Results of dynamic analysis of double-inlet screw conveyor machine assembly

. The article presents the results of theoretical studies of vertical and deflecting vibrations of two-stroke screws with a wavy surface and conveyor screws with a curved base and an elastic element. Based on the analysis of the obtained graphs of the relations of laws and motion parameters, their optimal values are justified. Here, the options for applying rubber gaskets to bearing bearings are considered in two versions, that is, with the same and two different types of stencils. When the rubber bushings of the bearing supports are taken in two different elasticities, the change laws of the vibration of the screw are obtained depending on the size of the supports, the moment of inertia of the screw and the change of the technological resistance force. Introduction


Introduction
The dynamic analysis of the machine unit is mainly to determine the movement laws and loads of the driver, coupling, belt transmission, drive pulley and screw depending on the resistance moment from the transported material, the frictional resistance of the oscillating bearing support, and the change of the friction-dissipative parameters. Based on the numerical solution of the obtained system of differential equations, the laws of change of rotor shaft, coupling, drive pulley and screw shaft angular velocities and driver loading were obtained.

Research methods
From the point of view of the theory of machines and mechanisms, it can be noted that the scientific innovation of the system is mainly due to the deformations of the screw bearings and the belt bushing, its vibrations are taken into account due to the changes in the torque of the frictional forces, and the belt transmission has a VTR and the drive pulley is equipped with an additional shock absorber. Therefore, it is of scientific importance to study their influence on the law of motion of masses. In the obtained laws, when the load is M t +M f = (95±1.5) Nm, the values of are on average 68.05 s -1 , and the angular speed of the driver is in the range of 72.1 s -1 . In this case, their average difference reaches 4.0 s -1 [1]. In this case, it is appropriate to emphasize the influence of technological resistance and the torque of frictional forces.
Мq=80,5 Nm+5,6 sinωt±1,5 Nm; Мmuf=(12÷14) Nm М q =140 Nm+8,2 sinωt±2,5 Nm; М t =(20÷25) Nm a) graphs of angular velocities of masses of the machine assembly and technological resistance and torque of the load on the drive shaft, b) vibration coverage of the angular velocities of the rotor shaft, clutch, drive pulley and screw shaft of the double-inlet screw conveyor machine assembly and torque on the drive shaft graphs of technological resistance and torque dependence of friction forces Accordingly, when the technological loading is on average (165±2.5) Nm, the values are on average (7.0÷7.5) s -1 and the values are (1.2÷1.6) s -1 . In this case, it can be seen that the angular velocity on the screw shaft is almost reduced to (2.1÷2.5) s -1 compared to the nominal value. It can be seen that the average values fluctuate between (14.9÷16.3) s -1 . By reworking the obtained laws, graphs of connection of parameters were constructed. Figure 2 shows graphs of dependence of the angular velocities of the mass of the machine and the technological resistance of the load on the drive shaft and the torque of the frictional forces [2].

1-
,25 kg m 2 ; 5-J u =0,128 kg m 2 Based on the analysis of graphs, the average values of (M q +M t ) increased from 0.9ꞏ10 2 Nm to 2.4ꞏ10 2 Nm, the average values increased from 0.726ꞏ10 2 s -1 to 0.584ꞏ10 2 s -1 , and the average values decreases from 0.695ꞏ10 2 s -1 to 0.56ꞏ10 2 s -1 in a nonlinear pattern, the values decrease from 1.58ꞏ10 s -1 to 0.91ꞏ10 s -1 , and the average values are M q , M t , c 1 , Depending on the values of c 2 , c 3 and moments of inertia, it decreases from 1.505ꞏ10 s -1 to 0.87ꞏ10 s -1 in a nonlinear pattern. In the expressions of technological resistances, the input, step, rotation frequency of the screw are taken into account. It is noted that the angular velocity of the screw shaft is higher than 19 s -1 , which ensures sufficient conveyor performance. Therefore, M q ≤[(120÷125)±(8.5÷11)] Nm in order for the conveyor to provide enough work output; It is recommended to have M t ≤(20÷23). It should be noted that when the load on the rotor shaft is J u =0.125 kg m 2 , it can be seen that the average values of M u go from 0.32ꞏ10 Nm to 3.1ꞏ10 Nm in a non-linear pattern. (Figure 2. Graph 5). It can be seen that the average values of Mu increase from 0.78ꞏ10 Nm to 4.61ꞏ10 Nm when the values of M q and M t increase, respectively, and the value of J u is 0.25 kg m 2 [3].
It is known that with the increase of the moment of inertia, the movement is smoothed, but the load and power consumption increase. Therefore, it is recommended to be in the range of J u ≤(0.2÷0.22) kg m 2 . Figure 3 shows graphs of dependence of technological resistance and torque of friction forces on the vibration range of angular speeds of the rotor shaft, clutch, drive pulley and screw shaft of the double-inlet screw conveyor machine unit, and the torque vibration range on the drive shaft. Based on the analysis of the resulting connections, the technological and frictional resistance moments generally increased from 0.4ꞏ10 2 Nm to 2.4ꞏ10 2 Nm, with values from 0.45 s -1 to 3.1 s -1 increases in a non-linear pattern up to, it can be seen that the values are on average (0.35÷0.4) s -1 more than it. Therefore, since the moments of resistance act directly on the screw, the values of its angular velocity decrease with respect to, and its values with respect to are greater. In this case, the impact of the screw on the transported product will be effective. However, according to experimental results, if the value of is greater than (3.0÷3.5) s -1 , the quality of the product will decrease and damage will increase. Therefore, M q ≤ [(120÷125) ± (8.5÷11)] Nm; It is desirable to be in the range of M t ≤ (20÷25) Nm. It should be noted that the values are not high and do not exceed (6.5÷7.5) s -1 , the rotation is stable. Correspondingly, when the range of vibration of the torque on the electric drive shaft is J u =0.128 kg m 2 , it does not exceed (4.2÷5.3) Nm.  6-∆М yu = f (М q +М ishq ); 5-J yu =0,25 kg m 2 ; 6-J yu =0,128 kgm 2

Results and discussion
Three belt elements were used in the machine assembly. Their actions directly affect the laws of motion of masses. Figure 4 shows the laws representing the influence of the coupling rubber bushing of the machine assembly, the rubber bushing of the drive pulley, VTR belt torque coefficients on the law of rotation of the screw, pulleys, coupling and rotor shaft, and on the engine load [4]. The analysis of the received laws shows that with the increase in the frequency of the belt elements of the machine assembly, the amplitudes of speed fluctuations decrease, but their average values also decrease. Also, the load on the driver increases accordingly. The main reason for this is that the increase in the weights is almost a mass in the interconnection of the masses, the movement is normalized, and the load increases, mainly the connection graphs were built. с1=430 Nm/rad; с2=380 Nm/rad; с3=320 Nm/rad; Мq=120 Nm+6,5sinωt±2,2 Nm; Мt=(20÷22) Nm  Fig. 4. Laws representing the influence of the coupling rubber bushing of the machine unit, the rubber bushing of the drive pulley with VTR, the belt friction coefficients on the law of rotation of the screw, pulleys, clutch and rotor shaft and the load of the engine. с 1 =400 Nm/rad; с 2 =320 Nm/rad; с 3 =290 Nm/rad; М q =120 Nm+6,5sinωt±2,2 Nm; Мt=(20÷22) Nm To increase the efficiency of the screw, its rotation frequency is increased. Also, when a double-inlet screw is used, the oscillation frequencies of the angular velocities on the shafts and the torque on the electric drive shaft increase by two times (Figure. 5). The main reason for this is that because the screw threads are displaced by half a step, the loading effect is almost twice the effect on the screw blades as a result of the spatial displacement. In this case, the laws of change of φyu, φ m , φ sh , and φ v depend not only on the moment of technological resistance and friction forces, but also on the changes in the thickness of the belt elements of the machine assembly. This is especially noticeable when double-threaded screws are used. Also, Figure 5 shows the laws of change of φ yu, φ m , φ sh , and φ v for M yu the double-inlet version of the machine assembly [5,6]. According to the analysis of the graphs, when the stiffness of the belt element that transmits motion to each mass increases from 2.2ꞏ10 2 Nm/rad to 5.5ꞏ10 2 Nm/rad, the values of are decreasing in a non-linear law. In this case, the values of M yu increase from 5.0 Nm to 3.52 Nm when J u =0.128 kg m 2 , and when M yu is 0.25 kg m 2 , the increase of M yu goes up to 5.23 Nm. It should be noted that the vertical vibration of the screw decreases with the increase of the uniformity coefficient of the rubber support. This also reduces the friction force. So, the frequency of change of the resistance of the screw increases twice, and affects the laws of change of the angular speed and load. Figure 6 shows the graphs of the dependence of the rotational speed coefficients of the corresponding belt transmissions on the vibration range of the rotor shaft, coupling, drive pulley and screw shaft angular velocities of the double-inlet screw conveyor machine assembly and the torque vibration range on the drive shaft. However, the reduction of this vibration causes the product to mix and brake less. Therefore, recommended values of sn are recommended in the range of (5.0÷7.0)ꞏ10 3 N/m. Accordingly, c 1 =(380÷450) Nm/rad, c 2 =(360÷400) Nm/rad; c 3 =(320÷350) Nm/rad values are desirable. It should be noted that when using a double-inlet screw, due to the equalization of the load distribution along its length, the amplitudes of the angular velocity change are up to (8.0÷12)% can be seen to decrease. and v 3 leads to a decrease in the angular velocities of the two lead screws and the driven pulley, which causes an increase in the loading of the driver. This, in turn, leads to an increase in power consumption. Therefore, the recommended parameters are: v 2 ≤(3.4÷3.6) Nms/rad; v 2 ≤(4.5÷4.8) Nms/rad; v 3 ≤(5.1÷5.4) Nms/rad [8,9].