Spiral Bevel Gear Pair Research Articles

Spiral Bevel Gears CNC Milled by Disc Cutter with Concave End

In order to solve the small cutting strip width and poor surface quality problems when spiral bevel gears are CNC machined by ball-end mills£¬a machining method of face milling spiral bevel gears by using a disc cutter with a concave end is presented. Based on the researches of spiral bevel gears geometry structure, through a bigger diameter disc cutter with a concave end selected, the setting order of cutter orientation angles changed, and the functions of cutter tilt and yaw angle separated, tooth surfaces machined with big cutting strip width and no bottom land gouge can be expected. Finally, taking a spiral bevel gear pair as an example, through machining and measurement experiments, the method feasibility and correctness are verified

Mathematical model and manufacture programming of loxodromic-type normal circular-arc spiral bevel gear

In this paper, loxodromic-type normal circulararc spiral bevel gear is proposed as a novel application of the circular-arc tooth profile at the gear transmission with intersecting axes. Based on the principle of molding-surface conjugation, the study develops a mathematical model for the tooth alignment curve and the computational flow at the design stage to enable the generation of the tooth surface. Machining of the tooth surface is then carried out to determine the interference-free tool path of the numerical control (NC). Moreover, a pair of loxodromic-type normal circular-arc spiral bevel gears is manufactured on computer numerical control (CNC) machine tools. The proposed theory and method are experimentally investigated, and the obtained results primarily reflect the superior performance of the proposed novel gear.

Pinion tooth surface generation strategy of spiral bevel gears

Aviation spiral bevel gears are often generated by spiral generated modified (SGM) roll method. In this style, pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances. For the optimal contact pattern and transmission error function, local synthesis is applied to obtain the machine-tool settings of pinion. For digitized machine, four tooth surface generation styles of pinion are proposed. For every style, tooth contact analysis (TCA) is applied to obtain contact pattern and transmission error function. For the difference between TCA transmission error function and design objective curve, the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established. Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function. The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers. The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair. This study is an expansion to generation strategy of spiral bevel gears, and offers new alternatives to computer numerical control (CNC) manufacture of spiral bevel gears.

NC Machining Simulation of Spiral Bevel Gear Based on VERICUT

Based on the traditional cradle-type spiral bevel gear machining theory, the mathematical model of tilt machining method for the pinion member of spiral bevel gear pair is created. Then, by applying coordinate transformation method from crade-type machine to CNC one, a five-axis virtual CNC machine model is established by VERICUT software. at the same time, the pinion cutting simulation is carried out under VERICUT according the properties of the general five-axis CNC system and the relevant configuration parameters. By using this method, the accuracy of the bevel gear cutting system based on a general five-axis CNC can be well verified.

Quantitative Evaluation of Aero Spiral Bevel Gear Meshing Quality

In order to precisely control the meshing performance of spiral bevel gear pair, this paper represents a quantitative evaluation method using transmission error curve and tooth face contact trace. The design, using local synthesis method, obtains the manufacturing parameters of gear pair and forms the tooth face of spiral bevel gear. This paper accomplishes the quantitative evaluation by the following methods: using tooth contact analysis (TCA) to obtain actual transmission error curve and tooth face contact trace; quantitatively evaluating the transmission error curve by comparing the web values of actual and preset theoretical transmission error curves; quantitatively evaluating the tooth face contact trace by comparing the requirements (such as in shape, size and position) defined for spiral bevel gear tooth face contact trace and the corresponding parameters of an externally-connected rectangle, which surrounds the tooth face contact trace and is used to describe tooth face contact trace. This paper conducts a meshing performance analysis and quantitative evaluation of an aero spiral bevel gear pair. The result shows that, the actual and preset theoretical transmission error curves are basically in coincidence and the tooth face contact trace meets the requirements. This quantitative evaluation method lays a foundation for analyzing the relationship between transmission error curve and tooth face contact trace and for analyzing the installation error sensitivity.

Quantitative Analysis of the Influence of Installation Errors on the Contact Pattern of Spiral Bevel Gears

A method—characteristic parameters analysis (CPA) is put forward, which is used for quantitative analysis of contact pattern of spiral bevel gears with installation errors. For forming the tooth surface of spiral bevel gears, local synthesis is used. To imitate rolling test machine, the pinion drive torque is calculated under the indentation depth 0.00635mm. Driven by this torque, the size, shape, location and variation of contact pattern are obtained by loaded tooth contact analysis (LTCA). A pair of aviation spiral bevel gears was taken to quantitatively analyze the various contact patterns under different installation errors. The results indicate that the contact pattern is more sensitive to pinion axis installation error.

Spiral Bevel Gear Dynamic Contact and Tooth Impact Analysis

A significant portion of the research on spiral bevel gear focused on contact stress and assembly flexibility (V and H check) values, while only a few studies investigated the relationship between transmission errors and rotational speed. This paper addresses and discusses an approach for 3D dynamic contact and impact analysis of spiral bevel gear drives. Dynamic models considering friction, gear clearance, and time-varying stiffness were established. Finite element software was utilized to analyze the dynamic responses of gear transmission, surface contact stress, and root bending stress of a spiral bevel gear pair. The dynamic model simulated the vibration behavior of an actual gear set under dynamic loading. The dynamic responses of the spiral bevel gear drives were obtained under differential rotational speeds of the driver and the driven resistance. The stiffness and elastic deformation of gear teeth were calculated using the finite element method with actual geometry and gear positions. After the impact analysis, the numerical simulation results of transient and steady-state transmission errors are obtained simultaneously. Using the fast Fourier transform method, frequency spectrums of the transient and steady states of the calculated transmission errors are obtained to enable the gearbox designer to avoid the resonance zone.

A Study on Spiral Bevel Gear Fault Detection Using Artificial Neural Networks and Wavelet Transform

Based on normal and defective gears of spiral bevel gear pair test, a study is represented to develop the performance of gear fault detection with artificial neural networks and wavelet transform. In order to research the relevant studies of gear failures, a gear fault test rig is designed and constructed, with which vibration test are processed for collecting the signals of a gearbox from this rig. The noise is removed from the original time-domain vibration signals by application of wavelet analysis threshold technique. The extracted energy features from those preprocessed signals are implemented by the wavelet transform, which are used as inputs to the artificial neural networks for two-pattern (normal or fault) recognition. The results show that the represented recognition accuracy of the ANN and WT method for gear fault diagnosis is 100% that is much higher compared with the results of application of ANN separately.

Study on Modeling and Simulating of Spiral Bevel Gears

Based on the theory of space meshing, the paper deduces the equation of tooth traces on the surface of the pitch cone of Gleason spiral bevel gears. The equation of tooth traces on the surface of the cone with given cone angles would be gained consequently. The 3-D models of a pair of Gleason spiral bevel gears used in the transmission system of a type of vehicle was built by the way of Pro/E parameter design software and spherical involutes function was adopted in this progress. The kinematical flank interference inspection of the gear pair was made and the satisfying gear pair was obtained through the adjustment of tangent modification coefficient. The work in this paper provides conditions for much more FEM analysis of Gleason spiral bevel gears.

Mathematical Modeling and Simulation of the External and Internal Double Circular-Arc Spiral Bevel Gears for the Nutation Drive

The purpose of this paper is to propose a pair of external and internal spiral bevel gears with double circular-arc in the nutation drive. Based on the movement of nutation, this paper develops equations of the tooth profiles for the gear set, leading to the mathematical modeling of the spiral bevel gear with a constant helical angle gear alignment curve, enabling the tooth surface to be generated, and permitting the theoretical contacting lines to be produced in light of the meshing function. Simulation and verification are carried out to prove the mathematical equations. Numerical control (NC) simulation of machining the external and internal double circular-arc spiral bevel gears is developed, and the spiral gears were manufactured on a NC milling machine. The prototype of the nutation drive is illustrated in the case study at the end of this paper.

Influence of Asymmetric Mesh Stiffness on Dynamics of Spiral Bevel Gear Transmission System

An 8‐DOF (degrees‐of‐freedom) nonlinear dynamic model of a spiral bevel gear pair which involves time‐varying mesh stiffness, transmission error, backlash, and asymmetric mesh stiffness is established. The effect of the asymmetric mesh stiffness on vibration of spiral bevel gear transmission system is studied deliberately with numerical method. The results show that the mesh stiffness of drive side has more effect on dynamic response than those of the coast side. Only double‐sided impact region is affected considerably by mesh stiffness of coast side while single‐sided impact and no‐impact regions are unchanged. In addition, the increase in the mesh stiffness of drive side tends to worsen the dynamic response of the transmission system especially for light‐load case.

Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to 5 are applied to conduct the variation in the cradle radial setting and in the cutting ratio in the process for pinion teeth generation. Two cases were investigated: In the first case, the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface; in the second case, the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation in the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation in the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase in transmission errors can be considerably reduced.

Head-cutter for optimal tooth modifications in spiral bevel gears

Abstract A method for the determination of optimal tooth modifications in spiral bevel gears based on improved load distribution and reduced maximum tooth contact pressure and transmission errors is presented. The modifications are introduced into the pinion tooth-surface by using a head-cutter with bicircular profile and with optimal diameter. In the optimization of tool parameters the influence of relative position errors of the mating gears is included. By using the computer program developed for load distribution calculation, the influence of head-cutter parameters and relative position errors of the mating gears on tooth contact and transmission errors is investigated. Based on the results obtained, the radii and the position of the circular tool profile arcs and the cutter diameter for pinion teeth finishing were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 45% and the maximum angular position error of the driven gear by 60%, in regard to the spiral bevel gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

Dynamic Characteristics of the Coupled System of the High Pressure Rotor and the Radial Driveshaft of a Turbofan Engine

In a turbofan engine, the high pressure rotor and the radial driveshaft, which transmit the power from the internal gear-box to the external gear-box, are geared by a spiral bevel gear pair. In this paper, a reasonably simplified dynamic model of the coupled rotors system is established, and then, the coupled stiffness matrix and coupled damping matrix of the spiral bevel gear pair are deduced. A shaft element method is proposed to investigate the lateral-torsional coupled vibration equations of the gear-rotor system. Furthermore, the mode shapes and unbalance responses of this two rotors coupled system are simulated. The results indicate that the system derives many new modes and the exciting forces on a rotor of the system would be passed to the other rotor for the gears meshing. When the rotor dynamics of a turbofan engine is being analyzed, the high pressure rotor and the radial drive shaft must be viewed as a whole. The dynamic balance precision of the rotors should be qualified properly, in order to improve the dynamic quality of the turbofan engine.

Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion machine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

On the Invariance of Gear Tooth Curvature

A method is presented for the determination of the principal curvatures along with their principal directions of two gear teeth in direct contact. The procedure used to determine these extreme curvatures and directions is based on the nominal position of contact. Moreover, these extreme curvatures and directions are invariant with tooth type (viz. involute and cycloidal) and manufacturing process. Such curvatures and directions depend on the instantaneous pressure angle, spiral or helix angle, and position of contact. This generalized method is applicable to cylindrical gears (spur and helical), conical gears (straight and spiral), as well as hyperboloidal gears (hypoid and worm). Three examples are included to illustrate the determination of principal curvatures and directions. The first example is a helical gear pair, the second is a spiral bevel gear pair, and the third example is a hypoid gear pair.

Estimation of Variation of Tooth Bearing in a Gear Pair by Image Processing Method and It's Influence on Dynamic Behavior of Gear. Variation in Spiral Bevel Gear Pair.

Estimation of Variation of Tooth Bearing in a Gear Pair by Image Processing Method and It's Influence on Dynamic Behavior of Gear. Variation in Spiral Bevel Gear Pair.

Method for Inspection of Spiral Bevel Gears in Klingelnberg Cyclo-Palloid System.

The pair of spiral bevel gears fabricated by Klingelnberg's cyclo-palloid method can be expected to have a good contact pattern because the gear tooth surfaces are fundamentally conjugate. In practice, however, the first gear pair having a good contact pattern is difficult to obtain because of the machine setting errors such as tool setting errors and workpiece setting errors in gear cutting. In this paper, an inspection method for detecting the machine setting errors in spiral bevel gear cutting in a Klingelnberg cyclo-palloid system is proposed. In this method, the coordinates of many points on the gear tooth surface are measured using a coordinate measuring machine and a geometrical gear tooth surface expressed as the functions of the machine settings is estimated by the method of least squares so that the surface can fit the measured data. The deviations of the estimated machine settings from the design values are considered to be the machine setting errors. The machine setting errors in gear cutting were detected using this method and corrective cutting which compensated for the errors was carried out. Consequently, more accurate gear could be obtained.

Helicopter transmission research

CURRENT HELICOPTER MAIN TRANSMISSION SYSTEMS must reduce the gas‐turbine engine speed by a typical ratio of 80:1 to drive the main rotor. Existing technology dictates that this ratio is achieved in 3 or 4 stages of gearing, where each stage is either an epicyclic gear assembly, a spiral bevel gear pair or a helical gear pair. Gear tooth reaction forces can be as high as 20,000lbf (90kN) both axially and radially, so large gears and as many as 3 heavy duty rolling elements bearings per gear shaft are required. Transmission systems thus typically account for 10 per cent of all‐up‐weight, the main gearbox taking up 75 per cent of this and the bearings accounting for 20 per cent of the gearbox weight. Scheduled overhaul periods are seldom more than 1,000 flying hr due partly to the likelihood of rolling element bearing fatigue failure and many require overhaul before this time is reached. Thus the research effort on transmission systems, and specifically on gearboxes, is directed in general terms towards achieving:—