Analysis of the physical features of the operation of stands with a closed power flow for testing v-belt gears

. Currently, there are practically no sufficiently satisfactory analytical methods for predicting the reliability of newly designed machines. Basically, the task is solved on the basis of information obtained largely during resource bench tests of parts, assemblies and aggregates. The stands used for carrying out resource tests of machine transmissions can be divided according to the type of loading into open loading stands and closed loading stands. Open loading stands are driven by an AC or DC electric motor and are decelerated by a special braking system. Closed loading stands load the transmission without the use of braking systems. This article discusses the physical features of the operation of stands with a closed power flow used for testing V-belt gears, which can significantly reduce energy costs. The analysis of the application of an analytical method for predicting the reliability of newly designed machines is carried out on the basis of information obtained largely during resource bench tests of


Introduction
Currently, there are practically no sufficiently satisfactory analytical methods for predicting the reliability of newly designed machines.
Basically, the task is solved on the basis of information obtained largely during resource bench tests of parts, assemblies and aggregates.The stands used for carrying out resource tests of machine transmissions can be divided according to the type of loading into open loading stands and closed loading stands [1].

Research methods
Open loading stands are driven by an AC or DC electric motor and are decelerated by a special braking system.Of the braking systems, the most reliable are DC generators with ballast resistances.In some cases, for example, if there is a DC power supply network in the laboratory, partial energy recovery is performed into the network.Closed loading stands load the transmission without the use of braking systems [2].Stands of this type are characterized by the fact that the loading of the elements of the tested gears is carried out by using the internal elastic forces of the system.Due to the closed loop, the initially created internal forces are preserved during the rotation of the transmission.These forces cannot carry out the work, therefore, the excited load in a closed-loop stand is called the apparent "circulating" power.
According to the method of loading the tested transmission, closed-loop stands can be divided into stands for testing gearing gears and stands for testing friction gears.
Closed-loop stands for gearing gears load the tested transmission by pre-twisting the shafts and other elastic elements of the gears using a special coupling 1 (Figure 1) in the stationary state of the transmission [3].This loading is maintained and controlled by a special planetary loader 2 (Figure 1) with additional loads 5 (Figure 1).
The torque reproduced in the test gear 3 where: Pi -circumferential force on the gear wheel of the planetary gearbox; r -gear radius; lshoulder; Ԛ -the total force applied to the shoulder l (the weight of the gearbox and the load).From the physical meaning of the occurrence of a load in a closed loop, it follows that the power consumed by the stand from the motor 4 (Figure 1) is spent on overcoming the friction resistance in preloaded kinematic pairs, therefore much less than the apparent power circulating in a closed loop [4].The total power circulating along the contour consists of the apparent N1 and the power N2 expended by the engine to overcome the friction forces: In closed-loop stands, it is important to know the direction of the circulating power flow.The direction of the power flow is counted from the link connected to the engine, from the corresponding leading links to the driven ones.To recognize the master and slave link, it is necessary to keep in mind the following obvious rule: at the leading link, the direction of its angular velocity ω does not coincide with the direction of the moment M of the forces acting on it; at the driven link, the direction ω coincides with the direction M.
Figure 1 shows the designations of the master and slave links, as well as the corresponding direction of the power flow N. The direction of the power flow allows you to evaluate the most loaded sections of the circuit.On the stand (Figure 1), the gear wheels of the gearbox 2 are loaded more than those of the gearbox 3.
In closed-loop stands for friction gears, it is impossible to load the tested transmission by pre-twisting the shafts and other elastic transmission elements, since these loads are balanced by the forces of friction bonds, which change when the stand is started, losing their original values.In these stands, loading is carried out due to a constant small kinematic misalignment of the gears entering the closed loop [5][6][7].
Figure 2 shows a diagram of a closed-loop test bench for V-belt gears.We have selected the diameters of the pulleys as follows: Due to this selection of pulley diameters, the pulley D22 tends to rotate the shaft at a higher speed than the pulley D21.This kinematic misalignment causes the appearance of elastic forces that create a constant torque in the closed circuit of the stand [8][9][10].
Using the above rule for determining the direction of the power flow for the stand circuit in Figure 2, we get: pulleys D12 and D21 are driving, and pulleys D22 and D11 are driven.The direction of the power flow is indicated by the arrow N and goes from the pulley D12 to the pulley D11.We determine the amount of torque that acts in a closed loop, with a given mismatch of diameters, noted in expression 2).
According to the direction of the power flow, the first drive pulley is D12, and the last driven pulley is D11.For this closed loop consisting of almost identical V-belt gears, the following expression can be written, which determines the relative slip of the V-belts due to kinematic mismatch of the pulley diameters: The torque M1, excited in a closed circuit due to mismatch of the pulley diameters, can be determined according to the sliding curve of each of the V-belt gears included in the circuit (Figure 3).If the reproducible load is within the permissible norms for V-belt transmission, then according to Figure 3 М1 = tgα ξ1; Hence the apparent circulating power The power expended to overcome the friction forces can obviously be expressed in terms of N1 as follows: where ƞ0 -the total efficiency of all elements of the transmission stand.
The total power of the leading link of the closed circuit of the stand N=N₁+N₂ =N₁(2-ƞ0)  From the consideration of the scheme of a closed-loop stand for testing belt drives (Figure 2), it follows: 1.When changing the direction of the angular velocity ω and preserving the condition of expression (2), the direction of the power flow and the value of expression (5) do not change.
2. When replacing the condition of expression ( 2) with a new one: D₁₂ < D₂₂ = D₂₁ = D₁₁ (7) the speed of the pulley D₂₂ will be less than the speed of the pulley D₁₂.Shaft 4 will be affected by a torque directed in the other direction [12][13][14].In this regard, the direction of the power flow will reverse, then the pulleys D₁₁ and d₂₂ are driving, and the pulleys d₁₂ and d₂₁ are driven.will give the same results as expression (7).
From the considered conditions of expressions ( 2), ( 7), ( 8) and ( 9) the general rules follow: -if D₁₂ˑD₂₁ > D₁₁ˑD₂₂, the direction of power flow will go from D₁₂ to D₁₁.If D₁₂ˑD₂₁ < D₁₁ˑD₂₂, the direction of power flow is from D₁₁ to D₁₂; -at the same time, the direction of the angular speed of rotation of the shafts does not change the direction of the power flow [15].

Conclusions
From all that has been considered, the following conclusions can be drawn: 1. Closed-loop stands have a number of advantages compared to stands with open loading using braking devices.
2. Closed-loop stands can significantly reduce energy costs and do not require special braking systems.
3. They are simpler in design, as well as in some cases simplify the adjustment and control of loading modes.
where: ξ1relative sliding of each of the two V-belt contours; n11; n12the corresponding rotational speeds of the pulleys.From here