78 CHAPTER 5 RANDOM ROAD ANALYSIS 5.1 INTRODUCTION In this chapter, the random runway profiles are generated using Matlab/Simulink. The developed full aircraft with active landing gear model is simulated on the different grades of runway profiles. In this work, random road profiles and their classification based on the international organization for standardization (ISO 8606) is considered (Figure 5.1).Lateral profiles show the superelevation and crown of the road design, plus rutting and other distress. Longitudinal profiles show the design grade, roughness and texture. ISO 8606 specifies the power spectral density values for road roughness, generally considered to be among road classes A to H. Figure 5.1 Road profile (Feng Tyan et al 2008) The most commonly adopted methods are shaping filter method and sinusoidal approximation method for generating one dimensional random
79 profile. These profiles are used in the simulation of full aircraft model with active landing gears. In the shape filter method, it is found that the time constant of first order transfer function generating the road profile is independent of the grade of road. While for the sinusoidal approximation method, a detail derivation of the amplitude of each sinusoidal function is re derived for completeness. 5.2 TYPES OF AIRFIELD SURFACE The Pavement is generally characterized as being rigid or flexible. The rigid pavement is made of concrete using Portland cement and the pavements under the jurisdiction of the port of Newyork and New jercy in which lime, cement and flyash are mixed with sand. The thickness is commonly 8 inch to 14 inch. Three types of loading are possible which are interior, edge and corner. The design of pavement is done based on the interior and edge load calculation. 5.2.1 Rigid Pavement This pavement design is based on westergaard s theories, which use radius of relative stiffness as a primary parameter in determining the equivalent single wheel load. The relative stiffness is a function of the concrete modulus of elasticity, concrete thickness, poison s ratio, and the modulus of sub grade reaction. 5.2.2 Flexible Pavement This pavement uses multiple layers of compacted materials beneath the surface course and total thickness is characterized between 8 inch and 60 inch.
80 5.2.3 Unpaved Air Field It includes bare soil, grass surfaces, mat-covered surfaces and surfaces that use a membrane between the natural surface and a landing mat. 5.3 RUNWAY SURFACE To analyze the dynamic behavior of a developed multi body system model, time histories have to be evaluated for a broad range of frequencies. The excitations used in the model should include a wide frequency range. The following existing runway disturbances (Wentscher et al 1995) have been considered for the ride comfort investigation. 5.3.1 General Roughness Airfield roughness affects both the landing gear and the airframe. Earlier until 1960 s, the roughness was specified in terms of step bumps and half sine waves. There are two reasons why roughness is receiving the increased attention, 1) Aircraft are becoming larger and therefore more flexible. Even on paved runways aircraft fatigue life is diminished due to roughness, 2) Military doctrine envisages operation from bomb damaged or unpaved airfields with associated roughness in each case. At one time it was assumed that if the tire section height was large enough to swallow a bump, then the bump could be accommodated. This simplistic approach is considered in determining aircraft response and the loads encountering step bumps. Runway profiles have been measured around the world and the data reduced to power spectral densities.the PSD are used to analyze the resultant effects on the airframe. Especially on older airports and on airports in the countries of former warsaw pact, the run and taxiways display undulations of all frequencies and with higher amplitudes than those measured on airports in western countries. These conditions led to dangerous situations. Pilots of
81 aircraft equipped with cathode ray displays (called glass cockpits) experienced difficulties to read the instruments due to vertical acceleration during the take off run. 5.3.2 Concrete Plate Deforming The runways are mostly laid down platforms using liquid concrete. These plates are separated from each other by gaps filled with rubber. Aging of concrete runways causes the plates to settle unevenly leading to long wave length bumps and steps at the gaps. 5.3.3 Center Line Lights All run and taxiways are equipped with lights indicating the middle line during night time operation. These lamps extend a few centimeters from the ground and exert a shock when hit by the tire. 5.4 MODELING OF RANDOM ROAD PROFILE In this work, the shape filter method (Feng Tyan et al 2008) is used for generating the road profiles. The road profile can be represented by Power Spectral Density (PSD) function. Power spectral densities of roads show a characteristic drop in magnitude with wave number. The road surface profile is measured with respect to reference plane. Random road profile can be approximated by a PSD in the form of ( ) =. (5.1) Or ( ) =. (5.2)
82 = in rad/m denotes the angular spatial frequency L is wave length ( ) in m²/ (rad/m) describes the values of the PSD at the reference wave number ( ) =1rad/m. = is the spatial frequency. = 0.1 cycle/m, is the waviness, for most of the road surface, =2 Appendix 1.8. The following guide lines are taken from the ISO 8608 as shown in 1) New roadway layers such as asphalt or concrete layers can be assumed to have a good or even a very good roughness quality. 2) Old roadway layers which are not maintained may be classified as having a medium roughness. 3) Road way layers consisting of cobble stones or similar material may be classified as medium (average) or bad (poor, very poor). It is well known that the amount of road excitation imposed at the vehicle tire depends on the road roughness which is a function of the road roughness coefficient and the velocity (v). Let s be the path variable by introducing the wave length =
83 And assuming that s=0 at t=0 the term can be written as = 2 = 2 = where (rad/s) is the angular velocity in time domain.then V= hence in the time domain the excitation frequency is given by = = For most of the vehicles the rigid body vibration are in between = 0.5 to = 15. This range is covered by waves which satisfy the condition 0.5 15.The random road profile is generated by shaping filter method. The profile can be approximated by PSD distribution ( ) = (5.3) where denotes the road roughness variance (m²) V the aircraft speed (m/s) depends on the type of road surface (rad/m) Hence if the vehicle runs with the constant velocity V, the PSD is given by the above equation(5.3)and the road profile signal may be obtained as the output of a linear filter expressed by the differential Equation (5.4), ( ) ( ) + ( ) (5.4) where (t) is a white noise process with the spectral density ( ) The road roughness standard deviations for various types of roads are as given in Table 5.1.
84 Table 5.1 Road roughness standard deviation Road class ( ) Roughness varience ( )( ), = power spectral density (rad/m) A(very good) 2 1 0.127 B(good) 4 4 0.127 C(average) 8 16 0.127 D(poor) 16 64 0.127 E(very poor) 32 256 0.127 5.5 SIMULINK MODEL OF RANDOM ROAD The road profiles are generated by using the values given in the Table 5.1 in the random road generator as shown in Figure 5.2. The random road generation is done through MATLAB/SIMULINK. Figure 5.2 Simulink model of random road generator
85 5.5.1 Grade B (good) Random Road The Grade B (good) random runway profile is generated by the random road generator. The runway profile is a good road which has a road roughness variance 0.004.The velocity of the aircraft is taken 5 m/s and =0.127.The generated grade B road profile is used for the series of simulations. The aircraft response is investigated with the road profile and the sprung mass acceleration, displacement and shock strut travel values are found from the simulations. 5.5.2 Grade C (average) Random Road The Grade C road profile is average roughness road and has a road roughness variance of 0.008, the velocity of the aircraft is taken as 5m/s and =0.127.The generated grade C road profile is used for the series of simulations and the sprung mass acceleration, displacement and shock strut travel values are calculated from the simulations. 5.5.3 Grade D (poor) Random Road The Grade D road profile is poor roughness road and has a road roughness variance of 0.016.The velocity of the aircraft is considered as 5 m/s and =0.127.The generated grade D road profile is used for the series of simulations and the sprung mass acceleration, displacement and shock strut travel values are calculated from the simulations. 5.5.4 Grade E (very poor) Random Road The road profile is generated in the mat lab simulink environment. The Grade E road profile is very poor roughness road and has a road roughness variance of 0.032.The velocity of the aircraft is considered as 5m/s and =0.127.The generated grade E road profile is used for the series of
86 simulations and the sprung mass acceleration, displacement and shock strut travel values are obtained from the numerical simulations. The performance of the landing gear on various simulated road conditions has been compared. 5.6 RIDE COMFORT ASSESSMENT The base measurements for ride comfort assessment are the vertical acceleration measurements. Since the individual perception is additionally influenced by other factors of the biomechanical human system, scales have been developed to weigh the fact that certain frequencies are perceived to be more uncomfortable than others for given amplitude. In ISO 2631, the frequencies between 4 Hz and 8 Hz are denoted as the most crucial for comfort. For Ride comfort improvement the vertical accelerations in the above frequency range, measured in the cockpit and passenger compartment is to be minimized. The ride quality of the vehicle is characterized based on the amount of weighted acceleration in the vehicle. It was measured to compare and validate the vehicle performance. Table 5.2 shows the level of acceptability of ride quality. Table 5.2 Level of acceptability for ride quality Weighted RMS of Body Acceleration (m/s²) Acceptability <0.315 Not Uncomfortable 0.315-0.63 A Little Uncomfortable 0.5 1 Fairly Uncomfortable 0.8 1.6 Uncomfortable 1.25 2.5 Very Uncomfortable >2 Extremely Uncomfortable
87 Guidelines for the measurement and evaluation of human exposure to whole body vibration are given by International Organisation for Standardisation ISO 2631-1 as shown in Appendix 1.9. The frequency range that is most often associated with the whole body vibration is approximately 0.5 Hz to 100 Hz. Vibration magnitude is generally measured in units of acceleration in rms values. The rms values are frequency weighted according to weighting curves defined in ISO 2631-1, and averaged over time and frequency. This is the basic method for evaluation of whole body vibration. The graphs are drawn such that horizontal axis denotes frequency, vertical axis denotes discomfort and the curves denote the exposure time period of vibrations as shown in Appendix 1.9. The curves for different exposure time period of vibrations look like each other in terms of their characteristics and the minimum regions of these curves are the region of 4 to 8 Hz. The vibration levels in this region are most important as the natural frequencies of certain body structures of a human fall in this range. For instance, in a human body the system of rib cage has a natural frequency value about 3-6 Hz and the structure of head and the neck 20-30 Hz. However the main limiting case changes between 4 and 8 Hz for discomfort. Human exposed to those resonance frequencies can have some health problem like motion sickness and in these frequencies ride comfort is described as worst case. For this reason, it is necessary either to keep the frequencies higher at about 15-20 Hz or to keep the frequencies lower than 4Hz. The simulink block diagram of aircraft with active landing gears is shown in Appendix 1.7. The dynamic response of aircraft to various runway random inputs are obtained considering the passive and active landing gears and the acceleration levels are compared with ISO curves.