The verification and demonstration of a unique course-profilemeasurement methodology

This paper presents an experimental methodology for regeneration of course profiles, with tire acceleration and speed, suspension force and pitch data collected from an instrumented trailer wheel running over the course profile to be identified. The collected data is used to derive the course profile as a function of time, while the speed data is used to map the ground elevation data from a time domain into a spatial domain. To verify the course re-generating rationale, the required test data was simulated with the data extracted from a trailer model running over selected course profiles. The regenerated course profiles are then compared against those used as the inputs to the trailer model, demonstrating the feasibility of using the methodology to regenerate course profiles which statistically align with real-world course profiles. The methodology may be used to develop the inputs statistically equivalent to realistic course profiles as needed in dynamic simulation of terrain-vehicle systems. INTRODUCTION Given that the excitations arising from ground roughness play a key role in the performance analysis of light armored vehicle systems, the need to use realistic ground inputs in dynamic modeling of terrain-vehicle systems is critically important. With today's advanced data acquisition technology, it is possible in reality to measure various offroad ground profiles at high degrees of precision. An extensive literature review, however, reveals that the majority of the reported course-profile-measurement techniques did not turn out to be as cost-effective and time efficient as expected. While certain techniques were reported to derive ground profiles based upon the data collected by an instrumented vehicle over different terrains, the accuracy and efficiency, as well as limitations of the approach used, have yet to be fully demonstrated and verified under specific ground inputs and operational conditions. A successful ground-profile-measurement technique should be based upon a fully verified rationale from both experimental and analytical perspectives. LITERATURE REVIEW Off-road profile measurement remains a challenging task in comparison to paved surface measurement, since the offroad profiles are generally more time-varying than pavedroads, leading to greater vehicle excitations and thus more severe vibration environments that may significantly deteriorate the quality of the test data collected. In addition, it is difficult to maintain a constant speed when traveling over extreme terrains and the dynamics of the suspension will be excited well beyond the points of small angle approximations and linearity assumptions [1]. A number of different methods, in use worldwide, involve either measuring the ground roughness directly with profile-meters [2-3] or deriving the ground profile from measured vehicle response to road roughness e.g., using Dynamic Force Measurement Vehicle (DFMV) developed by the Nevada Automotive Test Center [4-5]. There are also reports addressing specific profiling methods [6-9]. While a variety of profiling methods are available, a simple cost-effective Proceedings of the 2012 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) The verification and demonstration of a unique course-profile-measurement methodology, Zhang, et al. Approved for public release, distribution is unlimited, GDLS approved, Log No. 2012-61, dated 06/21/12 Page 2 of 8 yet efficient methodology remains to be investigated and demonstrated under specific inputs. This paper presents a unique experimental approach conceptually for regenerating longitudinal course profiles based on inputs from an instrumented trailer wheel running over course profiles to be identified. The efficiency and accuracy of the approach is demonstrated with simulation results from the trailer model under selected course inputs. METHODOLOGY An Adams model of a two-wheel trailer pulled by a fourwheel vehicle through a linkage frame, as shown in Figure 1 and Figure 2, was created to simulate the profiling hardware used in test scenarios. The trailer tires were designed with a significantly smaller radius in comparison to those of the tractor tires to ensure the measurement of short wave-length components of the profile. The tractor drives along a straight flat road, pulling the trailer run over the course profile to be regenerated. Compared to the method using DFMV, the geometric and stiffness characteristics of the trailer wheels can be designed solely for the purpose of data acquisition, with the effect from suspension dynamics of the tractor completely isolated from the instrumented trailer wheel (particularly in the simulation process). The sprung mass is supported by the suspension over the trailer wheel, which allows the translational and rotational movements between sprung mass and trailer wheel. The tire acceleration and speed, suspension force and pitch angular displacement of sprung mass of the trailer wheel are extracted from the Adams model (or measured by sensors in real profiling tests) in order to regenerate the course profile. The sprung mass, suspension characteristics and tire stiffness of the trailer wheel are designed to avoid any potential resonant vibrations arising from ground inputs at the speeds selected for simulations, with tire-ground contact maintained throughout the entire simulation process (corresponding to data collection process in a profiling test). Figure 1: Tractor and trailer model in Adams Figure 2: Trailer and its components in Adams By applying Fast Fourier Transform /Inverse Fast Fourier Transform (FFT/IFFT) techniques, the tire acceleration, suspension force and pitch angular displacement of sprung mass (extracted from the trailer in Adams model) are used to derive the course elevations as a function of time, while the speed data (measured at the center of the trailer wheel) is used to convert the regenerated ground elevations from a time domain into a spatial domain. The regenerated course profile is then compared to the course profile used as the inputs to the trailer model in terms of root-mean-square (RMS) values and illustrated in a time domain, showing the efficiency of the approach in regenerating realistic ground profiles. MATHEMATICAL MODEL Figure 3 and Figure 4 show the physical model of the trailer tire and its free-body-diagram. Figure 3: Physical model of trailer tire Trailer Tractor Tractor Linkage frame Suspension over trailer wheel Sprung mass Trailer wheel Profile to be measured Sprung mass Proceedings of the 2012 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) The verification and demonstration of a unique course-profile-measurement methodology, Zhang, et al. Approved for public release, distribution is unlimited, GDLS approved, Log No. 2012-61, dated 06/21/12 Page 3 of 8 Figure 4: Free-body-diagram of trailer tire In Figure 3 and Figure 4 where: x =Displacement at tire-ground interface, unit: m y =Displacement at tire center, unit: m F =Resultant of suspension forces, unit: N m =Mass of trailer tire assembly, unit: kg M =Sprung mass (over trailer wheel), unit: kg Ks =Suspension stiffness coefficient, unit: N/m Cs =Suspension damping coefficient, unit: Ns/m Kt =Trailer tire stiffness coefficient, unit: N/m Ct =Trailer tire damping coefficient, unit: Ns/m Applying Newton’s second law on the trailer wheel (in the vertical direction), it can be written: ) ( ) ( x y k x y c y m F (1) Note that in Equation (1), c and k (with subscript t omitted) are the damping and stiffness coefficients of the trailer tire, respectively, which are assumed to be constants. By re-arranging the items in equation (1) and noting F , x and y are functions of time, it can be written: ) ( ) ( ) ( ) ( ) ( ) ( t F t ky dt t dy c dt t y d m t kx dt t x d c (2)