CN111008354A - 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 PDF

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CN111008354A
CN111008354A CN201911283016.7A CN201911283016A CN111008354A CN 111008354 A CN111008354 A CN 111008354A CN 201911283016 A CN201911283016 A CN 201911283016A CN 111008354 A CN111008354 A CN 111008354A
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gravity
radial gate
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兰钦
岳汉东
廖玉海
段东旭
许勇刚
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PowerChina Zhongnan Engineering Corp Ltd
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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 stateiAnd equivalent gravity force arm rGi,j(ii) a Step 2, calculating the gravity force arm r of the radial gate in the fully closed statej(ii) a Step 3, calculating the gravity arm r of each component i of the radial gate in the fully closed stateGi,k(ii) a Step 4, calculating the gravity force arm r of the radial gate in the fully open statek(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 formulaG：sin(θG+Δθ)/sinθGF, wherein f is a constant coefficient, and Δ θ is an angle through which the radial gate rotates from the fully closed state to the fully open state; step 6, utilizing a formula rj＝rGsinθGCalculating the radial coordinate r of the center of gravity of the radial gate in the fully closed stateG. 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

Radial gate gravity center calculation method and gravity moment calculation method
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 water conservancy and hydropower engineering steel gate and the ' design specification NB 35055-2015 ' of the hydropower engineering steel gate ' in China 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 the calculation formulas of the dead weight and the force arm under different opening degrees of the arc door are not provided. 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 formula does not consider the actual weight distribution in the design of the arc door, and particularly, a large error is inevitably generated when the arc door is locally weighted or has a special-shaped structure.
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. But at present, the method is difficult to realize the optimization of the arc door structure and the optimization of the hoist arrangement 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. The idea of calculating the center of gravity of the arc door by a combination method is as follows: calculating the weight m of each component when the gate is in the fully closed stateiAnd center of gravity x to its main axis of inertia0CiFurther, the center of gravity (x) of each member in a rectangular coordinate system xoy is calculated by coordinate transformationCi,yCi) Then calculating the center of gravity (x) of the arc door under the rectangular coordinate systemC,yC) Then, the polar coordinate expression of the center of gravity of the arc door is easily obtained:
Figure BDA0002317272900000021
θG＝arctan(xC/yC) And the gravity moment of the arc door at any opening 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 stateiAnd equivalent gravity force arm rGi,j；
Step 2, calculating the gravity force arm r of the radial gate in the fully closed statej；
Step 3, calculating the gravity arm r of each component i of the radial gate in the fully closed stateGi,k；
Step 4, calculating the gravity force arm r of the radial gate in the fully open statek；
Step 5, calculating the circumferential coordinate theta of the gravity center of the radial gate in the fully closed state by using the following formulaG：
sin(θG+Δθ)/sinθG＝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 rj＝rGsinθGCalculating the radial coordinate r of the center of gravity of the radial gate in the fully closed stateG。
Preferably, in the first step, m isi＝ρδiBiAi，
Figure BDA0002317272900000031
Wherein rho is the material density of the radial gate, deltaiIs the radial height of the member i, BiFor the width of the member i in a direction parallel to the hinge of the radial gate, AiTaking the micro-element annular length of the component i, and taking the panel, the longitudinal beam front flange and the longitudinal beam web plate
Figure BDA0002317272900000032
For other members than panels, stringer front flanges and stringer webs, AiThe height of the ring is taken out in the circumferential direction,
Figure BDA0002317272900000033
is the radial average radius of the component i,
Figure BDA0002317272900000034
is the half-wrap angle of the component i,
Figure BDA0002317272900000035
the average value of the angle of the component i in the fully closed state of the radial gate.
Preferably, r isj＝Mj/(mg)＝(∑mirGi,j)/(∑mi) (ii) a Wherein M isjThe 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;
Figure BDA0002317272900000036
rk＝Mk/(mg)＝(∑mirGi,k)/(∑mi) (ii) a Wherein M iskIs the gravity moment of the radial gate in the 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, utilizing a formula rk＝rGsin(θG+ delta theta) calculating the gravity force arm r of the radial gate in the fully open statek；
Step 7, using formula Mk＝mgrGsin(θG+ Delta theta) calculation of the gravitational moment M of the radial gate in the fully open statekWherein 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 is 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 calculation of the gravity center 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 the fully closed stateiAnd an equivalent gravitational moment arm rGi,j；
step 2, calculating the gravity force arm r of the radial gate in the fully closed statej；
Step 3, calculating the gravity arm r of each component i of the radial gate in the fully closed stateGi,k；
Step 4, calculating the gravity force arm r of the radial gate in the fully open statek；
Step 5, calculating an included angle theta between the center line of gravity center and hinge center of the radial gate in the fully closed state and the vertical direction by using the following formulaGI.e. circumferential coordinate theta of center of gravity of the radial gate in the fully closed stateG：
sin(θG+Δθ)/sinθG＝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 rj＝rGsinθGCalculating the radial coordinate r of the center of gravity of the radial gate in the fully closed stateG。
In the step one, mi＝ρδiBiAi，
Figure BDA0002317272900000051
Wherein rho is the material density of the radial gate, deltaiIs the radial height of the member i, BiThe 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, AiTaking the micro-element annular length of the component i, and taking the panel, the longitudinal beam front flange and the longitudinal beam web plate
Figure BDA0002317272900000052
For other members than panels, stringer front flanges and stringer webs, AiThe height of the ring is taken out in the circumferential direction,
Figure BDA0002317272900000053
is the radial mean radius of the component i, i.e.
Figure BDA0002317272900000054
Wherein R isiIs the outer radius of member i;
Figure BDA0002317272900000055
being half-cornered of the member i, i.e.
Figure BDA0002317272900000056
In units of radian, θ1iIs 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), theta2iIs the upper limit value of the angle range surrounded by the circumferential direction of the component i (such as a panel, a main beam front flange and the like),
Figure BDA0002317272900000057
the average value of the angle of the component i in the fully closed state of the radial gate.
rj＝Mj/(mg)＝(∑mirGi,j)/(∑mi) (ii) a Wherein M isjThe 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;
Figure BDA0002317272900000058
wherein M iskIs the gravity moment of the radial gate in the full-open state.
In step 5, f is equal to Mk/Mj。
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 rk＝rGsin(θG+ delta theta) calculating the gravity force arm r of the radial gate in the fully open statek；
Step 7, using formula Mk＝mgrGsin(θG+ Delta theta) calculation of the gravitational moment M of the radial gate in the fully open statekWherein m is the mass of the radial gate; g isAcceleration 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
Figure BDA0002317272900000061
The analysis shows that the invention has strong practical value.
Two specific engineering examples are given below.
In the example ①, the width of the opening of the top-exposed type arc gate of the flood spillway is 20.0m, the height of the opening is 18.327m, the downstream is free of water, the curvature radius of a panel is 23.0m, the height of a rotary hinge is 10.327m, the height of a gate leaf is 18.8m, the gravity of the gate is 3000 kN., the rotary hinge frictional resistance force arm is 0.425m, the water seal frictional resistance force arm is 23.0m, the force arm of the water seal lifting force is 20.55 m.
According to the calculation example ②, the width of an orifice of a submerged-hole type radial gate of a Pan flood discharging tunnel is 8.0m, the height of the orifice is 10.0m, the curvature radius of a panel is 16.0m, the height of a rotary hinge is 13.10m, the height of a gate leaf is 10.15m, the gravity of the gate is 2334.5 kN., the force arm of rotary hinge frictional resistance is 0.35m, the force arm of water seal frictional resistance is 16.0m, the force arms of top and bottom water seal uplift forces are respectively 16.0m and 9.2 m.
And (3) related parameters: the density of the steel material is 7850kg/m3The Poisson's ratio is 0.31; the sliding friction coefficient of the hinge 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 6 MPa.
The gravity centers of the radial gates in the examples are calculated by respectively adopting an empirical formula, a three-dimensional model, a combination method and a rotation method, wherein the gravity centers are obtained by utilizing an APDL program in the three-dimensional finite element model, the combination method and the rotation method are realized by adopting MATLAB programming, the finite element model of the example ① is shown in figure 2, and the finite element model of the example ② is shown in figure 3.
In consideration of structural particularity, all steel structural components of the finite element model of the radial gate adopt shell units, and a water stopping part adopts friction units, wherein the case ① model has 71609 nodes and 35125 nodes, the case ② model has 53609 nodes and 30095 units, the types of the components of the radial gate are shown in a table 2, the calculation results of the four methods are shown in a table 4 and a table 5, and the calculation results of the three-dimensional model are used as real values in calculation.
TABLE 2 Unit type table for each component of radial gate
Figure BDA0002317272900000081
TABLE 3 EXAMPLES ① results of four methods and comparisons
Figure BDA0002317272900000082
TABLE 4 calculation of results and comparison of four methods of calculation ②
Figure BDA0002317272900000083
As can be seen from tables 3 and 4: when calculated by empirical formula, the inclination angle thetaGHas a maximum relative error of 3.78% and a radius rGHas a maximum relative error of 25.18%, and a tilt angle thetaGAre all much smaller than the radius rGA 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 the method which occupies a large-capacity memory and builds a complex three-dimensional platform by a 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 method is based on a combination method and a rotation methodThe calculation program can be combined with a gate structure and an arrangement optimization program of a hoist system, 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 (4)

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 stateiAnd equivalent gravity force arm rGi,j；
Step 2, calculating the gravity force arm r of the radial gate in the fully closed statej；
Step 3, calculating the gravity arm r of each component i of the radial gate in the fully closed stateGi,k；
Step 4, calculating the gravity force arm r of the radial gate in the fully open statek；
Step 5, calculating the circumferential coordinate theta of the gravity center of the radial gate in the fully closed state by using the following formulaG：
sin(θG+Δθ)/sinθG＝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 rj＝rGsinθGCalculating the radial coordinate r of the center of gravity of the radial gate in the fully closed stateG。
2. The method of calculating the center of gravity of a radial gate of claim 1, wherein in the first step, m isi＝ρδiBiAi，
Figure FDA0002317272890000011
Wherein rho is the material density of the radial gate, deltaiIs the radial height of the member i, BiFor the width of the member i in a direction parallel to the hinge of the radial gate, AiTaking the micro-element annular length of the component i, and taking the panel, the longitudinal beam front flange and the longitudinal beam web plate
Figure FDA0002317272890000012
For other members than panels, stringer front flanges and stringer webs, AiThe height of the ring is taken out in the circumferential direction,
Figure FDA0002317272890000013
is the radial average radius of the component i,
Figure FDA0002317272890000014
is the half-wrap angle of the component i,
Figure FDA0002317272890000015
the average value of the angle of the component i in the fully closed state of the radial gate.
3. The radial gate center of gravity calculation method of claim 2, wherein r is rj＝Mj/(mg)＝(∑mirGi,j)/(∑mi) (ii) a Wherein M isjThe 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;
Figure FDA0002317272890000021
rk＝Mk/(mg)＝(∑mirGi,k)/(∑mi) (ii) a Wherein M iskIs the gravity moment of the radial gate in the full-open state.
4. A radial gate gravitational moment calculation method, comprising the radial gate gravitational moment calculation method according to any one of claims 1 to 3, further comprising:
step 6, utilizing a formula rk＝rGsin(θG+ delta theta) calculating the gravity force arm r of the radial gate in the fully open statek；
Step 7, using formula Mk＝mgrGsin(θG+ Delta theta) calculation of the gravitational moment M of the radial gate in the fully open statekWherein m is the mass of the radial gate; g is the acceleration of gravity.
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