IntroductionTo reduce tangential stresses in the elements of the shaft line from torsional vibrations to the norms of classification societies – the Russian Maritime Register of Shipping (RMRS) [1] and the Russian Classification Society [2] use a damper (damper), which is installed at the bow end of the diesel engine. Silicone dampers are installed in marine propulsion systems with a design scheme: “medium – speed diesel shaft line – fixed – pitch propeller”. But the design schemes of modern ships are becoming more complicated and include gearboxes, couplings, screw steering columns in the composition of the engine-propulsion complex, which affects the development of torsional vibrations both in amplitudes and in the number of resonant frequencies. Silicone dampers may be ineffective in this case, so elastic-friction dampers are used. If silicone dampers are designed and manufactured by the domestic industry, then more complex spring dampers are produced only by foreign manufacturers. In this case, two ways can be chosen for import substitution – reverse engineering of foreign-made spring dampers available on domestic ships or the development of own technologies for the design, operation and repair of such devices, with the training of specialized specialists. Obviously, the second way is strategically important with the development of our own technologies, therefore, to confirm theoretical research, a laboratory base is needed, including test benches made with maximum similarity to real ship devices and structures. Setting the research taskOn Wartsila 6L20 marine diesels [3], Geislinger torsional vibration dampers of the D60/14/2 or D60/16/2 models are most often used [4], which combine damping due to spring springs and hydraulic filler – engine oil supplied under pressure from the diesel lubrication system through the crankshaft in the damper cavity. The general view of the damper with spring springs and its design are shown in Fig. 1.   Fig. 1. Design of the torsional vibration damper Geislinger D60/14/2 [4]: 1 – external housing; 2 – flywheel sector;3 – hole for fixing the flywheel with a lid;4 – inner rim for fixing spring springs;5 – flange for attaching the damper to the diesel crankshaft;6 – bolts for attaching the damper to the diesel crankshaft;7 – spring springs; 8 – cavities for oil passage The design feature of this damper is the presence of a combined elastic and hydraulic part of the damping area (Fig. 2) – for this purpose, oil is supplied to the housing from the engine under pressure, as a result it is located between the packages of spring plates and converts vibrations into thermal energy, heating the oil [4]. This complicates the design of the damper, but allows you to use the advantages of both spring dampers and hydraulic dampers, as well as cool its structural elements.   Fig. 2. Elastic and hydraulic damping in a spring damper [4]:a – the oil cavity before the spring package;b – the oil cavity after the spring package For dampers with spring springs from Geislinger, an oil supply system is used, the operation scheme of which is shown in Fig. 3 [4]. Fig. 3. The scheme of oil supply to the spring damperof torsional vibrations [4] Equipment and materialsThe model spring damper is supposed to be used as part of the laboratory stand (Fig. 4) of the Marine Technology Service test center of the ASTU (MTS TC).   Fig. 4. General view of the laboratory stand of the MTS TC: 1 – small measuring gear No. 1;2 – direct current generator; 3 – flywheel with a large measuring gear; 4 – shaft of the laboratory stand;5 – small measuring gear No. 2; 6 – direct current electric motor; 7 – silicone torsional vibration damper The laboratory stand simulates the operation of a marine engine and propulsion complex with a medium-speed diesel engine and direct transmission to the propeller. The direct current electric motor 6 simulates the operation of a marine internal combustion engine, with the possibility of creating a variable torque of variable amplitude and period of action. The presence of a long shaft 4 of small diameter and a large flywheel mass 3 models the design parameters of the ship's shaft line (high malleability and large flywheel mass). The direct current generator 2 simulates the operation of the propeller, with the possibility of changing the braking torque. The measurement of torsional vibrations is possible using two small flywheels with toothed rings 1 and 5 located at both ends of the laboratory stand, as well as one large measuring gear 3. The presence of a long shaft allows the measurement of tangential stresses using strain gauges. The model damper is planned to be manufactured on the basis of reverse engineering technology of the real Geislinger D60/14/2 damper available at MTS TC (Fig. 5), its drawing is shown in Fig. 6.   Fig. 5. Reverse engineering of the Geislinger D60/14/2 damper                                                                                 a                                                                            b Fig. 6. Drawing of the general view of the model spring damper of torsional vibrations: а – front view; b – side view;1 – side plate; 2 – flange; 3 – coupling ring; 4 – sprocket housing; 5 – intermediate block; 6 – plate spring; 7 – interplate spring;8 – bolt M14 × 1.25; 9 – disc washer; 10 – bolt M10 × 1.25; 11 – insert; 12, 13 – sealing ring, 14 – lubrication oil supplyNext, a schematic diagram of the oil supply system to the model spring damper was developed and formed (Fig. 7).   Fig. 7. Schematic diagram of the oil supply systemin a model spring damper of torsional vibrations:1 – pressure tank; 2, 15, 16, 19 – oil leak pan;3, 9 – oil temperature sensors at the inlet and outlet of the damper; 4, 11, 14 – taps; 5 – oil filter;6 – oil pumping pump; 7 – pressure sensor;8 – oil protection casing; 10 – oil flow control valve;12 – oil drainage tank; 13 – oil pumping pump;17 – flow meter; 18 – torsional vibration damper;20 – drainage line to drain the oil To calculate the thermal power, the Geislinger formula was used [4], according to which the thermal load in the Pkw, kW, damper for one harmonic order is calculated using the formula:  where i – the order of the harmonic oscillations; n – the rotation frequency, min–1; T – the vibration moment in the damper, N·m; CD – the stiffness of the damper, (N·m)/rad; kd – dimensionless damping coefficient.  According to the RMRS rules [1], when measuring torsional vibrations, it is necessary to consider the first 12 orders of harmonics.The heat that is transferred to the circulating oil in the damper Poil, J, will be determined by the formula:Рoil = сoilGoilΔtoil, where сoil = 1 670 J/(kg·degrees) – the heat capacity of the oil; Goil – mass oil consumption, kg/h; Δtoil – oil temperature difference at the inlet and outlet of the damper, °C.From here:                                                                                                                    (1) or, when recalculating from kW to J, formula (1) is converted to the formula: The excess oil pressure in the system must be at least: where Р0 – atmospheric pressure, bar; Т = 15,4 N·m – the damping moment in the damper, equated to the vibration moment; Trel = 143 (N·m)/bar – the relative value of the damping moment selected from the catalog of Geislinger spring dampers [4] for a model of similar geometric dimensions.Using the recommendations and methods of sources [5-7] in the MS Excel program, the necessary calculated data were obtained according to Tables 1, 2 and Fig. 7.Table 1Calculation of the parameters of the model torsional vibration damperParameterValueNumber of spring packages, pcs.2The number of plates in one spring package, pcs.2The average thickness of the plate, m0.001The width of the plate, m0.04The working length of the plate, m0.079The distance from the center to the place of sealing of the plate, m0.063The modulus of elasticity of the plate material, N/mm22.059·105The ductility of the calculated damper, rad/(N·m)0.001069291The stiffness of the calculated damper, (N·m)/rad935.20 Table 2Calculation of the parameters of the amplitude-frequency response of a model torsional vibration damperParameterValueMoment of inertia of the main oscillating system M, kg·m21.377Stiffness of the main oscillating system K, (N·m)/rad7 454Moment of inertia of the outer part of the damper m, kg·m20.1565Stiffness of the spring part k, (N·m)/rad935Disturbing force P0, kg15The oscillation frequency of the main system w1, Hz73.575Vibration frequency of the outer part of the damper w2, Hz77.29Ratio of moments of inertia m/M, n0.114Ratio of frequencies w2/w1, f 1.05Critical attenuation of oscillations Ck23.032Static oscillation amplitude xst0.002012Natural oscillation frequency without attenuation, HzThe frequency of the two-node waveform wc172.107The frequency of the single-node waveform wc282.864Frequency of forced oscillations w90.000Relative oscillation frequency w/w11.223Attenuation coefficient c5.095Amplitude of mass fluctuations M, x110.00373Dynamic gain factor x11/xst1.854       A stepwise change in the frequency of forced oscillations w and the calculation of the relative frequency of oscillations w/w1 allowed us to obtain data for plotting the amplitude-frequency response (Fig. 8) of the model damper with a characteristic increase in the dynamic gain coefficient to 5.1 with resonant oscillations, which are expected at a frequency of 0.87 (64 Hz) from the oscillation frequency of the system w1. The obtained dynamic gain coefficient corresponds to the range of its magnitude with effective operation of the damper according to the research of L. V. Efremov [8].Based on the results of calculations and theoretical studies, the elements of the working fluid supply system to the model spring damper were determined: a consumable oil tank, an oil supply pump, an oil pumping pump from the bath, an oil filter, a drainage tank from the oil bath, an oil pressure sensor, an oil temperature sensor at the inlet to the damper, an oil temperature sensor at the outlet of the damper, oil temperature control unit, fittings and taps.   Fig. 8. Graph of the amplitude-frequency response of the model damper For the operation of the damper, it is supposed to use Lukoil Navigo TPEO 30/40 oil [9], used for Wartsila 6L20, CAT engines, which include spring dampers of torsional vibrations.The oil supply to the damper housing will be carried out through the shaft and flange of the damper attachment from the nose end of the laboratory stand. The design pressure, taking into account the hydraulic resistance of the damper, must be at least 3 bar.The internal volume of the model damper is approximately 185 cm3, four inlet holes with a diameter of 4.9 mm are provided for lubrication of the inner surfaces of the damper, four holes with a diameter of 10 mm are provided for oil outlet in the lid. According to the calculation, the oil consumption for the operation of the model spring damper will be 32 kg/h, and the volume of the consumable oil tank will be 10 liters. ConclusionAccording to the conducted research, the following main conclusions can be drawn:1. The spread of spring dampers is justified by the design features of such devices, which allows the use of both elastic and hydraulic damping.2. The presence of a laboratory stand in the MTS TC allows for physical experiments with models of silicone torsional vibration dampers and for working with models of spring dampers, the system for supplying working fluid to the damper housing has been modernized. 3. According to the calculation, the oil consumption for the operation of the model spring damper will be 32 kg/h, the pressure, taking into account the hydraulic resistance of the damper, should be provided at least 3 bar.