# Analysis of the stress direction of the gear rack of the Three Gorges ship lift

There are two possibilities for the design water depth to be higher or lower than 3.5m in each ascending or descending motion. In this case, there are many changes in the force tooth surface and the force magnitude of the rack.

#### 1. Force bearing tooth surface of ship cabin when it moves upward

If there is positive water depth of false load, when the cabin moves upward, because the cabin mass is greater than the mass of the balance weight, the rack will exert an upward force on the shaft gear integrated with the cabin to overcome the resistance and push the cabin up. At this time, according to the relationship between the force and the reaction force, the upper gear surface of the rack bears a downward load, as shown in Figure 2A, The motor is now in drive mode.

If there is a small negative water depth, and the unbalanced gravity between the balance weight and the gravity of the cabin is not enough to overcome other running resistance (such as friction, wind), the upper tooth surface of the rack will still bear a downward load, and the stress condition of the rack is the same as the above situation.

If there is a large negative water depth, the gravity of the balance weight will be greater than the sum of the gravity of the cabin and other resistances. When the cabin moves upward, the balance weight will pull the cabin by the wire rope to accelerate together. In order to achieve the average speed and deceleration movement, the rack needs to exert a downward force on the shaft gear. At this time, the lower gear surface of the rack will bear an upward load, as shown in Figure 2B, At this time, the motor shall be in braking mode.

#### 2. Force bearing tooth surface when the ship box moves downward

If there is a large positive water depth of false load, when the cabin moves downward, because the weight of the cabin is greater than the sum of the weight of the balance weight and other running resistance, the cabin will pull the balance weight through the steel wire rope to accelerate the movement together. In order to achieve the average speed and deceleration movement, the rack needs to exert an upward force on the shaft gear, and the upper gear surface of the rack will bear a downward load, As shown in Figure 2c, the motor is in braking mode.

If there is a negative water depth of false load, the balance weight will be greater than the gravity of the cabin. When the cabin moves downward, the rack needs to exert a downward force on the shaft gear, and the lower tooth surface of the rack will bear an upward load, as shown in Figure 2D. At this time, the motor is in the driving mode.

If there is a small positive water depth of false load, when the unbalanced gravity between the cabin and the balance weight is not enough to overcome other running resistance (such as friction and wind), the lower gear surface of the rack will still bear an upward load, and the stress condition of the rack is the same as the above situation.

## Conclusion

(1) The gear rack device of the Three Gorges ship lift adopts the fully balanced vertical lifting mode. When the ship lift works, the weight of the equipment on the ship’s cabin, the ship and the 3.5m deep water body in the cabin are completely balanced by the same weight of the balance weight. The load on the rack is mainly related to the unbalanced weight caused by the water depth of the wrong load, which is basically irrelevant to the quality of the equipment.

(2) The direction and magnitude of the load on the rack are related to the positive and negative directions and magnitude of the water depth of the false load. When the ship lift works normally, the motor shall be in the driving mode as far as possible, that is, the upper tooth surface of the rack is stressed when it rises, and the lower tooth surface of the rack is stressed when it falls. In order to achieve this kind of working state, it is necessary to avoid large negative water depth and large positive water depth when the ship lift rises.

(3) The load of the gear rack of the ship lift consists of four kinds of loads: the water depth of the false load, the vertical wind force, the friction force and the acceleration force. Under the normal working condition of the ship lift, the force tooth surface and load of the rack are related to four working conditions, i.e. the moving direction of the ship box (ascending or descending), the water depth of the false load, the vertical wind direction (downwind or headwind) and the speed change (accelerating, uniform or decelerating). According to the different combinations of four working conditions, there are 24 kinds of stress conditions on the rack tooth surface when the ship lift rises and falls, among which 15 kinds of stress conditions are on the upper tooth surface when it rises and 15 kinds of stress conditions are on the lower tooth surface when it falls.

(4) The maximum load on the rack tooth surface of the ship lift appears under the conditions of + 10 cm water depth, headwind and acceleration when it rises; and under the conditions of – 10 cm water depth, headwind and acceleration when it falls. From the four types of load values, the load caused by the water depth of false load accounts for 52.4% of the maximum load. When the ship lift is running, by controlling the direction and size of the water depth of the false load reasonably, it can achieve the purpose of controlling the force direction of the rack and effectively reducing the load size, which is of great significance to ensure the safe and reliable operation of the ship lift and prolong the life of the rack and pinion of the ship lift.

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