Experimental study on continuous firing vibration response of the typical machine guns under different ground conditions

2.1. Typical machine gun and ground conditions

The selected typical machine gun is shown in Fig. 1. (All images in this paper were taken and produced by the author Liu Hengsha in the experiments involved in this paper).

Fig. 1Typical machine gun

As shown in the figure above, this typical machine gun adopts the air guiding automatic principle. The gun mount is a tripod, and the connection position with the gun body is close to the mass center of the gun body. The distribution of the tripod leg is two in the front and one in the rear, short in the front and long in the rear. The spade is of sled type, which can slide freely in the front and rear directions, and there are horizontal plates to prevent movement in left and right directions.

Position A is the muzzle, and its motion characteristics directly reflect the shooting accuracy. Positions B and C are the front tripod and the rear tripod respectively, which are in direct contact with the ground and reflect the movement characteristics of the gun rack. Position D is the butt of the gun, which together with the muzzle reflects the movement characteristics of the gun body.

Three ground conditions are selected: cement, sand and soil. The cement ground is the ground of the test site, and the sand and soil are packed in sandbags. As shown in Fig. 2.

Fig. 2Ground condition

a) Cement

b) Sand

c) Soil

Among them, the cement is cast cement, which is very hard and the surface is relatively smooth. The sand is dry and loose, the particle volume is very small, and it is easy to slide between each other. The soil is dry and there are agglomerated particles of different sizes. The particles are relatively hard and irregular in shape, and it is not easy to slide between each other.

For cement floors, the tripod is placed on it, and for sand and soil floors, the tripod is inserted.

2.2. Load

The loads in the firing process of a typical general machine gun mainly include the impact of the bolt when it locks, the pressure of gunpowder gas on the breech and gas chamber, and the impact of the bolt on the casing when it recoil. The former mainly causes the forward translation and forward turnover of the gun, followed by the jump of muzzle, and the latter mainly causes the backward translation and backward turnover of the gun.

Among them, the impact force is calculated by the existing simulation, and the breech force and chamber force are calculated by the internal ballistic formula according to the existing internal ballistic parameters.

The lock impact force and recoil impact force in continuous firing are shown in Fig. 3.

Fig. 3Lock impact force and recoil impact force

The breech force and chamber force in each shot are shown in Fig. 4.

Fig. 4Breech force and chamber force

2.3. Measuring method

2.3.3. Data processing

The key parameters are as follows: resolution: 512×384; sampling frequency: 5000 frames / second; Exposure time: 30 μ s.

Calculate the length of each pixel with a scale, get displacement curve. the scale is shown in Fig. 5.

The time interval between every two frames is calculated as 0.2 μs according to the frame frequency.

Calculate the velocity curve of the target according to the displacement and time interval, and take the derivative of velocity curve to get the acceleration curve.

Fig. 5Scale

2.4. Experimental scheme

Three sets of shots are fired under each ground condition. Each group has four spot shots (five shots in a row), and one group has a total of 20 shots. After each group completes shooting, replace the target paper and record. A total of nine groups, 180 shots.

In terms of high-speed photogrammetry, two high-speed cameras are used to shoot muzzle-front tripod, muzzle-rear tripod and muzzle-butt respectively for three groups of shots under each ground condition. Then the displacement and velocity are obtained.

The equipment arrangement is shown in Fig. 6.

Fig. 6Equipment arrangement

The marker points and ruler arrangement is shown in Figs. 7-10.

Fig. 7Location of muzzle marking points

Fig. 8Location of sign points of front tripod

3.1. Motion characteristics of each part

In order to analyze the vibration response of the gun body and tripod more carefully, four position points are selected. Therefore, it is necessary to understand the vibration response form of these four locations and the correlation between them.

Fig. 9Location of rear tripod mark point

Fig. 10Location of butt marker points

Take the results of sand ground conditions as an example to illustrate the displacement and velocity characteristics of muzzle, front tripod, rear tripod and butt, as shown in Figs. 11-14.

Fig. 11Displacement and velocity curve of muzzle

Fig. 12Displacement and velocity curve of front tripod

Fig. 13Displacement and velocity curve of rear tripod

Fig. 14Displacement and velocity curve of butt

On the whole, the displacement velocity curves of each parts show the same trend, different details and different values of displacement velocity. There is a backward offset in the front and rear direction and a downward offset in the vertical direction. The single cycle displacement amplitude in the front and rear direction is between 4 mm and 7 mm, and the maximum speed is between 250 mm/s and 400 mm/s. The single cycle displacement amplitude in the vertical direction is between 1 mm and 3 mm, and the maximum speed is between 50 mm/s and 250 mm/s.

On this basis, the translation and pitching movement of the gun can be analysed by combining the movement of each position point.

3.2. Comparison of gun pitching motion response under different ground conditions

The pitching quasi-periodic motion is the main factor affecting the dispersion of projectile in the vertical direction. Due to the elastic deformation of the gun mount, the pitching of the gun body and the pitching of the gun mount are considered separately. The line between the muzzle and the butt mark points represents the gun body, and the line between the front and rear tripod mark points represents the gun mount. The inconsistency of the pitching degree between the two represents the elastic deformation of the gun mount.

The plane is composed of front-and-back direction and up-and-down direction, and the motion trajectories of each part on the plane is obtained. Compare the different trajectories of each part under different ground conditions, the pitching movement of the gun can be seen. As shown in Figs. 15-18.

Take the single movement trajectories of cement ground as an example, as shown in Fig. 19.

The starting point is from the return of the bolt, the gun translates and Pitch down. Section A is the firing position, and there is a shaking peak at the muzzle, but it fails to change the movement trend of the gun. Section B is the recoil impact position, and the gun starts to translate and Pitch up.

The projection distance between the muzzle and butt marks is 900.1311 mm, and the projection distance between the front and rear tripod marks is 947.0739 mm. The two are similar, so in comparison, the displacement of each part in the up and down direction can be used to characterize the amplitude of pitching motion.

It can be seen from the figure that under the condition of cement ground, in a single firing cycle, the muzzle height movement amplitude in the forward stage is about 0.5 mm, and the muzzle height movement amplitude in the backward stage is about 1.3 mm, and the motion trajectory is mainly above the initial position.

Fig. 15Comparison of muzzle trajectories under different ground condition

Fig. 16Comparison of front tripod trajectories under different ground condition

Analyze the motion trajectory of each part. Under the condition of cement ground, the gun mainly pitch up relative to initial position. The pitching amplitude of muzzle-butt is larger than that of the front and rear tripods, which indicates that the tripod has large elastic deformation. The gun rely more on elastic deformation of the gun mount to counteract pitching motion.

Under the sand ground condition, in a single firing cycle, the muzzle height movement amplitude in the forward stage is about 3 mm, and the muzzle height movement amplitude in the backward stage is about 2.5 mm. The motion trajectory is mainly below the initial position.

Analyze the motion trajectory of each part. Under the condition of sand ground, the gun mainly pitch down relative to initial position. The front and rear tripods also have a large pitching amplitude. It indicates that the deformation of the gun mount is relatively small and the ground deformation is relatively large. The gun rely more on ground deformation to counteract pitching motion.

Under the soil ground conditions, the muzzle height movement amplitude in the forward stage is about 1.5 mm, and the muzzle height movement amplitude in the backward stage is about 1.6 mm. The motion trajectory is both above and below the initial position.

Based on the analysis of the motion trajectories of various parts, under the soil ground conditions, the gun pitch both down and up relative to initial position. The pitching amplitude of the front and rear legs indicates that the deformation of the soil is small, and the gun mount also has elastic deformation. The gun rely on both elastic deformation of the gun mount and ground deformation to counteract pitching motion.

The soil can better prevent the machine gun vibration to the side and forward, and better hold the balance potion of vibration.

Fig. 17Comparison of rear tripod trajectories under different ground condition

Fig. 18Comparison of butt trajectories under different ground condition

3.3. Comparison of translational motion response under different ground conditions

Take the forward and backward movement as an example. The translational motion response is composed of two parts, one is elastic vibration part, and the other is rigid body motion part.

The elastic vibration part comes from the elasticity of the gun mount, the elasticity of the shoulder and the elasticity of the ground. This part offsets the recoil impulse through the elastic vibration. The magnitude of the elastic vibration can be expressed by the vibration amplitude relative to the vibration balance position.

The rigid body motion part comes from the tripod slides relative to the ground, the ground deforms and the shooter's posture changes. The rigid body motion part offsets the recoil impulse through friction and deformation. The value of rigid body motion part can be expressed by the offset of the vibration balance position.

The two are mixed together. Therefore, in order to compare the vibration amplitude under different ground conditions, it is necessary to consider the offset of the vibration balance position before calculating the vibration amplitude.

Fig. 19Concrete. One shot movement trail example

The forward and backward displacement of each part under different ground conditions is shown in Figs. 20-23.

Fig. 20Comparison of muzzle forward displacement

Fig. 21Comparison of front tripod forward displacement

Fig. 22Comparison of rear tripod forward displacement

Fig. 23Comparison of butt forward displacement

It can be seen from the figure that there are two forms of displacement of the vibration balance position, one is a single large displacement, the other is a small number of multiple offsets, and the overall displacement is the result of multiple accumulation. The total offset can be expressed by the distance between the last vibration balance position and the initial position.

The final balance positions of the forward and backward movement displacement of each part under different ground conditions are obtained, as shown in Table 2. The size of the offset in each group of shooting has a certain randomness. The average value is calculated and compared.

It can be seen from the above that in the front and rear directions, the offset of the balance position under the cement ground is the largest, with an average of 6.41 mm, the offset of the sand ground is small, with an average of 4.15 mm, and the offset of the soil ground is the smallest, with an average of –0.085.

Combined with the displacement of vibration balance position, the average value of front and rear motion amplitude of each group under different ground conditions is obtained, as shown in Table 3.

It can be seen from the table that under the sand ground conditions, the average amplitude of elastic vibration in the front and rear directions in the four groups is greater than that under the soil ground conditions.

Under the condition of cement ground, the average value of motion amplitude has great randomness. By comparing the curve, it can be seen that under the cement ground, when the offset of equilibrium position is a large offset, the average value of motion amplitude is lower, and when the offset of equilibrium position is multiple and small offsets, the average value of motion amplitude is larger.

3.4. Comparison of projectile dispersion under different ground conditions

The impact points under different ground conditions are compared, as shown in Figs. 24-26.

Fig. 24Projectile dispersion under cement condition

Fig. 25Projectile dispersion under sand condition

Fig. 26Projectile dispersion under soil condition

Calculate and compare the firing dispersion under different ground conditions, as shown in Tables 4-6.

Shooting dispersion is represented by R50 and R100. R50 refers to the circle radius of the area with 50 % probability of the point of impact, and R100 refers to the circle radius of the area with 100 % probability of the point of impact.

It can be seen from the above table that the projectile dispersion under the cement ground condition is the largest, reaching 20.53 mm, the projectile dispersion under the sand and soil conditions is relatively close, and the soil condition dispersion is slightly smaller, 8.77 mm and 7.92 mm respectively.

In terms of horizontal dispersion, the horizontal dispersion of cement condition is very large, reaching 20.48 mm, and the sand and soil are similar, which are 7.65 mm and 7.44 mm respectively.

In the horizontal direction, the horizontal plate at the bottom of the hoe is mainly used to prevent the horizontal movement of the gun. The horizontal plate has no effect on the cement floor, so its horizontal dispersion is very large. Under the conditions of sand and soil, the translational stability of counteracting lateral movement is close, and sand is slightly better than soil.

In the vertical dispersion, the maximum cement is 6.27 mm, the second is sand, which is 5.88 mm, and the minimum soil is 3.82 mm.

The main factor affecting the vertical dispersion is the stability of gun overturning, which indicates that the stability of overturning motion under the soil ground condition is the best, the sand ground condition is the second, and the cement ground condition is the worst.