Purpose of the study is to develop a matrix method for studying the dynamics of a tractor as a multi-mass spatial system of rigid bodies with an arbitrary arrangement of elastic suspension of bodies on shock absorbers relative to a fixed support surface and the presence of elastic connections between the bodies, made in the form of beam elements. Research methods. The methodological basis of the work is the generalization and analysis of well-known scientific results regarding the dynamics of two-mass systems in resonance modes and the use of a systematic approach. The analytical method and comparative analysis were used to form a scientific problem, determine the goal and formulate the research objectives. When creating empirical models, the main provisions of the theory of stability of systems, methodology of systems analysis and research of operations were used. The results of the study. A wheeled vehicle is presented as an amortized continuous frame type structure with assemblies and assembly units located on it, as well as a methodology for calculating individual block matrices of stiffness and damping coefficients. In this case, it is assumed that a viscous damper can be connected in parallel to each elastic element. In this construction of the stiffness and damping matrix of the block matrix are formed in the same way. Damping matrices are derived from the corresponding matrices by substituting damping constants instead of stiffness constants. To determine the natural frequencies and vibration modes of an undamped system using a PC, the most effective method of diagonalization by successive rotations. This method provides a complete solution to the problem, allowing all frequencies and shapes to be determined simultaneously, and good convergence. Conclusions. The considered method for analyzing and calculating the dynamics and vibration damping of a tractor as a complex mechanical system is based on a matrix record of the problem of spatial vibrations of a system of rigid bodies with elastic bonds. Matrix equations seem to be especially useful in the study of complex tightly coupled systems with the obligatory use of a PC. The presented work provides a complete methodology for calculating a tractor as a complex mechanical system such as a spatial frame with equipment installed on it.
During rectilinear motion of a wheeled tractor on a deformable surface, its rear wheels move along the track formed by the front ones. The amount of soil compaction can be different depending on its physical and mechanical properties, the dimensions of the front wheels of the tractor, the weight load falling on the front axle, and the like. Accordingly, the traction abilities of the rear drive wheels will also be different. This circumstance should be taken into account when designing wheeled tractors, especially tractor-tractors with two driving axles, in which a change in any of the factors listed above, for example, the distribution of the load along the axles, affects not only the compaction of the surface on which the rear wheels move, but and on the traction qualities of the front. In the course of the research, it was found that with a decrease in the load distribution coefficient below 0.5, the role of the rear wheel, which is capable of developing a greater traction force than the front wheel at the same load, in the formation of the total traction force, decreases. Therefore, the total traction force of the driving wheels becomes lower. With an increase in this coefficient above 0.5, the amount of preliminary soil compaction by the front wheel decreases; as a result, the ability of the rear wheel to develop more traction than the front wheel under the same load is reduced. The greatest traction force of two driving wheels moving along the same track is achieved with the same weight loads. Thus, the position of the center of gravity of a tractor with four driving wheels of the same size should be chosen in such a way that the load on the front and rear wheels is equalized at the rated pull on the hook. When conducting research on a field prepared for sowing, with an active semi-trailer with different load distribution between the rear axle of the tractor and the axle of the semi-trailer, it was found that the center of gravity of the active semi-trailer can be selected in the same way as for the inactive one, i.e. taking into account the influence of the semi-trailer on traction performance. The dependences obtained in the work make it possible to analyze the traction qualities of several driving wheels when they roll along one track. With their help, it is possible to identify the effect of surface compaction on the traction qualities of the rear moving front wheels; the influence of load distribution along the axles of the driving wheels on their total traction force, etc.
In order to improve the smoothness of the course of the T-150K tractors, the possibilities of changing the main parameters of the suspension system and its influence on the intensity of low-frequency oscillations of the machine were considered. The stiffness and drag coefficient of the front suspension, as well as the base of the machine, were subjected to changes, and the range of variation was limited by the possibility of implementing the parameters without rearranging the units and changing the traction characteristics of the machine. As criteria for evaluating the smoothness of the ride, the values of the transfer function of the movements of various points of the frame, seat and root-mean-square accelerations during the movement of the tractor along natural irregularities were taken. Based on the results of these studies, it was found that an increase in the tractor base by 10% has an insignificant and contradictory effect on the root-mean-square accelerations of the frame point over the rear axle over the entire range of design speeds from 2.5 to 7 m/s, and acceleration over the front axle and on the seat - up to a speed of 5 m/s. With a further increase in speed to 7 m/s (25 km/h), an increase in the tractor base by 10% reduces frame acceleration over the front axle by 15%, and on the seat by 20%. In addition, 11-leaf springs (when removing the 5th and 7th sheets), installed in the suspension with tractor hydraulic shock absorbers with optimal parameters, created on the basis of automobile shock absorbers of the MAZ-500E type, have smaller dynamic deflections during compression, than 13-leaf springs (suspension without hydraulic shock absorbers). According to this, the dynamic load on the 11-leaf spring, compared to the serial suspension, is reduced by 51% when the KhTZ-150K tractor is moving along a dirt road and by 30% when plowing the field across the furrows. Consequently, the stress on the sheets of an 11-leaf spring in the presence of shock absorbers in the tractor suspension will be less than that of a 13-leaf spring (without shock absorbers), which will ensure increased durability of the 11-leaf spring. In addition, the resource of the last spring should be increased by reducing the number of load cycles, since the suspension with these springs reduces the frequency of the tractor by 10% (according to experimental data).
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