On problem of calculating longitudinal vibrations of piston engine crankshaft

One of the initial stages of calculating the crankshaft longitudinal vibrations is developing an oscillatory system model, which includes the determination of longitudinal pliability (rigidity) of elastic sections. If it is impossible to determine the pliability experimental, the empiric formulas or the final element method (FEM) are used. There are given the values of crank longitudinal pliability of the crankshafts of different marine engine types found by using the formulas of L. Gugliemotti – R. Machciotta, P. Draminsky, E. Y. Gorbunov, S. F. Dorey, N. S. Skorchev, V. S. Stoyanov, etc. It is shown that the calculation results obtained from these formulas for the same engine significantly differ; therefore, the choice of one or another empirical formula for practical calculations is difficult. The preference of using FEM for determining the longitudinal (axial) compliance of cranks and other areas with complex geometric shapes has been proven. The possibility of its application is also shown to determine the longitudinal disturbing force as the reaction of the crankshaft support against the action of the radial force exerted to the connecting rod journal. It is proposed to use, along with empirical formulas, regression equations connecting the longitudinal compliance of the cranks with a significantly larger number of their design dimensions.

Improving the Dynamic Characteristics of Precision Lathes Used in the Repair of Agricultural Machinery

A model of a friction unit of a lathe in the form of a thin layer of material of a honeycomb structure is described to determine the dynamic characteristics of a movable carriage to guide joint. The analysis of the mathematical model of friction for different sliding pairs with varying load and sliding speed is performed. It is shown that the presence of an abrasive impurity in the lubrication of the guide enhances the effect of the low-frequency component of the carriage vibrations on the dynamics of the machine tool and the presence of pockets for retaining the lubricant in the joint of the guide makes it possible to reduce the amplitude of the longitudinal vibrations of the carriage to 30-50 %.

Determination of the variable density of the rod from natural frequencies of longitudinal vibrations

Rods of various configurations are elements of many structures and machines. Therefore, the acoustic and vibration diagnostics of such parts has been widely developed. The paper considers the problem of determining the variable density of the rod from the natural frequencies of longitudinal vibrations. It is assumed that the density changes along the axis and is described by a polynomial function. This approach allows one to determine the law of density variation from a finite set of eigenvalues. The results of the study can find applications for finding hidden defects in steel and composite rods, which arise during the production process or due to corrosion.

Influence of dynamic properties on scaffoldings safety

Scaffoldings are used for works at height and in places that are hard to reach, which makes such works dangerous to employees and accidents occur frequently. Loads generated by scaffolding users cannot be avoided. Moving workers excite low-frequency (1–2 Hz) vibrations and scaffoldings as slender structures are prone to such dynamic action. The method for determining the probability of vibrations excitation is presented here. The quantity representing this probability is called the predictor of occurrence of a dangerous situation due to vibrations induced by a walking employee. The predictor of resonance with ith natural frequency requires an analysis of the scaffolding dynamic behavior. The frequencies and the natural mode shapes of vibrations were determined. Numerical dynamic simulations of the worker's movement on the penultimate decks of two scaffoldings were carried out, as well. Predictor analysis was made for single frequencies and combinations of frequency pairs. The predictor values calculated for the first frequency or combinations with it are the highest ones, however the probability of resonance is not only affected by the first frequency. To improve safety, the natural frequencies should be increased. For longitudinal vibrations, this can be done by adding more bracing or reducing lengths of anchors. Increasing the number of anchors gives good results in both directions. During scaffolding design of both typical and atypical constructions, one must determine the natural frequencies and then, if the first natural frequency is less than 4.0 Hz, perform a dynamic scaffolding analysis.

Ship control in storm conditions

Приведены выражения для определения периодов собственных поперечных и продольных колебаний судна, как точные, так и приближённые, но в тоже время достаточные для их практического использования на судне. Представлены формулы для расчёта поперечной метацентрической высоты после принятия груза судном перед выходом в море. Выведены формулы для определения критических зон резонансной качки по крену и дифференту, как по скорости судна, так и по курсовому углу по отношению к направлению распространения штормового волнения моря. Представлены формулы для определения кажущегося периода встречи судна с волной, которые являются основой для расчёта резонансных зон. Выведенные соотношения для определения зоны резонанса по скорости судна при заданном курсовом угле и по курсовому углу при заданной скорости судна представлены при условии известного периода штормового волнения моря и курсового угла судна по отношению к направлению распространения волнения моря. Приведены формулы для определения амплитуды качки в условиях резонанса, если отношение периода собственных колебаний судна к кажущемуся периоду волны находится в пределах 0,7 – 1,3. Представлены выражения для определения амплитуд качки по крену и дифференту, вызывающие морскую болезнь у персонала, а также критические значения боковых перегрузок, влияющих на правильность его действия. Expressions for determining the periods of the natural transverse and longitudinal vibrations of the vessel, both exact and approximate, are given, but at the same time sufficient for their practical use on the vessel. The formulas for calculating the transverse metacentric height after the cargo has been accepted by the vessel before going to sea are presented. Formulas are derived for determining the critical zones of resonant pitching in terms of roll and trim, both in terms of the ship's speed and in the heading angle in relation to the direction of propagation of storm waves of the sea. The formulas for determining the apparent period of the ship's meeting with the wave are presented, which are the basis for calculating the resonance zones. The derived relations for determining the resonance zone by the speed of the vessel at a given heading angle and by the heading angle at a given speed of the vessel are presented under the condition of a known period of stormy sea waves and the heading angle of the vessel in relation to the direction of propagation of sea waves. Formulas are given for determining the amplitude of pitching under resonance conditions if the ratio of the period of natural oscillations of the vessel to the apparent period of the wave is within 0.7 - 1.3. Expressions for determining the amplitudes of roll and pitch that cause motion sickness in personnel, as well as the critical values of lateral g-forces that affect the correctness of its action, are presented.

Experimental and numerical investigations on longitudinal vibration of suspended monorail trains induced by bogie pitching motion

The longitudinal harmonic vibrations found in the suspended monorail train (SMT) seriously affected the ride quality and dynamic behaviour. In this work, the experimental and simulated analyses are carried out to reveal the essential phenomenon, occurring mechanism and possible solutions to this issue. Firstly, the ride quality and vibration transmission of the tested SMT system are investigated. It is found that the longitudinal vibrations with the frequency of 2.7Hz occur to the carbody, bogie frame and suspension of the train system. Due to the secondary suspension is lower than the gravity center of the bogie frame, the bogie pitch motion with low damping ratio can be easily excited. The longitudinal components of the bogie pitch motion will transfer to the carbody and wheelset through traction rod and primary suspension, respectively. After that, the multibody dynamic model of a suspended monorail train is developed. Based on the numerical model, some parametric simulations, e.g. rubber stiffness, traction rod height and secondary damping, etc., are carried out to propose solutions to relieve the longitudinal vibrations. Finally, the field tests for the SMT arranging the longitudinal dampers are conducted to verify its improvement to longitudinal vibrations.