On Statistical Analysis of Gear Dynamic Loads

1986 ◽  
Vol 108 (3) ◽  
pp. 362-368 ◽  
Author(s):  
A. S. Kumar ◽  
M. O. M. Osman ◽  
T. S. Sankar
Keyword(s):  
Steady State ◽  
Statistical Analysis ◽  
Dynamic Load ◽  
Initial Conditions ◽  
Gear System ◽  
Computational Time ◽  
Statistical Linearization ◽  
Mesh Stiffness ◽  
Steady State Condition ◽  
Gaussian White Noise Process

Statistical analysis of the gear dynamic load is carried out using piecewise constant mesh stiffness approximation. The dynamics of the spur gear system is modeled as a nonlinear, nonstationary process, and the gear transmission error which acts as a random input to the gear system is generated by passing a Gaussian white noise process through a time invariant shaping filter. The equivalent discrete time state equation and the mean and covariance propagation equations are then written for the augmented system. Then starting from known initial conditions these propagation equations are used to compute the statistics of the steady state response and hence those of the dynamic load. A procedure is presented for the selection of proper initial conditions so as to reach the steady state condition faster, thereby reducing the computational time required. The variations in the statistics of the dynamic load with respect to changes in contact position, random error magnitude, and operating speed are also investigated with the help of a numerical example. The results show that the approach presented in this study provides truer results than the statistical linearization approach used by Tobe et al. [13]. Moreover, the proposed procedure has the advantage that it can be applied to higher-order systems with complex mesh stiffness and torque fluctuations and to systems with symmetrical or nonsymmetrical nonlinearities.

On Dynamic Tooth Load and Stability of a Spur-Gear System Using the State-Space Approach

1985 ◽  
Vol 107 (1) ◽  
pp. 54-60 ◽  
Author(s):  
A. S. Kumar ◽  
T. S. Sankar ◽  
M. O. M. Osman
Keyword(s):  
State Space ◽  
Dynamic Load ◽  
Initial Conditions ◽  
Gear Tooth ◽  
Spur Gear ◽  
The State ◽  
Gear System ◽  
Computational Time ◽  
Steady State Condition ◽  
The Stability

In this study, a new approach using the state-space method is presented for the dynamic load analysis of spur gear systems. This approach gives the dynamic load on gear tooth in mesh as well as information on the stability of the gear system. Also a procedure is given for the selection of proper initial conditions that enable the steady-state condition to be reached faster, conditions that result in considerable savings in computational time. The variations in the dynamic load with respect to changes in contact position, operating speed, backlash, damping, and stiffness are also investigated. In addition, the stability of the gear system is studied, using the Floquet theory and the well-known stability conditions of difference systems.

scholarly journals Computational Performance of Disparate Lattice Boltzmann Scenarios under Unsteady Thermal Convection Flow and Heat Transfer Simulation

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 65
Author(s):  
Aditya Dewanto Hartono ◽  
Kyuro Sasaki ◽  
Yuichi Sugai ◽  
Ronald Nguele
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Natural Convection ◽  
Lattice Boltzmann ◽  
Numerical Results ◽  
Convection And Heat Transfer ◽  
Steady State Condition ◽  
Physical Systems ◽  
Flow And Heat Transfer ◽  
Computational Performance

The present work highlights the capacity of disparate lattice Boltzmann strategies in simulating natural convection and heat transfer phenomena during the unsteady period of the flow. Within the framework of Bhatnagar-Gross-Krook collision operator, diverse lattice Boltzmann schemes emerged from two different embodiments of discrete Boltzmann expression and three distinct forcing models. Subsequently, computational performance of disparate lattice Boltzmann strategies was tested upon two different thermo-hydrodynamics configurations, namely the natural convection in a differentially-heated cavity and the Rayleigh-Bènard convection. For the purposes of exhibition and validation, the steady-state conditions of both physical systems were compared with the established numerical results from the classical computational techniques. Excellent agreements were observed for both thermo-hydrodynamics cases. Numerical results of both physical systems demonstrate the existence of considerable discrepancy in the computational characteristics of different lattice Boltzmann strategies during the unsteady period of the simulation. The corresponding disparity diminished gradually as the simulation proceeded towards a steady-state condition, where the computational profiles became almost equivalent. Variation in the discrete lattice Boltzmann expressions was identified as the primary factor that engenders the prevailed heterogeneity in the computational behaviour. Meanwhile, the contribution of distinct forcing models to the emergence of such diversity was found to be inconsequential. The findings of the present study contribute to the ventures to alleviate contemporary issues regarding proper selection of lattice Boltzmann schemes in modelling fluid flow and heat transfer phenomena.

Risk assessment in mission planning of uninhabited aerial vehicles

2019 ◽  
Vol 233 (10) ◽  
pp. 3499-3518 ◽  
Author(s):  
Giulio Avanzini ◽  
David S Martínez
Keyword(s):  
Initial Conditions ◽  
Mission Planning ◽  
Unmanned Aerial Systems ◽  
Steady State Condition ◽  
Motion Primitives ◽  
Uninhabited Aerial Vehicles ◽  
Aerial Systems ◽  
The Impact ◽  
Navigation Errors ◽  
Time Of Failure

A procedure for evaluating the risk related to the use of unmanned aerial systems over populated areas is proposed. A nominal trajectory, planned for performing a given mission, is represented by means of motion primitives, that is segments and arcs flown in a steady-state condition. The risk of hitting a person on the ground after catastrophic failure is evaluated as a function of vehicle reliability and population density (assumed known), and position of the impact point (which depends on initial conditions at the time of failure and trajectory flown afterwards). In the deterministic case, a lethal area is introduced and the risk at each point on the ground is proportional to the amount of time spent by the point inside the lethal area. Under the assumptions of a ballistic fall, the position of the lethal area with respect to the nominal trajectory depends only on altitude and velocity at the time of failure. When the effect of navigation errors is introduced, impact points are described by a statistical impact footprint, assuming that position and velocity errors at time of failure are normally distributed with known standard deviations. The two approaches are compared for a fictitious, yet realistic, mission scenario.

Steady-State Dynamic Response of a Limited Slip System

1968 ◽  
Vol 35 (2) ◽  
pp. 322-326 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Slip System ◽  
External Load ◽  
Initial Conditions ◽  
Viscous Damping ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
System Nonlinearity

The steady-state response of a system constrained by a limited slip joint and excited by a trigonometrically varying external load is discussed. It is shown that the system may possess such features as disconnected response curves and jumps in response depending on the strength of the system nonlinearity, the level of excitation, the amount of viscous damping, and the initial conditions of the system.

Continuous determination of the volume of a space in a non steady state condition

1974 ◽  
Vol 36 (1) ◽  
pp. 59-66
Author(s):  
Oscar A. Gómez-Poviña ◽  
Carmen Sainz de Calatroni ◽  
Susana Orden de Puhl ◽  
Mariano J. Guerrero
Keyword(s):  
Steady State ◽  
State Condition ◽  
Steady State Condition ◽  
Continuous Determination

An Approach for Snaky Well Productivity under Steady-State Condition

2006 ◽  
Author(s):  
Zhilin Qi ◽  
Zhimin Du ◽  
Baosheng Liang ◽  
Yong Tang ◽  
Shouping Wang ◽  
...  
Keyword(s):  
Steady State ◽  
State Condition ◽  
Well Productivity ◽  
Steady State Condition

Modeling the performance of biodegradation of textile wastewater using polyurethane foam sponge cube as a supporting medium

2010 ◽  
Vol 62 (12) ◽  
pp. 2801-2810 ◽  
Author(s):  
Yen-Hui Lin
Keyword(s):  
Steady State ◽  
Polyurethane Foam ◽  
Textile Wastewater ◽  
Pilot Scale ◽  
Biofilm Reactor ◽  
Column Test ◽  
Steady State Condition ◽  
Suspended Biomass ◽  
The Government ◽  
Carbon Dioxide Co2

A pilot-scale fixed-biofilm reactor (FBR) was established to treat textile wastewater to evaluate the feasibility of replacing conventional treatment processes that involve activated sludge and coagulation units. A kinetic model was developed to describe the biodegradation of textile wastewater by FBR. Batch kinetic tests were performed to evaluate the biokinetic parameters that are used in the model. FBR column test was fed with a mean COD of 692 mg/L of textile wastewater from flow equalization unit. The influent flow rate was maintained at 48.4 L/h for FBR column test. Experimental data and model-predicted data for substrate effluent concentration (as COD), concentration of suspended biomass in effluent and the amount of carbon dioxide (CO2) produced in the effluent agree closely with each other. Microscopic observations demonstrated that the biofilm exhibited a uniform distribution on the surface of polyurethane foam sponge. Under a steady-state condition, the effluent COD from FBR was about 14.7 mg COD/L (0.0213 Sb0), meeting the discharge standard (COD < 100 mg/L) that has been set by the government of Taiwan for textile wastewater effluent. The amount of biofilm and suspended biomass reached a maximal value in the steady state when the substrate flux reached a constant value and remained maximal. Approximately 33% of the substrate concentration (as COD) was converted to CO2 during biodegradation in the FBR test. The experimental and modeling schemes proposed in this study could be employed to design a full-scale FBR to treat textile wastewater.

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