Determination of ship shaft system torsional natural frequencies by Holzer method algorithm

The vessels are designed in such a way that they can keep their navigation tasks safe for many years, depending on the working conditions. In this context, it is very important that all the propulsion system components between the main engine and the propeller moving to the ship operate with high performance, stable and undamaged. If the torsional natural frequencies of the shaft system are close to the working speed of the main machine, the elements on this system are exposed to vibratory high angular displacements. As a result, high stresses on the rotating elements cause unexpected damage to these elements. This type of damage that can be encountered in the propulsion system while in the open sea causes great financial loss to the operators. Therefore, the shaft systems are an important part of the design process of the torsional vibration analysis of the shaft systems against the natural frequency probabilities that can occur at the operating speeds. Unexpected damages that may be encountered in the propulsion system, especially when the vessels used for freight transport are in the open sea, cause great loss of business for ship operators. The main causes of these losses are the delivery of the damaged ship by an auxiliary vessel from the open sea to the port, the compensation to be paid as a result of the transported cargo not being delivered in time, the shipyard costs for repairing damaged equipment and being the away from commercial duty for the ship. For this reason, it is necessary to calculate the torsional vibration of the system against the resonance vibrations that may occur in the shaft system while it is still in the design phase, and to avoid the natural frequencies that can be found at the working cycle. For this reason, in this study, it is aimed to develop an algorithm which can be used globally by using the classical approaches applied to the calculation of torsional natural frequencies and mode shapes of ship shaft systems. This algorithm is written using the Holzer method, which enables fast, easy and accurate results in multi-mass systems. In this respect, it is aimed to present a solution to the vibration problems that can be encountered before the shaft system is manufactured with the help of modern engineering tools and to present it to the manufacturer of a cheap solution that will shorten the design process. In the study, firstly, the general information about the ship propulsion system and ship vibrations is given and then the usage of Holzer method and the tabulation procedure are explained on simple structures. As a second step, the methods of reducing the complicated ship propulsion system components to the dynamic equivalent models in accordance with the Holzer method usage are described. In the next stage, as the main purpose of the study, the utilization procedures of the Holzer algorithm written in MATLAB mathematical calculation program are introduced. All subsequent chapters have been carried out on the basis of step-by-step proof that the calculations made by the algorithm are healthy. In this context, the torsional natural frequency analysis results of the written algorithm are compared with; i. For a two-mass sample system with the analytical method results, ii. For a three-mass sample system with the analytical method results, iii. For a four-mass sample system with the fem software ABAQUS results, iv. For a multi-mass sample system with the ABAQUS software results, v. For a geared sample system with the ABAQUS software results, and reliability of the algorithm has been confirmed. As a result of all the comparisons made, the Matlab Holzer algorithm proved to have a healthy outcome. Therefore, it has been demonstrated that the torsional natural frequency calculation of a real ship propulsion system, which is a representation of a multi-mass system, can be performed by only a written algorithm without the need for a method or software of another method. In this context, the torsional natural frequencies and mode shapes of the two different ships, one of which is a large oil tanker with a linear (non-geared) propulsion system and the other is a small passenger ship with a geared propulsion system, are determined by the Matlab algorithm written. The results obtained were compared with shipboard manufacturers' torsional vibration calculations (TVC). In the last part, an optimization study has been carried out regarding the displacement of natural frequencies that can be located in a critical region of a system. Since changing the flywheel weight or coupling flexibility is a frequently used method of frequency shifting, therefore it is added a section that can do flywheel and coupling optimization in the algorithm in a practical way. After requesting critical range inputs from the user for the optimization analysis, the algorithm performs a series of iteration operations and automatically shifts the natural frequency in the dangerous range by stepping through the flywheel coupling flexibility (according to user preference). When the natural frequency passes to the safe zone, the optimized flywheel mass / coupling flexibility is presented to the user. As a result of the analysis studies and the optimization studies that have been made during the whole study, it can be seen that this algorithm written in Matlab can be used in torsional natural frequency analysis of both linear and reducible ship shaft systems. And also by using flywheel and coupling optimization with vibration problems that can be encountered before the shaft system is manufactured. Moreover, this algorithm which can make flywheel and coupling optimization can provide a fast, convenient and inexpensive solution to the users.