Strength Analysis of the Marine Weapon’s Construction

DOI 10.17818/NM/2021/3.4 UDK 623.8./.9 :621.8 Preliminary communication / Prethodno priopćenje Paper accepted / Rukopis primljen: 12. 3. 2021. Stanisław Milewski Navigation and Naval Weapons Faculty Polish Naval Academy Gdynia E-mail: s.milewski@amw.gdynia.pl Bogdan Szturomski Mechanical and Electrical Engineering Department, Polish Naval Academy Gdynia E-mail: b.szturomski@amw.gdynia.pl Radosław Kiciński Mechanical and Electrical Engineering Department, Polish Naval Academy Gdynia E-mail: r.kicinski@amw.gdynia.pl


INTRODUCTION / Uvod
The design and construction of weapons are the subjects of interest and activity of many research and industrial centres worldwide [1]the density of which would be close to the lead density 11.3 Mg/m3. This material should also meet the requirements for ammo bullet cores. In order to check... ", "containertitle":"Advances in Science and Technology. Research Journal", "DOI" :"10.12913/22998624/115515", "ISSN":"2080-4075, 2299-8624", "issue ":"1", "journalAbbreviation":"Adv. Sci. Technol. Res. J. ", "language":"en glish", "note":"publisher: Polish Society of Ecological Engineering (PTIE. For various reasons, it is in the Armed Forces' good to have domestic-made weapons. In Poland, an example of such action is, among others, the prototype of the 35 mm Ship Weapons System (OSU-35), which was designed and built as a result of the implementation of a development project co-fi nanced by the National Center for Research and Development (NCBiR) [2]. Ultimately, the OSU-35 set is dedicated to the Polish Navy as the primary artillery armament of the Kormoran II minehunter. The main purpose of OSU-35 is a direct defence of a ship against lightly armoured air, surface, and shore threats.
The 35 mm Ship Weapon System consists of four autonomous modules: Integrated Tracking Head (ZGS-158M), 35 mm KDA type naval cannon, Multifunctional Operation Console (marked in the system as P-SKO), columns for mounting reserve gun sights -marked in weapon system as R-SKO (Fig.  1). The sea cannon, which is part of the OSU-35, is its primary element and is designed to fi re 35 mm FAPDS-T and TP-T artillery shells. The Fire Control System developed the gun settings based on data on target movement location and factors in the primary type of work. Those data are obtained from the ZGS-158M tracking head and other, determining shooting conditions -obtained from a multi-sensor data collection system, included in the system, e.g ., an artillery weather station, an IMU (Inertial Measurement Unit) cannon position sensor or a projectiles counter. The operator controls the system's operation using the console equipment interface (P-SKO) and dedicated software containing, among others, the Fire Control algorithm (KO) and the cannon condition control algorithm.
If a ZGS-158M or P-SKO failure fails, it is possible to operate the defence system in the backup type of work with a preliminary target indication for the ZGS-158M. The guidance and fi re control of the 35 mm cannon can also be carried out using the R-SKO operated manually by the operator. The direction of the fl ow of control signals in both system operation types is illustrated in Fig. 1.
During the project implementation, the ORP KASZUB warship was dedicated and used to test the OSU-35 prototype. It is a missile corvette that has been in the forces of the Polish Navy since 1987. The ship was built at the Northern Shipyard Heroes of Westerplatte in Gdansk. It is designed to search for and destroy submarines. The ship can protect teams of landing ships, transport, and other ships. The ship is adapted to operate in the Baltic Sea and the North Sea's meteorological conditions, with the possibility of sailing on crushed ice [3].
The installation and testing of the OSU-35 functionality on the ship confi rmed that one of the foremost tactical and technical requirements was met-the requirements related to the designed weapon system's autonomy, modularity, and scalability. As a result, it is possible to adapt it to various ships, both newly built and modernized, with diff erent operating conditions [4].

DESIGN OF THE SHIP'S WEAPON SYSTEM / Dizajn brodskog sustava naoružanja
Apart from the basic tactical requirements, each weapon system must meet several technical needs resulting from the operating conditions installed onboard the ship. Technical assumptions and standards [5,6]"issued":{"date-parts": [["1976"]]}}}], "schem a":"https://github.com/citation-style-language/schema/raw/ master/csl-citation.json"} defi ne the permissible values of mass and dimensions parameters and features, ensuring ergonomic and safe operation of the system on a limited area, such as the ship's deck. Due to its large dimensions and signifi cant weight of 675 kg [7], the system's crucial element is the 35 mm KDA gun. The gun was placed on a unique steel structure that uses servos for the gun guidance and control signals developed by the fi re control system. Additionally, for operation in the marine environment, the gun has a housing made of composite. Fig. 2 shows a photo of the 35 mm cannon that is part of the OSU-35 prototype mounted on the ORP KASZUB warship.
The gun consists of two primary assemblies: the foundation and the rotating unit (Fig. 3). The foundation is a fi xed part of the cannon mounted to the ship's deck in which a power supply and control blocks and safety elements are placed. The top surface of the foundation, on which the monoblock bearing with a toothed ring has been built, constitutes the rotary unit's mounting surface.
The rotary unit structure consists of the upper and lower cradles, which are mounted: a pivot assembly with a cradle, KDA artillery automatic machine, lifting control system, ammunition supply systems, and accessories and actuators enabling maintenance-free and automatic operation of the cannon. For the cannon assembly on the ORP KASZUB ship, the concept of a rotary unit on a foundation was adopted, the corners of which are attached to properly prepared mounting sockets on the deck. The cannon structure must meet several strength requirements under various load conditions. The variety of loads results from the needs of operation at sea and combat operations. All devices installed on the ship are exposed to shock eff ects caused by, e.g. non-contact explosion of a mine or torpedoes in the water. This approach is also defi ned by standards [5,6]"issued":{"date-parts":[["1976"]]}}}], "schema":"htt ps://github.com/citation-style-language/schema/raw/master/ csl-citation.json"} . Due to the project's prototype nature, the fi nite element method implemented in CAE programs was used to analyze the strength of the cannon structure.
Since there is no ready solution to mounting the ship's armament system, it was necessary to refer to the technical requirements based on defence standards and regulations of classifi cation societies such as PRS (Polish Register of Shipping), DNV (Det Norske Veritas), etc.

DISCRETIZATION OF THE WEAPON SYSTEM STRUCTURE / Diskretizacija strukture sustava naoružanja
The task was calculated using the Abaqus CAE software. The problem was solved by loading the gun with inertia forces from the set accelerations (d' Alembert forces), taking into account the materials' plastic characteristics the gun components. Mainly linear quadrilateral 4-node and triangular 3-node triangular elements and 8-node and tetragonal 3-node tetragonal solid elements in critical places were used. In total, the model consisted of 84,459 elements.
For numerical simulation purposes, individual parts of the cannon structure have been represented as shell and solid models [8][9][10][11]. During the geometry creation, appropriate geometric simplifi cations of the details were applied that do not aff ect the structure's overall strength. These parts were divided into linear triangular and rectangular shell elements and tetragonal and hexagonal solid elements fi rst-order elements. The components prepared in this way, using connectors and interactions, were combined into subassemblies intended for further, comprehensive analysis (Fig. 4).

SHIP'S WEAPONS SYSTEM STRUCTURE LOAD / Opterećenje strukture brodskog sustava naoružanja
To determine the distribution of reduced stresses in the analysed gun assembly structures, one should refer to a given reference load. When considering marine armaments' operation, one should refer to the worst possible variant: the load caused by a non-contact underwater explosion. [12,13]. An explosion is a violent combustion process with pressure build-up in fractions of a millisecond [14][15][16][17]. The nature of this process is determined by the dynamic conditions in which the explosive mixture is located, particularly the turbulence of the medium. Pressure waves, called shock waves, occurring during an explosion in liquids (underwater explosion) or solids, can reach up to 8000 m / s in the case of detonation. The expanding gas bubble acts on the surrounding water layer creating a spherical shock wave. In the initial phase, during detonation, this wave travels at a speed of v ≈ 5000 -8000 m / s [18]. Then the water molecules act on the adjacent water layers losing velocity and move further at the speed of sound in the water, which is approximately every ≈ 1500 m / s. Many researchers have described the pressure wave profi le and its value. The main one is R.H. Cole, whose publications form the basis of much research on the subject. The problem is also described by other authors [13,[19][20][21][22]. The criterion for the division of the degree of threat is also blurred, as described in work [23]and thousands of service members and civilians were injured or killed by underwater blast during WWII. The prevalence of underwater blast injuries and occupational blasting needs led to the development of many safety standards to prevent injury or death. Most of these standards were not supported by experimental data or testing. In this review, we describe existing standards, discuss their origins, and we comprehensively compare their prescriptions across standards. Surprisingly, we found that most safety standards had little or no scientifi c basis, and prescriptions across standards often varied by at least an order of magnitude. Many published standards traced back to a US Navy 500 psi guideline, which was intended to provide a peak pressure at which injuries were likely to occur. This standard itself seems to have been based upon a completely unfounded assertion that has propagated throughout the literature in subsequent years. Based on the limitations of the standards discussed, we outline future directions for underwater blast injury research, such as the compilation of epidemiological data to examine actual injury risk by human beings subjected to underwater blasts. ", "containertitle":"Diving and Hyperbaric Medicine", "ISSN":"1833-3516", "iss ue":"3", "journalAbbreviation":"Diving Hyperb Med", "language": "eng", "note":"PMID: 26415071", "page":"190-199", "source":"PubM ed", "title":"Underwater blast injury: a review of standards", "titleshort":"Underwater blast injury", "volume":"45", "author":[{"famil y":"Lance", "given":"Rachel M. "},{"family":"Bass", "given":"Cameron R. "}], "issued":{"date-parts": [["2015",9]]}}}], "schema":"https://github. com/citation-style-language/schema/raw/master/csl-citation. json"} . Since the explosion is an unpredictable phenomenon, individual countries refer to the standards [5,6]"issued":{"dateparts":[["1976"]]}}}],"schema":"https://github.com/citationstyle-language/schema/raw/master/csl-citation.json"} . As the explosion acts directly on the ship's hull, it is necessary to apply an equivalent load in the form of a kinematic input to the gun base. The deck on which the gun rests has been modelled as a perfectly stiff body, with appropriate accelerations. In the case of structures intended for use in the Polish Navy, the inputs are the appropriate acceleration values described in [5]. According to the standard, it is assumed that for devices rigidly fi xed to the foundation with a mass m > 200 kg, the shock acceleration graph has the shape of a full sinusoid or an unsymmetrical sine wave. The maximum acceleration of a symmetrical sinusoidal pulse shall be calculated from the formula: Additionally, according to the standard, the following designations of the directions of the coordinate system are assumed: -x -the direction determined by the intersection of the waterplane plane and the planeship symmetry (along with the ship); -y -the direction determined by the intersection of the waterplane plane and the midships plane the ship (across the ship); -z -the direction determined by the intersection of the midships plane and the symmetry plane of the ship (vertically). However, depending on the place of installation, the device is divided into three groups: -A -devices at the level of the second bottom and bulkheads near their centre, not closer than 2 m from the side; -B -devices on the ship's sides and underwater decks as well as on bulkheads within a distance of 2 m from the side; -C -equipment on decks, platforms, superstructures and masts.
Depending on the device's location and the direction of the impact, the specifi ed acceleration values should be multiplied by an appropriate factor (Tab. 1). The arms inspectorate, based on the standard, determined the parameters which are respectively (Fig. 5): -a x = 85 m/s 2 during 10 ms -along the ship's axis a y = 250 m/s 2 during 8 ms -transversely to the ship's axis a z = 500 m/s 2 during 5 ms -vertical Calculations should be performed in the time interval equal to 0 ÷ 0.04 s (40 ms).

MECHANICAL PROPERTIES OF OSU-35 CONSTRUCTION MATERIALS / Mehanička svojstva OSU-35 konstrukcijskih materijala
The structural elements of the weapon system are made of various materials. These are steels of higher quality, construction steels, non-ferrous metal alloys, plastics, composites, etc. [2]. For CAE strength calculations, it is necessary to know the mechanical properties such as density, Young's modulus, Poisson's ratio, yield point and strength. To obtain those data, a series of static tensile tests were performed. For the simulation, plastic characteristics of materials were determined, which were described by constitutive equations presented by the simplifi ed (neglecting the temperature term and strain rate) Johnson-Cook equation [24]: (1) where: A, B, n -material constants; σ pl -plastic stress; ε pl -plastic strain.
Due to the project's military (classifi ed) nature, the results of all tests and material models used cannot be presented in this article. An example of the characteristics of one of the materials used (high-quality steel) is shown in Fig. 6.

CONSTITUTIVE EQUATION / Konstitutivna jednadžba
Under certain operating conditions, the weight of the machines may constitute a dangerous load on the structure. Machine elements always work in the fi eld of gravity. Thus they are loaded with their weight. This load is constant and can be ignored for many static problems. In dynamic situations, where machine elements experience signifi cant acceleration values, mass loads can lead to failure in improperly designed structures. The leading cause of high-value accelerations is shock loads caused by a sudden change in speed resulting from a collision with another object or the impact of a pressure wave generated by an explosion. In the analysed case, the acceleration source is the eff ect of the pressure wave from the non-contact explosion of an underwater explosive charge, e.g. a sea mine, torpedo, etc. The source of acceleration is rotation. Rotating machine elements, such as the ship's propeller shafts, rotors of electric motors, crankshafts, connecting rods of combustion engines, gas turbines, and many other devices, reach speeds of up to tens of thousands of revolutions per minute. During rotation, machine elements are in the fi eld of centrifugal forces, represented by average acceleration [10]: (2) where: -components of linear accelerations; ω -angular velocity vector; r -radius vector.
According to the above equation, the mass (centrifugal) loads depend not only on the value of the angular velocity ω, but also on the distance from the axis of rotation r. For this reason, in large-size structures, in elements extremely distant from the axis of rotation, relatively high values of centrifugal acceleration may occur, even at low speeds. Such an object is a ship that heels, heave and pitch due to the sea waves that lead to rotation about all three axes. In practical analyses where the occurring accelerations or the speed of rotating machine elements is constant, especially where the axis of rotation is constant and the rates are fi xed in time, a static problem is solved. There is then a complete analogy between fi xed rotation and uniform rectilinear motion. The load is, therefore, the mass and centrifugal forces added to the static loads.
Besides, the task considers the plastic characteristics of materials and large deformations, which aff ect the constitutive equation. The constitutive matrix equation then takes the form [10,12]: (3) where: M -mass matrix; -nonlinear stiff ness matrix taking into account plastic properties of materials and deformations; U -displacement vector; F -load vector.

FEM SIMULATION RESULTS / Rezultati FEM simulacije
Several simulations using the explicit dynamic method were carried out following the methodology's load [5]. The states of displacements, strains, stresses, and motion parameters were obtained. The Polish defence standard does not specify precise endurance guidelines. Other standards allowing the use of FEM for the analysis of this type of structure was used. According to the shipbuilding regulations for Bundeswehr 0430 (Schocksicherheit Experimenteller und rechnerischer Nachweis für Überwasserschiff e und Uboote), the stresses due to shock loading must not normally exceed the static yield point. Only where limited plastic deformation of the foundation does not aff ect the device's effi ciency, the theoretical stress may exceed the static yield point. So, the Huber-Mises-Hencky (HMH) reduced stresses [24] is the most crucial parameter. The extreme  Fig. 7.
Based on the simulations, it was found that the geometry was modelled correctly because the load was transferred to all structural elements. Moreover, most elements of the cannon structure can withstand the given load. Particular attention should be paid to the gun bed, as it is exposed to the highest loads. Mounting the cannon to the ship's deck should withstand the designed load. Other observations concerning the cannon construction cannot be disclosed due to the military nature of the work. However, they were used to modernize the cannon structure, making it more resistant to loads caused by the non-contact explosion.
Another important aspect is the acceleration values in the construction of the cannon. The reaction of the model base on the kinematic excitation caused by acceleration is shown in Fig. 8. The fi gure shows that in the initial phase, the load and the structure response coincide, however, after about 1 ms, the base acceleration decreases, and then its value above the set value increases due to inertia cannon construction. Then the accelerations in the base oscillate according to the vibration theory [25] and approach zero. The acceleration wave in the structure did not manage to return to the bottom in the considered loading time of 40 ms.
From the results of the calculations, it was noticed that in the middle of the height of the armament system, there is an accelerations concentration caused by the kinematic load accumulation from the inertia structural response forces. At this point, the resonance causes the acceleration values to be even several times greater than in the load. The above thesis is also confi rmed by the location of the node where the greatest displacements were noticed. Fig. 9 shows the displacements of the base and displacements in the node. The diagram shows that this node moves in the direction opposite to the acceleration in the initial phase, which is the result of the mass inertia of the gun.