Complex Research of Perspective Suspension for Locomotives

In this article questions on creation and calculation of a perspect ive design of adaptive torsion suspension for the locomotives, including hydromechanical dampers of fluctuations of adaptive type. The design procedure of the main kinemat ic and geometrical characteristics on a locomotive example 2ТЭ10Л, supplied with the specified technical solutions, and studying of fluctuations and power loading of its running gears is offered. Thus, the dynamic settlement scheme on the basis of Foygt-Kelv in's elastic and viscous model is developed. The bench pilot studies, allowed to specify parameters and characteristics of the above-stated designs are carried out. Expected economic effect of possible introduction of development will make 850 thousand rubles a year on one locomotive. Materials of this art icle were discussed at various conferences of leading higher education institutions of the Russian Federation. Results of researches are recommended to design, research and machine-building structures for their possible use in practice.


Introduction
Modern rolling stock, including loco motives, passenger and freight cars is the most important constituent part of the technical facilities of railway transport characteristics, properties and parameters of which are determined by the growth of traffic, increase traffic speed, ensuring operational reliability, increase the comfort of passengers and the smooth progress of railway carriages, cargo safety, etc. Such requirements are d irect ly connected with the imp rovement of their spring suspension, aimed at reduction of dynamic loads transmitted fro m the track of the body and crews and thus increasing the smoothness of the rail vehicles. The existing design elements spring suspension of rolling stock have a number of drawbacks, such as a high metal content, complexity of design, low reliability and, most importantly, the inability to change in the automatic mode of their damping characteristics.

Objectives
In view of the foregoing at the chair "Applied mechanics and engineering graphics" Yelets State University name I.A. Bunin for a nu mber of years carried out the research works

Methods
To solve this problem and provide the most detailed picture of the dynamic p rocesses occurring in adaptive torsion suspension, formu lated requirements to the developed calculation scheme and of the elaborated mathematical model, describing the damping characteristics of such a device.
At the first stage, to assess the efficiency of adaptive torsion spring suspension, with respect to the jaw cart trunk or industrial locomotive (Fig. 1) were carried out preliminary calculations of the basic parameters of the proposed technical solution on the basis of the adopted scheme (Fig.  2).  When forming of the mathematical model, according to a design diagram (Fig.2), used the equations of dynamics, theory of elasticity and hydromechanics. As the base of the calculation of the ratio was adopted by the equation of motion of a concentrated mass m 0 , which for the cases of power, kinemat ic and mixed excitation is of the form: In this case, the damping factor α ∑ , depending on the hydraulic resistance in the channel, fluid v iscosity, flow turbulence, as well as the relevant parameters, characterizing the working fluid in the throttle channels adaptive hydro-mechanical shock absorbers were defined in the following dependencies: As a result of calcu lations performed for the locomot ive 2TE10L were identified piston diameter D P = 80 mm, the diameter of the butterfly channel d К = 1.5 mm, nu mber of channels n = 4, stem diameter d S = 20 mm, hydro-mechanical damping factor α ∑ = 374.8 N· s/cm, the force o f resistance to the movement of the piston R ∑ = 206,96 N.
For pre -practical calculation o f a torsion spring suspension used approximate method of determin ing the equivalent damping ratios proposed W. Kirp ichew and further developed I. Chelnokow. In this case used the following differential equation and is included in the parameters describing the fluctuations of the concentrated masses on the springs in the form o f: As a result, were pre -installed with the most important geometric characteristics of the proposed adaptive torsion springs, designed just for jaw cart above mentioned locomotive 2TE10L. In this case it is considered, that the rod of the torsion springs made of steel 65С2ВА GOST 14959-79, and its diameter is equal to d t = 60 mm. When you change the length of the working area, for examp le, fro m 600 mm in the statics of up to 550 mm under dynamic loading changing the torsional stiffness of the torsion increased in 1.6 times and amounts to, respectively, the c s = 1127.6 N/mm and c d = 1805 N/mm, which, in the end, allows you to reduce the movement of the crew part of the loco motive with Δ s = 47 mm to Δ d = 36.7 mm.
For the redetermined settlement, characterizing the smoothness of the locomotive 2TE10L, equipped with the technical solutions, and the study of oscillation and force loading its chassis is designed dynamic calculat ion scheme on the basis of elastic-plastic model Vo igt-Kelvin (figure 3).
Under the С φ provided torsional stiffness of the torsion springs, and under the α ∑ -total damping factor of hydromechanical shock absorbers.
At drawing up of the mathematical model uses the following assumptions: 1. Not taken into account bending oscillations of the rod, and other parts of hydromechanical damper.
2. Coefficient of friction of mating surfaces is taken constant.
3. The law o f excitement due to the irregularities of the micro -and macro-profile conditional pavement changes in time according to the harmonic law.
4. Is not taken into account the gyroscopic effect of a rotating mass of wheels, as well as air resistance when its translational motion.
5. The processes occurring in the hydro mechanical damper, believe isothermal to the specified coefficients of viscosity of the working body.
6. To reflect the movement of the piston and the rod relative to the frame with the longitudinal oscillations applied inverse form of the assignment of coordinates, and with torsional direct.
7. Vectors of dry friction forces in the forward kinematic pair the piston -working cylinder were heading in the opposite direction relat ive to the coordinate system. 8. The movement of the loco motive is on the straight stretch of road without bias.
9. Profile path under the two wheels of each wheelset is the same.
For a description of the rectilinear mot ion of the locomotive bogie choose the following generalized coordinates the movement's centre of gravity of the locomotive in the d irection of motion; vertical movement of the centre of gravity Z loco motive; angular d isplacement φ crew of the locomotive in the vertical p lane with respect to the transversal axis, passing through its center of gravity. The systems of generalized coordinates accept the Cartesian lefts. Using the technique of linearization, which gives opportunity to carry out, both quality and quantitative study of nonlinear systems of suspension with a high eno ugh for practical tasks degree of accuracy, we write the equation of the oscillations of the crew part of the loco motive: The force of P i can be presented in the form of two forces: where PTiforce caused by the movement o f the leaf suspension and characterized by the torsional rig idity of the shaft torsion; PHM Diforce caused by the resistance of hydromechanical damper.
It is seen that the forces of P i , attached to the wheels and motors unit of irregularities way, can be exp ressed in terms of generalized coordinates of φ, z, y, and the frequency of the external excitat ion p = 2πυ/α, where α is a dimensionless variable associated with the time t is a linear dependence of α=pt.
Then equation (1) can be written as follows: Analyzing the formula (16) we see that the variable total hydro-mechanical damp ing factor α Σ of the proposed hydromechanical damper will depend on the hydraulic resistance in the channel, the viscosity of the working flu id and flow turbulence α (t) arising in the channels of the piston and the rod, as well as fro m mechanical α m (t), which are characterized by the torsional stiffness С φS variable cross-section of the piston rod. Such an integrated its constructive characteristics allows to efficiently in the automatic mode and in a wide range of impact of the dynamic loadings arising in spring suspension rail crew, to produce vibration dampening the crew part o f the locomotive.
The General solution of equations (15) Solving equation (15) we can determine the amplitude of the steady-state oscillations of spring mass z 0 and the amp litude of φ 0 , respectively, on dependencies: For the resonance modes depending have the form: For the decision of ordinary d ifferential equations describing the fluctuations of the locomotive bogie, used widely professional applied mathemat ical package MATLAB 6.5., designed for the solution of practical engineering problems. Construction of the model includes the solution of differential equations for the serial spring suspension of the above locomotive and the perspective of a torsion under the same in itial conditions. For the series production of springs of the suspension of the locomotive equations describing the forced vibrations, have the form: and for torsion, as it was mentioned above, according to equation (15).
The init ial conditions: For clarity perfo rmed analytical and numerical solution of the presented differential equations. The analytical solution obtained when using dsolve built-in package Tool Box Symbolic Math, the input argu ments, which are the line to the equation, boundary conditions, if any, and the independent variable for which is the default t.
Nu merical solution of a set of differential equations with initial conditions, i.e., the Cauchy problem, carried out with the help of built-in functions of MatLab, called solvers. For the above equations used solver ode45, which is based on the method of Runge-Kutta method of the fourth and fifth order of accuracy. The input arguments solvers are: the name of the file functions in apostrophes, vector with an init ial and a final t ime value observations of the movements and the vector of init ial conditions. Output argument two: the vector of values of t ime and a mat rix o f values of unknown functions. The values of the functions are located at the columns of the matrix in the first colu mn is the value of the function, in the second -its first derivative.
Scheme of location of the nu merical solution consists of the following stages: 1. Adjusting the differential equation to a system of differential equations of the first order. For the presented equations were obtained the following systems: -for the series production of springs of the suspension: -for the perspective torsion suspension: Writ ing a special file of functions for the system of equations obtained. File -function must have two input arguments: the variable t, wh ich is the differentiat ion, and the vector, the amount of which is equal to the number of unknown functions of the system. File -function for the initial equations (15) and (20) eq_serZ, eq_serFI and eq_modZ, eq_modFI are in the Listings.
3. Call solver ode45. 4. Visualization of the obtained results. An analytical solution of the differential equations (20) after the start of the file -program solv_serial has the form presented in figure 4.
An analytical solution of the equations (15) split into 2 parts: figure 5, a -solution for Z, and figure 5  After the solution of the d ifferential equations are constructed, amp litude-frequency characteristics for a torsion spring suspension. The formu la for the amp litude of forced oscillat ions, has the form: Taking into account the dynamic factor built a family of curves, the host various values of the ratios of n/p. The family of such curves presented in figure 7. Th is graph of the family of curves constructed for the perspective adaptive torsion suspension, shows that at the approach of the frequency perturbations ω to the frequency of oscillation of the p, dynamic factor increases, and the maximu m amp litude of oscillat ion is achieved approximately in respect of ω/p=1. At the same time fro m 5 p resented in figure 7 plots the most removed fro m the resonance zone chart with the ratio n/p=0.6 and maximu m coefficient of dynamic equal to 1.7, which is characteristic o f the proposed design of adaptive torsion spring suspension with adaptive damping elements at a total coefficient of damping α Σ =420,0 kN•s/m. While the decline in the last possible input suspension in resonance.
To determine the resonance mode of the amplitude of steady-state oscillat ions was used by the known method and then was used by the file -program rezonans, showing the dependence of the resonance amp litudes fro m the stiffness of the suspension in various types of dithering. The graphs obtained are shown in figure 8.  For a more co mplete study of the oscillat ion process of the locomotive bogie with use of the developed models were calculated basic parameters characterizing the dynamics of motion of a loco motive at different values of F 0 , α Σ and с φ , which, in particu lar reflect the change during the time interval in 10 seconds with the vert ical movement of the body Z and the speed of this movement Z'. As a result of such calculations show that using the proposed design of adaptive torsion suspension of amplitude of oscillations of the body and the speed of its movement in the vertical plane much lower than the cart, equipped with leaf springs.
To confirm the correctness of the calculation was developed method benchmark test of experimental studies of the proposed design of perspective suspension.
The basic scheme of the test stand, shown in figure 9, represents the elastic rod, motionless fixed in support B and mobile, with the help of splines, in support A, which are established on the table hydraulic press, creating effort of compression of up to 160 kN.
were calcu lated rational parameters and characteristics of the perspective of adaptive torsion suspension, with respect to locomotives 2TE10L, which amounted to diameter equal to d t = 69,5 mm, length of the working area of the rod of the torsion 637 mm with torsional stiffness C = 1213,0 N/mm. Such values of a good agreement with previously obtained estimates.

The Results
As a result of the bench experimental research, as well as using methods of mathematical modeling, received rat ional geometric and жесткостные characteristics of a nu mber of torsions, which can be widely used in various models of the rolling stock.
According to the results of the research proposed a number of technical solutions, created at the level of 8 inventions of the Russian Federation, which are modifications of the above construction, and in each case, that permits to use them not only in the desig ns of locomotives, but also passenger and freight rolling stock. For such structures as the calculations on the substantiation of their rat ional kinemat ic and geometric parameters.
With account of the above-mentioned, the carried out researches have allowed to expand the well-known classification of the running parts of the ro lling stock, as shown in figure 10.

Conclusions
Developed by promising adaptive torsion suspension, designed for the main and industrial loco motives, including adaptive hydro-mechanical dampers, established on the level of inventions (RU2427737 and a positive decision of FIPS fro m 25.04.2012, according to the application №2011121597/ 11), schematic d iagram of wh ich is shown in Fig. 1 allows you to: firstly, to reduce consumption of metal chassis of the rolling stock, secondly, to simplify the des ign of the spring suspension, third, to increase the maintainability of it and in the fourth increase the smoothness of the crew at the expense of its ability in the automatic mode effectively mitigate any dynamic components of the loads caused by the irregularit ies of the way when the motion of the rolling stock.
The results of the research are reco mmended both domestic and foreign scientific research institutes, design and production structures heavy machinery for further study and elaboration of p roposed constructions of adaptive torsion spring suspension with a view to the possible introduction of it in p ractice.