Gear Face Width Research Articles

3D Optimization of Gear Train Layout Using Particle Swarm Optimization Algorithm

Optimization of the volume/weight in the gear train is of great importance for industries and researchers. In this paper, using the particle swarm optimization algorithm, a general gear train is optimized. The main idea is to optimize the volume/weight of the gearbox in 3 directions. To this end, the optimization process based on the PSO algorithm occurs along the height, length, and width of the gearbox to achieve the smallest possible gearbox. The constraints are divided into three types named geometrical, design and control constraints. The optimization process is presented for two and three-stage gear trains and by choosing different values for the gear ratio, input power and hardness of gears. The practical graphs for the optimum value of the weight/volume and all necessary design parameters of gearbox such as the number of stages, position, modulus of gears, face width of gears, and diameter of shafts are also presented. The results are validated by comparing with the results reported in the previous publications.

ISO Stress Analysis and Micro Geometry Corrections of Parallel Axis Gearbox Using Dontyne Systems Gear Production Suite

This paper shows the design procedure of a parallel axis gearbox for an electric power steering system using Dontyne Gear Production Suite (GPS) software. It will also investigate the effect of microgeometry correction on contact stress values. Initially, the quantitative design procedure of gears geometry is implemented through an iterative selection process. This includes a proper selection of several geometrical parameters to match the design requirements. Then, ISO 6336, which is the most common analytical gear stress analysis approach, is applied for calculating surface contact and root bending stresses in involute gears. Applying a good macro geometry technique is desirable in order to optimize gear design. However, the increasing demand for reliable and compact gear pair requires specifying proper micro geometry corrections in order to ensure minimum peak stress, low noise, and vibration. Thus, the tooth profile is modified by applying for tip relief from the start to the end of active profiles taken into consideration the value of the mean mesh deflection and the profile error. Similarly, tooth flank is crowned to compensate for equivalent misalignment and to achieve a uniform load distribution over the gear face width. The amount of crowning is determined by adding shaft deflection error to manufacturing error and torsional deflection. The results suggest that there is a significant improvement in contact stress value after applying tip relief and helix crowning.

Dimensional Optimization of Helical Gear Pair Through Finite Element Analysis Using Subproblem Approximation Method

Traditional helical gear stress analysis techniques such as AGMA and ISO standards provides very often over-dimensioned gear pairs with bulky design. Therefore, it is required to optimize the gear pair design using latest techniques like finite element analysis. Stress analysis technique chosen to investigate the feasibility of dimensional optimization of a gear was Finite Element Analysis platform ANSYS 12.1. ISO 6336 standards and Hertz contact theory neglect friction between contact teeth. This work reflects coefficient of friction between contact teeth using FEA predicts more accurate results for contact stress. In this work, case hardened steel helical gear is optimised for optimum tooth root stress level subsequently to reduce the face width of gears with other geometrical parameters unaffected. Efforts has been carried out to verify contact stress value using Lagrange multiplier algorithm of optimised helical gear pair. Subproblem approximation method was implemented for searching of optimal solution of design variable. Optimized gear pair was manufactured and experimentally investigated for actual stresses and strains, as per loading condition mention in the rules of TED. Percentage saving in the material for optimised gear pair also been included in this work.

Effects of PTO gear face width on safety factors

Gears are components of transmission which transmit the power of an engine to a machine and offer numerous speed ratios, a compact structure, and high efficiency of power transmission. Gear train design in the automotive industry uses simulation software. However, PTO (Power Take-Off) gear design for agricultural applications uses the empirical method because of the wide range of load fluctuations in agricultural fields. The PTO is an important part of agricultural tractors which transmits the power to various tractor implements. Therefore, a simulation was essential to the optimal design of the PTO. When the PTO gear is optimally designed, there are many advantages such as low cost, reduced size, and light weight. In this study, we conducted the bending and contact safety factor simulation for the PTO gear of an agricultural tractor. The bending and contact safety factors were calculated on ISO 6336 : 2006 by decreasing the face widths of the PTO pinion and wheel gear from 18 mm at an interval of 1 mm. The safety factor of the PTO gear decreased as the face width decreased. The contact safety factors of the pinion and wheel gear were 1.45 and 1.53, respectively, when the face width was 18 mm. The simulation results showed that the face width of the PTO gear should be greater than 9 mm to maintain the bending and contact safety factors higher than 1. It would be possible to reduce the weight of the PTO gear for different uses and working conditions. This study suggests that the possibility of designing an optimal PTO gear decreases as its face width decreases.

Gear train optimization based on minimum volume/weight design

In this study, the general form of objective function and design constraints for the volume/weight of a gearbox has been written. The objective function and constraints can be used for any number of stages for gearbox ratio but in this paper one, two and three-stage gear trains have been considered and by using a Matlab program, the volume/weight of the gearbox is minimized. Finally, by choosing different values for the input power, gear ratio and hardness of gears the practical graphs from the results of the optimization are presented. From the graphs, all the necessary parameters of the gearbox such as number of stages, modules, face width of gears, and shaft diameter can be derived. The results are compared with those reported in the previous works and an example is presented to show how the practical graphs can be used.

Oil Churning Power Losses of a Gear Pair: Experiments and Model Validation

This paper presents the results of an experimental study on load-independent (spin) power losses of spur gear pairs operating under dip-lubricated conditions. The experiments were performed over a wide range of operating speed, temperature, oil levels, and key gear design parameters to quantify their influence on spin power losses. The measurements indicate that the static oil level, rotational speed, and face width of gears have a significant impact on spin power losses compared with other parameters such as oil temperature, gear module, and the direction of gear rotation. A physics-based gear pair spin power loss formulation that was proposed in a companion paper (Seetharaman and Kahraman, 2009, “Load-Independent Spin Power Losses of a Spur Gear Pair: Model Formulation,” ASME J. Tribol., 131, p. 022201) was used to simulate these experiments. Direct comparisons between the model predictions and measurements are provided at the end to demonstrate that the model is capable of predicting the measured spin power loss values as well as the measured parameter sensitivities reasonably well.

Experiments on Root Stresses of Helical Gears With Lead Crown and Misalignments

In this study, the results of an experimental parametric study of the combined influence of shaft misalignments and gear lead modifications on the load distribution and tooth bending stresses of helical gear pairs are presented. A set of helical gear pairs having various amounts of total lead crown was operated under loaded, low-speed conditions with varying amounts of tightly controlled shaft misalignments. Gear teeth were instrumented through strips of strain gages along the face width of gears at the tooth fillet region at a roll angle that is near the start of the active profile. Variations of root strains along the face width were quantified for different levels of shaft misalignments and gear lead crown. The results presented demonstrate the direct link between the lead crown and gear misalignments as well as the effectiveness of the lead crown in preventing edge loading conditions due to misalignment. The results presented here form a database that should be available for a validation of gear contact models in terms of their ability to simulate misalignments.

Investigation of the Thermal Behaviour of Non‐metallic Curved‐Face‐Width Spur Gears

AbstractThis paper describes a curved‐face‐width spur gear, specially designed for manufacture from non‐metallic materials. The benefits of this gear are the higher contact ratio, bending and Hertzian contact resistance, and greater tooth stiffness compared to standard spur gears. A modified geometry is proposed for the gear tooth, the height of which varies along the gear face width. Due to the reduction in tooth height, in sections away from the gear centre, lower sliding friction is expected, with consequences for the gear's thermal behaviour. The complex gear geometry makes the design of a die difficult; therefore the gears were cut on a milling machine, using a special kinematic generation process and related equipment. The tooth flank profile, an involute or near involute in sections away from the gear half‐width plane, as well as the flank surface quality determined by the single‐cutter tool used for gear manufacture, influence the meshing condition, and can be detrimental to the thermal behaviour of the gear. Experimental tests were carried out to examine the influence of load and speed on the temperature of the curved‐face‐width spur gears with modified geometry. The measured temperature of the non‐standard gear is further compared with the predicted temperature of plastic standard spur gears of the same specification.