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We consider a discrete version of reaction-diffusion equations. A typical example is the fully overdamped Frenkel–Kontorova model, where the velocity is proportional to the force. We also introduce an additional exterior force denoted by σ . For general discrete and fully nonlinear dynamics, we study traveling waves of velocity c = c (σ) depending on the parameter σ . Under certain assumptions, we show properties of the velocity diagram c (σ) for σ ∈ [ σ - , σ + ] . We show that the velocity c is nondecreasing in σ ∈ (σ - , σ +) in the bistable regime, with vertical branches c ≥ c + for σ = σ + and c ≤ c - for σ = σ - in the monostable regime. [ABSTRACT FROM AUTHOR]

This paper proposes a stage flow parameter analytical model for rapid evaluation of a counter-rotating compressor's performance for design optimization and its application in the design of a transonic counter-rotating fan. In the first part, the velocity diagram method, considering the influence of flow-path geometry variation for enhancing the accuracy, is used to correlate the aerodynamic parameter between the inlet guide vane (IGV), the upstream rotor (R1), and the downstream CR rotor (R2). A profile loss correlation based on Lieblein's diffusion factor and a shock loss model from a high-speed fan database are incorporated for predicting the rotor efficiency. In the second part, to verify its effectiveness, the analytical model is used for aiding in the aerodynamic design of a transonic CR fan for indicating the optimized combination of design parameters for good efficiency and a high pressure ratio. According to the analytical model and the simulation results, the final selected samples have higher efficiency, with a moderate pressure ratio (0.949/2.67, 0.890/2.99, and 0.841/2.99 for R = 0.1, 0.5, and 0.9, respectively). Finally, the aerodynamic characteristics of the designed transonic CR fan at a relative rotating speed of N = 1.05~0.8 are calculated by using the CFD software Numeca. Simulations indicate that the designed transonic CR fan has a pressure ratio of 2.76, with an efficiency of 0.8405 at the design point, and the efficiency is maintained above 0.821 with a stall margin of 13.3% for N=1.0. The maximum pressure ratio of this CR fan reaches 3.08 and 3.36 for N = 1.0 and 1.05, respectively. If used to provide thrust, calculations indicate that the thrust of this transonic CR fan is 71.8, 65.9, and 35.8 kN for N = 1.05, 1.0, and 0.8 at the near-choke point for the sea-level condition. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to propose a new graphical method for a planetary gear train (PGT) analysis. This is a fully graphical method that determines the rotational speeds of all transmission components, as well as the torque, power flow, power losses, and efficiency of any PGT. With this method, a sketcher workbench available in any modern computer-aided design (CAD) system can be used. This provides an interactive way to work. Both the construction of the geometric model and the interpretation of the results are intuitive, which facilitates error identification. Observing the impact of the selected input data or model parameters on the model behavior is extremely easy and can even be animated. It is believed that the presented method can streamline the PGT design process.

The main purpose of this paper is to propose a new graphical method for a planetary gear train (PGT) analysis. This is a fully graphical method that determines the rotational speeds of all transmission components, as well as the torque, power flow, power losses, and efficiency of any PGT. With this method, a sketcher workbench available in any modern computer-aided design (CAD) system can be used. This provides an interactive way to work. Both the construction of the geometric model and the interpretation of the results are intuitive, which facilitates error identification. Observing the impact of the selected input data or model parameters on the model behavior is extremely easy and can even be animated. It is believed that the presented method can streamline the PGT design process. [ABSTRACT FROM AUTHOR]

This paper proposes a stage flow parameter analytical model for rapid evaluation of a counter-rotating compressor’s performance for design optimization and its application in the design of a transonic counter-rotating fan. In the first part, the velocity diagram method, considering the influence of flow-path geometry variation for enhancing the accuracy, is used to correlate the aerodynamic parameter between the inlet guide vane (IGV), the upstream rotor (R1), and the downstream CR rotor (R2). A profile loss correlation based on Lieblein’s diffusion factor and a shock loss model from a high-speed fan database are incorporated for predicting the rotor efficiency. In the second part, to verify its effectiveness, the analytical model is used for aiding in the aerodynamic design of a transonic CR fan for indicating the optimized combination of design parameters for good efficiency and a high pressure ratio. According to the analytical model and the simulation results, the final selected samples have higher efficiency, with a moderate pressure ratio (0.949/2.67, 0.890/2.99, and 0.841/2.99 for R = 0.1, 0.5, and 0.9, respectively). Finally, the aerodynamic characteristics of the designed transonic CR fan at a relative rotating speed of N = 1.05~0.8 are calculated by using the CFD software Numeca. Simulations indicate that the designed transonic CR fan has a pressure ratio of 2.76, with an efficiency of 0.8405 at the design point, and the efficiency is maintained above 0.821 with a stall margin of 13.3% for N=1.0. The maximum pressure ratio of this CR fan reaches 3.08 and 3.36 for N = 1.0 and 1.05, respectively. If used to provide thrust, calculations indicate that the thrust of this transonic CR fan is 71.8, 65.9, and 35.8 kN for N = 1.05, 1.0, and 0.8 at the near-choke point for the sea-level condition.

An electric-powered lateral torque-vectoring differential utilizes the output torque of an electric motor for generating the torque difference between the right and the left wheels. Compared with conventional torque-vectoring differentials which utilize the slipping clutch or brake for torque vectoring, electric-powered lateral torque-vectoring differentials have advantages, namely the response and the control accuracy of the torque difference. However, an electric-powered lateral torque-vectoring differential is complex as it is composed of a single electric motor and some planetary gear units; therefore it is difficult to understand its mechanism and characteristics. This paper describes the classification and analysis of electric-powered lateral torque-vectoring differentials. Electric-powered lateral torque-vectoring differentials are studied using the velocity diagram which is utilized for analysis of the conventional torque-vectoring differentials. The analysis shows that the simplest electric-powered lateral torque-vectoring differential is a mechanism of five elements with two degrees of freedom; the mechanism is composed of a single electric motor, one differential gear unit and two planetary gear units; the gear ratios of the planetary gear units are equal to each other. The simplest mechanisms are classified into nine kinds and these have two differences in their characteristics, namely the torque amplification factor between the electric motor and the vectoring torque, and the revolution speeds of one rotational element. Finally, the best mechanism is evaluated from the differences of the characteristics. [ABSTRACT FROM AUTHOR]

This paper describes the classification and analysis of lateral torque-vectoring differentials using velocity diagrams, which are frequently used for the gear-shifting analysis of an automatic transmission. A lateral torque-vectoring differential is composed of the mechanism of torque vectoring from the right wheel to the left wheel, and the similar mechanism of torque vectoring from the left to the right. The analysis shows that, when only the mechanism part of one-way torque vectoring is considered, then the smallest number of the rotational elements composing the one-way torque-vectoring mechanism is four. This is the simplest mechanism. The mechanism is classified into seven kinds of mechanism, namely six clutch-type mechanisms and one brake-type mechanism. The expressions for the clutch torque for torque vectoring, the clutch slip speed, and the energy loss generated by clutch are presented for these mechanisms. As a result, the theoretical value of energy loss is completely the same in these seven kinds of mechanism in the ideal state, in which the transmission efficiency of gears, agitation loss, etc., are assumed to be neglected. Finally, from an actual mechanism design point of view, the best mechanism is evaluated. [ABSTRACT FROM AUTHOR]