بررسي اثر افزايش سرعت بر روي شاخص راحتي سفر و عمر سيستم تعليق واگن هاي اكسپرس

An Investigation on the Speed Increasing Effects on the Ride Quality and Fatigue Life of Suspension Systems in Express Coaches

In this paper dynamic performance of a passenger coach is investigated in higher speeds in presence of rail surface irregularities. The research is directed to study how increasing the operating speed may affect two important dynamic parameters ; ride quality index as well as the fatigue life of the springs used in both primary and secondary suspension systems. Rail surface corrugation is modeled by its Power Spectral Density (PSD) for three classes of rails according to the USA classifications of tracks. Using random vibration theory, dynamic matrix of the system (H(co)) is obtained and then for the response matrix of the system one can find: Sxe(o) = H(w)Slt(w)Hri„) (1) where, Sff represents the PSD of the rail corrugation having the general form ^ (CI) = ^ (2) ^ (Q2 +n?xn2 + q2) where Q is spatial frequency and the other parameters are all constants dependent on the rail classifications. Power Spectral Density of the acceleration is abstained by 4*?]= J(3) —oo In order to evaluate Sperlingʹs ride quality index one may use the filter given by its gain of ^ i 1.911 f2 + (0.25f2 )2 H(f) = 0.588 (1 - (0.277f2 )2 + (1.563f -(0.0368f3): to filter the acceleration PSD. After the filtration procedure, Sperlingʹs comfort index can be expressed as Comfort Index = 4.42 (amMSf3 (5) Comfort index Physical denotation 1.0 Just noticeable 2.0 Clearly noticeable 2.5 More pronounced but not unpleasant 3.0 Strong, irregular, but still tolerable 3.25 Very irregular 3.5 Extremely irregular, unpleasant, annoying 4.0 Extremely unpleasant Each comfort index has a physical meaning according to Table 1. In order to obtain fatigue life of the springs used in the primary and secondary suspension systems, random fatigue theory is utilized. Rayleigh technique is used and fatigue life can be obtained as: ʹ&1 2\ -in n I 2 J . x \ y K " J J (6) In e(ad)\ a. k e(t) (7) where m and n are two constants dependent on the spring material and Xq and are spectral moments as follows: = VTXG))dG) j— 00 A2 = f co2tAcojdco J-CO and stress expected value jix 8 d Mx = Tr 2C+1 2C and C represents spring index that is D/d. and finally for the Power Spectral Density of the acting force one can obtain Sʹiia)-s£(a>)+ S£(a>)) (12) Using the above procedure, a computer program has been provided using MATLAB software. A comprehensive parametric study has been carried out to investigate how various parameters like, traveling speed, rail corrugation level, eccentricity ratio, body mass, bogie mass, wheelset mass, primary and secondary suspension system may affect dynamic performance of the coach. Figure 1 illustrates variation of the ride quality index versus the operational speed for three classes of rails. As it is seen, one can divide the diagram into two parts before and after 60 km/hr. It is seen that before 60 km/hr comfort index increases rapidly by very sharp gradient with respect to operational speed. It is also seen that the rail corrugation has smaller effects on the comfort index in this area. But for speeds higher than 60 km/hr, the story is different. Comfort index is approximately a linear function of the speed and its slope is almost independent of the rail class. Furthermore, in this region, comfort index is more affected by the rail class than the operational speed. It is also found that the wheel set and bogie mass have smaller effects than the body mass on the level of the ride comfort index. Moreover, stiffness of the secondary suspension system has greater effects than the primary suspension system on the ride comfort index. Speed( Km/hr) Figure 1: Ride comfort index versus operational speed for eccentricity of 0.1Variation of the fatigue life of the springs used in rear bogie versus operating speed is illustrated in Figure 2. As it is seen, bolster springs have more critical situation than others. Similarly it is seen that the fatigue life of the springs is almost a linear function of the operational speed in high speed region. Figure 2: Fatigue life of the rear bogie springs versus operational speed for eccentricity of 0.1 Variation of the fatigue life of the springs used in rear bogie versus operating speed is illustrated in Figure 2. As it is seen, bolster springs have more critical situation than others. Similarly it is seen that the fatigue life of the springs is almost a linear function of the operational speed in high speed region. Figure 2: Fatigue life of the rear bogie springs versus operational speed for eccentricity of 0.1