Pitch Curve Research Articles

Flow fluctuation abatement of high-order elliptical gear pump by external noncircular gear drive

Large flow ripples restrict the development and application of high-order elliptical gear pumps badly. A new approach is proposed to reduce the flow fluctuations effectively by using a varying angular speed drive. Firstly the instantaneous flow rate model of the elliptical gear pump is established to analyze the effect of the eccentric ratio, number of order and module of the rotors on the flow rate. Then on the basis of the flow characteristics of the pump, an external noncircular gear drive is presented to cancel the low-frequency and large-amplitude flow ripples given by noncircular rotors completely, whose pitch curves are identified to be closed by the residue theorem. Finally, a pump prototype is made to prove that the flow pulsation of the elliptical gear pump can be reduced effectively by the external noncircular gear drive, which provides a favorable support for the design of high-performance pump with lager displacement and uniform flow.

Research on design method of non-circular planetary gear train transplanting mechanism based on precise poses and trajectory optimization

Among all kinds of transplanting mechanisms which are the important parts of transplanters, the planetary gear train transplanting mechanism is widely used for its excellent transmission performance, but it is difficult to design the gear pitch curves and structural parameters according to the trajectory and pose requirements of transplanting. The current design method of the non-circular planetary gear train transplanting mechanism cannot ensure the precise position and posture in the crucial points of transplanting trajectory, nor take both the anticipated trajectory and the smoothness of the gear pitch curves into account, it will only get one solution which is available for mechanism design. In order to solve those problems, the non-circular planetary gear train transplanting mechanism is analyzed as a combination of the bar-group and gear train system. According to the transplanting requirements, three points with precise position and posture which called pose points in the trajectory are given to obtain the solution domain of the parameters of bar-group, and then trajectory shape control points are inlet to design the desired shape of the transplanting trajectory and obtain the transmission ratio curve which can be used to get the gear pitch curve. The most suitable parameters of bar-group in solution domain are selected based on the smoothness of the gear pitch curves. This article establishes three-dimensional model of the mechanism and utilizes the ADAMS to carry out a motion simulation; all simulation results are consistent with theoretical design results, which confirm that the design method based on prescribed pose points and trajectory control points is adequate for the transplanting mechanism. With the proposed method, the selectivity of the mechanism’s parameters solution is increased, and transmission performance benefits from the integrated design of trajectory control and the smoothness of the pitch curves.

Geometric design and kinematics analysis of coplanar double internal meshing non-circular planetary gear train

A new type of non-circular planetary gear train is proposed, in which the planetary gear is internally meshed with the sun gear and the ring gear at the same time. The structural form and transmission principle are analyzed, and the design method of non-circular gear pitch curves and related parameters of the gear train are discussed. The input–output relationship under various working conditions of the gear train is deduced. The precise tooth profile of the non-circular gears is obtained by the Boolean operation of MATLAB, then the virtual prototype model of the planetary gear train is established, and the kinematics simulation is carried out in the ADAMS software. The simulation results verify the correctness of the transmission principle and the theoretical analysis of the motion law.

Comparative assessments of binned and support vector regression-based blade pitch curve of a wind turbine for the purpose of condition monitoring

The unexpected failure of wind turbine components leads to significant downtime and loss of revenue. To prevent this, supervisory control and data acquisition (SCADA) based condition monitoring is considered as a cost-effective approach. In several studies, the wind turbine power curve has been used as a critical indicator for power performance assessment. In contrast, the application of the blade pitch angle curve has hardly been explored for wind turbine condition monitoring purposes. The blade pitch angle curve describes the nonlinear relationship between pitch angle and hub height wind speed and can be used for the detection of faults. A support vector machine (SVM) is an improved version of an artificial neural networks (ANN) and is widely used for classification- and regression-related problems. Support vector regression is a data-driven approach based on statistical learning theory and a structural risk minimization principle which provides useful nonlinear system modeling. In this paper, a support vector regression (a nonparametric machine learning approach)-based pitch curve is presented and its application to anomaly detection explored for wind turbine condition monitoring. A radial basis function (RBF) was used as the kernel function for effective SVR blade pitch curve modeling. This approach is then compared with a binned pitch curve in the identification of operational anomalies. The paper will outline the advantages and limitations of these techniques.

A pair of kinematically related space curves

We investigate the relation between two types of space curves, the Mannheim curves and constant-pitch curves and primarily explicate a method of deriving Mannheim curves and constant-pitch curves from each other by means of a suitable deformation of a space curve. We define a “radius” function and a “pitch” function for any arbitrary regular space curve and use these to characterize the two classes of curves. A few non-trivial examples of both Mannheim and constant pitch curves are discussed. The geometric nature of Mannheim curves is established by using the notion of osculating helices. The Frenet–Serret motion of a rigid body in theoretical kinematics is studied for the special case of a Mannheim curve and the axodes in this case are deduced. In particular, we show that the fixed axode is developable if and only if the motion trajectory is a Mannheim curve.

Comparative analysis of binning and Gaussian Process based blade pitch angle curve of a wind turbine for the purpose of condition monitoring

Several studies have used the power curve as a critical indicator to assess the performance of wind turbines. However, the wind turbine internal operation is affected by various parameters, particularly by blade pitch angle. Continuous monitoring of blade pitch angle can be useful for power performance assessment of wind turbines. The blade pitch curve describes the nonlinear relationship between pitch angle and hub height wind speed which to date has been little explored for wind turbine condition monitoring. Gaussian Process models are nonlinear and nonparametric technique, based on Bayesian probability theory. Such models have the potential give results quickly and efficiently. In this paper, we propose a Gaussian Process model to predict blade pitch curve of a wind turbine for condition monitoring purposes. The obtained Gaussian Process based blade pitch curve is then compared with a conventional approach based on a binned blade pitch curve for identifying operational anomalies purposes. Finally, the weaknesses and strengths of these methods are summarised. SCADA data from healthy wind turbines are used to train and evaluate the performance of these techniques.

근접 복사 유형화를 통한 미국인과 한국인의영어 억양 분석

A comparative analysis of English intonations produced by 22 Americans and 21 Koreans was conducted using a close-copy stylization of pitch curves....

Optimal shape and motion planning for dynamic planar manipulation

This paper presents a framework for optimizing both the shape and the motion of a planar rigid end-effector to satisfy a desired manipulation task. Both shape and motion play key roles in determining contact interaction, and while both are commonly seen as design/control freedoms, their synergies are rarely formally explored. In this paper we study quasistatic problems like cam design, or dynamic problems like ball throwing, where both the shape and motion of the surfaces at contact are relevant. We frame this design problem as a nonlinear optimization program, where shape and motion are decision variables represented as splines. The task is represented as a series of constraints, along with a fitness cost, which force the solution to be compatible with the dynamics of frictional hard contact while satisfying the task. We illustrate the approach with the example problem of moving a disk along a desired path or trajectory, and we verify it by applying it to three classical design problems: the rolling brachistochrone, the design of teeth of involute gears, and the pitch curve of rolling cams. We conclude with a case study involving the optimization and real implementation of the shape and motion of a dynamic throwing arm.

Cam Profile Generation for Cam-Spring Mechanism With Desired Torque

Commercial springs have linear characteristics. Nevertheless, in some cases, nonlinear behavior (e.g., nonlinear torque) is desired. To handle that, a cam-spring mechanism with a specified cam profile was proposed in our previous work. In this paper, to further study the cam profile generation, a new convenient design method is proposed. First, the model of cam-spring mechanism considering the friction force is analyzed. Based on this model, sorts of derivation processes are conducted for obtaining the expression of spring torque. When the friction coefficient is zero, the analytical solution of the equation (spring deformation) is derived. However, in practice, where the friction coefficient is not zero, an analytical solution is not available. Therefore, a numerical solution is sought. Then, with the obtained spring deformation, the cam profile and pitch curve are generated. Results of an experiment conducted to verify the new method show that the cam profile generated by the direct derivation method can precisely mimic the desired torque characteristics. In addition, the hysteresis induced by the friction force in the cam-spring mechanism is also studied. By increasing the spring stiffness, spring free length, and the cam eccentricity, the hysteresis in the cam-spring mechanism can be decreased.

Design of Accurate Steering Gear Mechanism

Abstract This article focuses on the synthesis of a steering mechanism that exactly meets the requirements of steering geometry. It starts from reviewing the four-bar linkage, then discusses the number of points that a common four-bar linkage could precisely trace at most. After pointing out the limits of a four-bar steering mechanism, this article investigates the turning geometry for steering wheels and proposes a steering mechanism using servo motors and ARDUINO board. The pitch curves, addendum curves, dedendum curves, tooth pro les and transition curves of the noncircular gears are formulated and designed. Finally, kinematic simulations are executed to demonstrate the target of design

Design of a Compact Gravity Equilibrator With an Unlimited Range of Motion

A gravity equilibrator is a statically balanced system which is designed to counterbalance a mass such that any preferred position is eliminated and thereby the required operating effort to move the mass is greatly reduced. Current spring-to-mass gravity equilibrators are limited in their range of motion as a result of constructional limitations. An increment of the range of motion is desired to expand the field of applications. The goal of this paper is to present a compact one degree-of-freedom mechanical gravity equilibrator that can statically balance a rotating pendulum over an unlimited range of motion. Static balance over an unlimited range of motion is achieved by a coaxial gear train that uses noncircular gears. These gears convert the continuous rotation of the pendulum into a reciprocating rotation of the torsion bars. The pitch curves of the noncircular gears are specifically designed to balance a rotating pendulum. The gear train design and the method to calculate the parameters and the pitch curves of the noncircular gears are presented. A prototype is designed and built to validate that the presented method can balance a pendulum over an unlimited range of motion. Experimental results show a work reduction of 87% compared to an unbalanced pendulum and the hysteresis in the mechanism is 36%.

Study on the pitch curve with minimal rotary inertia for the noncircular gears

Aimed at the high load and slow response of the noncircular gears design, a general mathematical model for designing the pitch curve with minimal rotary inertia of the noncircular gear is proposed by resorting to kinematics principle and calculus of variations. To achieve the closure design, the constraint conditions and smoothness characteristics of N-lobed noncircular gear pitch curve with minimal rotary inertia are established and calculated analytically. In addition, the unified design method of the conjugate pitch curves with minimal rotary inertia for the noncircular gears is given in this paper. Unclosed and closed N-lobed conjugate pitch curves that satisfy the desired transmission requirements can be easily solved by using the proposed method, and each lobe has identical profile to ensure the periodical motion of the pitch curves. Numerical examples are implemented in computer and demonstrate the feasibility of the above method.

Synthesis of Shaped Noncircular Gear Using a Three-Linkage Computer Numerical Control Shaping Machine

Gear shaping, commonly regarded as the most widely used machining method for cylindrical gear, is in fact an ideal manufacturing method for noncircular gear due to its merit of not being restricted by gear type or pitch curve in contrast to gear hobbing. However, concerning researches are mainly focused on the generation of noncircular straight external gear, paying rare attention to noncircular internal gear and noncircular helix gear. Considering that this paper, through using a three-linkage computer numerical control (CNC) shaping machine, aims to synthesize shaped noncircular gear, covering external, internal, straight, and helix gear. The mathematical model, a three-linkage model, is first established. The corresponding manufacturing process in practice is subsequently discussed. Finally, with practical shaping experiments, the correctness of the proposed model and the appropriateness of the manufacturing process are verified.

Cylindrical Gears with Changing Ratio

Changing ratio gears are noncircular. It means that if they are combined with a conventional cylindrical gear a changing axis distance will be given. Changing axis distance can generate a lot of difficulties and additional costs in the construction. Our goal was to create changing ratio gears that have cylindrical geometry and interlock with conventional cylindrical gears at a constant axis distance. This can be achieved by applying continuously changing profile shift. Profile shift modifies the diameter of the gears, however it does not have any effect on the ratio; regardless if that is constant or changing. The point of our calculation is that some gears with noncircular rolling curves can have circular pitch curve with the help of changing profile shift.

Influence of tooth profile on the noncircular gear tooth contact

With noncircular gears, the continuous modification of the tooth meshing, in terms of variation of the tooth profiles and the line of action position and inclination, makes difficult the implementation of a general standard procedure for the analysis of the noncircular gears tooth contact. In this paper, the authors present a graphical approach that enables the tooth contact static pattern to be produced and evaluated in case of a noncircular gear with complex geometry of the pitch curve. The study is virtually developed, in AutoCAD environment, by animating and investigating the gear solid models in mesh. The tooth static contact analysis enables the path of contact area and distribution to be evaluated in correlation with the following variable initial data: gear pitch curve geometry, tooth profile geometry, as a consequence of different generating procedures, and the gear pressure angle. It was found out that the noncircular gear tooth contact could be improved by choosing different procedures for the tooth flank generation in concave and convex zones and by increasing the gear pressure angle.

Optimal Control to Increase Energy Production of Wind Farm Considering Wake Effect and Lifetime Estimation

In a wind farm, the upstream wind turbine may cause power loss to the downstream wind turbines due to the wake effect. Meanwhile, the energy production is determined by the power generation and the lifetime of the wind turbine. In this paper, an optimal active power control method is proposed to maximize the energy production of wind farms by considering the wake effect and the lifetime of wind turbine. It starts with the analysis of the pitch angle curve and active power curve seen from the Maximum Power Point Tracking (MPPT) of individual wind turbines. Taking the wake effect into account, the pitch angle curve and active power curve are optimized with the aim of Maximum Power Generation (MPG) of the wind farm. Afterwards, considering the lifetime of wind turbines, a comparison is offered between the MPPT method and the MPG method for energy production using a simplified two-turbine wind farm as an example. Due to the small range of the effective wake area, it is found that the energy production is almost the same. Finally, the pitch angle curve and active power curve are optimized according to the Maximum Energy Production (MEP) of a wind farm. Upon considering and contrasting the MPPT method and the MEP method, it can be seen that the energy production of wind farms can be increased even in the case of there not being an effective wake area.

Evidence of secondary tooth contact in harmonic drive, with involute toothed gear pair, through experimental and finite element analyses of stresses in flex-gear cup

Stresses in flex spline/gear cup in harmonic drives with involute toothed gear pair and conventional strain wave generating cam are analyzed using finite element method in ANSYS® environment and experiments. The most innovative part of this investigation is establishing the evidence of secondary contacts and probable load shared by those contacts experimentally over the finite element analysis. Aiming at the performance improvement of gearing in harmonic drives, with involute toothed gear pair, the investigations are carried out through the following analyses. (a) Initial stresses in flex gear cup due to cam insertion only. (b) Stresses in flex gear cup at no load in fully assembled harmonic drive components i.e. flex gear, ring gear, and strain wave generating cam. (c) Stresses in flex gear cup at full load passing through the two pitch points, i.e. the intersection points of ring gear pitch circle, flex gear pitch curve, and major axis on both sides. Finally, (d) stresses in flex gear cup at full load distributed over all possible primary and secondary contacts, in proportion to their contact intensities. Recorded strains of the flex-gear cup while the cam being rotated showed very good agreement with the results obtained by finite element analysis with proper modeling of loading.

Transmission principle and geometrical model of eccentric face gear

Noncircular gears acquire wide application in various filed. A novel spatial noncircular gear set comprised of a cylinder gear and an eccentric face gear is presented, which has advantages of light weight, high interchangeability and convenient installation. The transmission mechanism of the eccentric face gear is expounded by kinematical analysis, with the pitch curves and drive ratio deduced. Based on the spatial meshing theory of gears, the mathematical model of the tooth surface of the eccentric face gear is built. Defining the basic design parameters of the eccentric face gear, an kinematical simulation and tooth contact analysis of the eccentric face gear and a cylinder gear are made, which demonstrate the feasibility of the transmission and the correctness of the mathematical model of the eccentric face gear.

A Study on the Features of the Japanese Intonation of Beginner level of Japanese language learners : An Analysis through Pitch Curve

A Study on the Features of the Japanese Intonation of Beginner level of Japanese language learners : An Analysis through Pitch Curve

A numerical analysis to evaluate Betz's Law for vertical axis wind turbines

The upper limit for the energy conversion rate of horizontal axis wind turbines (HAWT) is known as the Betz limit. Often this limit is also applied to vertical axis wind turbines (VAWT). However, a literature review reveals that early analytical and recent numerical approaches predicted values for the maximum power output of VAWTs close to or even higher than the Betz limit. Thus, it can be questioned whether the application of Betz's Law to VAWTs is justified.To answer this question, the current approach combines a free vortex model with a 2D inviscid panel code to represent the flow field of a generic VAWT. To ensure the validity of the model, an active blade pitch control system is used to avoid flow separation. An optimal pitch curve avoiding flow separation is determined for one specific turbine configuration by applying an evolutionary algorithm. The analysis yields a net power output that is slightly (≈6%) above the Betz limit. Besides the numerical result of an increased energy conversion rate, especially the identification of two physical power increasing mechanisms shows, that the application of Betz's Law to VAWTs is not justified.