The simulation of regular shock wave (e.g., halfsine) can be achieved by the traditional rubber shock simulator, but the practical highpower shock wave characterized by steep prepeak and gentle postpeak is hard to be realized by the same. To tackle this disadvantage, a novel highpower hydraulic shock wave simulator based on the live firing muzzle shock principle was proposed in the current work. The influence of the typical shock characteristic parameters on the shock force wave was investigated via both theoretical deduction and software simulation. According to the obtained data compared with the results, in fact, it can be concluded that the developed hydraulic shock wave simulator can be applied to simulate the real condition of the shocking system. Further, the similarity evaluation of shock wave simulation was achieved based on the curvature distance, and the results stated that the simulation method was reasonable and the structural optimization based on software simulation is also beneficial to the increase of efficiency. Finally, the combination of theoretical analysis and simulation for the development of artillery recoil tester is a comprehensive approach in the design and structure optimization of the recoil system.
In modern shooting range construction process, the consumption was significantly increased due to the real firing practice. Four sorts of capability, that is, reliability, security, testability, and supportability, were the critical aims for the examinations [
With the fast development of hardware and software resource, computational simulation is gradually introduced in the design of fire shock simulation tester. Yangwu innovatively reported the build of a numerical simulation model of artillery recoil system simulator with applying the classical internal ballistics and systematic dynamic related theories [
A further optimization of the simulation model was proposed by Hang and Zhang which considered the load conditions and structure parameters of DSII artillery recoil system [
In shock simulation tests, the shock wave simulator played an important role in energy transferring and conversion. In addition, it could also achieve the recoil simulation of various cannons under various loading conditions with adjusting the structure parameters. For a regular wave test, a rubber shock wave simulator was usually used. However, practical shock wave was a complex shock curve; traditional rubber shock wave simulator was not fit for practical shock wave.
Therefore, in the current work, a novel highpower hydraulic shock wave simulator was proposed to simulate the real shock wave. In the paper, the shock process and working principle were described and optimization design analysis of reasonable shock’s characteristic parameters was achieved. Finally, the similarity evaluation of shock wave simulation was achieved for evaluating the simulation method based on the curvature. The analysis results indicated that the novel highpower hydraulic shock wave simulator could solve the reappearance problem of practical highpower shock wave, which replaced a traditional rubber wave simulator, and also supplied theoretical references for designs of artillery fire shock simulation test.
Breech resultant force
Firing shock simulation test system (shown in Figure
Firing shock simulation test system.
The shock simulation tester used in the firing shock simulation test system was shown in Figure
Shock simulation tester with rubber shock simulator.
Controlling firing rate, firing angle and shock load simulation were realized, which were used to test reliability and durability of the big bore ground and selfpropelled and tank artillery. Hydraulic subsystem drove big mass block with shock wave simulator; then the highvelocity big mass block impacted artillery muzzle and simulated the deflagration effect. The simulations made artillery shock test system generate similar recoil motion with artillery live firing.
Shock and restoration processes were shown in Figure
Shock and restoration process.
The rubber shock simulator was usually used for the regular shock wave reappearance such as a halfsine shock wave. Additionally, practical shock force wave simulating the breech force had the characteristic of steep prepeak and gentle postpeak relatively (dotted line in Figure
Shock simulation system adopted the principle of the momentum transfer; that is, a shock wave simulator with a certain velocity transferred momentum into cannon barrel during the shock, and the large shock force and the shock acceleration were formed on cannon barrel, and the shock wave could be adjusted by the damping and rigidity of the shock wave simulator. Structure sketch of the highpower hydraulic shock wave simulator was shown in Figure
Structure stretch of the highpower hydraulic shock wave simulator.
The inner diameter of the fixed block was 440 mm, and its initial length was 100 mm. The inner diameter of the moving block was 310 mm, and its initial length was 80 mm; there were two throttle holes in the throttle spindle. The piston chambers were fully filled with silicone oil.
The shock wave simulator was accelerated to certain velocity before shock, and then shocking the cannon barrel through the highpower hydraulic shock wave simulator produced instantaneous shock force. During the shock, the moving block moved to the right relative to the fixed block, which led to the oil pressure rise; silicone oil was squeezed to the left side of moving cylinder block through orifice plunger; then isolating piston was pushed to compress Nitrogen for the energy storage. The damping force varied with oil cavity pressure changes.
When an external shock force was applied to the left of the shock wave simulator, the moving block moved toward the right. The oil in the right fixed block chamber was compressed and flew through the throttle gap into the left chamber (as the red arrow shown in Figure
In the highpower shock simulation test, the whole simulation process could be divided into two stages. The sketch of the whole model is shown in Figure
Coupling model for the highpower shock simulation test.
The shock was the first stage; in this process, the rubber pad located on the pounding head of a highpower hydraulic shock wave simulator collides with the canon muzzle and supplies velocity to the cannon barrel and accelerates the canon barrel including recoil buffer device and the cannon suffered shock force from the shock system and the resistance from the recoil system. In the second process, the moving block part will be braked by the damper part of the highpower hydraulic shock wave simulator.
Although the corresponding throttling bar diameters under different recoil displacement are different, throttling bar diameter remains constant.
In conclusion, the force balance equation of the shocked cannon is expressed as follows when firing angle is 0°:
For the shock wave simulator, considering oil compressibility, formula (
Throttling groove adopts slender hole; flow state is laminar flow because the flow is not free when viscous fluid flows through the throttling groove. The flow of slender hole is related to the viscosity of the fluid. The viscosity of oil changes with its temperature.
When the area
Using Matlab/Simulink software, firstly, import into the characteristic parameters
From the building process of mechanical model, the factors affecting shock wave characteristics were mainly divided into three classes: the first class was test parameters including
The influences of typical parameters on the shock force wave were analyzed, and these typical parameters included initial velocity
The influence of initial velocity
Shock force curve of the highpower hydraulic shock wave simulator under various initial velocity
In characteristic parameters, the dynamic viscosity
Shock force curve of the highpower hydraulic shock wave simulator under various dynamic viscosity
Shock force curve of the highpower hydraulic shock wave simulator under various bulk elastic modulus
According to the building process of mechanical model, the bulk elastic modulus
In controlled parameters, the diameter
Shock force curve of the highpower hydraulic shock wave simulator under varying throttle diameter
Shock force curve comparison generated by the highpower hydraulic shock wave simulator and live firing test, respectively.
By the optimization design analysis of typical shock parameters, a set of reasonable shock parameters were received as shown in Table
Main shock parameter list.
Main shock parameter 








Value  3000  2540  15  0.5  800  0.08  0.27 
The throttle diameter
The shock force wave was simulated adopting the optimized shock parameters in Figure
The simulation curve was similar to the test curve under the live firing. It was indicated that the above mathematical model had good precision by optimization and correction of numerical simulation tests under various working conditions, and the highpower hydraulic shock wave simulator adopting the optimized shock parameters realized the shock wave reappearance of the shock force on artillery muzzle in the live firing test.
Using the above data, similarity evaluation was carried out for the simulation method based on the numerical similarity and shape similarity.
Assume that the test data consequence was
When
The shape similarity was calculated according to the curvature distance between the two time sequences [
Firstly, primitive sequence
Nonnegative subsequence was generated according to AGO (Accumulated Generating Operation), and the consequence presents approximate exponential increase law, which decreased the randomness, possessed statistical significance, and kept the relevance of primitive consequence. Nonnegative subsequence
We can get
For increasing the fitting model accuracy of time consequence, the subsequence
Assume that the curvature of each section in time consequence was
Assume that the curvatures of the two time consequence were
The curvature distance of subsequences
Numerical similarity and shape similarity were, respectively, calculated based on the two time consequences. Based on the multiattribute integrated evaluation theory, we use multiplication relationship to obtain comprehensive similarity.
So the comprehensive similarity of
In cannon recoil motion process, recoil time consequence was divided into recoil section and counterrecoil section. Recoil section was from original point to displacement peak point; counterrecoil section was from displacement peak point to the end point. In recoil section, cannon motion velocity was high and had serious vibration and the maximum velocity existed in the section; cannon motion velocity was low and had small vibration. The weights of recoil section and counterrecoil section were, respectively, 0.67 and 0.33.
The two long subsequences were divided into multiple short subsequences. The length of each short subsequence was 8; numerical similarity and shape similarity of each short subsequence were calculated by the above method; then the numerical similarity and shape similarity of each long subsequence and the total consequence were calculated. Using the data in simulation, the integrated similarity of the shock wave was calculated as in Table
Similarity of shock wave simulation.
Subsequence 1  Subsequence 2  Total consequence  

Numerical similarity  0.95  0.78  0.894 
Shape similarity  0.92  0.73  0.857 
The evaluation result indicated that the highpower hydraulic shock wave could simulate the dynamic process of live firing accurately. Therefore, the optimization of shock characteristic parameters could improve the simulation accuracy.
Theoretical analysis and numerical simulation result analysis demonstrated that the highpower hydraulic shock wave simulator could be adopted for simulating the shock force generated on the artillery muzzle; the similarity evaluation of shock wave simulation indicated that high similarity existed between the shock force in simulation test and the practical shock force in live firing test. In other words, the simulation method was reasonable. Finally, the analysis supplied references for the utility of artillery fire simulation technology. The novel highpower hydraulic shock wave simulator replaced a traditional rubber wave simulator to realize practical highpower shock wave reappearance, which also supplied references for the artillery dynamic recoil simulation test.
The authors declare that there are no conflicts of interest regarding the publication of this paper.