Novel methodology for turbine gas meters error curve modelling across a wide range of operating parameters

In this paper, performance of turbine flowmeters was investigated for different flowmeter ranges and working gas operating pressures. Variation of these parameters was represented in dimensionless form as a function of Reynolds Number and gas density ratio, while the relative flow measurement error was selected as the most important operating characteristic. A novel error curve model based on turbine machine theory and dimensionless analysis was introduced for the purpose of error data fitting across a wide range of gas flow rates and operating pressures. The main advantage of the presented model is the capability of accurate error data fitting with a single continuous equation, as demonstrated by high R 2 {R^{2}} values for the vast majority of flowmeters analyzed in this study. The acceptability criterion was designed based on the fact that the expanded measurement uncertainty of the relative error must not exceed 0.5 %. Besides an accurate interpolation, our model can also be utilized for prediction of turbine flowmeter performance at modified flow conditions (pressure and flow rate, working gas properties), and for assessment of the drift of flowmeter performance over time. The novel error curve model is demonstrated to outperform the standard polynomial-based model regardless of the independent variable used.

Nonlinear Optimization Method for Transmission Error of Hypoid Gear Machined by the Duplex Helical Method

In this study, synchronous cutting of concave and convex surfaces for hypoid gear was achieved using a duplex helical method. Precise, nonlinear optimization of the transmission error driven by machine tool parameters was performed to reduce the vibration noise of the gear pair. First, the transmission error curve and contact path of the tooth surface of the initial pinion were solved using tooth contact analysis. Second, according to the preset parabolic transmission error curve, the initial gear was used to generate the target pinion, which coincided with the contact path of the initial pinion. Finally, a deviation correction model of the discrete points, corresponding to the contact paths on the concave and convex surfaces of the target and initial pinions, was established. This model was solved using the Levenberg–Marquard algorithm with the trust region strategy, to obtain optimized machine tool parameters. Synchronous optimization of the transmission errors of concave and convex surfaces of the pinion was achieved by correcting the deviations of the contact points. The effectiveness of the proposed method was verified by a numerical example and by performing a contact area rolling test.

Advantages of an Innovative Crossed Four Bar Steering Mechanism of a Novel Vehicle

A crossed four-bar steering mechanism has been considered for a novel four-wheel vehicle which has different wheel locations compared to a conventional four-wheel vehicle. The present paper discusses the advantages of this newly proposed steering mechanism and the novel vehicle. The steering error curve of this novel vehicle has been compared with that of a conventional four-wheel vehicle having Ackermann steering. When both vehicles move on a curved road, the required angle of rotation of the vehicle wheels due to steering effort will be different and depend on the radius of curvature of the road from place to place. It has been found that the vehicle wheels of novel vehicle need to be rotated by smaller angle for steering. The steering error of the novel vehicle is far less. The swept path width will be reduced if the novel vehicle is used instead of the conventional vehicle.

Back to Basics: Meaning of the Parameters of Fractional Order PID Controllers

The beauty of the proportional-integral-derivative (PID) algorithm for feedback control is its simplicity and efficiency. Those are the main reasons why PID controller is the most common form of feedback. PID combines the three natural ways of taking into account the error: the actual (proportional), the accumulated (integral), and the predicted (derivative) values; the three gains depend on the magnitude of the error, the time required to eliminate the accumulated error, and the prediction horizon of the error. This paper explores the new meaning of integral and derivative actions, and gains, derived by the consideration of non-integer integration and differentiation orders, i.e., for fractional order PID controllers. The integral term responds with selective memory to the error because of its non-integer order λ , and corresponds to the area of the projection of the error curve onto a plane (it is not the classical area under the error curve). Moreover, for a fractional proportional-integral (PI) controller scheme with automatic reset, both the velocity and the shape of reset can be modified with λ . For its part, the derivative action refers to the predicted future values of the error, but based on different prediction horizons (actually, linear and non-linear extrapolations) depending on the value of the differentiation order, μ . Likewise, in case of a proportional-derivative (PD) structure with a noise filter, the value of μ allows different filtering effects on the error signal to be attained. Similarities and differences between classical and fractional PIDs, as well as illustrative control examples, are given for a best understanding of new possibilities of control with the latter. Examples are given for illustration purposes.

Evaluation of Handle Rotational Feeling in Fishing Reel by Coordinate Measurement and Gear Transmission Error Measurement

This report discusses how a transmission error curve is derived by a coordinate measuring machine, and the result by a coordinate measuring machine is compared with the result by a transmission error measuring machine. A vibration based on a gear pair engagement in fishing reel occurs when a handle of the reel rotates. When this vibration is large, an angler feels uncomfortable. In author’s previous reports, it is known that a rotational feeling depends on the transmission error curve. The result indicates that the rotational feeling can be improved if the accuracy of a tooth flank is improved. In order to reduce the transmission error, the error should be measured in high accuracy. In this research, a measurement method for evaluating the rotational feeling was reported using a face gear pair via a coordinate measuring machine and a transmission error measuring machine. As a result, it was confirmed that the result of measurement by the coordinate measuring machine agrees very well with the result of measurement by the transmission error measuring machine.