Torsional Deformation Analysis of Large Miter Gate under Different Operating Conditions

Abstract

As an important part of the navigation facilities for water conservancy and electricity in Gezhouba, the operation safety of herringbone gates is critical. Due to the minor torsional stiffness of the gate, it is easy to produce torsional deformation during operating under the water pressure, wind load, and gravity, which may lead to fatigue damage. In this study, a gate model with a combination of plate unit and the solid unit was developed, taking a ship lock herringbone gate as an example. According to the gate load under different working conditions, such as self-weight, surge, etc., in this research, we used the finite element analysis software ANSYS to analyze and calculate the stress and strain of the gate, with and without a back tie, and obtained the characteristics of the gate torsional deformation under various working conditions. The results show that the gate’s deformation degree and the direction under different working conditions vary greatly. The maximum deformation point mostly appears in the upper or lower corners of the oblique joint column. The gate deformation can be significantly reduced by adding the back tie. The research results provide a theoretical basis for further optimizing the design of the gate and installation of the back tie to reduce the fatigue damage of the miter gate.

1. Introduction

Miter gates are widely used in ship locks in navigable rivers. The mass and size of the gate leaf of large miter gates are significant, and belong to a typical super large open thin-walled structural member [1], in structure. However, the torsional stiffness is slight. Therefore, torsional deformation will occur under the action of self-weight, water pressure, and wind load during operation, especially in the gate operation [2]. Thus, the large miter gate is designed with a prestressed back tie rod to enhance the stiffness. The US Army Corps of Engineers took the lead in putting forward the calculation theory of a prestressed back tie rod, through which the prestress range of a back tie rod can be calculated [3,4,5,6]. With computer technology and optimization algorithms, the gate and back tie rod can be optimized by finite element software. He Wenjuan et al. took the vertical displacement of the lower corner of the gate miter column as the optimization objective function to determine the prestress [7,8,9]. Still, a single objective function cannot accurately reflect the deformation characteristics of the gate. Liu Lihua et al. used flatness and sag as objective functions to determine prestress, which improve the accuracy of calculation [10], but it is difficult to reflect the direction and change law of deformation.

By coupling multiple factors and the influence of the gate’s structure, the gate is bound to produce vibration during the operation. P. Billeter et al. conducted an experimental study of the multi-degree-of-freedom gate vibration problem to illustrate the hydrodynamic coupling mechanism of the two vibration modes and determine the non-constant lift interaction and drag forces [11]. DK. Singh et al. established the coupling effect of the gate structure and fluid domain using the finite element method and studied the effects of different fluid domain ranges on the gate intrinsic frequency [12,13]. The frequent opening and closing of the gate under multiple stresses are bound to cause fatigue damage to the corresponding components. MA Vega and Dang TV et al. illustrated how to find the optimal time for a maintenance plan in a herringbone gate, and they proposed a new Bayesian approach to estimate the error rate in OCA scores, thus improving the accuracy of OCA score-based predictions [14,15]. Ye and H. Mahmoud et al. used finite element calculations to analyze the stresses on the backstop horizontal surface steel gate structure, the displacement and stresses on the gate leaves of herringbone gates under different operating conditions, the structural deformation and stress distribution of curved steel gates under other operating conditions, and the assessment of the full life cycle of fatigue fracture of herringbone gates [16,17,18,19]. Loïc and Yan et al. used finite element software to evaluate the gate’s structural resistance after impact and assessed the drive shaft’s structural safety [20,21]. S Khatir [22] used the isogeometric analysis (IGA) method to establish the model of the FGM plate, which is more effective than the traditional finite element method.

Using the miter gate at the lower head of the Gezhouba no. 2 ship lock as an example, this study establishes the 3D model of the miter gate by using the finite element software, Ansys Workbench. Then, simulating and calculating the gates with and without back tie rods under different working conditions, this essay analyzes the torsional deformation under various working conditions and provides some theoretical basis for optimizing the design and installation of the back tie rod.

2. Modeling

2.1. Stress Analysis of Gate under Different Operating Conditions

The downstream threshold elevation of the ship lock is 34.0 m, and the downstream navigable water level is 39 m. When the navigable water level is below 54.5 m, there is a difference of 0.2 m between the upstream and downstream. The direction of wind load points from the downstream to the upstream, and the influence of water pressure and wind pressure are different under different operating conditions. The operation state of the gate mainly includes the opening, closing, and static. The stress and deformation of each state are different. The closed static state is divided into the lowest and highest cases according to the upstream water level. As shown in Figure 1, through the analysis of gravity, water pressure, and wind load, the stress conditions of the gate under different operating states are mainly divided into the following four types:

State 1: the gate hangs freely and is only affected by its gravity.

State 2: the ship is located in the lock chamber and the gate is closed and static. The lock chamber begins to fill water. When the water level reaches the upstream navigable water level, there is the water pressure at both upstream and downstream. The water level difference between the upstream and downstream of the gate reaches the maximum, and the wind load acts on the downstream surface of the gate.

State 3: the gate is in the open state. Taking the maximum wind load as an example and at the moment of gate opening, the rotation trend makes the upstream water pressure become resistant. As a result, the downstream water pressure is almost zero.

State 4: the gate is closed. Taking the maximum wind load as an example and the moment the gate is about to close, the rotation trend makes the downstream water pressure resistant, and the upstream water pressure is almost zero.

2.1.1. Wind Load

When the herringbone gate is subjected to wind load, it is assumed that the wind pressure is $p$. The gate opening degree is $\alpha$. The force schematic is shown in Figure 2a. The wind load can be a positive or negative force, as shown in Figure 2b.

According to Design of Hydraulic Steel Structures, the wind pressure $p$ acting on the gate is calculated as follows:

$$p=u_1{u}_2{p}_0$$

(1)

where, $p_0$—basic wind pressure, $p_0=\frac{V^2}{1600}$, $V$ is the average wind speed; $u_1$—wind pressure body type factor. The gate generally takes the value of 3u₁ = 1.3; $u_2$—wind pressure height factor. It can be selected according to

Table 1. Wind pressure height variation factor.

Height above Ground (m)	10	15	20	30
$u_2$	1	1.15	1.25	1.42

.

As shown in Figure 2, it can be seen that the gate is subjected to a total wind pressure of:

$$P_v=p\cdot \sin \alpha \cdot h_1\cdot b$$

(2)

Combined with Gezhouba monitoring data and reference materials [23,24], the maximum wind speed in the navigable water of Gezhouba locks is 15.24–3.12 m/s with the average wind speed V = 19.18 m/s. Wind pressure body type factor is taken as u₁ = 1.3; wind pressure height factor u₂ = 1.0. The average wind pressure p acting on the gate is calculated according to Equation (1) as:

$$p=1.3\times 1.0\times \frac{{19.18}^2}{1600}=0.3 \mathrm{kN}/{\mathrm{m}}^2$$

Gate width $b=19.6 \mathrm{m}$; panel windbreak height $h_1=29.4 \mathrm{m}$; gate opening $\alpha =67.5°$. Calculate the total wind pressure on the gate according to Equation (2).

$$P_v=0.3\times \sin 67.5°\times 19.6\times 29.4=159.7 \mathrm{kN}$$

2.1.2. Water Pressure

Although the herringbone gate is opened and closed in the still water where the upstream and downstream water levels are the same, the rotation of the gate leaves in the water causes congestion in front of the gate. Banked-up height $\Delta h$ is generally approximated by the following equation:

$$\Delta h=1.2V_m^2$$

(3)

where, $Vm$ is the average tangential linear velocity at the end point of the door lobe (m/s), and often chosen to be about 0.2 m in design.

The dynamic water pressure generated by the water level difference between the upstream and downstream of the gate is trapezoidally distributed on the front and back of the gate leaf, and its plane force schematic diagram is shown in Figure 3. Assuming that the water level difference is $\Delta h$; the depth of inundation of the dynamic water resistance surface is $h_3$; the density of water is $\rho$.

The size of the liquid pressure depends only on the type and depth of the liquid, and the quality of the liquid. The total dynamic water pressure per unit width of the door leaf panel along the door axis direction is

$$P_2={\displaystyle \underset{0}{\overset{h_3}{\int }}\rho ghdh}-{\displaystyle \underset{0}{\overset{h_3-\Delta h}{\int }}\rho ghdh}=\frac{1}{2}\rho g{h}_3^2-\frac{1}{2}\rho g{\left(h_3-\Delta h\right)}^2=\rho g\left(h_3\Delta h-\frac{1}{2}\Delta h^2\right)$$

(4)

The average dynamic water pressure $p_2$ and total dynamic water pressure $p_h$ acting on the panel are:

$$p_2=\frac{P_2}{h_3}=\rho g\left(\Delta h-\frac{1}{2}\Delta h^2/h_3\right)$$

(5)

$$P_h=p_2{h}_{3}b=\rho gb\left(h_3\Delta h-\frac{1}{2}\Delta h^2\right)$$

(6)

As the surge impact load variation law is a non-constant value and the impact on the door body is small, the simulation analysis will not be considered. The gate panel dynamic water action when submerged water depth $h_3=5 \mathrm{m}$; gate width $b=19.6 \mathrm{m}$. According to Equations (5) and (6), the total dynamic water pressure can be calculated as:

$$P_h=p_2{h}_{3}b=1.95\times 5\times 19.6=191.1 \mathrm{kN}$$

2.2. Model Establishment and Grid Division

The gate size is large, and the ratio of length to width to thickness of the plate is too large. Therefore, to obtain a high-quality grid, the grid size must be reduced, which will increase the number of grids, resulting in the doubling of the amount of calculation. Therefore, it is necessary to simplify the model.

The plate shell structure means that the thickness (t) of the plate is much smaller than the dimensions in the other two directions. Whether the design can be simplified as a plate and shell problem requires determining the ratio of thickness to other azimuth dimensions. If 1/80 ≤ t ≤ 1/10, it can be attributed to a problem of a plate (thin shell). If it is in the interval [1/10–1/5], it belongs to a thick shell problem. If it is greater than 1/5, it does not belong to a plate and shell structure problem. The mechanical model of the plate and shell element is taken as the neutral surface of the structural element. Each neutral surface is represented as a combination of plate or shell elements with different thicknesses to simulate the structural body [25,26,27], as shown in Figure 4.

The miter gate is mainly composed of gate leaf structure, supporting part, water stop part, and other auxiliary parts. The gate leaf structure includes the panel, main beam, secondary beam, transverse diaphragm, vertical diaphragm, back tie rod, door shaft column, and miter column. The panel, main beam, secondary beam, diaphragm, and vertical diaphragm are plate parts with large lengths, widths, and thickness ratios. They can be set as plate elements in modeling, and the rest are solid elements, including 200 plate elements and 19 solid elements. As shown in Figure 4, the coordinate system selects the x-axis as the axial direction of the main beam of the gate, y-axis as the direction from the upstream to the downstream that is perpendicular to the axial direction of the main beam, and z-axis as vertical upward. The grid type is mainly the hexahedral grid [28]. The common nodes are set for the plate element, and the thickness of the plate element is set according to the thickness of specific parts. Finally, the finite element analysis model of 137,296 elements and 160,573 nodes is generated. The finite element model is shown in Figure 5. In the analysis process, the material of the model is 16 Mn; the elastic modulus is 206,000 mpa; Poisson’s ratio is 0.3; the density is 7850 kg/m³; and the gravity acceleration is 9800 mm/S². Other attribute parameters adopt default values.

2.3. Setting of Load and Boundary Conditions

Take State 3, the gate open working condition as an example. The finite element simulation boundary conditions are set based on the gate operation force situation as shown in Figure 1c and Figure 6. Because the surge and the friction of the top and bottom pivots on the operation of the gate is relatively small, they are ignored in the analysis process. There is no corresponding support for the gate shaft column and tilt joint column during the opening process, so no constraints are set.

Load setting: (1) considering the effect of gravity of the gate, gravitational acceleration g = 9.8 m/s² is applied at the center of the gate weight, along the negative direction of the gate axis. (2) Wind pressure 159.7 kN, blowing from downstream to upstream. (3) The upstream water level is 5 m when the door is opened, and the dynamic water pressure is 191.1 kN.

Boundary conditions: according to the operation and components of the herringbone gate, the top pivot, bottom pivot, push–pull rod, and gate body are set with constraints. (1) The top pivot is constrained with 5 degrees of freedom, and the Z-direction movement is not constrained. (2) The bottom pivot is constrained with 6 degrees of freedom. (3) Push–pull rod on the door body is of the constraint 6 degrees of freedom.

The above is the load and constraints under the gate opening condition. The other three states can be obtained in

Table 2. Stress load and constraint of the gate under different states.

State	Gravity	Wind Load	The Minimum Water Pressure in Upper Reaches	Water Pressure in Lower Reaches	The Maximum Water Pressure in Upper Reaches	Bottom Pivot Constraint	Top Pivot Constraint	Miter Column Constraint	Push–Pull Rod Restraint
1	✔					✔	✔
2	✔	✔		✔	✔	✔	✔	✔
3	✔	✔	✔			✔	✔		✔
4	✔	✔		✔		✔	✔		✔

Note: “✔” indicates that there is such a load or boundary condition.

. Figure 7 shows the different states of the gate load and constraints. The gate is in a quiescent closed state, and the fixed restraint of the inclined joint column is increased within 6 degrees of freedom [29,30].

3. Results and Discussion

According to the stress analysis of the gate under different working conditions, the gate model is loaded, and the deformation of the gate without and with the back tie rod under different working conditions is obtained. Furthermore, by comparing the deformation of the gate shaft column and miter column in different directions, the deformation characteristics of the gate under different working conditions are obtained.

3.1. State 1

In the state of no external force and self-weight, only the gravity of the gate itself is considered. Therefore, the mushroom head is fixed on the ground and the gate is placed on the mushroom head. The bottom pivot plays a supporting role, and the top pivot is matched with the bottom pivot to make the gate hang freely.

When the back tie rod is not installed on the gate, the calculated deformation of the gate is shown in Figure 8. Under the condition of self-weight and free suspension, the herringbone gate produces obvious torsional deformation. The upper half of the gate body bends downstream, and the lower half of the gate body tilts upstream. It can be seen that the maximum deformation occurs at the upper corner of the miter column, and the door shaft column and miter column have different degrees of deformation. Figure 9 shows the deformation diagram of the gate shaft column and miter column in different positions and directions.

It can be seen from Figure 9a that the deformation of the door shaft column gradually increases from the bottom to the top, and the deformation is the largest at the gate height of 30,000 mm, with the deformation of about 8 mm. The deformations in the X, Y, and Z directions shows that the deformation of the door shaft column is mainly curved and inclined to the upstream. In Figure 9b, the deformation of mitered column decreases gradually in the range of 0–7500 mm and increases linearly in the range of 7500–34,000 mm. The maximum deformation is more than 175 mm. There is almost no deformation in the X-direction. The deformation in the Z direction is basically stable at 26 mm. The deformation trend in the Y direction is consistent with the total deformation. It can be seen that the deformation of the miter column is much larger than that of the gate shaft column. The maximum deformation of the upper corner of the miter column is along the positive direction of the Y-axis, and the lower corner is along the negative direction of the Y-axis. Therefore, when the gate is suspended freely, the upper half of the gate body bends downstream and the lower half of the gate body tilts upstream, and the dividing point in the middle is at the gate height of 7500 mm.

According to the actual installation position of the back tie rod on the general miter gate, four back tie rods are, respectively, installed in the upper half and lower half of the gate. The centroid position of the upper half is the center, which is respectively connected with the top of the door shaft column, the middle of the door shaft column, the upper corner of the miter column, and the middle of the miter column in a cross shape. Similarly, the centroid position of the lower half is the center, which is respectively connected with the bottom end of the door shaft column, the middle of the door shaft column, the lower corner of the miter column, and the middle of the miter column. The eight back tie rods have the same size and material. The finite element calculation of the gate with the back tie rod under the same conditions shows that the deformation nephogram of the gate, gate shaft column, and miter column is shown in Figure 10, and the maximum deformation of the whole gate and different parts is shown in

Table 3. The maximum deformation of the gate with or without the back tie rod under no external force and self-weight mm.

The Setting of Back Tie Rod	Total Deformation of Gate	Gate Shaft Column				Miter Column
		X	Y	Z	Total Deformation	X	Y	Z	Total Deformation
No back tie rod	186.96	2.8475	−6.639	−2.881	7.7098	2.9945	183.19	−30.752	185.77
Back tie rod	30.219	−0.549	−2.333	−2.825	3.0792	−0.501	29.231	−6.9884	30.05

Note: the “−” in the table only represents the direction.

.

It can be seen from Figure 8 and Figure 10 that under the condition of no external force and self-weight, the deformation trends of the gate with and without the back tie rod are the same. The upper half of the gate body bends downstream, the lower half of the gate body tilts upstream, and the maximum deformation is near the upper corner of the miter column. As shown in Table 3, the maximum deformation of the gate shaft column can be reduced by 60%, and the deformation of the overall gate and miter column can be reduced by more than 80% using the back tie rod. This huge deformation reduction indicates that the back tie rod plays an important role in reducing the deformation of the gate under no external force and self-weight condition.

3.2. State 2

When the door is opened, the gate opens in the water under the action of the hoist. During the opening process, the wind pressure decreases as the opening and closing angles decrease. Take the maximum wind load as an example. The moment the door is opened, the turning trend makes the upstream water pressure resistant. The downstream water pressure is almost zero, mainly due to the water resistance in the opposite direction of the door opening.

As shown in Figure 11 and Figure 12, the upstream water level rises to the navigable water level under static conditions, and the upstream water level is 69 m. The downstream water level is 39 m, and the water level difference is 30 m, resulting in large deformations of the gate, mainly the middle part of the gate shaft column. The deformation gradually decreases toward the edge of the gate. The deformation of the door shaft column primarily occurs in the Y direction, and the deformation in the X and Z directions is small. The gate height is in the range of 12,500–17,500 mm, and the deformation is the largest. The direction is toward downstream.

The same finite element analysis is performed on the gate with back tie rods, and the deformation cloud diagram of the gate, the gate shaft column, and the miter column is shown in Figure 10. The maximum deformation of the gate as a whole and different parts are detailed in

Table 4. The maximum deformation of the gate with or without the back rod in the static state mm.

Back Tie Rod Setting Situation	Total Gate Deformation	Door Shaft Post
		X Direction	Y Direction	Z Direction	Total Deformation
Backless tie rod	276.3	−13.533	275.21	43.005	275.81
With back rod	266.71	−12.431	265.7	40.136	266.23

Note: “−” in the table only represents the direction.

.

It can be seen from Figure 11 and Figure 13 that the overall deformation characteristics of the gate with the back rod and without the back rod and the deformation trend of the door shaft column are similar. The maximum deformation is near the midpoint of the door shaft column, and the primary deformation is in the Y direction. The overall deformation of the gate is centered on the middle of the gate shaft column and gradually decreases toward the edge of the gate. The deformation directs to the downstream. According to Table 4, in the static state, the maximum deformation of the tie rod with the back is 276.3 mm, and the maximum deformation of the tie rod without the back is 266.71 mm, and the deformation is reduced by 3.6%. The deformation effect is small.

3.3. State 3

When the door is opened, the gate opens in the water under the action of the hoist. During the opening process, the wind pressure decreases as the opening and closing angle decreases. Take the maximum wind load as an example. The moment the door is opened, the turning trend makes the upstream water pressure become resistant, and the downstream water pressure is almost zero, mainly due to the water resistance in the opposite direction of door opening.

In the door-opening process, the action direction of water pressure and wind pressure on the gate is opposite. Therefore, as shown in Figure 14, the lower right part of the gate is deformed downstream, and the deformation is gradually reduced around the door body, based on this. It can be seen from the deformation cloud map of the door shaft column and the miter column that the deformation of the door shaft column and the miter column is gradually reduced from the bottom to the top, and the overall deformation of the miter column is relatively large.

Figure 15 illustrates the deformation of the door shaft column and the miter column, mainly in the Y direction. The overall deformation trend is that the amount of deformation gradually decreases from the bottom to the top. The deformation of the door shaft column in the Z direction is less than 3 mm, and the deformation in the X direction is only about 10 mm, which is smaller than that of the miter column. The total deformation of the miter column decreases linearly from the bottom to the top. The deformation in the Y direction is almost the same as the total deformation. The deformation points to the positive direction of the Y axis, while the deformation in the X and Z directions is stable from the bottom to the top. The maximum deformation is 725 mm at the lower corner of the miter column. It can be seen that the lower half of the gate close to the miter column is tilted downstream in the opening condition.

The same finite element analysis was carried out for the gate with the back tie, resulting in the deformation clouds for the gate. The gate shaft post and the diagonal joint post are provided in Figure 16, and the maximum deformation for the gate as a whole and the different parts of the gate are listed in

Table 5. Maximum deformation of the gate with and without a back tie rod in a state of 3 mm.

Back Tie Rod Setting Situation	Total Gate Deformation	Door Shaft Post				Miter Post
		X Direction	Y Direction	Z Direction	Total Deformation	X Direction	Y Direction	Z Direction	Total Deformation
Backless tie rod	730.46	14.704	−34.949	−5.1192	37.922	16.635	720.89	76.159	725.07
With back rod	330.58	6.3417	−14.677	−3.7689	15.998	6.4437	326.8	29.318	328.13

Note: “−” in the table only represents the direction.

.

It can be seen from Figure 14 and Figure 16 that in the opening condition, through the deformation cloud diagram of the gate with or without back tie rod, the addition of the back tie rod has no obvious effect on the deformation trend of the gate. Still, it can effectively reduce the gate in the opening condition—the shape variable. As shown in Table 5, the maximum deformation of the gate is 730.46 mm when there is no back tie rod and 330.58 mm when there is a back tie rod. The deformation is reduced by 55%. At the same time, the maximum deformation of the door shaft column and the miter column is reduced by more than 50%. Hence, the back tie rod has a good effect on restraining the deformation of the gate under the condition of opening.

3.4. State 4

When the door is closed, the gate is closed in the water under the action of the hoist. During the closing process, the wind pressure increases with the increase of the opening and closing angle. Taking the maximum wind load as an example. At the moment of closing, the turning trend makes the downstream water pressure become resistant. The upstream water pressure is almost zero, mainly due to the water resistance in the opposite direction of door closing. As a result, the gate has been warped upstream, which is illustrated in Figure 17. It can be seen from the deformation cloud map of the door shaft column and the miter column that the deformation of the door shaft column and the miter column is gradually reduced from the bottom to the top, and the overall deformation of the miter column is relatively large.

As shown in Figure 18, when the door is closed, the deformation of the door shaft column in the X and Y directions gradually decrease from the bottom to the top, and there is almost no deformation in the Z direction. It can be seen that the deformation of the door shaft column is mainly in the Y direction. The deformation of the miter column in the X and Z directions is almost a constant value. The deformation in the Y direction decreases linearly from the bottom to the top, which is consistent with the trend of the total deformation of the miter column. The deformation points to the negative direction of the Y axis, where the largest deformation lies. It is also at the lower corner of the miter column, and the deformation is greater than 1025 mm. Therefore, the Y-direction deformation of the gate is mainly considered when setting the back tie rod.

The same finite element analysis is performed on the gate with back tie rods. The deformation cloud diagram of the gate, the gate shaft column, and the miter column is shown in Figure 19, and the maximum deformation of the gate as a whole and different parts are provided in

Table 6. The maximum deformation of the gate with and without back lever in the closed state mm.

Back Tie Rod Setting Situation	Total Gate Deformation	Door Shaft Post				Miter Post
		X Direction	Y Direction	Z Direction	Total Deformation	X Direction	Y Direction	Z Direction	Total Deformation
Backless tie rod	1032.9	−21.248	48.881	−1.0649	53.3	−23.458	−1018.8	−114.52	1025.4
With back rod	455.73	−9.2346	19.779	−1.26	21.828	−9.1849	−449.96	−46.911	452.42

Note: “−” in the table only represents the direction.

.

According to Table 6, in the closed state, the maximum deformation of the gate without a back tie rod is 1032.9 mm, and the maximum deformation of the gate with a back tie rod is 455.73 mm. The installation of the back tie rod reduces deformation by 55%. After installing the back tie rod, the deformation in all directions has been significantly reduced. Still, the addition of the back tie rod in the Y direction of the door axis column increases the deformation by 18%, indicating that the back tie rod structure can significantly improve the deformation of the gate in the closed state. However, it has the opposite effect on the deformation in some directions.

4. Conclusions

The herringbone gate is an important part of navigation facilities. Frequent opening and closing will inevitably cause fatigue damage to the gate. Therefore, it is particularly important to improve the torsional rigidity of the gate so that it is always in a state of no deformation or less deformation; adding a back tie rod is currently the primary means of this problem. In the operation process, regardless of the amount of deformation or the direction of deformation under each working condition, the position of the back tie rod and the direction of the pre-tightening force should also be changed according to different working conditions.

This study analyzes the deformation of the gate under different working conditions:

(1)

The herringbone gate has obvious torsional deformation under its weight and when it is suspended freely. The door’s upper half bends to the downstream, and the lower half tilts to the upstream. The demarcation point in the middle is at the gate height of 7500 mm.

(2)

Under static State 1 of the herringbone gate, because the upstream and downstream have water pressure, and the difference is only 0.2 m, the deformation of the gate is not large, mainly in the Y direction, and the deformation is less than 1 mm. However, under static State 2 of the herringbone gate, the water level difference between the upstream and downstream is large, and the deformation in the Y direction is large. The main body of the gate is deformed toward the downstream.

(3)

Under the door opening and closing conditions, the gate is actuated by the push–pull rod and rotates around the door shaft column. The resistance generated by the upstream and downstream water level causes the gate to be deformed greatly in the lower half of the gate close to the miter column when the gate is closed. When the gate is closed, the gate is tilted to the upstream.

(4)

Adding a back tie rod can effectively reduce the deformation of the gate under free-hanging, door opening, and closing conditions, but the effect of reducing the deformation of the gate in a static state is not very obvious. At the same time, under some working conditions, the back tie rod is still. Therefore, it will have an opposite effect on the deformation of the door shaft and increase the deformation. Thus, according to the deformation characteristics of the gate under different working conditions, the back pull rod should be set correspondingly to achieve the effect of reducing the deformation of the gate.