Coupled multi-DOF dynamic contact analysis model for the simulation of intermittent gear tooth contacts, impacts and rattling considering backlash and variable torque

2015 ◽  
Vol 230 (7-8) ◽  
pp. 1022-1047 ◽  
Author(s):  
C Spitas ◽  
V Spitas
Keyword(s):  
Numerical Models ◽  
Gear Tooth ◽  
Dynamic Contact ◽  
Spur Gear ◽  
Accurate Solution ◽  
Operating Conditions ◽  
Analytical Models ◽  
Analysis Model ◽  
Tooth Contact ◽  
Lateral Displacements

Variable torque conditions in geared powertrain applications are known to lead to tooth contact loss, contact reversal, tooth impacts, rattling vibration and noise. Displacements/ deflections dominate the low-torque high-vibration responses and, besides backlash, the real-time dynamic lateral deflections of the gear bodies and the occurrence of simultaneous double-sided tooth contact influence the instantaneous mesh excitation strongly. The faster deterministic and stochastic analytical models do not consider this coupling, whereas the numerical models that do so implicitly by simulating the contact of discretised tooth surfaces/ volumes are significantly limited by the accuracy and computational overhead of their discrete meshes. To provide a both fast and accurate solution of the contact problem, especially in displacement-dominated operating conditions, this work analyses the dynamic contact of gears starting from basic principles and derives an accurate analytical model for the coupling between the compliance, contact geometry, the backlash, and the torsional and lateral displacements and deflections in the general three-dimensional multi-DOF system. This serves as a foundation for a series of dynamical simulations of a single-stage spur gear transmission under different variable-torque excitations to predict tooth contact loss and contact reversal and the basic interactions that lead to impacts and rattling vibration. This approach can be used to predict critical torque fluctuation levels, beyond which these phenomena emerge.

scholarly journals Lubricated Loaded Tooth Contact Analysis and Non-Newtonian Thermoelastohydrodynamics of High-Performance Spur Gear Transmission Systems

Lubricants ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 20 ◽  
Author(s):  
Gajarajan Sivayogan ◽  
Ramin Rahmani ◽  
Homer Rahnejat
Keyword(s):  
High Speed ◽  
High Performance ◽  
Spur Gear ◽  
Contact Analysis ◽  
Operating Conditions ◽  
Tooth Contact Analysis ◽  
Transmission Systems ◽  
Tooth Contact ◽  
Contact Kinematics ◽  
Loaded Tooth Contact Analysis

Energy efficiency and functional reliability are the two key requirements in the design of high-performance transmissions. Therefore, a representative analysis replicating real operating conditions is essential. This paper presents the thermoelastohydrodynamic lubrication (TEHL) of meshing spur gear teeth of high-performance racing transmission systems, where high generated contact pressures and lubricant shear lead to non-Newtonian traction. The determination of the input contact geometry of meshing pairs as well as contact kinematics are essential steps for representative TEHL. These are incorporated in the current analysis through the use of Lubricated Loaded Tooth Contact Analysis (LLTCA), which is far more realistic than the traditional Tooth Contact Analysis (TCA). In addition, the effects of lubricant and flash surface temperature rise of contacting pairs, leading to the thermal thinning of lubricant, are taken into account using a thermal network model. Furthermore, high-speed contact kinematics lead to shear thinning of the lubricant and reduce the film thickness under non-Newtonian traction. This comprehensive approach based on established TEHL analysis, particularly including the effect of LLTCA on the TEHL of spur gears, has not hitherto been reported in literature.

UV disinfection of water: the need for UV reactor validation

2003 ◽  
Vol 3 (4) ◽  
pp. 293-300 ◽  
Author(s):  
Y.A. Lawryshyn ◽  
B. Cairns
Keyword(s):  
Legionella Pneumophila ◽  
Uv Light ◽  
Numerical Models ◽  
Operating Conditions ◽  
Analytical Models ◽  
Human Consumption ◽  
Average Dose ◽  
Reactor Performance ◽  
Uv Reactor ◽  
Bioassay Data

Disinfection by ultraviolet light (UV) has received wide endorsement as an important contribution to the multiple barrier approach for protection of public health. UV can be used both to disinfect wastewater discharged to the environment, and to disinfect that water when it is picked up again for human consumption. UV readily blocks infectivity by such chlorine-resistant pathogens as Cryptosporidium parvum, Giardia lamblia and Legionella pneumophila. Multiple disinfectant use is now being discussed to broaden the spectrum of pathogens that can be inactivated by using disinfectants in their most strategically advantageous dose and function. Optimizing multiple barrier strategies requires attention to validation of the concepts and technologies involved. UV technology validation ensures that the equipment can deliver the target UV design dose, and that the monitoring/control technology modulates the dose appropriately with changes in water quality or operating conditions. The bioassay approach for UV reactor validation is recommended over analytical and numerical models. Analytical models, which provide an average dose estimate, have been shown to be inadequate. Numerical models, which utilize Computational Fluid Dynamics (CFD) and UV light intensity models to predict reactor performance, can be accurate when used by skilled professionals but require significant validation and/or calibration against bioassay data.

Effect of Gear Tooth Crack on Spur Gear Dynamic Response by Simulation

2011 ◽  
Author(s):  
Yimin Shao ◽  
Xi Wang ◽  
Zaigang Chen ◽  
Teik C. Lim
Keyword(s):  
Dynamic Response ◽  
Gear Tooth ◽  
Sudden Change ◽  
Element Model ◽  
Spur Gear ◽  
Operating Conditions ◽  
Lumped Parameter Model ◽  
Mesh Stiffness ◽  
Heavy Load ◽  
High Rotational Speed

Geared transmission systems are widely applied to transmit power, torque and high rotational speed, and as well as change the direction of rotational motion. Their performances and efficiencies depend greatly on the integrity of the gear structure. Hence, health monitoring and fault detection in geared systems have gained much attention. Often, as a result of inappropriate operating conditions, application of heavy load beyond the designed capacity or end of fatigue life, gear faults frequently occur in practice. When fault happens, gear meshing characteristics, including mesh stiffness that is one of the important dynamic parameters, can be affected. This sudden change in mesh stiffness can induce shock vibration as the faulty gear tooth passes through the engagement zone. In this study, a finite element model representing the crack at the tooth root of a spur gear is developed. The theory is applied to investigate the effect of different crack sizes and the corresponding change in mesh stiffness. In addition, a lumped parameter model is formulated to examine the effect of tooth fault on gear dynamic response.

The Stress Analysis on Spur Gear Meshing Simulation

2013 ◽  
Vol 392 ◽  
pp. 151-155
Author(s):  
Zheng Li ◽  
Yang Chen
Keyword(s):  
Gear Tooth ◽  
Nonlinear Behavior ◽  
Element Model ◽  
Spur Gear ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Reliable Model ◽  
Nonlinear Behaviors ◽  
Meshing Process

The gear meshing is a very complicated process due to the nonlinear behaviors during the teeth contact. It is necessary to build a reliable model to simulate gear meshing process which can consider geometry and boundary conditions nonlinear behavior in gear tooth contact analysis. This paper propose a 3D finite element model to simulate the meshing process of a pair of spur gears, and then carry out the gear tooth contact analysis with the consideration of nonlinear behaviors. The results and relevant discussions will indicate and explain some significant phenomena of the gear tooth contact characteristics in gear meshing process.

DrillString Vibration With Hole-Enlarging Tools: Analysis and Avoidance

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Robello Samuel ◽  
Dongping Yao
Keyword(s):  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Technical Conference ◽  
Careful Consideration ◽  
Operating Conditions ◽  
Drilling Process ◽  
Analysis Model ◽  
Incidence Data ◽  
Lateral Displacements

In high-risk, high-cost environments, such as ultra-deep waters, refining advanced technologies for the successful completion of wells is paramount. Challenges are still very much associated with complex bottomhole assemblies (BHAs) and with the vibration of the drillstring when used with hole enlarging tools. These tools with complex profiles and designs become additional excitation sources of vibration. The more widespread use of downhole tools for both directional telemetry and logging-while-drilling (LWD) applications, as part of the front line data acquisition system within the drilling process, has made reliability a prime area of importance. This paper presents and validates an existing model to predict severe damaging vibrations. It also provides analysis techniques and guidelines to successfully avoid the vibration damage to downhole tools and to their associated downhole assemblies when using hole enlarging tools, such as hole openers and underreamers. The dynamic analysis model is based on forced frequency response (FFR) to solve for resonant frequencies. In addition, a mathematical formulation includes viscous, axial, torsional, and structural damping mechanisms. With careful consideration of input parameters and the judicious analysis of results, we demonstrated that drillstring vibration can be avoided by determining the three-dimensional vibrational response at selected excitations that are likely to cause them. In addition, the analysis provides an estimate of relative bending stresses, shear forces, and lateral displacements for the assembly used. Based on the study, severe vibrations causing potentially damaging operating conditions that had been a major problem in nearby wells were avoided. Steps required to estimate the operating range of the drilling parameter such as weight on bit and rotational speeds to mitigate and avoid the downhole tool failures due to vibration are given. Extensive simulations were performed to compare the data from the downhole vibration sensors; this paper includes severe vibration incidence data from three case studies in which the model estimated, predicted, and avoided severe vibration (Samuel, R., et al., 2006, “Vibration Analysis Model Prediction and Avoidance: A Case History,” Paper SPE 102134 Presented at the IADC India Conference, Mumbai, India, Oct. 16–18; Samuel, R., 2010, “Vibration Analysis for Hole Enlarging Tools” SPE 134512, Annual Technical Conference, Florence, Italy).

Effect of structural design parameters on nonlinear dynamic characteristics of the gear transmission

2021 ◽  
pp. 095440702110294
Author(s):  
Tiancheng Ouyang ◽  
Rui Yang ◽  
Yudong Shen ◽  
Jingxian Chen ◽  
Nan Chen
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
High Speed ◽  
Gear Tooth ◽  
Spur Gear ◽  
Operating Conditions ◽  
Design Parameters ◽  
Meshing Stiffness ◽  
Nonlinear Dynamic Characteristics ◽  
Potential Energy Method

The calculation of time-varying meshing stiffness caused by the alternate contacting of the gear tooth is an essential prerequisite to obtain real and effective nonlinear dynamic characteristics of the transmission system, so that the significance of which cannot be overemphasized. Accordingly, this work proposes an improved method to get meshing stiffness with taking fillet-foundation and gear rim deflection into consideration. Compared to the traditional potential energy method, the proposed method has more superior accuracy and performance, and its effectiveness has been further verified by the finite element analytical model. After that, an ideal eight degree of freedoms (DOFs) dynamic model of one stage mass-spring-damper involute spur gear, including lateral and torsional motions, is established to study the dynamic characteristics. Due to the complexity of the gear system operating conditions, we also investigate the influence of various parameters including hub bore radius, transmitting load, and rotation speed on dynamic features, especially in heavy-load and high-speed conditions. From the results, it can be concluded that these parameters will play a prominent role in the spur gear pair dynamic behaviors, providing a certain guidance for gear design.

scholarly journals Analytical Models for Seawater and Boron Removal through Reverse Osmosis

2021 ◽  
Vol 13 (16) ◽  
pp. 8999
Author(s):  
Michael Binns
Keyword(s):  
Reverse Osmosis ◽  
Numerical Models ◽  
Total Concentration ◽  
Transport Coefficients ◽  
Operating Conditions ◽  
Analytical Models ◽  
Boron Removal ◽  
Modelling Methodology ◽  
Membrane Modules ◽  
Similar Accuracy

Regarding the purification of seawater, it is necessary to reduce both the total concentration of salt and also the concentration of boron to meet purity requirements for safe drinking water. For this purpose reverse osmosis membrane modules can be designed based on experimental data supported by computer models to determine energy efficient configurations and operating conditions. In previous studies numerical models have been suggested to predict the performance of the removal with respect to difference pressures, pH values, and temperatures. Here, an analytical model is suggested which allows for both the simplified fitting of the parameters required for predicting boron transport coefficients and also the simple equations that can be used for the design of combined seawater and boron removal systems. This modelling methodology is demonstrated through two case studies including FilmTec and Saehan membrane modules. For both cases the model is shown to be able to predict the performance with similar accuracy compared with existing finite-difference type numerical models from the literature.

Calculation of Spur Gear Tooth Flexibility by the Complex Potential Method

1985 ◽  
Vol 107 (1) ◽  
pp. 38-42 ◽  
Author(s):  
A. Cardou ◽  
G. V. Tordion
Keyword(s):  
Singular Point ◽  
Complex Potential ◽  
Gear Tooth ◽  
Contact Point ◽  
Spur Gear ◽  
Potential Method ◽  
Complex Potentials ◽  
Spur Gears ◽  
Tooth Contact ◽  
Complex Potential Method

Complex potentials have already been used to calculate analytically spur gear stresses. However, their application to the calculation of tooth flexibility is not so straightforward since displacements of interest are at the tooth contact point, which is a singular point for the equations being used. A method has been devised to circumvent this difficulty and to obtain the value of the displacement at each point of the line of action, and thus, the flexibility of a given pair of spur gears.

Investigation of Contact Characteristics of Long-Fiber Reinforced Plastic Gears Based on Observation With a High-Speed Camera

2010 ◽  
Author(s):  
Tomoki Otawa ◽  
Toshiski Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Temperature Distribution ◽  
High Speed ◽  
Gear Tooth ◽  
Dynamic Contact ◽  
Operating Conditions ◽  
Back Surface ◽  
High Speed Camera ◽  
Contact Ratio ◽  
Contact State ◽  
Plastic Gears

We also observed the dynamic contact state of gear meshing in operating conditions with a high-speed camera. The temperature distribution when driving was measured by thermography. Contact ratio is often used to show contact state, but there are currently no reports that describe the dynamic contact ratio of FRP gears although there are some reports on plastic gears. We therefore considered a contact ratio formula based on a new contact model that the dynamic real deflections of the gear tooth. The temperature distribution measurement was done from the side and the upper surface of the gear. The characteristics of heat generation on the surface of each gear tooth were analyzed, and the temperature distribution was analyzed according to the time and each point of the tooth. (1) FRP gears over heated as a result of driving by the metal gear for a long time. The rise in temperature was rapid and was compounded by heat dissipated from the metal gear. (2) The pitch point of the FRP gear tooth had the highest temperature. The reason for this is that the hysteresis heating is large. It is not easy for the gear to dissipate heat. (3) The temperature rose as a result of hysteresis heating. At high torque, the back surface contact and deflection of the teeth also increased because the gear became viscoelastic.

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