Bevel Pinion Research Articles

Dynamic simulation of the differential gear in road vehicles

The differential gear is a mechanism that is part of the kinematic chain of the vehicle’s transmission. The differential gear has the role of dividing the self-propulsion power flow received from the main drive into two branches, each transmitted to a drive wheel, giving them the possibility to rotate with different angular velocities, depending on the driving conditions. The present work presents the possibilities of computer-aided design and 3D modeling of the main drive and differential gear, respectively the bevel pinion, the crown wheel, the planet pinions and the satellites, using Autodesk Inventor Professional. The 3D model of the main drive - differential gear assembly, considered as a mechanism, was subjected to a dynamic study, using the Dynamic Simulation module. This involves the modeling of the kinematic couplings, the definition of the drive movement parameters and the external loads, respectively the graphical visualization of the kinematic and kinetostatic results for the various components of the mechanism, in real operating conditions, during a kinematic cycle. At the same time, based on the obtained results, the analysis by the finite element method of the most critical component elements, under straight-line driving and turning conditions, is presented.

Dynamic Simulation of Cracked Spiral Bevel Gear Pair Considering Assembly Errors

The tooth root crack fault is a common fault type of the spiral bevel gear pair (SBGP). Affected by the strong bearing capacity, the early crack fault of the SBGP cannot be found in time. In this study, a finite element (FE) model of the SBGP is established and assembled through the tooth contact analysis. The maximum tooth root stress is analyzed considering the variation of assembly errors. Meanwhile, this study simulates the tooth root crack fault of the bevel pinion with different crack degrees. The initial position of the crack is located where the maximum tooth root stress appears. The time-varying mesh stiffness (TVMS) of the SBGP considering different degrees of the pinion tooth root crack fault is obtained. The TVMS and the non-load transmission error are brought into a hybrid FE dynamic model, and steady responses are solved. Based on this, the sensitivities of various statistical indicators for identifying the tooth root crack fault of SBGP under the influence of assembly errors are verified. This paper can provide the necessary theoretical basis for the analysis and diagnosis of tooth root crack faults in the SBGP transmission system.

Practical Example of Modification of a Gearbox Lubrication System

This paper presents the optimization of the lubrication method of a helical bevel gearbox, which is part of a pickling line. The first gear stage of this gearbox showed frequent failures. The bevel gearing and bearings were damaged. Damage analysis was performed, based on which a change in bevel gearing and bearing lubrication was proposed. In this case, the original transmission was lubricated by dip lubrication. The bevel gear wheel was insufficiently submerged below the lubricating oil level. Due to insufficient lubrication of the bevel gearing, both gear wheels, the bevel pinion, and the bevel wheel were damaged. Central circulating lubrication has been proposed for the bevel gear pair and first gearbox shaft bearings. This paper deals with the design of circulating lubrication components. Changes and modifications to an existing lubrication system are proposed. The layout of the gearbox in question was not originally designed and adapted for the circulating lubrication required. To improve the original lubrication system, it was decided that it should be redesigned with central circulating lubrication, which meant implementing the necessary gearbox casing modifications. Our novel contribution is the proposition of an innovative transmission lubrication system aimed at increasing the service life parameters of the transmission. After the implementation of the proposed modifications to the lubrication method, a period of monitoring the operating characteristics of the gearbox followed. With the modification of the lubrication system of the bevel gear pair, the temperature on the gearing surface was lowered by 39%. The service life of the gearbox increased from the original 1.9 years to at least 5 years. On the basis of the long-term monitoring of changes caused by the adjustment of the lubrication method, we can state that the requirement was met, and the frequent failures of this gearbox were eliminated.

Computational approach to design face-milled spiral bevel gear drives with favorable conditions of meshing and contact

The micro-geometry of the tooth surfaces of spiral bevel and hypoid pinions has to be fine-adjusted to obtain enhanced meshing and contact characteristics during the meshing process with their corresponding mating gears. In this paper, a new methodology is proposed to design face-milled spiral bevel gear drives to, firstly, derive favorable orientation and dimensions of the contact pattern between the mating surfaces of the gears and, secondly, obtain a predesigned parabolic function of negative transmission errors with limited magnitude of maximum transmission errors. The proposed approach is based on the definition of the desired topography for the active surfaces of the pinion followed by a numerical derivation of their finishing machine-tool settings through a bound-constrained optimization algorithm. Increasing mechanical strength and reducing the levels of noise and vibration of face-milled spiral bevel gear drives constitute the main objectives of the proposed design process. A numerical example is provided to illustrate the applicability of the developed theory .

GEAR GEOMETRY AS FUNCTION OF PRODUCTION METHOD

In the frame of the activity of JSME RC-268 committee, new bevel gear i.e. Invo-Planar bevel gear is developed, the tooth flank of which wheel is plane or whose transverse tooth profile is straight line. The cutting/grinding time of this bevel wheel can be more than 10 times shorter than the working time for conventional bevel gear wheel, when it is cut with 5-axis machine, because it cuts or grind the tooth flank through one path of tool movement. The finished tooth flank is far smoother than the curved tooth flank manufactured by many paths of cutting blades of tool. The production rate of the mating pinion with 5-axis machine is same as that of conventional bevel pinion. Some experiences in the production, quality of the product gears and performance survey of this new bevel gear is introduced to promote the discussion.

Experimental Setup and Methodology to Carryout Fatigue Testing of Spiral Bevel Gears Used in Differential Gear Box Using NVH Approach

Currently the fatigue testing of bevel gears are being done by using non rotating type of fixtures that applies fatigue load on a single tooth, which does not resemble the actual loading condition in an automotive differential gear box. This paper discusses the experimental setup with the noise and vibration analysis approach to determine the signature of failures of spiral bevel gears. The proposed experimental setup seems promising for further research and development in the fatigue testing of spiral bevel gears. The Crown pinion and wheel assembly is used for the testing. The pinion is connected to the electric 3 phase AC motor of 75HP with a suitable coupling and the crown wheel is mounted on the half axle shaft, which in turn is connected to an electric dynamometer. The speed/torque of electric motor and the load applied by the dynamometer can be varied. The acoustic sensor is mounted near the differential gear box and the accelerometers are mounted on the Pinion bearing, Crown wheel bearing and the half axle bearing. A four channel data acquisition system is used to log data in time domain (raw data) by three accelerometers and an acoustic sensor. The variations of sound pressure(dB) v/s time, sound Pressure(FFT-(RMS)) amplitude v/s Frequency, Acceleration v/s Time, Octave analysis i.e., Band power v/s Frequency, Noise spectrum Power v/s Frequency, Histogram, Power density v/s Time can be obtained. These data are then used to plot vibration and SPP levels in frequency domain to develop the noise and vibration signature of that crown pinion for given cycles of operation. The tests on Bevel pinion and gear set were performed in the BEC, Bagalkot NVH lab facility. The gear set run successfully at double the rated torque for 30 million pinion cycles. And the signature of pinion failure was obtained. The results demonstrated the suitability of using the given bevel crown pinion and gears set for specified speed, high load application in differential gear box of an automobile.

DESIGN OF A SPHERICAL CAM-ROLLER MECHANISM FOR AN AUTOMOTIVE DIFFERENTIAL

Spherical cam-follower mechanisms are attractive alternatives to bevel gears, as they provide low backlash and low friction losses. The design of such a mechanism is reported here, to be incorporated in an automotive differential, whose bevel pinions and side gears are substituted by spherical cams and rollercarriers, respectively. Critical to the design of cam mechanisms is the generation of the cam-profile, free of undercutting. The profile, generated using computer algebra, is analyzed for singularities, including cusps and double points. The pressure angle, an important factor that governs the effective force transmission of cam mechanisms, is duly kept within acceptable limits. Conclusions are drawn on the suitability of cam mechanism developed for automotive applications.

Reconstruction of real tooth surfaces of spiral bevel pinions with modified offset

Reverse engineering has been successfully applied in many fields; however, it is not the case for spiral bevel gears. In order to reconstruct the real tooth surfaces of spiral bevel pinions based on the original tooth surface grids (OTSG) provided by coordinate measuring machine, meshing performances were achieved by tooth surface scanning method. Three meshing conditions necessary for local synthesis, i.e. the directional angle, the magnitude of major axis of contact ellipse and the second derivative of transmission errors at the mean contact point, were filtered from the meshing performances obtained by discrete tooth contact analysis. Computational tooth surface grids (CTSG), corresponding to OTSG node to node, were expressed by manufacturing parameters derived by local synthesis. Tooth surface grid difference was formed by making the centre node of CTSG through rotation operation coincided with that of OTSG. Optimization objective was built up by summing up the deviations of all nodes on either OTSG or CTSG. The three meshing conditions, the mean contact point position and the higher order coefficients of blank offset correction were taken as the design variables. The internal function fminsearch of MATLAB was chosen to minimize the tooth surface grid difference. After the manufacturing parameters were achieved, the pinion tooth surfaces were reconstructed based on the reversed CTSG. A zerol spiral bevel pinion in an aviation engine accessory gear box was employed to demonstrate the proposed methodology. The results show that OTSG is unable to give perfect meshing performance. The convergent results of reversing show that many of the field of distance between the reversed CTSG and OTSG is less than 1 μm. This demonstrates the feasibility of the proposed reversing techniques.

Reverse engineering of machine-tool settings with modified roll for spiral bevel pinions

Although a great deal of research has been dedicated to the synthesis of spiral bevel gears, little related to reverse engineering can be found. An approach is proposed to reverse the machine-tool settings of the pinion of a spiral bevel gear drive on the basis of the blank and tooth surface data obtained by a coordinate measuring machine(CMM). Real tooth contact analysis(RTCA) is performed to preliminary ascertain the contact pattern, the motion curve, as well as the position of the mean contact point. And then the tangent to the contact path and the motion curve are interpolated in the sense of the least square method to extract the initial values of the bias angle and the higher order coefficients(HOC) in modified roll motion. A trial tooth surface is generated by machine-tool settings derived from the local synthesis relating to the initial meshing performances and modified roll motion. An optimization objective is formed which equals the tooth surface deviation between the real tooth surface and the trial tooth surface. The design variables are the parameters describing the meshing performances at the mean contact point in addition to the HOC. When the objective is optimized within an arbitrarily given convergence tolerance, the machine-tool settings together with the HOC are obtained. The proposed approach is verified by a spiral bevel pinion used in the accessory gear box of an aviation engine. The trial tooth surfaces approach to the real tooth surface on the whole in the example. The results show that the convergent tooth surface deviation for the concave side on the average is less than 0.5 μm, and is less than 1.3 μm for the convex side. The biggest tooth surface deviation is 6.7 μm which is located at the corner of the grid on the convex side. Those nodes with relative bigger tooth surface deviations are all located at the boundary of the grid. An approach is proposed to figure out the machine-tool settings of a spiral bevel pinion by way of reverse engineering without having known the theoretical tooth surfaces and the corresponding machine-tool settings.

Static and dynamic models for spiral bevel gears

This paper synthesizes a whole of work carried out on the spiral bevel gears from quasi-static and dynamic models viewpoint. A sophisticated quasi-static model makes it possible to calculate the tooth loads, the pressures, the instant mesh stiffness, and the deflections on the flanks of spiral bevel gears. Based on these results, two three-dimensional lumped parameter dynamic models are presented. The mechanical system under consideration comprises: a spiral bevel pinion and gear connected by a time-varying non-linear mesh stiffness function, and mounted on two shafts simulated by Timoshenko’s beams supported by bearings. Two variants are considered which rely on different contact stiffness simulations: (a) using an averaged mesh stiffness function acting at the centroid of the loaded areas on tooth flanks and (b) a more local approach based on a discrete distribution of the local mesh stiffness, elements over the contact areas. A number of results are presented and commented which illustrate the interest of these dynamic models.

Numerical Model of Bevel Gears Cutting by Duplex Helical Method

In the paper it was presented a mathematical model of tooth generating of spiral bevel pinion and gear. Geometry as well as kinematic functions of the 116 machine tool were defined and mathematical model of the technological gear was built, which allows for the simulation of tooth generating.

Finger Milling-Cutter NC Generating Spiral Bevel Gear Tooth Surfaces & its Machining Simulation

Based on the in-depth study the principle of NC generating gear tooth surfaces by application of the disc milling-cutter, finger milling-cutter NC generating spiral bevel gear tooth surfaces is presented in this paper. Through using a 5 shaft 4 linkage machining center, the finger milling-cutter is mounted on the imagination disc milling-cutter, in fact, 2 NC axes are used simultaneously to control the finger milling-cutter motion, imitating a blade motion of disc milling-cutter, and the motion of the blank is not change, to generate the spiral bevel gear tooth surfaces. A spiral bevel pinion is simulation machined by using machining simulation system VERICUT and the feasibility of the machining method is verified.

Generation and curvature analysis of conjugate surfaces via a new approach

In the first part, the alternative formulation of the theory of gearing presented in [F. Di Puccio, M. Gabiccini, M. Guiggiani, Alternative formulation of the theory of gearing, Mechanism and Machine Theory 40 (5) (2005) 613–637] is generalized to cope with the case of modified roll and translating axes of the mating surfaces, that is with a setting typical of some computer numerically controlled (CNC) machine. The peculiarity of the proposed approach is that it always deals with vectors as such, thus avoiding the need of a chain of reference systems, necessary when components are used as in the traditional method. It results in a more compact and clearer formulation. In the second part the proposed approach is applied to obtain the normal curvatures and geodesic torsions of two conjugate surfaces in a way that fully exploits the rigid-body relative motions involved in gear generation. In order to prove the ease of use and effectiveness of the proposed approach, the curvature analysis of a spiral bevel pinion generated on a CNC face-milling machine is performed.

Premature failure of a spiral bevel pinion in a turbine condenser gear reducer

Within several months of service, a spiral bevel pinion inside a gear reducer failed resulting from serious pitting and associated tooth breakage. The failure was investigated using metallographic, scanning electronic microscopic techniques, and microhardness testing. The study indicates that the pinion suffered surface contact fatigue initially due to the repeated contact stresses, and later normal fatigue under the repeated bending stresses. Misalignment (or spiral angle error) of the pinion with the mating gear could cause the premature failure of the spiral bevel pinion, not due to materials deficiencies and/or poor mechanical properties. The alignment of the pinion should be checked carefully after assembly. This could be done by applying “engineering blue” to the gear teeth and manually rotating the gears to check the contact pattern.

Three-dimensional, parallel, finite element simulation of fatigue crack growth in a spiral bevel pinion gear

This paper summarizes new results for predicting crack shape and fatigue life for a spiral bevel pinion gear using computational fracture mechanics. The predictions are based on linear elastic fracture mechanics theories combined with the finite element method, and incorporating plasticity-induced fatigue crack closure and moving loads. We show that we can simulate arbitrarily shaped fatigue crack growth in a spiral bevel gear more efficiently and with much higher resolution than with a previous boundary-element-based approach [Spievak LE, Wawrzynek PA, Ingraffea AR, Lewicki DG. Simulating fatigue crack growth in spiral bevel gears. Engng Fract Mech 2001;68(1):53–76] using the finite element method along with a better representation of moving loads. Another very significant improvement is the decrease in solution time of the problem by employing a parallel PC-cluster, an approach that is becoming more common in both research and practice. This reduces the computation time for a complete simulation from days to a few hours. Finally, the effect of change in the flexibility of the cracking tooth on the location and magnitude of the contact loads and also on stress intensity factors and fatigue life is investigated.

Modelling, Implementation, and Manufacturing of Spiral Bevel Gears with Crown

The operational performance of gears in terms of smoothness, quietness, wear and life span is largely affected by how gear and pinion teeth make contact. To enhance the operational performance, a crown is often applied to a standard (nominal) gear tooth surface. Regardless of the presence of a crown, all the gears are machined by special types of machine tools, such as gear hobbers and shapers. This paper develops a tooth surface for a spiral bevel gear with a crown so that it can be machined by numerically controlled machine tools. Specifically, we derived: 1. A bi-parametric tooth surface model for a standard spiral bevel gear. 2. A crown model along the spiral curve direction. 3. A crown model along the involute curve direction. The developed algorithm was tested and implemented in a prototype software system called GearCAM. With the GearCAM system, a set of spiral bevel gear and pinion was machined using a 4-axis CNC milling machine to check the validity and effectiveness of the crowning method. Through various verifications, it is shown that the models developed for the standard and crown gears can be used as a means for design and verification of spiral bevel gears.

Simulating fatigue crack growth in spiral bevel gears

The boundary element method and linear elastic fracture mechanics theories are used to predict three dimensional fatigue crack trajectories in a spiral bevel pinion under a moving load. It is found that the moving load produces a non-proportional load history in a gear’s tooth root. An approach that accounts for fatigue crack closure effects is developed to propagate the crack front under the non-proportional load. The predictions are compared to experimental results. The sensitivity of the predictions to variations in loading conditions and crack growth rate model parameters is explored. Critical areas that must be understood in greater detail prior to predicting more accurate crack trajectories and crack growth rates in three dimensions are identified.

Improving the Stiffness of Overhung Bevel Pinion Mountings

SUMMARY Conventional two-bearing mounting arrangements for overhung bevel pinions do not provide the highest available stiffness at the pinion head. In smaller sizes, the shaft contribution to flexibility dominates; in larger sizes, the contribution of the bearings dominates. A three-bearing arrangement provides a substantial improvement. If bearing types are selected with a view to maximizing the stiffness of the front bearing, a non-traditional arrangement is possible which reduces deflections at the pinion head by up to 70% compared with a corresponding traditional two-bearing arrangement. Advantages accrue throughout the design.

Straddle Design of Spiral Bevel and Hypoid Pinions and Gears

The design of spiral bevel and hypoid gears that have a shaft extended from both sides of the cone apex (straddle design) is considered. A main difficulty of such a design is determining the length and diameter of the shaft that might be undercut by the head cutter during gear tooth generation. A method that determines the free space available for the gear shaft is proposed. The approach avoids collision between the shaft being designed and the head cutter during tooth generation. The approach is illustrated with a numerical example.

Load Support System Analysis-High Speed Input Pinion Configuration

Structural assemblies which transmit power, helicopter gearboxes for example, require accurate evaluation of load and displacement distributions to ensure system design optimization. Particular performance parameters which depend on detailed understanding of the distributions are operating life and rigidity. The coupling complexity of system components; gears, shafts, bearings and the housing itself, prevents meaningful evaluation of performance from the study of isolated components. The entire load support system has to be examined in its interacting entirety. In this paper a theoretical study has been made to determine the performance of a load support system, consisting of a shaft and two taper roller bearings for the high-speed input pinion of an advanced helicopter transmission. SHABERTH, a computer program designed to perform thermo-mechanical analyses of arbitrarily configured rolling element bearing-shaft systems, was employed to analyze, both, a straddle arrangement where the spiral bevel pinion gear is located axially between the two bearings, and a cantilevered arrangement where the pinion is outboard of the bearings. The effects of preload, shaft wall thickness, bearing spacing and misalignment of bearing races were examined. Their influence on load distributions and bearing rating lives including simulation of bearing and shaft elastic deformations were evaluated for both support geometries. Additional effort was expended to detail the performance of the pinion designs over a range of shaft rotational speeds. Lubrication and friction effects were included. Particular attention was directed to local as well as global heat generation rates (HGR) to provide design information for proper lubrication of the bearings. The results provide guidance for improved design of transmissions and the load vector control within them. In particular, the relative merits of the straddle versus the cantilever design have been exposed so that their individual characteristics may be exploited to increase system survivability.