Engineering topics
Publications and source records attributed to Clark, S. K..
A method is presented for calculating the stress-strain relations in a multi-layer composite made up of materials whose individual stress-strain characteristics are non-linear and possibly different. The method is applied to the case of asymmetric tubes in tension, and comparisons with experimentally measured data are given.
Reinforced elastomers form the basis for most of the structural or load carrying applications of rubber products. Computer based structural analysis in the form of finite element codes was highly successful in refining structural design in both isotropic materials and rigid composites. This has lead the rubber industry to attempt to make use of such techniques in the design of structural cord-rubber composites. While such efforts appear promising, they were not easy to achieve for several reasons. Among these is a distinct lack of a clearly defined set of material property descriptors suitable for computer analysis. There are substantial differences between conventional steel, aluminum, or even rigid composites such as graphite-epoxy, and textile-cord reinforced rubber. These differences which are both conceptual and practical are discussed.
A method was developed for calculating the internal temperature distribution in an aircraft tire while free rolling under load. The method uses an approximate stress analysis of each point in the tire as it rolls through the contact patch, and from this stress change the mechanical work done on each volume element may be obtained and converted into a heat release rate through a knowledge of material characteristics. The tire cross-section is then considered as a body with internal heat generation, and the diffusion equation is solved numerically with appropriate boundary conditions of the wheel and runway surface. Comparison with data obtained with buried thermocouples in tires shows good agreement.
An analytical model was developed to approximate the internal temperature distribution in an aircraft tire operating under conditions of unyawed braked rolling. The model employs an array of elements to represent the tire cross section and considers the heat generated within the tire to be caused by the change in strain energy associated with cyclic tire deflection. The additional heating due to tire slip and stresses induced by braking are superimposed on the previously developed free rolling model. An extensive experimental program was conducted to verify temperatures predicted from the analytical model. Data from these tests were compared with calculations over a range of operating conditions. The model results were in reasonably good agreement with measured values.
A method was developed for calculating the internal temperature distribution in an aircraft tire while free rolling under load. The method uses an approximate stress analysis of each point in the tire as it rolls through the contact patch, and from this stress change the mechanical work done on each volume element may be obtained and converted into a heat release rate through a knowledge of material characteristics. The tire cross-section is then considered as a body with internal heat generation, and the diffusion equation is solved numerically with appropriate boundary conditions of the wheel and runway surface. Comparison with data obtained with buried thermocouples in tires shows good agreement.
A method was developed for calculating the internal temperature distribution in an aircraft tire while free rolling under load. The method uses an approximate stress analysis of each point in the tire as it rolls through the contact patch, and from this stress change the mechanical work done on each volume element may be obtained and converted into a heat release rate through a knowledge of material characteristics. The tire cross-section is then considered as a body with internal heat generation, and the diffusion equation is solved numerically with appropriate boundary conditions of the wheel and runway surface. Comparison with data obtained with buried thermocouples in tires shows good agreement.
The properties were measured during static, slow rolling, and high-speed tests, and comparisons were made between data as acquired on indoor drum dynamometers and on an outdoor test track. In addition, mechanical properties were also obtained from scale model tires and compared with corresponding properties from full-size tires. While the tests covered a wide range of tire properties, results seem to indicate that speed effects are not large, scale models may be used for obtaining some but not all tire properties, and that predictive equations developed in NASA TR R-64 are still useful in estimating most mechanical properties.
A review of the tire research programs which address the various needs identified by landing gear designers and airplane users is presented. The experimental programs are designed to increase tire tread lifetimes, relate static and dynamic tire properties, establish the tire hydroplaning spin up speed, study gear response to tire failures, and define tire temperature profiles during taxi, braking, and cornering operations. The analytical programs are aimed at providing insights into the mechanisms of heat generation in rolling tires and developing the tools necessary to streamline the tire design process and to aid in the analysis of landing gear problems.
Effort is directed toward construction of a rational method for evaluating internal temperatures of aircraft tires. Enhanced predictability of tire temperature buildup is a design tool in both the tire and airframe industries.
The data bank constructed provided two basic advantages for the user of aircraft tire information. First, computerization of the data bank allowed mechanical property data to be stored, corrected, updated, and revised quickly and easily as more reliable tests and measurements were carried out. Secondly, the format of the book which can be printed from the computerized data bank can be easily adjusted to suit the needs of the users without the great expense normally associated with reprinting and editing books set by ordinary typography.
The principle of utilizing geometric interaction between runway asperities and tire pattern design is discussed, and a theoretical basis is presented for substantial enhancement of frictional effects by this process. Test data confirming this is given. First order analytical expressions are given for the increased friction coefficients and for the engagement distances required. High speed friction data on a 7.00 x 8 aircraft tire is presented confirming this. Example design geometries are shown for the tire tread groove pattern, and designs and materials are discussed for the asperity grid and its attachment system.
Fore-aft, lateral, and vertical spring rates of model and full-scale pneumatic tires were evaluated by testing techniques generally employed by industry and various testing groups. The purpose of this experimental program was to investigate what effects the different testing techniques have on the measured values of these important static tire mechanical properties. The testing techniques included both incremental and continuous loadings applied at various rates over half, full, and repeated cycles. Of the three properties evaluated, the fore-aft stiffness was demonstrated to be the most affected by the different testing techniques used to obtain it. Appreciable differences in the fore-aft spring rates occurred using both the increment- and continuous-loading techniques; however, the most significant effect was attributed to variations in the size of the fore-aft force loop. The dependence of lateral stiffness values on testing techniques followed the same trends as that for fore-aft stiffness, except to a lesser degree. Vertical stiffness values were found to be nearly independent of testing procedures if the nonlinear portion of the vertical force-deflection curves is avoided.
A research program has investigated the use of the von Schlippe string-type tire model for predicting the dynamic behavior of aircraft tires. The transfer-function method was used for theory evaluation. A more flexible two-constant modification to the string theory tire model is presented. Experiments were conducted on four types of scale model aircraft tires. Two types were of conventional bias construction, one type was an isotropic toroid, and one type was of unbelted radial construction. The conventional string theory and model gave predictions that were in good agreement with experimental data for bias constructed tires. The two-constant modification to string theory provided better agreement between predictions and experiment for the unconventional tires. The results indicate that the string theory tire model using static and slow-rolling tire properties predicts dynamic aircraft tire properties that have the same trends as the measured dynamic properties and, in most cases, provides good quantitative agreement.
A variety of tests was undertaken to determine the nature of heat generation associated with a pneumatic tire operating under various conditions. Tests were conducted to determine the magnitude and distribution of internally generated heat caused by hysteresis in the rubber and ply fabric in an automobile tire operating under conditions of load, pressure, and velocity representative of normal operating conditions. These included tests at various yaw angles and tests with braking applied. In other tests, temperature sensors were mounted on a road to measure the effect of a tire rolling over and an attempt was made to deduce the magnitude and nature of interfacial friction from the resulting information. In addition, tests were performed using the scratch plate technique to determine the nature of the motion between the tire and road. Finally, a model tire was tested on a roadwheel, the surface covering which could be changed, and an optical pyrometer was used to measure rubber surface temperatures.
The dynamic properties of four model aircraft tires of various construction were evaluated experimentally and compared with available theory. The experimental investigation consisted of measuring the cornering force and the self-aligning torque developed by the tires undergoing sinusoidal steering inputs while operating on a small scale, road-wheel tire testing apparatus. The force and moment data from the different tires are compared with both finite- and point-contact patch string theory predictions. In general, agreement between finite contact patch theory and experimental observation is good. A modified string theory is also presented in which coefficients for cornering force and self-aligning torque are determined separately. This theory improves the correspondence between the experimental and analytical data, particularly on tires with relatively high self-aligning torques.
A theoretical and experimental investigation of the feasibility of determining the mechanical properties of aircraft tires from small-scale model tires was accomplished. The theoretical results indicate that the macroscopic static and dynamic mechanical properties of aircraft tires can be accurately determined from the scale model tires although the microscopic and thermal properties of aircraft tires can not. The experimental investigation was conducted on a scale model of a 40 x 12, 14 ply rated, type 7 aircraft tire with a scaling factor of 8.65. The experimental results indicate that the scale model tire exhibited the same static mechanical properties as the prototype tire when compared on a dimensionless basis. The structural modeling concept discussed in this report is believed to be exact for mechanical properties of aircraft tires under static, rolling, and transient conditions.
The string theory was evaluated for predicting lateral tire dynamic properties as obtained from scaled model tests. The experimental data and string theory predictions are in generally good agreement using lateral stiffness and relaxation length values obtained from the static or slowly rolling tire. The results indicate that lateral forces and self-aligning torques are linearly proportional to tire lateral stiffness and to the amplitude of either steer or lateral displacement. In addition, the results show that the ratio of input excitation frequency to road speed is the proper independent variable by which frequency should be measured.
Tire shimmy calculations for scale model aircraft tires