Optimum Gear Tooth Geometry for Minimum Fillet Stress Using BEM and Experimental Verification With Photoelasticity

2005 ◽  
Vol 128 (5) ◽  
pp. 1159-1164 ◽  
Author(s):  
Vasilios A. Spitas ◽  
Theodore N. Costopoulos ◽  
Christos A. Spitas
Keyword(s):  
Gear Tooth ◽  
Optimization Procedure ◽  
Computational Time ◽  
Design Parameters ◽  
Gear Teeth ◽  
Design Variables ◽  
Maximum Root ◽  
Stress Minimization ◽  
Complex Algorithm ◽  
Root Stress

This paper introduces the concept of nondimensional gear teeth to be used in gear stress minimization problems. The proposed method of modeling reduces the computational time significantly when compared to other existing methods by essentially reducing the total number of design variables. Instead of modeling the loaded gear tooth and running BEA to calculate the maximum root stress at every iterative step of the optimization procedure, the stress is calculated by interpolation of tabulated values, which were calculated previously by applying the BEM on nondimensional models corresponding to different combinations of the design parameters. The complex algorithm is used for the optimization and the root stresses of the optimum gears are compared with the stresses of the standard gears for the same transmitted torque. Reduction in stress up to 36.5% can be achieved in this way. This reduction in stress has been confirmed experimentally with two-dimensional photoelasticity.

Geometry optimization of the rolling tool for gear roll-forming process

2020 ◽  
pp. 095440542095110
Author(s):  
Bo Peng ◽  
Yang Luo ◽  
Yuanxin Luo ◽  
Ziyong Ma
Keyword(s):  
Gear Tooth ◽  
Geometry Optimization ◽  
Roll Forming ◽  
Utilization Rate ◽  
Forming Process ◽  
Bending Performance ◽  
Maximum Root ◽  
Standard Profile ◽  
Roll Forming Process ◽  
Root Stress

Gear roll forming process is an innovative near-net-shape gear manufacturing technology for efficient manufacturing, high material utilization rate, high products strength, and outstanding surface quality. The profile of the Tooth of the Rolling Tool (TRT) has a direct impact on its strength/stiffness which further affects its life duration and the accuracy of the formed products. Research has been carried out to design the involute curve of TRT, however, the transaction curve of TRT which also has a significant impact on tooth strength and service durability remains to be designed and optimized in order to further improve the rolling performance. In this paper, an elliptical gear tooth root transaction curve is proposed to replace the traditional fillet curve for the enhancement of tooth bending performance. The maximum root stress and stiffness of the gear tooth with elliptical transaction curve are calculated and compared to the standard profile with different parameters (modulus, pressure angle, and coefficient of bottom clearance). The results show that proposed elliptical tooth reduces the maximum root stress and increase the strength and stiffness of TRT especially significant for rolling tools with small number of teeth and coefficient of bottom clearance.

A new criterion for comfort assessment of in-wheel motor electric vehicles

2020 ◽  
pp. 107754632097718
Author(s):  
Hossein Salmani ◽  
Milad Abbasi ◽  
Tondar Fahimi Zand ◽  
Mohammad Fard ◽  
Reza Nakhaie Jazar
Keyword(s):  
Electric Vehicle ◽  
Degrees Of Freedom ◽  
Optimization Technique ◽  
Optimization Procedure ◽  
Linear Quadratic Regulator ◽  
International Organization ◽  
Design Parameters ◽  
Linear Quadratic ◽  
International Organization For Standardization ◽  
Design Variables

A novel optimization technique was implemented to investigate the effects of vibrations on comfort of occupants to maintain oscillations in an acceptable zone in accordance with the International Organization for Standardization 2631 standard. In this regard, a newly introduced comfort indicator was defined as discomfort criterion (DiC). The effectiveness of the proposed measure was investigated throughout the suspension optimization of an in-wheel motor electric vehicle which almost doubled the unsprung mass by adding an electric motor to the wheel assembly. First, a spatial oscillatory model of the electric vehicle with eight degrees of freedom was developed, and the linear quadratic regulator control scheme is selected to control an actuator in an active suspension. Road excitations were then generated by applying the power spectral density of road class B–C provided by the International Organization for Standardization 8608 standard. The exceedance from the reduced comfort limit (in accordance with the International Organization for Standardization 2631 standard) and wheel travel (WT) of the vehicle were considered as design objectives. Finally, using a novel optimization procedure, the optimum condition and impact factor of the design variables, as well as counterplots of the design objectives with respect to the effective design parameters, were extracted and analyzed. Results proved the proposed indicator, that is, discomfort criterion (DiC) as a reliable measure to assess suspension systems’ performance effectively.

An Aerodynamic Optimization Procedure for the Preliminary Design of Centrifugal Compressor Stages

2008 ◽  
Author(s):  
Omar Elshamy ◽  
Nidal Ghizawi ◽  
Ce´line Yon ◽  
Simone Pazzi ◽  
Denis Guenard
Keyword(s):  
Centrifugal Compressor ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Computational Time ◽  
Preliminary Design ◽  
Trial And Error ◽  
Aerodynamic Optimization ◽  
Peak Efficiency ◽  
Stage Design ◽  
Design Variables

This paper presents an automated aerodynamic optimization procedure for the preliminary design of centrifugal compressors. The proposed procedure interfaces a well-validated prediction tool with a GE in-house developed optimization code (PEZ). In GE Oil & Gas this tool is used to predict the performance of a single centrifugal compressor stage the outline of which requires more than thirty geometric parameters to be set. In the early phase of a new stage design, the designer manually varies all related parameters in the framework of a trial-and-error approach. The optimization procedure eliminates the inconvenience of a vast amount of manually launched simulations required by variations of the large number of design variables. Additionally, this procedure can perform trade-off studies and sensitivity analysis. In this case the optimization plan consists of a differential evolution (DE) genetic algorithm followed by a simplex-based optimization method (AMOEBA). The procedure was challenged with several existing designs by setting different objective/constraints combinations. The optimizer was often able to improve the predicted performance, as for an old 2D design where it was possible to increase the peak efficiency of approximately 2.6%. Also, the algorithm proved able to maximize the polytropic head (+12% with respect to baseline), while keeping unaltered both surge and choke limits. The computational time was about 40 hours per case on a Windows workstation (3.20 GHz, 3.5 GB RAM).

Computerized Tooth Profile Generation and Undercut Analysis of Gears Manufactured With Pre-Shaving Hobs

2009 ◽  
Vol 16-19 ◽  
pp. 1278-1282
Author(s):  
Xiang Wei Kong ◽  
Jing Zhang ◽  
Meng Hua Niu
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Design Parameters ◽  
Gear Teeth ◽  
The Mathematical Model

This paper investigated the feature of pre-shaving hob contour and the generated gear tooth profile. By tooth generation method, a complete geometry of the gear tooth can be mathematically derived in terms of the design parameters of the pre-shaving hob cutter. The mathematical model consisted of equations describing the generated fillet and involute profiles. The degree of undercutting and the radii of curvatures of a fillet were investigated by considering the model. Finally, a computer program for generating the profile of the gear teeth was developed by simulating the cutting methods. The methods proposed in this study were expected to be a valuable guidance for pre-shaving hob designers and manufacturers.

Optimization of Cold Rolling by Nonlinear Programming

1978 ◽  
Vol 100 (2) ◽  
pp. 186-192 ◽  
Author(s):  
S. S. Rao ◽  
A. Kumar
Keyword(s):  
Nonlinear Programming ◽  
Optimization Procedure ◽  
Design Parameters ◽  
Strip Rolling ◽  
Single Pass ◽  
Design Variables ◽  
In Series ◽  
Induced Stresses ◽  
Cold Strip Rolling ◽  
Neutral Angle

The problem of determining the optimum design parameters of single pass and multipass cold strip rolling is considered. The problem is formulated and solved as a constrained nonlinear programming problem by considering the radius of rolls, and the front and back tensions as design variables. Two objectives, namely, the minimization of the deflection of rolls and the minimization of the power required for rolling, are considered in the case of single pass rolling. The minimization of the sum of deflections of all the rolls lying in series is considered as the objective in the case of tandem mill rolling. Constraints are placed on the induced stresses, neutral angle and the angle of bite. Example problems are presented to illustrate the efficiency of the optimization procedure presented.

Improvement of engine performance using an optimization procedure

2007 ◽  
Vol 221 (8) ◽  
pp. 1001-1014 ◽  
Author(s):  
B Kegl ◽  
S Pehan ◽  
M Kegl
Keyword(s):  
Optimal Design ◽  
Data Exchange ◽  
Engine Performance ◽  
Optimization Procedure ◽  
Design Parameters ◽  
Analysis Software ◽  
Design Variables ◽  
Gradient Based ◽  
Data Files ◽  
Engine Power

This paper presents a simple and effective approach to improve engine performance of a racing car with special requirements. Attention is focused on optimal design of the intake system, using a gradient-based approximation method of mathematical programming. Since optimization relies on accurate numerical analysis of engine processes, the sub-models and parameters needed in the analysis software are carefully determined by experiment. Subsequently, the influence of different design parameters of intake and exhaust systems on engine performance is investigated numerically. The most influencing parameters are selected to be the design variables in the optimization process. In order to improve engine power at several engine speeds, two different forms of the optimal design problem are proposed, solved, and compared as a means to identify the most appropriate one. Since the analysis software is a black-box program, the optimization procedure is implemented by employing the optimization software as a master (driver) program while the analysis software acts as the slave program. The data exchange between these programs is established by XML data files and suitable wrapper programs. The results obtained confirm the usefulness of the approach presented.

scholarly journals Towards design optimization of high-pressure gasoline injectors using Genetic Algorithm coupled with Computational Fluid Dynamics (CFD)

2017 ◽  
Author(s):  
Robin Hellmann ◽  
Paul Jochmann ◽  
Karl Georg Stapf ◽  
Erik Schuenemann ◽  
László Daróczy ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
High Pressure ◽  
Pareto Front ◽  
Nozzle Geometry ◽  
Computational Time ◽  
Design Parameters ◽  
Nozzle Flow ◽  
Long Distance ◽  
Penetration Length ◽  
Design Variables

The spray pattern of high-pressure multi-hole injectors as well as the atomization process are of uttermost impor-tance regarding efficiency and emissions in gasoline combustion engines. Ensuring optimal homogenization while meeting the engine individual specifications regarding spray targeting and massflow is a crucial development goal. High effort is put on the layout of the nozzle seat to meet the engine requirements. Success is only possible with a deep knowledge of the influencing quantities, considering that many design parameters affect the inner nozzle flow. Based on this knowledge improvement in spray penetration length and atomization can be achieved.In the current investigation a segment model of the injector is considered. A fully automated, highly parallelized workflow enables a systematic examination of the constrained design space with acceptable computational time. The CFD workflow is implemented in the OPtimization Algorithm Library++ (OPAL++) developed at the “Otto von Guericke” University of Magdeburg.First, inner nozzle flow 3D-CFD calculations of two selected nozzle geometries are validated by comparison with shadowgraphy and Long-Distance-Microscope (LDM) measurements. Using these simulations, correlations be- tween nozzle flow parameters and the key spray characteristics, serving as optimization objectives, are analyzed. Second, a Design-of-Experiment (DoE) is created to understand the interdependency between design variables and objectives. Based on the DoE, metamodels are constructed, validated, compared with each other and used for optimization. Afterwards, a direct 3D CFD-optimization is carried out for the nozzle geometry. It relies on a Genetic Algorithm in OPAL++ to identify the Pareto front of the multi-objective problem. Finally, the Pareto front is analyzedand conclusions are drawn for future research.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4586

Stress and Mesh Stiffness Evaluation of Bimaterial Spur Gears

2019 ◽  
Author(s):  
Fatih Karpat ◽  
Tufan Gürkan Yılmaz ◽  
Oğuz Doğan ◽  
Onur Can Kalay
Keyword(s):  
Weight Reduction ◽  
Gear Tooth ◽  
High Stress ◽  
Design Parameters ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Root Region ◽  
Stress Region ◽  
Stress And Deformation ◽  
Root Stress

Abstract Lightweight spur gears have been a trending topic in aerospace and automotive applications recently. Traditionally, weight reduction could be ensured by using gear body with holes or thin rim design which result in to fluctuate mesh stiffness or it may increase stress and deformation levels. Indeed, high stresses occur in only contact and root region of gear tooth during the meshing process, so other regions are subjected to low stress. Based upon this point; various materials with low density and adequate strength could be used in low stress region while gear steel remains for high stress region. In this study, two different lightweight materials (Aluminum alloy and Carbon fiber reinforced polymer) were used for low stress region. The effect of these materials was investigated in view of stiffness and root stress for the same gear design parameters. Unidirectional CFRP laminas were used in a symmetric lay up to ensure quasi-isotropic laminate properties. Finite element analyses were conducted to obtain root stress and then total deformation of the tooth for stiffness calculation. Interface properties of ring and core regions were assumed as pure bonded. Meshing load was applied on the highest point single tooth contact (HPSTC) line. Weight reduction ratios were also compared. According to results, the steel/composite design is superior to steel/aluminum hybrid design in view of stress, stiffness and weight.

Probabilistic Analysis of MEMS Asymmetric Gear Tooth

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Fatih Karpat ◽  
Stephen Ekwaro-Osire ◽  
Morshed P. H. Khandaker
Keyword(s):  
Gear Tooth ◽  
Load Capacity ◽  
Probability Of Failure ◽  
Mems Devices ◽  
Contact Ratio ◽  
Microelectromechanical System ◽  
Gear Teeth ◽  
Failure Theory ◽  
Gear Drives ◽  
Root Stress

Currently, there is an increased interest in the application of microelectromechanical system (MEMS) gear drives. Additionally, requirements for transmitted power and related reliability issues have increased. Reliability issues often occur due to uncertainties of material, geometry, and loading conditions of the MEMS gears. Asymmetric gear teeth are used to improve the performance of gears by increasing the load capacity or by reducing vibrations. In this paper, asymmetric gear teeth are proposed for MEMS applications. The objective of this research is to investigate the feasibility of applying asymmetric gears for MEMS devices while accounting for uncertainty. The Weibull failure theory was applied to four different MEMS gear configurations. The following analyses were carried out in this research: (i) for the calculation of root stress, four different asymmetric gears were used; (ii) for the calculation of the probability of failure, the Weibull failure theory formulization was used, and (iii) the efficacy of the various asymmetric tooth configurations was discussed. Specifically, the probability of failure of the asymmetric gear was extracted for various parameters. The parameters considered included pressure angle, tooth height, and contact ratio. The efficacy of using asymmetric gear teeth was shown in this study.

Load Distribution in Double Enveloping Worm Gears

1993 ◽  
Vol 115 (3) ◽  
pp. 496-501 ◽  
Author(s):  
V. Simon
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Design Parameters ◽  
Distribution Factor ◽  
Axial Deformation ◽  
Gear Teeth ◽  
Worm Gears ◽  
New Type ◽  
Alignment Errors ◽  
Gear Drives

A method for the determination of load sharing among the instantaneously engaged worm threads and gear teeth of double enveloping worm gears and for the calculation of load distribution along their instantaneous contact lines is presented. The bending and shearing deflection of worm thread and gear tooth, the contact deformation, the axial deformation of worm body, and the manufacturing and alignment errors of worm and gear are included. The obtained system of integral equations is solved by using approximations and an iterative technique. The corresponding computer program is developed. By using this program, the load distribution in the classical and in a new type of double enveloping worm gear drives is calculated. The influence of design parameters on load distribution factor and on maximum tooth pressure is investigated and discussed.

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