Vehicle Evaluation During Sustained Solid Axle Tramp: Part 1 — New Testing Methods and Novel Approaches to Data Analysis

Abstract

EI Consultants (formerly The Engineering Institute) has been studying solid rear axle tramp for well over a decade, and contributed several publications to the literature outlining recommended test methods and their results. Throughout the history of EI’s research, sustained tramp inputs have been achieved by use of a tire featuring affixed lumps of rubber to induce wheel hop at one end of the axle. The principal methodological guide for studying the vehicle response to this input has been the test methods and data analysis recommendations of test standard SAE J266: Steady-State Directional Control Characteristics for Passenger Cars and Light Trucks. More specifically, past testing has been patterned almost exclusively on the circle test (constant-radius/slowly-increasing-speed) method discussed in J266. Historically, the J266 recommendation for data analysis and presentation, i.e. understeer/oversteer gradients derived from a wheel angle versus lateral acceleration plot, were principally used. Recent research, along with fresh analysis of previous testing results, revealed limitations of the circle test and the J266 recommended manner of data analysis in the context of tramp resonance testing. During a constant-radius/slowly-increasing-speed test, a single control variable (speed) has the effect of changing both the lateral acceleration and the tramp input frequency simultaneously. This effect results in a non-steady-state test event where only a narrow portion of each test run expresses the resonant axle tramp phenomenon that is the intended object of the observation. To provide a wider view of vehicle response characteristics during sustained axle tramp, EI Consultants selected and evaluated expanded test methods in a recent testing project. These methods included performing circle tests at multiple radii, performing continuous tests modeled after the J266 constant-speed/variable-radius method, and performing path-following tests modeled after the slowly increasing steer method. Expanded data analysis and presentation methods were developed to quantify and understand the vehicle oversteer response in more effective ways than those recommended by J266. Due to the abrupt discontinuity in the vehicle’s response upon reaching the resonant tramp frequency, novel methods of data presentation were shown to be more useful in assessing vehicle characteristics during resonant tramp. Of particular value was examining the steering input delta in the vehicle speed and tramp input frequency domains during the phase of resonant axle response; and examining the difference between the actual yaw rate and the theoretical Ackerman yaw rate derived from the measured steer angle. This paper will detail the data analysis techniques that were developed to overcome the limitations of the J266 standard’s steer gradient methodology, and thus introduce a more useful approach to evaluating understeer/oversteer characteristics during non-steady-state test events. This paper is the first of two companion papers presenting theory and results from EI Consultants’ most recent axle tramp testing. This paper focuses on new understandings of test data analysis theory, while the second paper will summarize the results of numerous tests and their application to various suspension design strategies for improving solid rear axle tramp control, with a motivation for enhancing vehicle controllability and highway safety.

Vehicle Evaluation During Sustained Solid Axle Tramp: Part 2 — Application of Methodology to Shock Absorber Design Strategies

“…Previous publications by the authors have described the results of some of these test projects. [2,3,5,7] The general methodology has also been employed by other authors. [9,10] The most recent test projects utilized a lumped tire that had the outermost tread cap removed and three equally spaced blocks of rubber, 1-¼" thick, vulcanized onto the tire.…”

“…The most recent test programs of late 2014 and early 2015 added two other maneuver types based on the J266 standard. [7] For brevity and consistency with prior publications, only analysis from subsets of the circle testing will be presented here.…”

“…Test data was plotted and evaluated in the time domain for initial review, as well as in other novel formats described in the companion paper [7]. The principle of the J266 steer gradient data presentation method, whereby steer is plotted in the domain of measured lateral acceleration, was emulated by plotting the steer angle of the road wheels in the speed domain, in the tramp input frequency domain, and against the nominal (centripetal) lateral acceleration as derived from the intended circle radius.…”

“…A computational measure of this oversteer may be found by plotting the difference between the measured yaw rate around the circle and the Ackerman yaw rate derived from the measured steer [7].…”

“…As detailed in this paper's companion work [7], recent expansions to the authors' test methodologies and data analysis techniques have provided a greater ability for quantifying the effectiveness of these shock absorber design strategies, by proposing new methods for observing and describing the vehicle's oversteer characteristic during maximum axle tramp.…”