Method for strength calculating of structural elements of mobile machines for flash butt welding of rails

Purpose. The subject of this study is the strength of the loaded units of mobile machines for flash butt welding by refining high-strength rails. The theme of the work is related to the development of a technique for strength calculating of the insulation of the central axis of these machines. The aim of the paper is to establish the mathematical dependence of the pressure on the insulation on the magnitude of deflections of the central axis under the action of the upset force. Design/methodology/approach. Using the Mohr’s method, the displacements of the investigated sections of the central axis under the action of the upset force and the equivalent load distributed along the length of the insulation were calculated. The magnitude of the load distributed along the length of the insulation equivalent to the draft force was determined from the condition that the displacements of the same cross sections are equal under the action of this load and under the action of the upset force. Results. An analytical expression for establishing the relationship between the pressure acting on the insulation and the magnitude of the upset force and the geometric dimensions of the structural elements of the machine was obtained. Based on the condition of the strength of the insulation for crushing, an analytical expression for establishing the relationship between the length of insulation and the size of the upset force, the geometric dimensions of the structural elements of the machine, and the physical and mechanical properties of the insulation material was obtained. Originality/cost. The proposed methodology was tested in the calculation and design of the K1045 mobile rail welding machine, 4 of which is currently successfully used in the USA for welding rails in hard-to-reach places.


Introduction
When laying railroad tracks, as well as during their repair, contact butt welding is used in more than 90% of cases. This welding method ensures equal static and fatigue strength of welded joints with base metal, including the welding of railway frogs with rail ends [1,2]. E.O. Paton Electric Welding Institute of NAS of Ukraine (PEWI) has many years of experience in the integrated development of equipment for flash butt welding of rails in stationary and field conditions [3]. Serial production of stationary and mobile rail welding machines based on the PEWI's inventions was set up by PJSC "Kakhovka Plant of Electric Welding Equipment" (KZESO). Among the mobile machines produced at KZESO company, the most widely used models are K255, K355A and K828 [4], and since the 2000s, taking into account the need to weld thermally strengthened rails, К76F type (manufactured by PAO «МК «Аzovstal'») [5], new generation machines K920, K922 and K1000 are widely used [6,7].
Today an actual problem for existing mobile welding machines is the welding of rails in hard-to-reach places, for example, in the subway or at the jointing of the main track rails with track switches [8].

Purpose
To solve this problem in the PEWI was developed the K1045 machine ( Fig. 1) [9]. In the course of its design, it was necessary to take into account that the process of flash butt welding is associated with the application of a large upset force, as a result some certain design elements of the welding machine is affected by a high operational load. One of the loaded structural elements is the insulation of the central axis of the machine, seeing that this axis is bent and presses on the insulation during the welding. Therefore among other loaded elements of the machine it is necessary to ensure the strength of the insulation for crushing. The main input parameter for the calculation of structural elements for strength is the magnitude of the load acting on them. However, in the case under consideration, the relationship between the upset force and the load on the insulation is not obvious. Therefore, the purpose of this work is to establish the relationship between the pressure acting on the insulation and its length with the magnitude of the upset force, the geometric dimensions of the structural elements of the machine, and the physical and mechanical properties of the insulation material.

Investigation
When the rails are welded, the machine transfers the force to them with the help of a hydraulic cylinder of upset 1, the central axis 2 which consists of two parts isolated from each other is flexing and pressing on insulation 3 (Fig. 2). Inasmuch as the pressure on the insulation is associated with the movements of the central axis during its bending, it is necessary to determine the vertical displacement of section A on the action of the upset force P. In order not to violate the symmetry, we determined the total displacement of the section A and section B, which are located symmetrically with respect to the joint of the welded rails (Fig. 3).

Fig. 3. The calculation scheme of machine loading during the welding
According to the Mohr's method, bending is determined by the formula [10] where f i is the desired displacement; M i is the equation of the bending moment from the unit force which is applied in the direction of the desired displacement; M Pj is the equation of the bending moment from the corresponding active or reactive external load; E is the modulus of elasticity of material; J is the moment of inertia of the cross section of the central axis.
To determine the necessary equations of bending moments, let us construct an equivalent system by conditionally cutting the contour along the cross-section of the central axis opposite the joint (Fig. 4).
According to the diagram (Fig. 4), the bending moment acting on the central axis due to the application of the upset force has a constant value Let us load the equivalent system by unit loads F = 1, applied in the direction of vertical displacement of sections A and B and plot the bending moment diagram from these forces (Fig. 5). According to the loading scheme (Fig. 5), the bending moment caused by the application of unit loads in the direction of vertical displacement of sections A and B is determined by the formula (3)

Fig. 5. Diagram of bending moments from the action of unit loads
Substituting (2) and (3) into (1) we determine the total displacement of sections A and B, from the action of the upset force 2 2 To determine the pressure acting on the insulation, instead of the upset force, we apply to the equivalent system a linear force q uniformly distributed along the length of the insulation (see Fig. 3), and plot the diagram of the bending moments caused by this force (Fig. 6).
To determine the total displacement of the cross sections A and B from the equivalent load q, substitute (5) and Equating the right-hand parts (4) and (6), we establish the relationship between the pressure acting per unit length of insulation, with the magnitude of the upset force   According to [11], the strength of the insulation for crushing will be ensured if where [σ] br is the allowable stress of insulation material for crushing; d is the diameter of the central axis, which can be determined by knowing the maximum value of the bending moment acting on the central axis (see Fig. 4), according to the known formula [11]   where [σ] is the allowable stress of the material of the central axis. Substituting the expression for q from (7) into (8), we obtain Thus, the relationship between the length of insulation with the amount of upset force, the geometric dimensions of the structural elements of the machine, and the physical and mechanical properties of the insulation material was established.

1.
A technique for calculating the strength of central axis insulation of mobile machines for flash butt welding of rails was developed. This technique consists in finding an analytical expression that establishes the relationship between the pressure acting per unit length of insulation, the amount of upset force and the geometric dimensions of the structural elements of the machine.
2. Based on the condition of the insulation strength for crushing, an analytical expression that establishes the relationship between the length of insulation and the size of the draft force, the geometric dimensions of the structural elements of the machine, and the physic al and mechanical properties of the insulation material is obtained.
3. The proposed methodology was tested in the calculation and design of the K1045 mobile rail welding machine, which is currently successfully used in the US for welding rails in hard-to-reach places.