Browse Topic: Splines
A new guidance optimization scheme for spacing waypoints on spline trajectories is proposed. This scheme, the bounded area minimization algorithm, examines sequences of 3 waypoints that sample a given spline trajectory at its constituent knot locations and moves the interior waypoint to a location on the spline trajectory that minimizes the bounded area, computed using Green’s theorem, between the trajectory and the straight-line paths (legs) that connect adjacent waypoints. For spline trajectories defined by more than 3 knots, the algorithm can be applied sequentially to cover the entire chain of knots. Five motion primitives were chosen to test the performance of the optimization scheme on piecewise cubic polynomial spline trajectories. Two of these motion primitives (sinusoid and exponential) as well as two real-world trajectories that have been flight-tested on an MD530F platform were then simulated in a full nonlinear rotorcraft flight dynamics simulator to quantify and compare the effects of optimized versus baseline waypoint spacing. The bounded area minimization algorithm was extremely effective at reducing cumulative cross track error when the waypoint spacing was large enough that the aircraft trajectories closely matched the straight-line waypoint legs used in the algorithm. A method of determining the smallest waypoint spacing at which the optimization algorithm is still beneficial was proposed based on varying the wavelength of the ADS-33 Slalom MTE. For densely sampled spline trajectories that do not have knot spacings large enough to realize the benefits of the optimization algorithm, knot removal can sometimes reduce the number of waypoints required to represent the trajectory while maintaining the cumulative cross track error. However, there is no guarantee that subsequent bounded area minimization results in better performance than the baseline waypoint spacing. Determination of waypoint spacing for densely sampled spline trajectories is a recommended area of future work. A practical benefit of the bounded area minimization algorithm is that it requires very little modification to in-service coupled waypoint guidance flight director and autopilot schemes on existing aircraft, which improves the likelihood of its adoption by reducing the effort required for formal qualification and certification.
This paper addresses the uncertainty quantification of time-dependent problems excited by random processes represented by Karhunen Loeve (KL) expansion. The latter expresses a random process as a series of terms involving the dominant eigenvalues and eigenfunctions of the process covariance matrix weighted by samples of uncorrelated standard normal random variables. For many engineering appli bn vb nmcations, such as random vibrations, durability or fatigue, a long-time horizon is required for meaningful results. In this case however, a large number of KL terms is needed resulting in a very high computational effort for uncertainty propagation. This paper presents a new approach to generate time trajectories (sample functions) of a random process using KL expansion, if the time horizon (duration) is much larger than the process correlation length. Because the numerical cost of KL expansion increases drastically with the size of time horizon, we partition it into multiple subdomains of equal length (time), perform a KL expansion for only the first subdomain and then extend it to the remaining subdomains by imposing a correlation between the KLE coefficients of adjacent subdomains. Additionally, to ensure continuity at the junction between subdomains, a cubic spline interpolation is implemented. The proposed approach is demonstrated using two examples.
This ARP applies to turbine engines that are to be used in helicopters. It provides the engine designer guide lines in achieving a satisfactory turbine engine drive shaft connection.
This paper takes a review of fretting phenomenon on splines of the engaging gears and corresponding splines on shaft of automotive transmission and how it leads to failure of other components in the gearbox. Fretting is a special wear process which occurs at the contact area of two mating metal surfaces when subject to minute relative oscillating motion under vibration. In automotive gearbox, which is subjected to torsional vibrations of the powertrain, the splines of engaging gears and corresponding shaft may experience fretting, especially when the subject gear pair is not engaged. The wear debris formed under fretting process when oxidizes becomes very hard and more abrasive than base metal. These oxidized wear particles when comes in mesh contact with nearby components like bearings, gears etc. may damage these parts during operation and eventually lead to failure. In this paper, a case study is presented wherein fretting has been identified as the root cause of failures of some child parts in a gearbox. A parametric study was carried out, evaluating design and operational parameters to identify the causes of fretting and their relative impact on gearbox durability, through rig testing. Corrective action and their correlation in addressing the failures of other child parts was further proved though rig testing.
The advancement in embedded systems and positional accuracy with base station GPS modules created opportunity to develop high performance autonomous ground vehicles. However, the development of vehicle model and making accurate state estimations play vital role in reducing the cross track error. The present research focus on developing Linear Quadratic Gaussian (LQG) with Kalman estimator for autonomous ground vehicle to track various routes, that are made with the series of waypoints. The model developed in the LQG controller is a kinematic bicycle model, which mimics 1/5th scale truck. Further, the cubic spline fit has been used to connect the waypoints and generate the continuous desired/target path. The testing and implementation has been done at APS labs, MTU on the mentioned vehicle to study the performance of controller. Python has been used for simulations, controller coding and interfacing the sensors with controller. From the results, it has been confirmed that, the vehicle is able to track the given path within the cross track error of ±0.2m.
This concept for measuring worn splines provides a direct wear depth dimension by utilizing the unworn involute surface as a contact point from which to measure the depth of wear on the spline tooth at the pitch diameter. Fig. 1 shows spline wear patterns and pitch diameter gaging points.
A real-time path planning algorithm is developed to generate time-optimal trajectory for helicopter shipboard landing. The trajectory optimization problem is translated to the lower dimensional flat output space by exploiting the differential flatness property of the simplified helicopter model. Then, the flat outputs are parameterized using piecewise spline functions with adjustable coefficients, which are used to shape the trajectory and approximate the optimal solution. Further, by allowing the flexible selection of each spline segment's time-duration and enforcing additional path constraints, the time-optimality of the planned trajectory is largely preserved without violation of state and input bounds. Compared to pure temporal discretization methods, the proposed algorithm employs considerably less decision variables and significantly reduces the computational time by 75%, which only leads to a 0.5% growth in the optimal flight time as the trade-off. The improvement in computational efficiency enables the real-time recalculation of the time-optimal trajectories on-the-fly if there are unforeseen deviations from the planned flight path.
This specification, in conjunction with the general requirements for steel heat treatment covered in AMS2759, establishes the requirements and procedures for three classes of gas, vacuum, liquid, and low pressure (LPC) carburizing and related heat treatment of parts fabricated from carburizing grade steels. Parts made from steels other than those specified in the detail specifications may be heat treated in accordance with the applicable requirements using processing temperatures, times, and other parameters recommended by the material producer unless otherwise specified by the purchaser. This specification does not cover pack carburizing.
This SAE Aerospace Standard (AS) is intended for use by those involved in the design of aircraft, missile, or space systems, and their support equipment to define the various types of fastener torque.
This specification, in conjunction with the general requirements for steel heat treatment covered in AMS2759, establishes the requirements and procedures for three classes of gas, vacuum, liquid, and low pressure (LPC) carburizing and related heat treatment of parts fabricated from carburizing grade steels. Parts made from steels other than those specified in the detail specifications may be heat treated in accordance with the applicable requirements using processing temperatures, times, and other parameters recommended by the material producer unless otherwise specified by the purchaser. This specification does not cover pack carburizing.
In the emerging commercial vehicle sector, it is very essential to give a product to customer, which is very reliable and less prone to the failures to make the product successful in the market. In order to make it possible, the product is to be validated to replicate the exact field conditions, where it is going to be operated. Lab testing plays a vital role in reproducing the field conditions in order to reduce the lead time in overall product life cycle development process. This paper deals with the design and fabrication of the steering column slip endurance test rig. This rig is capable of generating wear on the steering column splines coating which predominantly leads to failure of steering column. The data acquired from Proving Ground (PG) was analyzed and block cycles were generated with help of data analyzing tools. Those block cycles were run with the help of this rig it consists of Variable Frequency Drive (VFD) to change the velocity of steering column, and torque applied on component to reproduce field conditions.
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