American Gear Manufacturers Association Research Articles

An evaluation methodology for the circumferential position error of the V-shaped apex of the double-helical gear.

Aiming to achieve an accurate evaluation of the circumferential position error of the V-shaped apex of double-helical gear, the definition of the V-shaped apex of double-helical gear and the evaluation method of the circumferential position error is studied based on the geometric characteristics of double-helical gear and the definition of shape error. First, the definition of the V-shaped apex of double-helical gear based on the helix and its circumferential position error is presented based on the (American Gear Manufacturers Association) AGMA940-A09 standard. Second, based on the basic parameters, the tooth profile characteristics, and the tooth flank forming principle of double-helical gear, the mathematical model of double-helical gear in a Cartesian space coordinate system is established, and the auxiliary tooth flank and auxiliary helix are constructed to generate some auxiliary measurement points. Finally, the auxiliary measurement points are fitted using the least-squares principle to calculate the position of the V-shaped apex of the double-helical gear in the actual meshing condition and its circumferential position error. The simulation and experimental results show that the simulation results verify the feasibility of the method, and the experimental results (the circumferential position error of the V-shaped apex is 0.0187mm) are consistent with the results of the literature [Bohui etal., Metrol. Meas. Technol. 36, 33 (2016)]. This method can effectively realize the accurate evaluation of the double-helical gear V-shaped apex position error, providing some guidance for the design and manufacture of double-helical gear.

Optimization of spur gear pairs for aerospace applications

Abstract High power applications at high speed create contact problems, increase heat sink values and transmission error (TE) during gear meshing. Hence, analyzing the gear mesh including helix angle effect, the optimization in terms of contact pressure and the transmission error reduction are all crucial for high-speed applications. In this study, meshing characteristics including helix angle based on different approaches, optimization of spur gears pairs in terms of the transmission error and contact stresses obtained from improved analytical method besides transmission design tools are all investigated for high-speed aerospace applications. Results reveal that significant transmission error reduction could be achieved by applying tip relief starting from the highest-point of single tooth contact for spur gears in aerospace applications. Hence, the need for higher contact ratio by helix angle inclusion for smoother transmission could be compensated by using tip-relief modified spur gears in gearbox since the heat sink values also need to be minimized by using relatively lower contact ratio. Results obtained from the improved analytical method by directly considering gear geometry including gear foundation effects based on direct deformation–summation approach are found in between AGMA (American Gear Manufacturers Association) standard and ISO (International Organization for Standardization) standard results.

Stress and Fatigue Analysis of Picking Device Gears for a 2.6 kW Automatic Pepper Transplanter

A seedling picking device is an essential component for an automatic transplanter to automatically convey the seedling to the dibbling part. It is necessary to find the appropriate material and dimensions for the picking device gears to avoid mechanical damage and increase their durability. Therefore, the objectives of this research were to analyze the stress of a picking device gear mechanism in order to select suitable materials and dimensions, and to predict the fatigue life by considering the damage level. The picking device gear shaft divided the input power into two categories, i.e., crank and cam gear sets. Finite element analysis simulation and American Gear Manufacturers Association standard stress analysis theory tests were conducted on both of the crank and cam gear sets for different materials and dimensions. A test bench was fabricated to collect the load (torque) data at different gear operating speeds. The torque data were analyzed using the load duration distribution method to observe the cyclic load patterns. The Palmgren–Miner cumulative damage rule was used to determine the damage level of the picking mechanism gears with respect to the operating speed. The desired lifespan of the transplanter was 255 h to meet the real field service life requirement. Predicted fatigue life range of the picking mechanism gears was recorded as from 436.65 to 4635.97 h, making it higher (by approximately 2 to 18 times) than the lifespan of the transplanter. According to the analyses, the “Steel Composite Material 420H carbon steel” material with a 5 mm face width gear was suitable to operate the picking device for a 10-year transplanter service life. The analysis of stress and fatigue presented in this study will guide the design of picking device gears with effective material properties to maintain the recommended service life of the pepper transplanter.

Proračun jačine pitinga kod materijala od livenog gvožđa i legura bakra

An attempt is made to predict the pitting strength of cast iron and copper alloy materials from their compressive yield or compressive proof strength for a reliability of 99% at 107 load cycles. The compressive yield or compressive proof strength is related to the tensile strength of ductile cast iron and copper alloy materials by a proportionality factor. Two proportionality factors are used for brittle cast iron materials. The pitting strength formulation incorporates a nominal design factor at 99% reliability which is estimated from a probabilistic model based on the lognormal probability density function. Pitting strength estimates from the predictions are compared with those of American Gear Manufacturers Association (AGMA) estimates and data from other sources. The predicted values for gray cast irons had variances in the range of -11.28% to 25%. Ductile cast iron pitting strength estimates deviated from those of AGMA by -30.28% to 1.73% and 16.76% to 36.34% for Austempered ductile irons. The variances obtained for cast bronze were from 11.17% and 14.73%, but the sample size was small. These variances appear to be reasonable due to the many factors that can influence pitting resistance. Since pitting strength data for many grades of cast iron and copper alloys are not available (especially in the public domain), they may be estimated by the expressions developed in this study for initial design sizing. Also, the pitting strength of new cast iron and copper alloy materials could likewise be estimated for initial design sizing. This will eliminate long and costly contact fatigue testing at the initial design phases, which of course is necessary for design validation.

Proračun otpornosti na piting čeličnih materijala

A single expression for estimating the nominal pitting strength of steel materials, based on surface hardness, is developed from first principles for a reliability of 99% at 107 load cycles. It requires the hardness values to be measured in Vicker's hardness scale. The expression may be used for any steel material processed by hot rolling, cold drawing, quenching and tempering or case-hardening. The formulation incorporates a nominal design factor at 99% reliability which is estimated from a probabilistic model based on the lognormal probability density function. Pitting strength estimates from the expression are compared with those of American Gear Manufacturers Association (AGMA) estimates and data from other sources as indicated in Tables 3 and 4. The expression predicts lower values at low hardness but higher values at high hardness. The variance is between - 15.21% and 10.13% for through-hardened steels. For case-hardened steels, the variances range from 14.23% to 20.26% between the estimates and available data. These variances appear to be reasonable considering the many factors involved in pitting resistance. The main advantage of this study is that pitting strength of new steel materials may be estimated for initial design sizing without long and costly contact fatigue testing which of course is necessary for design validation. Also, the estimation method developed may be applied to other materials, metallic and non-metallic. Suggestions are made for estimating some pertinent pitting strength adjustment factors when considering field or service pitting strength.

Revised Lewis Bending Stress Capacity Model

Background: During operation, cylindrical gearset experiences tangential, radial, and axial (helical gears only) force components that induce bending, compressive, and shear stresses at the root area of the gear tooth. Accurate estimation of the effective bending stress at the gear root is a challenge. Lewis was the first person who attempted estimating the root bending stress of spur gears with some reasonable accuracy. Various gear standards and codes in use today are modifications and improvements of the Lewis model. Objective: This research aims at revising the Lewis model by making adjustments for dynamic loads, shear stresses, axial bending stress for helical gears, and stress concentration factor that is independent on the moment arm of tangential or axial force component. Methods: An analytical approach is used in formulating a modified formula for the root bending stress in cylindrical gears starting with the original Lewis model. Intermediate expressions are developed in the process and works from many previous authors are reviewed and summarized. The new model developed is used to estimate the root bending stress in four example gearsets of 0o to 41.41o helix angle and the results are compared with those of AGMA (American Gear Manufacturers Association) formula. Results: Analysis from the examples shows that neglecting the radial compressive stress over-estimated the root bending stress by 5.27% on average. When shear stresses are ignored, the root bending stress is under-estimated by 7.49% on average. It is important, therefore, to account for both compressive and shear stresses in cylindrical gear root bending stress. When the root bending stress estimates from the revised Lewis model were compared with AGMA results, deviations in the range of -4.86% to 26.61% were observed. The stress estimates from the revised Lewis formulae were mostly higher than those of AGMA. Conclusion: The new root bending stress model uses stress concentration factors (normal and shear) that are independent of the point of load application on the gear tooth. This decoupling of stress concentration factor from the load moment arm distinguishes the new model from AGMA formula and brings bending stress analysis in gear design in line with classical bending stress analysis of straight and curved beams. The model can be used for both normal contact ratio and high contact ratio cylindrical gears.

Stress and stiffness analysis of a 7-teeth pinion/rack jacking system of an Offshore jack-up rig

In offshore mobile jack-up rig, platforms are generally supported by movable jacking system in which strength of rack and pinion are very crucial in determining the design life of the superstructure. In this study, a series of finite element (FE) models has been developed and analysed for a 7-teeth pinion with rack to investigate the strength, stiffness and fatigue life of the jacking system before its practical application in an offshore rig. Since rack/pinion contact patterns change with the rotation of the shaft, FE models are developed for each 10-degree rotations starting from 0 to 50 degree where elasto-plastic properties of both rack and pinion are considered in the FE analyses. A geometric analysis is also performed to determine shape and contact position between the rack and pinion at different angle of rotation. Finite element analyses are conducted for worst possible load cases of the jacking system including self-weight of the platform, wind load, hydrodynamics force as per American Bureau of Shipping (ABS) guideline. The stress distribution of the pinion shows that maximum stress occurs at the root of the tooth, mainly due to bending effect resulting from external torque. The FE analysis reveals that maximum von mises stress of pinion and rack are found to be 1105 MPa and 688 MPa, respectively which are very close to the corresponding strength of the materials. The FE results are validated with the established Lewis formula and American Gear Manufacturers Association (AGMA) guideline. Considering the design life of the offshore platform, fatigue performance of the pinion is investigated for different operational loading of the platform. A separate 3D FE model has been developed to check the stiffness of the gear box that actually presents the serviceability of shaft beam and pinion teeth. In the stiffness analysis, the maximum deflection of the beam and individual tooth are found to be 1.2 mm and 2.1 mm, respectively. The outcome of this study is expected to contribute in designing future rack/pinion system for offshore jack-up rigs and similar other structures.

Effect of module variation on a 100watt horizontal axis wind turbine spur gear drive

Spur gears are simple to design and construct to actualize their usage in power transmission as well as for speed reduction or increase. The aim of this research work is to determine the effect of module variation on a 100Watt horizontal axis wind turbine (HAWT) spur gear drive. The solution is to determine and appropriately select gear parameter values based on design considerations and the significance is for enhanced machine reliability and balance with economic production. The method used involved the application of gear design principles, modelling the gears with AutoCAD, module variation and evaluation of induced bending stress at the gears root; gear diameter, tooth thickness and face width become bigger with choosing higher modules for cutting tooth size, with the largest diameter of 168.4mm and 80mm for driver and driven gear respectively and face width of 60mm from using a module of 6mm. Although, the total torque exerted remains constant at 7.9Nm and 3.8Nm for a 100W HAWT. The tangential force in meshed operation of the gears and induced bending stress kept reducing as module increased. The highest tangential force is 282.4N and corresponding induced bending stress is 26.1N/mm2 based on American Gear Manufacturers Association (AGMA) standard and the range of data analyzed, at the lowest module of 2mm. Selecting lower modules means that higher bending stresses will be induced at the gears root, but smaller production cost and more compact system with less space requirement. The lower bending stresses with increasing module will support higher load capacity of the gears due to the increasing face width and enhance the reliability of the HAWT in respect of its performance.
 Keywords: Module, Spur Gear, Power Transmission, Bending Stress, Wind Turbine

Pinion Failure Analysis of a Helical Reduction Gearbox in a Kraft Process

This paper reports investigations related to addressing the cause of pinion teeth deformation of a helical reduction gearbox in a kraft process. The American Gear Manufacturers Association (AGMA) design methodology was employed to determine the safety factor under bending and surface fatigue strengths of a pinion and gear at two operating loads (3 and 3.75 MW). In addition, finite element analysis (FEA) of the pinion and gear assembly was also performed to check the misalignment (due to deformation) at 3.75 MW load. Based on the investigations presented herein, it is found that the pinion portion near the thrust disc became excessively deformed at the axial thrust corresponding to the 3.75 MW load, causing misalignment that resulted in the plastic deformation of the pinion teeth.

Projektovanje veličine para cilindričnih pužnih zupčanika

A method for the design sizing task of cylindrical worm gearsets is presented that gives an estimate of the initial value of the normal module. Expressions are derived for the worm pitch diameter of integral and shell worms as well as for the active face width of the gear and the threaded length of the worm. An attempt is made to predict the contact strength of bronze materials against scoring resistance. Four Examples of design sizing tasks of cylindrical worm gears are carried out using the approach presented and the results are compared with previous solutions from other methods. The results for first three examples show excellent comparisons with previous solutions of American Gear Manufacturers Association (AGMA) method. The results of the fourth example are slightly more conservative than those of DIN3999 but are practically similar. Therefore, it appears that a systematic, reliable and more scientifically based method for cylindrical worm drive design sizing has been developed.

Practical Optimal Design on Two Stage Spur Gears Train Using Nature Inspired Algorithms

The accurate design of spur gear drive has a tremendous impact on size, weight, transmission and machine performance. Also, the demand for lighter gears is high in power transmission systems, as they save material and energy. Hence this paper presents an enhanced method to solve a two stage spur gear optimization problem. It consists of a mathematical model with a nonlinear objective function and 11 constraints. A two stage spur gear is considered. To obtain minimum volume of spur gear drive is objective of the problem. The considered design variables are: Module, number of teeth, base width of the gears and, shaft diameter and power. Besides considering regular mechanical constraints based on American Gear Manufacturers Association (AGMA) requisites, six more additional critical constraints on contact ratio, load carrying capacity, power loss, root not cut, no involute interference and line of action are imposed on the drive. Nature inspired optimization algorithms, namely, Simulated Annealing (SA), Firefly (FA) and MATLAB solver fmincon are used to find solution in MATLAB environment. Simulation results are analyzed, compared with literature and validated.

Development of Computer-Based Model for Design and Analyses of Worm Gearing Mechanism

Current computer software for designing gear systems have limited flexibility and few offer multiple gearing design options. The objective of this study was to develop an interactive package for the design and analyses of worm gearing mechanisms. The worm gears were designed based on full-depth involute teeth. Mathematical models were developed to compute geometry factors for surface durability of single-enveloping worm gearing cases which were extracted from established American Gear Manufacturers Association (AGMA) standards. Maximum percentage errors from the geometry features, bending loads and wear loads are 0.97%, 3.27% and 1.77% respectively and insignificant. A software capable of computing geometry parameters, bending and wear loads, and selecting appropriate materials for worm mechanisms with good accuracy has been developed.

Development of Computer-Based Model for Design and Analyses of Worm Gearing Mechanism

Current computer software for designing gear systems have limited flexibility and few offer multiple gearing design options. The objective of this study was to develop an interactive package for the design and analyses of worm gearing mechanisms. The worm gears were designed based on full-depth involute teeth. Mathematical models were developed to compute geometry factors for surface durability of single-enveloping worm gearing cases which were extracted from established American Gear Manufacturers Association (AGMA) standards. Maximum percentage errors from the geometry features, bending loads and wear loads are 0.97%, 3.27% and 1.77% respectively and insignificant. A software capable of computing geometry parameters, bending and wear loads, and selecting appropriate materials for worm mechanisms with good accuracy has been developed.

Development of knowledge based parametric CAD modeling system for spur gear: An approach

In almost every mechanism, gears are extensively used machine parts to transmit power from one shaft to other with or without change of speed or direction. The need for better and efficient power transmission has increased the demand for effective gear design systems. All renowned formal gear design systems use AGMA (American Gear Manufacturers Association) standards for design. The conventional processes demand 150 to 200 man-hours to design the new optimized typical gear. Significant time reduction in design calculations can be obtained by using the soft computing tool. Additionally, advanced CAD Modeling techniques like parametric modeling can further trim down the design time. Hence, the present work is aimed to develop a knowledge-based parametric CAD modeling system for Spur Gear Design. This framework or system utilizes Knowledge Based Engineering (KBE) incorporating the rules of AGMA in design computations and parametric modeling in CAD. SolidWorks customization is carried out to generate the spur gear CAD model based on AGMA standards. Further, this system is proven as standard, faster, and simpler gear design system when compared with conventional design system. Results of this system are reasonably close to AGMA results under specific conditions.

Internal spur gear root bending stress: A comparison of ISO 6336:1996, ISO 6336:2006, VDI 2737:2005, AGMA, ANSYS finite element analysis and strain gauge techniques

The Association of German Engineers VDI 2737:2005 and the International Organisation for Standardisation ISO 6336:2006 are universally accepted analytical procedures for the analysis of internal gears. There is no official American Gear Manufacturers Association standard for internal gear stress analysis due to the validity of inscribing the Lewis parabola within internal concave profiles and the resulting errors associated with the location of maximum root bending stress. This research investigates the differences associated with using ISO 6336, VDI 2737 and an unofficial American Gear Manufacturers Association method, all of which are compared against a potentially more accurate numerical (ANSYS) method and strain gauge techniques.

Search method applied for gear tooth bending stress prediction in normal contact ratio asymmetric spur gears

Various analytical methods have been developed by designers to predict gear tooth bending stress in asymmetric spur gears with an intention to improve the accuracy of predicted results and to reduce the need for time consuming finite element analysis at the early stages of gear design. Asymmetry in the drive and coast side of asymmetric spur gears poses difficulty in direct application of well-known procedures like American Gear Manufacturers Association and International Organization for Standardization in the prediction of gear tooth bending stress. In earlier works, ISO-6336-3 methodology was suitably modified and adapted to predict asymmetric spur gear tooth bending stress. This approach is based on certain assumptions on the location of critical section which could introduce error in the predicted maximum bending stress. The present work is to analytically predict gear tooth bending stress in normal contact ratio asymmetric spur gears based on a more rigorous analytical approach. This includes a fundamental study on the gear tooth orientation used to define the coordinate system, determination of maximum bending stress by search along the fillet profile and to obtain stress profile along the fillet. Gear tooth bending stress obtained from the present work using Search method is compared against the results obtained from earlier adapted International Organization for Standardization method and Finite Element Analysis. This study recommends a new coordinate system and method for analytical prediction of gear tooth bending stress in normal contact ratio asymmetric spur gears.

Modeling of the kinematic geometry of spur gears using matlab

The analytical method of gear design is calculation-intensive and it is usually difficult to achieve optimum backlash and interference-free involute profile that are required to generate geometrical compatibility in a pair of meshing gears when design procedure is entirely based on this method. Some amount of backlash is often required in the assembly of gears but excess backlash can lead to increase vibration and wear of the gear assembly. Also, interference-risk profile can result in undercutting of gear tooth. This paper optimized a spur external involute-profile gear by developing an application for the modeling of its geometrical compatibility using Matlab®. The application uses existing models to test for interference and a proposed model to determine effective backlash in a gear. The backlash values resulting from the application are more confined and the model is applicable to a wider range of modules suggested by American Gear Manufacturers Association. Simulation of the gear-set in Solidworks® for kinematic geometry presents an interference-free tooth contour and an effective backlash.

Finite Element Simulation of Bending Stress on Involute Spur Gear Tooth Profiles

This study investigated bending stress distribution on involute spur gear tooth profiles with pressure angle of 20 ̊ but different modules 2.5, 4.0 and 6.0 mm, using a finite-element-based simulation package - AutoFEA JL Analyzer. The drafting of the geometry for the three gear tooth profiles were implemented on the platform of VB-AutoCAD customized environment, before importing to the package. These were separately subjected to analysis for bending stresses for a point at the tooth fillet region with appropriate settings of material property, load and boundary conditions. With the same settings, the bending stresses were computed analytically using American Gear Manufacturers Association (AGMA) established equation. The results of the two approaches were in good agreement, with maximum relative deviation of 4.38%. This informed the confidence in the implementation of the package to investigate the variation of bending stress within the gear tooth profile. The simulation revealed decrease in the bending stresses at the investigated regions with increase in the module of the involute spur-gear. The study confirms that Finite element simulation of stresses on gear tooth can be obtained accurately and quickly with the AutoFEA JL Analyzer.

Optimum design of straight bevel gears pair using evolutionary algorithms

Straight bevel gear is a type of gear which is widely used in mechanical systems to transmit power between perpendicular rotating axes. Designing straight bevel gears with the least possible volume is of great importance in industry since it results in a decrease in energy consumption and the material requirement in manufacturing. In this paper, employing two powerful optimization algorithms, simulated annealing algorithm (SA) and genetic algorithm (GA), techniques for advanced optimization, coupled with American Gear Manufacturers Association (AGMA) instructions the volume of straight bevel gears pair is minimized and the corresponding design variables are obtained. These variables include majors, including teeth number, module and face width. Using a traditional technique, recommended values of the design variables by AGMA, a design example was performed and the values were obtained. Then, the suggested techniques were utilized to get the values. The comparison between the results of all techniques shows that proposed optimization algorithms are considerably capable of minimizing the volume. It indicates that improvement in the attained volume varies between 1.56 and 17.40% for SA and 9.28 and 23.15% for GA.

External spur gear root bending stress: A comparison of ISO 6336:2006, AGMA 2101-D04, ANSYS finite element analysis and strain gauge techniques

The International Organisation for Standardisation ISO 6336:2006 and the American Gear Manufacturers Association AGMA 2101-D04 are the two most predominant empirically based analytical gear stress analysis methods for establishing contact and root bending stress in involute spur and helical gears. Although based on the same fundamental principles, they have evolved to such an extent that, for various reasons, they are not necessarily in agreement. The use of commercial universal numerical finite element software has become an increasingly popular alternative for gear stress analysis and this research compares the root bending stresses in external spur gears established using ISO 6336:2006, AGMA 2101-D04 and numerical finite element analysis (ANSYS) with experimental strain gauge validation.