Creature forcing and large continuum: The joy of halving

For $f,g\in\omega^\omega$ let $c^\forall_{f,g}$ be the minimal number of uniform $g$-splitting trees needed to cover the uniform $f$-splitting tree, i.e., for every branch $\nu$ of the $f$-tree, one of the $g$-trees contains $\nu$. Let $c^\exists_{f,g}$ be the dual notion: For every branch $\nu$, one of the $g$-trees guesses $\nu(m)$ infinitely often. We show that it is consistent that $c^\exists_{f_\epsilon,g_\epsilon}=c^\forall_{f_\epsilon,g_\epsilon}=\kappa_\epsilon$ for continuum many pairwise different cardinals $\kappa_\epsilon$ and suitable pairs $(f_\epsilon,g_\epsilon)$. For the proof we introduce a new mixed-limit creature forcing construction

Evaluation of operation in piston–con–rod system of ship propulsion engine on the basis of harmonic torque

The following article includes the analysis of mechanical and thermal load criteria of combustion engine. Those criteria have been divided into tribological, technical in detail and technical in general. The above criteria have been related to piston-con-rod system, in which, two tribological centres were specified. One centre included, piston-piston rings and cylinder, in which, piston rings serve as labyrinth seal and the cylinder constitutes piston guides. Crank bearings and main bearings of engine crankshaft constitute the second centre. From the point of tribological view, piston-piston rings and cylinder constitute slide and thrust bearing lubricated hydrodynamically, while crankshaft bearings a-c-t as slide and journal bearings also lubricated hydrodynamically. In the description of thermal load of the above-mentioned tribological centres, special attention was paid to criteria that ensure their motion reliability and durability of engine operation. Whereas in the description of mechanical load of elements constituting investigated centres, some criteria were determined resulting from their functionality and fatigue strength of the material they were made of. Criteria of thermal loads were based on mean density flux of heat conducted through the walls of engine elements, paying attention to their low precision of evaluation. It has been emphasized that synthetic criteria indicators are the most precise. They are determined on the basis of engine load measurements during its operation. Those criteria allow us to describe the operating process of con-rod-piston diesel engines and at the same time it is possible to expose their technical condition which is of essential practical meaning. The wear process of tribological centres that takes place during operating in piston-con-rod system, affects the course of engine working process and its techno-economic indicators

Determination of nondimensional arguments in dimensional functions of ship propulsion engine operation

The following article describes different ways for determining dimensionless arguments in dimensional functions of ship propulsion engine operation. Dimensional space has also been characterized in relation to properties it possesses. An attention has been paid to the fact that it creates Abelian group, where involution fulfils multiplication axiom by scalar, and positive numbers that belong to dimensional space create dimensionless subspace. The conception of dimensional dependence has also been explained. There are also described conditions, which should be fulfilled by dimensional quantities to be dimensionally independent. Fundamental theorems of dimensional analysis have also been characterized. There is also given the definition of dimensional function of ship propulsion engine operation concerning values and dimensional arguments. It has been explained what requirements are to be fulfilled. One can also learn what limitations are imposed on dimensional function of ship propulsion engine operation concerning dimensional homogeneity and invariance. The ways of dimensional function transformation into a numerical one have been described. In addition, some conditions have been given which must be applied at given method of dimensional function transformation. An attention has been paid to the fact that dimensionless arguments are similarity invariant as a result of transformation by the similarity method of mathematical model of ship propulsion engine operation. In this study, the ship propulsion engine performance is expressed by product of Joule and second interpreted as transfer of energy in the form of work. Identification of ship propulsion engine operation by dimensional analysis performed in terms of its usefulness for diagnosis of ship propulsion engines. The basic problem of marine diesel exploitation is the monitoring of its technical condition. Diagnosis of marine diesel propulsion increases the safety of the ship and thus protects the marine environment against pollution

Load analysis of propulsion engine during ship's speed acceleratio

The following paper presents load analysis of propulsion engine during ship's speed acceleration. This process is carried out after manoeuvring in order to receive, as fast as possible, exploitation speeds of the ship, achieved during the voyage. The analysis concerns direct propulsion power system of low-speed engine of constant pitch propeller. Wrong steering process of engine load changes in temporary states, can cause engine overloading, as the result of its operation on the external limiting characteristic and can end up in engine seizure. Control of engine operation is carried on through selecting of adequate setting of rotational speed governor, which for specified external conditions can result in adequate position of fuel link and the choice of adequate fuel index arm dose. Equalization of the power delivered by the engine in given conditions of work with power required by the ship’s propeller cooperating with the hull, will establish adequate rotational speed of the engine and finally the speed of the vessel. In order to speed up the sip's motion, there must occur an overflow of propeller thrust over the required thrust (resistance) and this, in turn, is connected with the necessity to ensure the engine power surplus over the power required for a given range of operation or in other words sailing speed. This article presents the working model of ship propelling system during speed acceleration and concerns mainly nonoverload running of the engine. The model described above has been verified during tests in real conditions at sea

Operation of diesel engine in direct ship propulsion

In the paper an identification of low speed diesel engine operation in direct propulsion plant equipped with fixed pitch propeller during ship manoeuvring. It was starting of engine and gathering speed of ship. Analysis of engine operation was based on changes of engine torque and time of ship bring up to speed. Operation of reciprocating internal combustion engine consists in converting the supplied fuel energy and delivering it to ship propeller. This condition implicates converting different amounts of energy in different time. The main attention was given to operation of engine caused by crank pin forces in wide range of revolutions and their influence on mechanical load of ship propulsion plant. The torque is the major component determining the engine load. As a matter of fact its mean value is low, but a passing torque can be four times higher than the rated torque. The second important component of propulsion engine operation is the time of ship acceleration from one speed to another. It determines dynamic properties of the ship describing its reductional feature. This time is determined in dependence on other parameters characterizing operation of ship propulsion plant and ship motion by means of dimensional analysis. These parameters were regarded as dimension quantities of three-dimensional space. Thus the three independent in dimension parameters can be noted in digital form in dimensional functions. The knowledge of operation parameters of ship propulsion plant and the knowledge of ship motion dynamics makes possible rational manoeuvring. It increases safety of ship motion and failure-free operation of ship propulsion engine. The proper operation of engine requires delivery to the propeller such amount of energy, which ensure the motion of ship with required speed in given sailing conditions

Symptoms of states included in the performance of con-rod-piston combustion engines systems

The following article describes energetic states symptoms, included in correct and incorrect performance of crankpiston combustion engines systems. Special attention has been paid to accompanying processes of such performance, with regard to, heat generation effect in combustion chamber and friction in joined frictional movements. Combustion chamber is a moving space formed by connection of the piston through piston rings with the cylinder liner and the engine head. Heat generation process takes place above the piston, generated by burning of fuel. It causes an increase of gas pressure in the combustion space, which results in the movement of the piston tightened by the rings, followed by an increase of the space volume. In this way energy is emitted from fuel burning, influencing the elements of piston-conrod system in the form of heat and work. The ability of such thermodynamical system to convert energy into an effective one is limited. Internal energy of exhaust gases can be divided into the part which cannot be converted into work. The process of heat generation in engine cylinder is of irreversible character which results in the loss of energy. In piston combustion engines, work is performed by heat generated in cylinders. Energetic performance in piston-crank system results from internal exchange of exhaust gases in combustion chamber with the engine surroundings. Analysis of such energetic performances allows us to isolate symptoms of correct operation of piston con-rod combustion engine systems. Such symptoms include: exhaust gases temperature, temperature of piston surface, momentary values of torque and the speed of pressure increase during combustion. Piston-con-rod system is a component part of the engine. Evaluation of its performance allows to identify the present technical condition of the engine. Diagnostic advantages of some, above mentioned symptoms of piston-con-rod combustion engine operation, have been verified by means of adequate laboratory testing and during engine operation on the ship

Material consumption criteria of piston – con – rod elements system of combustion engine

The following article includes the analysis of mechanical and thermal load criteria of combustion engine. Those criteria have been divided into tribological, technical in detail and technical in general. The above criteria have been related to piston-con-rod system, in which, two tribological centres were specified. One centre included, piston-piston rings and cylinder, in which, piston rings serve as labyrinth seal and the cylinder constitutes piston guides. Crank bearings and main bearings of engine crankshaft constitute the second centre. From the point of tribological view, piston-piston rings and cylinder constitute slide and thrust bearing lubricated hydrodynamically, while crankshaft bearings a-c-t as slide and journal bearings also lubricated hydrodynamically. In the description of thermal load of the above-mentioned tribological centres, special attention was paid to criteria that ensure their motion reliability and durability of engine operation. Whereas in the description of mechanical load of elements constituting investigated centres, some criteria were determined resulting from their functionality and fatigue strength of the material they were made of. Criteria of thermal loads were based on mean density flux of heat conducted through the walls of engine elements, paying attention to their low precision of evaluation. It has been emphasized that synthetic criteria indicators are the most precise. They are determined on the basis of engine load measurements during its operation. Those criteria allow us to describe the operating process of con-rod-piston diesel engines and at the same time it is possible to expose their technical condition which is of essential practical meaning. The wear process of tribological centres that takes place during operating in piston-con-rod system, affects the course of engine working process and its techno-economic indicators

Operation valuation of volumetric compressors by means of dimensional analysis

The following article introduces determination method of displacement compressors basing on its work parameters, by means of dimensional analysis. Operation of displacement compressors as volumetric compressing devices, according to J. Girtler, has been treated as a new physical quantity of [J·s] dimension. Such operation can be interpreted as mechanical energy transfer, through working organ, to gas factor volume in working space of the compressor in a definite time. Operation of volumetric compressor in which energy transfer, takes place, can be an information carrier of its technical condition. It expresses transformation of energy delivered to the gas, being forced through, by the compressor. This quantity can be determined, on the basis of, algebraic diagram of dimensional analysis, constructed by S. Drobot. The above diagram allowed us to control correctness of inference rules, in relation to mathematics, used in numerical functions of volumetric compressors operation, fitted in installations. Constructional solutions of compressors depend on the kind of compressed factor, the way of cooling, size of compressor and on the kind of propulsion and destination of compressor