Helical Gear Teeth Research Articles

Investigating the effect of helix angle and pressure angle on bending stress in helical gear under dynamic state

PurposeThe aim of this paper is to study the effect of pressure angle and helix angle on bending stress at the root of helical gear tooth under dynamic state. Gear design is a highly complex process. The consistent demand to build low-cost, quieter and efficient machinery has resulted in a gradual change in gear design. Gear parameters such as pressure angle, helix angle, etc. affect the load-carrying capacity of gear teeth. Adequate load-carrying capacity of a gear is a prime requirement. The failure at the critical section because of bending stress is an unavoidable phenomenon. Besides this fact, the extent of these failures can be reduced by a proper gear design. The stresses produced under dynamic loading conditions in machine member differ considerably from those produced under static loading.Design/methodology/approachThe present work is intended to study the effect of pressure angle and helix angle on the bending stress at the root of helical gear tooth under dynamic state. The photostress method has been used as experimental methods. Theoretical analysis was carried out by velocity factor method and Spott’s equation. LS DYNA has been used for finite element (FE) analysis.FindingsThe results show that experimental method gives a bending stress value that is closer to the true value, and bending stress varies with pressure angle and helix angle. The photostress technique gives clear knowledge of stress pattern at root of tooth.Originality/valueThe outcomes of this work help the designer use optimum weight-to-torque ratio of gear; this is ultimately going to reduce the total bulk of the gear box.

Dynamic State or Whole Field Analysis of Helical Gear

To determine the true bending stresses at the root of the tooth is an important and crucial step in accurate design of the gears. The present work has been intended for bending stress analysis at critical section of helical gear tooth under dynamic state by different methods. The photo stress coating method along with reflection polariscope was used as experimental method. Velocity factor method and Spott’s equation method have been used to estimate dynamic load and bending stress at critical section of tooth. LS DYNA software has been used for finite element analysis under dynamic state. The results show that the experiment photo stress method gives bending stress closer to the true value in dynamic conditions amongst all method under consideration. Finally, the study proposes the correction factor for velocity factor method and Spott’s equation method to estimate true bending stress at tooth root with respect to experimental method.

Generation of a double-crowned involute helical gear with twist-free tooth flanks by a CNC hobbing machine with three synchronous axes

In the conventional hobbing process, a double-crowned involute helical gear is generated by the hob cutter with parabolic-curve tooth profiles for the cross-profile crowning and varied the center distance between the hob and work gear for the longitudinal crowning. Therefore, to cut a double-crowned helical gear not only requires at least four synchronous axes and hob cutter regrinding (which increases production costs) but also induces twisted tooth flanks on the generated work gear. In this paper, I propose a hobbing method by applying a modified work gear rotation angle that enables double-crowning of involute helical gear's tooth flanks using a standard hob cutter and a computer numerical control (CNC) hobbing machine with only three synchronous axes. The proposed method has also verified by using two computer simulation examples to compare the meshing-conditions, contact ellipses, and transmission errors of the double-crowned gear pairs with that produced by applying the conventional hobbing method. Computer simulation results reveal the advantages of the proposed novel hobbing method.

Helical gear multi-contact tooth mesh load analysis with flexible bearings and shafts

A multi-contact tooth meshing model for helical gear pairs considering bearing and shaft deformations is proposed. First, to easily incorporate into the system model, the complicated Harris\'s bearing force-displacement relationship is simplified applying a linear least square curve fit. Then, effects of shaft and bearing flexibilities on the helical gear meshing behavior are implemented through transformation matrices which contain the helical gear orientation and spatial displacement under loads. Finally, true contact lines between conjugated teeth are approximated applying a modified meshing equation that includes the influence of tooth flank displacement on the tooth contact induced by shaft and bearing displacements. Based on the model, the bearing\'s force-displacement relation is examined, and the effects of shaft deformation and external load on the multi-contact tooth mesh load distribution are also analyzed. The advantage of this work is, unlike previous works to search true contact lines through time-consuming iterative strategy, to determine true contact lines between conjugated teeth directly with presentation of deformations of bearings and shafts.

Mathematical Model of Helical Gear Topography Measurements and Tooth Flank Errors Separation

During large-size gear topological modification by form grinding, the helical gear tooth surface geometrical shape will be complex and it is difficult for the traditional scanning measurement to characterize the whole tooth surface. Therefore, in order to characterize the actual tooth surfaces, an on-machine topography measurement approach is proposed for topological modification helical gears on the five-axis CNC gear form grinding machine that can measure the modified gear tooth deviations on the machine immediately after grinding. Combined with gear form grinding kinematics principles, the mathematical model of topography measurements is established based on the polar coordinate method. The mathematical models include calculating trajectory of the centre of measuring probe, defining gear flanks by grid of points, and solving coordinate values of topology measurement. Finally, a numerical example of on-machine topography measurement is presented. By establishing the topography diagram and the contour map of tooth error, the tooth surface modification amount and the tooth flank errors are separated, respectively. Research results can serve as foundation for topological modification and tooth surface errors closed-loop feedback correction.

Local fault detection in helical gears via vibration and acoustic signals using EMD based statistical parameter analysis

Gear is a vital transmission element, finding numerous applications in small, medium and large machinery. Excessive loads, speeds and improper operating conditions may cause defects on their bearing surfaces, thereby triggering abnormal vibrations in whole machine structures. This paper describes the implementation of empirical mode decomposition (EMD) method for monitoring simulated faults using vibration and acoustic signals in a two stage helical gearbox. By using EMD method, a complicated signal can be decomposed into a number of intrinsic mode functions (IMF) based on the local characteristic time scale of the signal. Vibration and acoustic signals are decomposed to extract higher order statistical parameters. Results demonstrate the effectiveness of EMD based statistical parameters to diagnose severity of local faults on helical gear tooth. Kurtosis values from EMD and that obtained from vibration and acoustic signals are compared to demonstrate the superiority of EMD based technique.

Study on the Anti-Twist Helical Gear Tooth Flank With Longitudinal Tooth Crowning

To attain an anti-twist helical gear tooth flank with longitudinal tooth crowning, a novel additional rotation angle is proposed for the work gear during its hobbing process. A congruous nonlinear function with two variables is proposed and supplemented to this additional rotation angle of work gear. Two numeral examples are presented to illustrate the effects of coefficients of the proposed nonlinear function on the twist and evenness of generated helical gear tooth flanks. The twist of the crowned helical tooth flank is reduced significantly by applying the proposed longitudinal crowning gear method.

Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method

ABSTRACTIn this paper, the fatigue crack growth in helical gear tooth root has been simulated using linear elastic fracture mechanics. The extended finite element method has been used to simulate 3D fatigue crack growth and obtain growth path. Paris equation has been used to calculate the fatigue life of the gear. The modelling time has reduced considerably compared to previous works carried out on 3D crack growth in gears. Some verifications have been carried out to ensure the reliability of the results.

A Finite Element Approach to Bending, Contact and Fatigue Stress Distribution in Helical Gear Systems

In the face of extensive research into the theoretical basis and performance characteristics of helical gear design, a complete mathematical description of the relationship between the design parameters and the performance matrices is still to be clearly understood because of the great complexity in their interrelationship. The objective of this work is to conduct a comparative study on helical gear design and its performance based on various performance metrics through finite element as well as analytical approaches. The theoretical analysis for a single helical gear system based on American Gear Manufacturing Association (AGMA) standards has been assessed in Matlab. The effect of major performance metrics of different helical gear tooth systems such as single, herringbone and crossed helical gear are studied through finite element approach (FEA) in ANSYS and compared with theoretical analysis of helical gear pair. Structural, contact and fatigue analysis are also performed in order to investigate the performance metrics of different helical gear systems. The benefit of such a comparison is quickly estimating the stress distribution for a new design variant without carrying out complex theoretical analysis as well as the FEA analysis gives less scope for manual errors while calculating complex formulas related to theoretical analysis of gears. It will significantly reduce processing time as well as enhanced flexibility in the design performance.

Design and Static Analysis of an Addendum Modified Helical Gear Tooth

A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. We have several types of gears among which spur gears are used as pinion and gear between parallel shafts.. When the involute portion of the tooth mates with the non-involute portion of the other tooth an undercut is formed. Due to this the mating gear will try to scoop out metal from the interfering portion. In order to avoid undercutting and interference, addendum modification of the gear tooth is carried out. This paper describes about the modeling meshing and the analysis techniques. Effort has been taken to develop the tooth profile involute as well as the fillet region by calculating the co-ordinates using C-language. The output file of the C-program is converted to modeling software PRO/E for 3-D modeling with the help of a coupler software DXF file converter. Those PRO/E models are imported to an analysis software ANSYS for the proposed stress analysis.

Simulation Research on Tooth Root Dynamic Stress of Marine Helical Gear Meshing Impact

Finite element model of helical gear meshing of large burden marine is built based on explicit dynamics finite element method, dynamics stress variation of helical gear tooth is simulated under multiple working conditions, research is focused on the impact of changes in working conditions on the dynamic stress of the tooth root. The results show that helical gear pair speed and center distance error have great impact on dynamic stress of tooth root. The results provide reference for dynamic performance optimization of marine gears.

Contact stress calculation of high transverse contact ratio spur and helical gear teeth

For contact stress calculations of spur and helical gears, the Hertz equation can be used in combination with a model of load distribution along the line of contact. This load distribution is not uniform due to the changing rigidity of the pair of teeth along the path of contact and has decisive influence on the location and the value of the critical contact stress to consider for calculations. Moreover, the load distribution can be highly influenced for non-standard gearing conditions as the presence of undercut, enlarged tooth addendum or reduced center distance, often present in high transverse contact ratio gears. In this paper, a new calculation method of the contact stress of spur and helical gears with transverse contact ratio greater than 2 is developed. It is based on the Hertz equation and an enhanced model of load distribution, obtained from the minimum elastic potential criterion, suitable for non-standard gearing conditions. A complete study on the critical load conditions and the value of the critical contact stress has been carried out. As a result, a recommendation for pitting load capacity calculations is proposed.

Research on the Parametric Design of Involute Helical Gear Based on Pro/Program

Involute helical gear has advantages of larger overlap coefficient, steady transmission, lower impact and noise, higher load bearing capacity, longer life, so it is widely used in machinery, mining, metallurgy, aerospace and other fields. However, due to the involute helical gear tooth profile shape is more complex, and some low-level CAD software is difficult to directly generate a three-dimensional helical gear tooth profile. According to involute helical gear formation principle, this paper presents an effective method to establish the three-dimensional model for involute helical gear .In this paper, a parametric design method of realizing involute helical gear 3D model by using Pro/E modeling functions and Pro/Program programming is discussed. This method can enable designers to obtain helical gear 3D solid model quickly and accurately by inputting a little geometry characteristic parameters. It can also enables designers quickly update design based on the existing 3D gear model, so as to improve the design efficiency.

Enhanced model of load distribution along the line of contact for non-standard involute external gears

The presence of undercut at the tooth root, non-equal addendum on pinion and wheel, non-standard tooth height or non-standard center distance may have decisive influence on the load distribution along the line of contact of spur and helical gear teeth. The curve of variation of the meshing stiffness along the path of contact, quite symmetric respect the midpoint of the interval of contact, loses its symmetry for non-standard geometries and operating conditions. As a consequence, the critical contact points for bending and wear calculations may be shifted from their locations for standard gears. In this paper, a non-uniform model of load distribution along the line of contact of standard spur and helical gears, obtained from the minimum elastic potential criterion, has been enhanced to fit with the meshing conditions of the above mentioned non-standard cylindrical gear pairs. The same analytical formulation of the initial model may be used for the non-standard gears by considering appropriate values of a virtual contact ratio, which are also presented in the paper.

Multi-tooth contact behavior of helical gear applying modified meshing equation

In tooth contact analysis, the numerical process of searching for true contact lines or points is always a daunting task. The true contact lines for ideal helical gear transmission can be easily obtained through the helical gear meshing theory; however, in practice, this approach does not work well due to effect of tooth elasticity that shifts the contact lines from their ideal position. To address this problem, an approximate method to seek the true contact positions is proposed applying a modified meshing equation for a pair of helical gear with error free and no shaft deformation. First, the helical gear tooth deformation is calculated with the combination of contact mechanics and finite element method. Second, the deformed tooth flanks are fitted with Chebyshev polynomials. Third, the modified meshing equation is formulated by accounting for the influence of not only gear rigid body movement but also the gear deformation on the meshing process. Finally, the true contact points are determined by solving the correlated tooth flank equations, meshing equations, and force balance equations. The deformations of the gear and pinion teeth within the meshing plane are analyzed, and the contact load distributions along with the Von Mises stresses over a mesh cycle are examined. The study indicates that the proposed numerical method can yield true contact lines quickly while avoiding costly computational time in the traditional true contact line searching process that searches iteratively in the whole meshed tooth flank.

A FEM Analysis of Cross-Wedge Rolling of Toothed Shafts

This paper presents a new concept for forming toothed shafts based on the cross-wedge rolling process (CWR). This method consists in using special inserts in the shape of flat rack bars, which, acting on a billet, extrude material from tooth spaces to tooth points. These inserts are placed at the finish end of a wedge tool. Numerical calculations (based on FEM) and experimental rolling tests unequivocally demonstrate the effectiveness of the proposed method for forming spur (straight-cut), helical, curved and herringbone gear teeth.

Contact stress calculation of undercut spur and helical gear teeth

The presence of undercut at the pinion root may affect the load sharing among couples of spur gear teeth in simultaneous contact, as well as the load distribution along the line of contact of helical gears . This occurs if the outside points of the wheel profile do not find, due to undercut, mating profile to mesh with, which is called vacuum gearing. Under these conditions, the effective contact ratio is reduced, and the critical contact points may be shifted from their locations at non-undercut profiles. In this paper, a non-uniform model of load distribution along the line of contact, obtained from the minimum elastic potential criterion, has been used combined with the Hertz equation for the calculation of the contact stress. A complete study on the critical load conditions and the value of the critical contact stress has been carried out, considering a wide range of the values of the geometrical parameters. As a result, a recommendation for pitting load capacity calculations of vacuum-gearing spur and helical gears is proposed. ► A model of load distribution along the line of contact is proposed for undercut gears. ► A study on the critical load conditions and critical contact stresses is carried out. ► Recommendations for load capacity calculation are proposed for vacuum gearing contact.

Critical stress and load conditions for pitting calculations of involute spur and helical gear teeth

Calculation methods of spur and helical gear drives for preliminary designs or standardization purposes available in technical literature, use the Hertz equation to evaluate the contact stress, assuming the load to be uniformly distributed along the line of contact. However, this model presents some discrepancies with experimental results because the changing rigidity of the pair of teeth along the path of contact produces a non-uniform load distribution, which implies that some load distribution factors are required to compute the contact stress. In this paper, a non-uniform model of load distribution along the line of contact, recently developed, obtained from the minimum elastic potential criterion, has been used. This model combined with the Hertz equation yields more accurate values of the contact stress. As the load per unit of length at any point of the line of contact and any position of the meshing cycle has been described by a very simple analytic equation, a complete study of the location and value of the critical contact stress has been carried out. From this study, a recommendation for the calculation of the pitting load capacity of spur and helical gears is proposed.

A NEW BALL SET FOR TUBE SPINNING OF THIN-WALLED TUBULAR PARTS WITH LONGITUDINAL INNER RIBS

Tube spinning is one of the old incremental forming manufacturing processes. Recently, tube spinning using balls as forming tools, has been extensively utilized in producing tubular components with longitudinal or helical internal gear teeth, internal grooves or internal ribs. Thin-walled tubular parts with longitudinal inner ribs emerge in order to adapt to the development of aeronautic, aerospace and military industry. Recent development of tube spinning of macro and micro inner grooved tubes and inner geared drums face many challenges. The most important ones are; material built up formation in front of the forming balls, material folding at the tube inner surface, and the forming mandrel failure due to load fluctuations at the root of the forming tooth. These problems have been addressed separately in the literature without a unified approach to simultaneously overcome them. The current study proposes a new ball set design that is claimed to be able to overcome these problems simultaneously. A finite element simulation model for the conventional and the new proposed designs is built and verified. The conventional ball set contains four balls lie in the same plane. The proposed design contains 24 balls distributed in four planes, having 6 balls in each plane. The first plane is set to suppress the built up formation, the second and third plane are set for the main forming process, the fourth plane is set for suppressing the load fluctuation. Each two consecutive planes are shifted by 60 deg from each other to suppress the folding creation. By examining the achieved results, the new design has shown the potential to significantly reduce the built up formation in the front of the forming balls. Also, the reactions at the inner surface of the spun tube have shown significant improvements in both the radial load fluctuation which is responsible of the folding problems and the load in the tangential direction which is responsible of the tooth root failure.

Prevention of helical gear tooth damage in wind turbine generator: A case study

The transmission error between the driving and driven gears originating because of manufacturing error or misalignment in the gearbox assembly causes noise and vibrations during the functioning of the gearbox. This research article discusses a novel method to prevent tooth damage in the helical gear due to transmission error by providing tip relief on the gear tooth and introducing a combination of epi-cycloid and involute profiles called composite profile for the gear tooth. Analysis is carried out using finite-element analysis package for the existing involute as well as the modified composite helical gear pair to evaluate the performance. The study reveals that the modified design (tip relief with composite profile) is superior to the existing involute gear for windmill applications because the wind turbine generators are subjected to fluctuating wind force, sudden grid drops, failure of pitching, braking, etc.