 3.
Considering the structural particularity, the steel structural members of the finite element model of the radial gate all adopt shell units, and the water stopping part adopts a friction unit. Wherein, the case (1) model has 71609 nodes and 35125 cells; the case (2) model has 53609 nodes and 30095 units. The types of the respective component units of the radial gate are shown in table 2. The calculation results and comparison of the four methods are shown in table 4 and table 5, and the calculation results of the three-dimensional model are used as true values in the calculation.
TABLE 2 Unit type table for each component of radial gate
TABLE 3 EXAMPLES (1) results of four methods and comparison
TABLE 4 calculation example (2) calculation results and comparison of four methods
As can be seen from tables 3 and 4: when the inclination angle theta is calculated by adopting an empirical formula G Has a maximum relative error of 3.78% and a radius r G Has a maximum relative error of 25.18%, and a tilt angle theta G Are all much smaller than the radius r G A minimum difference of about 1 times; the results calculated by adopting the combination method and the rotation method are equivalent, the maximum relative error is 7.58 percent, and the total error is much smaller than that of an empirical formula. Compared with a three-dimensional platform occupying a large-capacity memory and building a complex model, the combination method and the rotation method can be realized by only programming a small program, and are more convenient for a designer to master and use. In addition, the calculation program compiled according to the combination method and the rotation method can be combined with the gate structure and the hoist system arrangement optimization program, so that the overall optimization design of the radial gate is realized. In comparison, the rotation method does not need to calculate the gravity center of each component separately, and does not need coordinate transformation, which is simpler and more convenient than the combination method.
In conclusion, the empirical formula can be used for estimating the opening and closing force of the radial gate and analyzing the change rule of the opening and closing force along with the opening; the analytic method has the outstanding advantages of high precision and strong universality, and compared with a combination method, the calculation process of the rotation method is simpler, so that the calculation method of the arc gate is better in gravity center.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (2)
1. A method for calculating the gravity center of a radial gate is characterized by comprising the following steps:
step 1, calculating the weight m of each component i of the radial gate in the fully closed state i And equivalent gravity force arm r Gi,j ；
Step 2, calculating the gravity arm of force r of the radial gate in the fully closed state j ；
Step 3, calculating the gravity arm r of each component i of the radial gate in the fully closed state Gi,k ；
Step 4, calculating the gravity force arm r of the radial gate in the fully open state k ；
Step 5, calculating the circumferential coordinate theta of the gravity center of the radial gate in the fully closed state by using the following formula G ：
sin(θ G +Δθ)/sinθ G ＝f
Wherein f is a constant coefficient, and delta theta is the angle of the radial gate from the fully closed state to the fully open state;
step 6, utilizing a formula r j ＝r G sinθ G Calculating the radial coordinate r of the center of gravity of the radial gate in the fully closed state G ；
In step 1, m i ＝ρδ i B i A i ，
Wherein rho is the material density of the radial gate, delta i Is the radial height of the member i, B i The width of the member i in a direction parallel to the hinge of the radial gate, A i Taking the infinitesimal circumferential length of the component i as the length of a panel, a longitudinal beam front flange and a longitudinal beam web
For other members than panels, stringer front flanges and stringer webs, A i Get the ring to the height and get the ring to the height>
Is the radial mean radius of component i->
Is half a wrap angle of component i, is>
The average value of the angles of the component i in the fully closed state of the radial gate is obtained;
r j ＝M j /(mg)＝(∑m i r Gi,j )/(∑m i ) (ii) a Wherein M is j The gravity moment is the gravity moment when the radial gate is in a fully closed state; m is the mass of the radial gate; g is the acceleration of gravity;
r k ＝M k /(mg)＝(∑m i r Gi,k )/(∑m i ) (ii) a Wherein M is k Is the gravity moment of the radial gate in the full-open state.
2. A radial gate gravitational moment calculation method, comprising the radial gate gravitational moment calculation method of claim 1, further comprising:
step 7, using formula r k ＝r G sin(θ G + delta theta) calculating the gravity force arm r of the radial gate in the fully open state k ；
Step 8, using formula M k ＝mgr G sin(θ G + Delta theta) calculation of the gravitational moment M of the radial gate in the fully open state k Wherein m is the mass of the radial gate; g is the gravitational acceleration.
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| JP2002285533A (en) * | 2001-03-26 | 2002-10-03 | Marsima Aqua System Corp | Non-power type gate |
| CN102968518A (en) * | 2012-10-08 | 2013-03-13 | 蔡坤 | Topology optimization design method for novel down-the-hole arc-shaped hydraulic steel gate |
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