Standard Spur Gears Research Articles

Exploring Tribological Behaviors of Profile-Shifted Spur Gears: An Experimental Investigation

The tribological behavior of an addendum modified altered tooth sum optimized spur gear set were experimentally compared with that of the standard spur gear under several loading conditions including the wear morphology study and wear debris analysis. The temperature, viscosity, elastohydrodynamic oil film thickness, specific film thickness, and combined surface roughness variation under increasing operating load were analyzed experimentally. Finally, the performance impact of addendum shifted altered tooth sum optimized gear was examined. Results show that the tribological improvement strongly depends on the addendum alteration and modified tooth sum condition. The modification of the addendum in gears with a negatively altered tooth sum facilitates the transition from single-tooth contact to two-tooth contact, broadening the lubrication range while preserving optimal film thickness and improving wear resistance. However, it is reverse to decrease the film thickness and increase wear for standard and profile-modified positively altered tooth sum gear. The gear tribological performance can be significantly improved by profile modification and negatively altered tooth sum approach with a lower rate of degradation of oil and damage on the tooth contacting surface.

Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears

Numerical methods have gained momentum among specific engineering problems that must be solved in such a manner that accuracy and speed are the two most important aspects to consider regarding the output. This paper presents a fast, semi-analytical method (SAM) and original mathematical algorithms to determine the pressure distribution and von Mises stress for spur gears’ meshing teeth. The SAM begins with the Hartnett approach, based on Boussinesq’s equation for the half-space theory of linear elasticity, which implicitly means an infinite width of the gear flank. To simulate more realistic quarter-space conditions, corrections based on virtual mirror pressure are introduced in the computational algorithm. Mathematical surfaces modeling is an important aspect for spur gears as an intermediate stage to determine the pressure distribution and von Mises stress. Shaft misalignment changes the contact problem from symmetric, in which the half- or quarter-space model can be used, to asymmetric. In the latter case, the model must determine the entire contact area. The obtained output is validated by comparisons between our original FEA results and results from the literature using SAMs and FEA.

A Novel Inductive Angular Displacement Sensor With Multi-Probe Symmetrical Structure

This articledevelops a novel probe-type inductive angular displacement sensor based on time-grating, which is suitable for large-diameter hollow rotary table position detection of the heavy-duty machine tools. It abandons the traditional sensor precise marking lines in spatial domain, and integrates the tested mechanical component with the sensor, which realizes the angular displacement measurement directly. The sensor is divided into three parts: 1) a permalloy probe, which is adopted the simple structure to reduce the assembly errors; 2) a 45-steel rotor, which is a standard spur gear in a heavy-duty machine tool rotary table transmission system; 3) three groups of copper coils, which include sinusoidal coils, cosine coils and inductive coils. The theoretical model of angular displacement measurement is derived by means of mathematical equation in detail. Then the feasibility of the sensor structure is verified by finite element simulation. After that, a sensor prototype is built and tested in the laboratory, showing that the sensor has an original error of ±0.018° (approximately ± <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$64^{\prime \prime }$ </tex-math></inline-formula> ) over a full 360° range. The error analysis found that the systematic error is the main component. As a result, the mechanical structure and angular displacement algorithm of the sensor are optimized, which can significantly reduce the original errors of the sensor. After optimization, the final accuracy of the sensor is within ±0.0012° (approximately ± <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.4^{\prime \prime }$ </tex-math></inline-formula> ) in the range of 0°–360°.

Rotor Profile Design and Motion Simulation Analysis of Hydrogen Circulating Pump

With the development of automotive fuel cells towards high power and high efficiency, higher requirements are put forward for the speed and boost ratio of hydrogen circulation pump, while high speed and boost ratio increase the pulsation characteristics and accelerate the aging of hydrogen fuel cells. Cam type hydrogen cycle pump has the advantages of compact structure, high efficiency under low boost ratio, and good adaptability to low temperature, so it has become an important research direction. The efficient and reasonable rotor profile design can improve the volumetric efficiency of the cam rotor pump. It can reduce the pressure pulsation and flow pulsation in the pump. The equation of multi-stage circular arc rotor profile is established according to the meshing principle of the rotor. Motion Simulation module in UG NX is employed to conduct dynamic interference detection of rotor mechanism and simulation analysis of rotor mechanism meshing motion on the rotating parts of the hydrogen circulating pump. So the angular velocity curve and meshing force change curve of the driven gear is obtained. In order to verify the rationality of rotor profile design, the meshing force is compared with the standard spur gear.

Effect of Profile Shift Factor on Contact Stress and Natural Frequencies of Spur Gear

High levels of contact stress between mating teeth can damage the contact surface and hall structure of spur gears, driving research that has aimed to minimize this stress. This study analyzed the effects of the profile shift factor (x) on the contact stress between a pair of spur gear teeth. Five profile shift factors were considered, from x = 0 (standard spur gear) to x=0.2. For each case, theoretical results were calculated based on the Hertzian contact theory and ISO-equations of contact stress and subsequently compared with results generated in the ANSYS Workbench software using the finite element method. Modal analysis was performed to compare the mode shape frequencies of all profile shift factor values. The harmonic responses indicate that the stresses generated by our geometry are less than the maximum material stress.

Modified geometry of spur gear drives for compensation of shaft deflections

One of the main problems when standard spur gears are in mesh is the appearance of edge contact on the gear tooth surfaces caused by misalignments. Those misalignments are caused partially by deflections of gear supporting shafts. As a result of an edge contact, a non-favorable condition of the bearing contact occurs, yielding high level of contact stresses. An intensive research and many practical solutions have been directed to modify the gear tooth surfaces in order to avoid edge contact. An innovative procedure is proposed here for: (1) determination of errors of alignment caused by shaft deflections, (2) compensation of predicted shaft deflections during generation of spur gears, and (3), obtaining a favorable function of transmission errors for the design load. A finite element model of a spur gear drive that comprises pinion and gear supporting shafts is used for the determination of errors of alignment along a cycle of meshing. Compensation of misalignments caused by shaft deflections in gear generation is then accomplished by modification of pinion tooth surfaces whereas the gear tooth surfaces are kept unmodified. Additional modifications of pinion tooth surfaces may be required for obtaining a favorable function of transmission errors. The effect of several misalignment compensations in the reduction of contact stresses has been investigated. Postprocessing of load intensity functions and loaded transmission errors is included. The developed approach is illustrated with numerical examples.

The evaluation of contact fatigue strength for 20MnCr5 carburized gear

A FZG test rig for determining the contact fatigue characteristics of gear teeth was used in this paper. Under the range of operating conditions, experiments were performed by using standard spur gear test specimens which were made from 20MnCr5 gear alloy steel. Test rig, spur gear test specimens, the properties of the gear material were also introduced as well as the method to determine the stress levels. After the test, a small spalling pitting phenomenon was observed in the vicinity of the test pinion pitch line which is close to the gear tooth root portion. The tooth is subjected to the highest load due to the single tooth pair contact. The test data was analyzed and processed by statistical methods, and the equation parameters of gear contact fatigue and the contact fatigue limit were obtained. The analyzed results showed that the three-parameter Weibull distribution was best to fit the given stress for the contact fatigue life of 20MnCr5 carburized gear with better precision and adaptability. Finally, the P-S-N (Probability-Stress-Life) curves for the contact fatigue strength had been obtained by the reliability theory. It would provide a reliable basis for the reliability design for 20MnCr5 carburized gear fatigue life.

A study on the evaluation of bending fatigue strength for 20CrMoH gear

A test apparatus for determining the bending fatigue characteristics of gear teeth was used in this paper. Experiments were performed in the test apparatus using a standard spur gear test specimens made from 20CrMoH gear steel. Test apparatus, specimen fixture, spur gear test specimens, the properties of gear material were also introduced as well as the method to determine the stress levels. The test data was analyzed and processed by statistical methods, and the equation parameters of gear bending fatigue and the bending fatigue limit were obtained. The analysis results showed that the three-parameter Weibull distribution was to fit the given stress for the bending fatigue life of 20CrMoH carburized gear with better precision and adaptability. And the P-S-N (Probability-Stress-Life) curves for the bending fatigue strength had been obtained by the reliability theory. It would provide a reliable basis for the reliability design for 20CrMoH carburized gear fatigue life.

Research on Parametric Design Platform of Gear Based on Pro/E

A development system on gear parametric design and check based on Pro/E4.0 and Visual C++ was built in the paper. The system included three modules: the standard spur gear, helical gear and bevel gear. According to the human-machine interface, the 3D parameterization model and 2D engineering drawing of the gear were achieved. And according to the actual situation of the load, the gear was automatically calculated, checked and output results. The system was adjusted successfully

Development on Inspection System for Gear’s Dimension Based on Machine Vision

A noncontact inspection system for gear based on machine vision is developed in this work, according to the mathematical model of lens distortion; the calibration of the camera was realized by the MATLAB calibration toolbox, obtained the distortion coefficients, by which the pixel is proofread. After then the key parameters of gear could be automatically acquired with proposed algorithm. In this work, the algorithm is applied to a practical case of a standard spur gear; the experimental results reported here confirm the effectiveness of the approach.

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.

Optimal Tooth Numbers for Compact Standard Spur Gear Sets

The design of a standard gear mesh is treated with the objective of minimizing the gear size for a given ratio, pinion torque, and allowable tooth strength. Scoring, pitting fatigue, bending fatigue, and the kinematic limits of contact ratio and interference are considered. A design space is defined in terms of the number of teeth on the pinion and the diametral pitch. This space is then combined with the objective function of minimum center distance to obtain an optimal design region. This region defines the number of pinion teeth for the most compact design. The number is a function of the gear ratio only. A design example illustrating this procedure is also given.

Closure to “Discussions of ‘Optimal Tooth Numbers for Compact Standard Spur Gear Sets’” (1982, ASME J. Mech. Des., 104, pp. 757–758)

Closure to “Discussions of ‘Optimal Tooth Numbers for Compact Standard Spur Gear Sets’” (1982, ASME J. Mech. Des., 104, pp. 757–758)

Distortions and Residual Stresses of Gears Caused by Hardening : 2nd Report, Through-Hardening of Gear Made of S45C Carbon Steel

In this paper, the authors investigated experimentally and theoretically the distortions and the residual stresses of gear tooth of standard spur gears made of S35C carbon steel generated by induction-hardening. The main results obtained from this investigation are summarized as follows. (1) Analytical method introduced by the authors is available for the estimation of distortions in the case of induction-hardening of gears. Comparing analytical distortions, such as outside diameter, whole depth and tooth profile, with experimental ones, there are no remarkable difference except pressure angle. (2) Residual stresses from theoretical analysis agree in the tendency with the experimental ones. Consequently, possibility of theoretical analysis of residual stresses of gears in the induction-hardening process could be expected.

Equations of Shifted Helical Gears by Cutters with Standard Normal Tooth Profile

According to the present methods, we have two difficulties in calculation of shifted helical gears by cutters with standard normal tooth profile, because of the existence of helix angle β : one is the displacement of cutting pitch circle, and the other the variation of cutting face pressure angle of gears. So, I will suggest to adopt the imaginary pitch circle which is the same as that of standard spur gears and unrelated to the helix angle, and to utilize the '''table of β-Vv-V function which is newly derived. Then, the calculation of helical gears would be so simple as that of spur gears.