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To improve transmission performance and reduce the impact of meshing in and out, a design method based on a sinusoidal profile cutter for the tooth surface crowning of spiral bevel and hypoid gears is proposed. Initially, a mathematical model for the sinusoidal blade profile and gear cutting process is established, and the influences of blade profile parameters on tooth surface mismatch are obtained using numerical analysis methods. The optimization model of the tool profile parameters is proposed by presetting the tooth contact characteristics with the objective function of minimizing the angular acceleration of the peak relative motion. Finally, the transmission performance simulations and rolling test results of two pairs of gears, before and after blade profile optimization, demonstrate that spectral analysis comparison significantly reduces maximum acceleration on the driving and coast sides, and decreases transmission noise by 1.8 dB, evidently enhancing the transmission performance of the gear pair.

The prevention of excessive roll acceleration is one of the fundamental requirements of an oceangoing vessel at sea. In this paper, aiming at this requirement, we propose a new theoretical method for calculating roll angular acceleration, called “PDF line integral method.”. This paper presents the derivation of this method and a numerical comparison with Monte Carlo simulation (MCS) results; also, its validity is shown. Although the utilized GZ curve (restoring curve) exhibits strong asymmetricity, the proposed method can provide for such a condition. With only the information of roll and roll rate joint probability density function (PDF), this method can approximately calculate the roll angular acceleration, which is a high-order differential property. In addition, a relatively good agreement is achieved between the theory and MCS results.

So far, we have developed a calculation method for roll angular acceleration and its derivative, which is a jerk. In this study, using the probability density function (PDF) line integral method and the joint PDF (JPDF) of roll angle and angular rate, we obtain a theoretical method for the evaluation of the two properties. In particular, the estimation method of acceleration is considered crucial, as the angular acceleration is directly related to inertial forces or moments of onboard objects. Moreover, to consider the strength of container stacks, as well as the lashing strength of cargo and track on board, a separate evaluation of roll angle and roll angular acceleration is insufficient. Further, although the new-generation intact stability criteria for excessive acceleration have been discussed by the International Maritime Organization, the evaluation of JPDF of roll angle and roll angular acceleration could contribute to the efficient evaluation of the safety of crews on board. Meanwhile, no JPDF of roll angle or angular acceleration has been calculated for an arbitrary nonlinear system so far, and there is no doubt that it is a challenging problem. In this study, by applying and extending the idea of the PDF line integral method, we proposed a method for evaluating the JPDF of roll angle and angular acceleration.

Current aerodynamic parameter identification methods take the consistency between the response of the motion model reconstructed with the identified aerodynamic parameters and flight data as an optimization index. Since there is only one index constraint in aerodynamic parameter optimization, and more than ten aerodynamic parameters to be identified simultaneously have different sensitivity to the optimization index, the accuracy of identification results of parameters with low sensitivity is poor, especially for those with small absolute value. To solve these problems, a new idea, having aerodynamic parameters solved by balance equations and identified in stages, is proposed. Based on the motion characteristics of different lateral-directional maneuvers, the scheme of combined maneuvers is designed, and the step-by-step identification procedure is established. An estimation method of angular acceleration with angular velocity equivalent model is proposed to solve the problem that angular acceleration cannot be measured directly. A lateral-directional aerodynamic parameter identification method using segmented adaptation of flight data and identification models is established based on the identifiability of flight data. The lateral-directional aerodynamic parameter identification results of a large civil aircraft show the identification results can be obtained with higher accuracy by adopting the proposed identification method and the flight test scheme.

The time derivative of acceleration is called a jerk, which is an important property to evaluate ride comfort in elevators, cars, and so on. Likewise, evaluation of motion sickness or ride comfort on a vessel could be achieved by this jerk property in the future. In this paper, we utilize the PDF Line Integral Method (PLIM), which was newly contrived in our previous research, for calculating not only roll angular acceleration but also roll angular jerk. The derivation of this theory, as well as numerical comparison with Monte Carlo simulation (MCS) results, are presented. Although the utilized restoring curve (GZ curve) exhibits strong asymmetricity, the proposed method successfully calculates roll angular jerk for such a condition. Since roll angular jerk is a high-order differential property, the biggest advantage of PLIM is that it only requires the information of roll and roll rate joint probability density function (PDF) to provide the PDF of jerk.

Angular acceleration sensors are attracting attention as sensors for monitoring rotational vibration. Many angular acceleration sensors have been developed; however, multiaxis measurement is still in a challenging stage. In this study, we propose a biaxial angular acceleration sensor with two uniaxial sensor units arranged orthogonally. The sensor units consist of two rotational-symmetric spiral channels and microelectromechanical system (MEMS) piezoresistive cantilevers. The cantilever is placed to interrupt the flow at the junctions of parallelly aligned spirals in each channel. When two cantilevers are used as the resistance of the bridge circuit in the two-gauge method, the rotational-symmetric spiral channels enhance the sensitivity in the target axis, while the nontarget axis sensitivities are canceled. The fabricated device responds with approximately constant sensitivity from 1 to 15 Hz, with a value of 3.86 × 10−5/(rad/s2), which is equal to the theoretical value. The nontarget axis sensitivity is approximately 1/400 of the target axis sensitivity. In addition, we demonstrate that each unit responds according to the tilt angle when the device is tilted along the two corresponding rotational axis planes. Thus, it is concluded that the developed device realizes biaxial angular acceleration measurement with low crosstalk.

In contrast to driverless cars and other three-wheeled and four-wheeled motorcycle vehicles, driverless two-wheeled motorcycles have the problem of maintaining balance. In this paper, we propose the design of an SGCMG frame angular velocity controller to realize the balance control of the motorcycle under static and dynamic working conditions. Meanwhile, since the roll angular acceleration of the actual body movement of the cross roll cannot be obtained directly, this paper proposes a Kalman filtering method based on the nonlinear dynamics model of the motorcycle to obtain a reliable angular acceleration signal. First, we modeled the dynamics of the motorcycle by analyzing the various types of moments generated by the motorcycle equipped with the SGCMG under static and dynamic conditions; Then, the design of the angular velocity control of the SGCMG frame was carried out with the feedback and through MATLAB/Simulink simulation to restore various types of actual working conditions to verify the controller has good robustness; Finally, we have completed the test of the controller using the above filtering method on the real vehicle with an embedded system and compared the effect with other controllers, obtained the results that the body is stable and balanced under static conditions and the applied load can automatically find a new balance point, so as to prove the effectiveness of the designed control.

Focusing on the inverse synthetic aperture radar (ISAR) imaging of targets with complex motion, this paper proposes a modified version of the Fourier transform, called non-uniform rotation transform, to achieve cross-range compression. After translational motion compensation, the target’s complex motion is converted into non-uniform rotation. We define two variables—relative angular acceleration (RAA) and relative angular jerk (RAJ)—to describe the rotational nonuniformity. With the estimated RAA and RAJ, rotational nonuniformity compensation is carried out in the non-uniform rotation transform matrix, after which, a focused ISAR image can be obtained. Moreover, considering the possible deviation of RAA and RAJ, we design an optimization scheme to obtain the optimal RAA and RAJ according to the optimal quality of the ISAR image. Consequently, the ISAR imaging of targets with complex motion is converted into a parameter optimization problem in which a stable and clear ISAR image is guaranteed. Compared to precedent imaging methods, the new method achieves better imaging results with a reasonable computational cost. Experimental results verify the effectiveness and advantages of the proposed algorithm.

This paper investigates the design of intermittent mechanisms for external energy launching mechanisms, focusing on analysing parallel indexing cam mechanisms. Common laws of motion, including the improved sine and cosine laws of motion, are introduced, and the cosine law of motion and the improved sine law of motion are compared. Simulation analysis was also carried out, and the angular acceleration of the improved sinusoidal motion law is 10%of the pre-optimisation one under high-speed and heavy load environment, which improves the stability and service life of the intermittent mechanism. The paper is of reference value for the design of parallel cams and the optimisation of the intermittent mechanism of external energy chain launching mechanisms.

A dynamically unbalanced rotor in viscoelastic orthotropic supports equipped with a two-plane automatic ball balancer (ABB) is considered. Based on an analysis of the equations describing the stationary modes of motion of the system, the possibility of the existence of the balanced mode is shown and the necessary conditions for its existence are found. Critical rotor speeds are found for a case of a rotor without an ABB. Amplitude-frequency responses for rotors in isotropic and orthotropic supports are constructed. Autobalancing process for the cases of rotation at constant angular velocity and constant angular acceleration is investigated.