Article citation information:Vinogradov, B. Mechanical systems with air spring flexible elements. Scientific Journal of Silesian University of Technology. Series Transport. 2019, 103, 199-207. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2019.103.16. Borys VINOGRADOVMECHANICAL SYSTEMS WITH AIR SPRING FLEXIBLE ELEMENTSSummary. The purpose of this study was to assess the effectiveness of flexible air-spring systems operating in parallel to share the total load, taking into account installation and in-operation errors. This study presented experimental and calculated characteristics of the air spring flexibility and its dependence on the polytropic index and additional volume. It considered patterns of load distribution between the air springs when they are operating in parallel to share the total load for the case when the air springs were used as the supporting elements for various machines and units, and between transmission lines containing flexible couplings, where air springs were installed as flexible elements.Keywords: air spring, rubber-cord shell, load distribution, flexible1. INTRODUCTIONA wide standard size series of rubber-cord air springs with a load capacity from 350 N to 230,103 Nwas developed and is being produced. Prospects for effective use of air springs as hydraulic inertial transducers of motion [1], vibration dampers and shock absorbers for rail vehicles [2] are being considered. The use of pneumatic couplings in machine drives solved the problem of limiting dynamic loads [3, 7]. One of the most important features of pneumatic couplings is the ability to control their stiffness and, accordingly, torsional vibrations of mechanical systems [4]. Furthermore, air springs may be effectively used as flexible elements sharing the total load, and in systems with a branched power flow.2. FLEXIBILITY CHARACTERISTICS OF AIR SPRINGSWhen choosing a reference point in the static equilibrium position, the characteristics of the air spring flexibility has the form QUOTE (1)where QUOTE , QUOTE are the gas volume and overpressure in the air spring bellows in the static equilibrium position; QUOTE is atmospheric pressure; QUOTE is the air spring effective area depending on the displacement x.The experimental studies of the flexibility characteristics were carried out for the Connect MD 1895 double convolution air spring, according to the manufacturer’s company catalogue, its features are: weight - 2.95 kg; working pressure - 0.5 MPa; maximum pressure - 0.8 MPa; minimum pressure - 0 MPa; working diameter - 265 mm; assembly height 210 mm; load capacity - 900 kg. The internal volume of the air spring with its design height of 140 mm is 3.64 litres. Based on experimental studies, the dependence of the air spring effective area on its deformation is represented by a first-order polynomial. QUOTE (2)where QUOTE is the effective area in the static equilibrium position, m2, P is the external load, β = 0.118 m.The difference between the experimental and calculated flexibility of the air spring, when compared by the formula (1) given (2), does not exceed 2%, which allows for further consideration of it as an actual flexibility [5].Expanding the expression (1) considering (2) in a Taylor series and retaining only the first two terms, we obtain QUOTE ,(3)where QUOTE , QUOTE (4)Figure 1 shows the linearised flexibility characteristics, determined by the formula (4), with the actual flexibility determined by the formula (1)The rubber-cord flexible element is a closed system, where heat will be evolved due to internal air friction during each cycle of air compression and expansion. The value of the polytropic index depends on the conditions of heat removal. The environmental conditions being the same, the number of compression and expansion cycles over the same time period grows with an increase in the vibration frequency; with the lack of proper heat removal, the polytropic index can take values n > 1.4. In most cases, the calculations take n = 1.3. As n increases, for example, from 1.3 to 1.6, as it follows from expression (4), the air spring stiffness and the natural frequency increase by 1.13 (Figure 2a) and 1.06 times, respectively, which in practice can be neglected in most cases. Fig. 1. Actual and linearised flexibility characteristics of the air springавFig. 2. The dependence of the air spring stiffness on the polytropic index (a) and the additional volume (b): k is the ratio of the total volume of gas (including the added gas) to the initial volumeThe rubber-cord flexible element is a closed system, where heat will be evolved due to internal air friction during each cycle of air compression and expansion. The value of the polytropic index depends on the conditions of heat removal. The environmental conditions being the same, the number of compression and expansion cycles over the same time period grows with an increase in the vibration frequency; with the lack of proper heat removal, the polytropic index can take values n > 1.4. In most cases, the calculations take n = 1.3. As n increases, for example, from 1.3 to 1.6, as it follows from expression (4), the air spring stiffness and the natural frequency increase by 1.13 (Figure 2a) and 1.06 times, respectively, which in practice can be neglected in most cases. One of the advantages of systems that use air springs as flexible elements is the ability to control their flexibility by adding an additional volume (Fig. 2b)3. LOAD DISTRIBUTION BETWEEN AIR SPRINGS OPERATED IN PARALLEL TO SHARE THE TOTAL LOADConsider the case where air springs are used as support for various machines and units. These mechanical systems include vibratory machines or other aggregates that apply air springs as flexible elements. This is the case, where installation errors may occur when the support of one air spring is displaced by Δ relative to the other (Fig. 3).When pressure is supplied to the bellows of each air spring, the error is compensated and the air springs will attain equal pressures. Interconnected air springs adjust the pressure automatically. In the state of static equilibrium position, the first air spring will undergo a deformation smaller by the value of Δ. As a result, the effective areas of the air springs in the static equilibrium position will be different; pressures pm0 being the same, the load between the air springs will not be uniformly distributed.Fig. 3. Flexible system with air springs mounted in parallel: 1, 2 - air springs; 3 - common pipeline; P - external load; Δ - the errorFor the case of independent operation of air springs, the equilibrium equations will take the form:, , ,where QUOTE , QUOTE Substituting S (x1), S (x2), p1 , p2 from (1), we obtain the system of equations QUOTE