Double Helical Gears Research Articles

Investigation of a design modification for double helical gears reducing vibration and noise

To reduce vibration and noise and increase transmission efficiency, a three segment method for modifying the pinion profile was proposed. Cutter surface equations were deduced by changing the shape of the cutter-edge, substituting three segment parabolas for the line. The influence of longitudinal tooth modifications on tooth surface load distributions was discussed. Transmission error minimization and uniformity of tooth surface load distribution were chosen as optimization goals and the modified parameters were obtained by applying the complex method. Finally, an experiment comparing the loaded transmission error, vibration, and noise both before and after modifications was carried out. The results indicate that the modified design is reliable.

Computerized design and simulation of meshing of modified double circular-arc helical gears by tooth end relief with helix

The contents of the paper cover: (i) computerized design, (ii) method for modification, (iii) simulation of meshing, and (iv) finite element analysis of the unmodified and modified double circular-arc gears. The approach proposed of tooth end relief with helix is based on the curves of circumferential displacement differences between before and after tooth surfaces entering in mesh and exiting out mesh. And the solutions under the conditions of different modification parameters are investigated. The results demonstrate that the method enables to decline transmission errors, decrease the maximum contact stress, lessen the tooth end stress, and cut down the circumferential displacement difference, effectively. Therefore, the purposes for modification of reducing noise and vibration and avoiding edge contact are achieved. In comparison with conventional double circular-arc gears, the developed theory is illustrated with numerical examples that confirm the advantages of the gear drives of the modified geometry.

The Analysis and Modeling for Nutation Drives with Double Circular-Arc Helical Bevel Gears

Based on the nutation movement of a rotating coin on a table, the formulae for calculating the transmission ratio between two nutation gears is developed. The tooth profile with a double circular arc for helical bevel gears in nutation drives is proposed and then the meshing equation during the nutation process and the universal equation of the crown gear tooth surface with helical double circular arc profiles are obtained based on the gear meshing theory. Further, the modeling for nutation drives with the proposed profile is carried out in a virtual working process.

ホブ切り円弧歯すじ歯車に関する研究 : 第3報,歯当たり解析(O.S.03-1 歯車の加工・製造(1))

The curvilinear-tooth gear was developed as a gear having the same function as the double helical gear. The double helical gear has disadvantages that necessitate a special bobbing machine for fabrication and a high-grade technique for assembly. The curvilinear-tooth gear was devised as a solution to these disadvantages. In general, curvilinear-tooth gears were previously fabricated using gear-mill cutters. However, the authors have devised a bobbing method that uses a CNC bobbing machine. The present report introduces a method of hobbing a curvilinear-tooth gear.

Effect of gear width and helix angle on factor of dynamic load of double circular arc helical gearing

Effect of gear width and helix angle on factor of dynamic load of double circular arc helical gearing

Compensating analysis of a double circular-arc helical gear by computerized simulation of meshing

A mathematical model of a stepped double circular-arc helical tooth profile with two centre offsets is developed. The conditions of gear meshing that reflect manufacturing and assembly errors are simulated. The locations of bearing contact and the contact path pattern of mating tooth surfaces are determined by tooth contact analysis (TCA). By applying the proposed mathematical model and TCA, single error impact can be determined. To compensate for offset and angular misalignment, the authors propose an adjustable bearing whereby transmission errors can be minimized. The investigation is illustrated with several numerical examples.

DETECTION OF GEAR FAULTS BY DECOMPOSITION OF MATCHED DIFFERENCES OF VIBRATION SIGNALS

This paper describes a series of seeded fault tests performed on the double-helical gears in a marine gearbox and presents analyses of the vibration signals measured at two locations on the gearbox for each of five faults. It is shown that by applying recently developed techniques for the matching of consecutive synchronous averages and for the decomposition of synchronous averages into their components, clear indications of all but one of the sets of seeded faults can be obtained.

Theoretical investigation on state of load distribution among contact bearings of double circular arc helical gears

Theoretical investigation on state of load distribution among contact bearings of double circular arc helical gears

Dynamic Gear Loads Due to Coupled Lateral, Torsional and Axial Vibrations in a Helical Geared System

In this paper we investigate the rotordynamics of a geared system with coupled lateral, torsional and axial vibrations, with a view toward understanding the severe vibration problems that occurred on a 28-MW turboset consisting of steam turbine, double helical gear and generator. The new dynamic model of the shaft line was based on the most accurate simulation of the static shaft lines, which are influenced by variable steam forces and load-dependent gear forces. The gear forces determine the static shaft position in the bearing shell. Each speed and load condition results in a new static bending line which defines the boundary condition for the dynamic vibration calculation of the coupled lateral, torsional and axial systems. Rigid disks and distributed springs were used for shaft line modeling. The tooth contact was modeled by distributed springs acting normally on the flank surfaces of both helices. A finite element method with distributed mass was used for lateral and torsional vibrations. It was coupled to a lumped mass model describing the axial vibrations. The forced vibrations due to unbalances and static transmission errors were calculated. The eigenvalue problem was solved by means of a stability analysis showing the special behavior of the coupled system examined. The calculation was successfully applied, and the source of the vibration problem could be located as being a gear-related transmission error. Several redesign proposals lead to a reliable and satisfactory vibrational behavior of the turboset.

Computerized design and generation of double circular-arc helical gears with low transmission errors

The authors have computerized the simulation of meshing and contact of double circular-arc helical gears, and determined the impact of gear misalignment on transmission errors. A modified geometry of the gears for absorption of transmission errors caused by misalignment has been developed. The generation and the geometry of the gears are represented in the Appendices. Numerical examples that illustrate the developed theory are represented.

Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

Load share and finite element stress analysis for double circular-arc helical gears

The authors analyze the tooth surface contact and stresses for double circular-arc helical gear drives. The geometry of such gear drives has been represented by the authors in their previous paper [1]. The proposed approach is based on application of (i) computerized simulation of meshing and contact of loaded gear drives, and (ii) the finite element method. Load share between the neighboring pairs of teeth is based on the analysis of position errors caused by surface mismatch and elastic deformation of teeth. The authors have investigated the conditions of load share under a load and determined the real contact ratio for aligned and misaligned gear drives, respectively. Elastic deformation of teeth and the stress analysis of the double circular-arc helical gears are accomplished by using the finite element method. The finite element models for the pinion and gear are constructed, respectively. Contact pressure is spread over elliptical area. The stress analysis for aligned and misaligned gear drives, respectively, has been performed. The numerical results have been compared with those obtained by other approaches.

Computerized simulation of generation, meshing and contact of double circular-arc helical gears

The authors have investigated the generation, geometry, meshing and contact of double circular-arc helical gears. Such gears have been proposed in extension of the idea of single-arc Wildhaber-Novikov gears with the purpose: (i) to obtain two zones of meshing and reduce the bending stresses, and (ii) keep the advantage of reduced contact stresses of W.-N. gears. The proposed methods and developed computer programs cover the solution to the following problems: 1. Determination of the paths of contact on the gear tooth surfaces. 2. Determination of the bearing contact as the set of instantaneous contact ellipses. 3. Determination of transmission errors caused by gear misalignment. The investigation is illustrated with numerical examples.

A three dimensional photoelastic study of the stress distributions in double helical epicyclic gears

This paper reports on part of a research programme which was carried out using two‐ and three‐dimensional photoelastic model techniques in order to analyse the stress distributions in a double‐helical epicyclic gear design incorporating typical features of production gear units.The paper describes the testing of two three‐dimensional models, one subjected to torque loading, i.e. tooth forces; the other to combined rotational and torque loading. Note is made of some of the problems inherent in the design and loading of complex models such as those used in the tests and of the solutions developed to overcome the difficulties.Attention is devoted to the analysis of contact loads and load distribution, maximum sub‐surface stresses, maximum root fillet bending stresses and the geometry of the lines of contact. General conclusions are drawn and an indication given of the subsequent extensive two‐dimensional test programme which was carried out.

Strength Calculation of Large Helical Gears

A way to calculate the state of tooth fillet stress, contact stress and flash temperature on tooth flank of large helical gears with profile-, longitudinal form error and simultaneous pitch error is shown. The calculated tooth fillet stress and the contact pattern on tooth flank are compared with the values and figures measured on large double helical gears of 366000 DWT tanker ship drive during test voyage, in order to show the reliability of this calculating method. A hint is shown, to decide the order of accuracy of transverse tooth profile and longitudinal tooth form as input data for this calculation.

The Effects of Direction of Rotation in Double-Helical Gear Pumps on Delivery Characteristics

In double-helical gear pumps, it is clarified theoretically that delivery characteristics differ in accordance with the direction of gear rotation (called "forward rotation" when central part of the tooth curve first enters the gearing region, and "backward rotation" when ends of the tooth first enter the gearing region), and experiments are conducted using spur gear, single-helical gear and double-helical gear pumps. Results obtained are as follows : (1) Owing to fluid flow across the tooth curves being unfavourable, the theoretical characteristics at backward rotation are worse than at forward rotatio. (2) When there were pressure release ports on both sides of delivery and suction, or on delivery side only, the pumps operating under forward rotation always showed better total efficiencies than pumps operating under backward rotation and having the same type of release ports. (3) When the release port was on suction side only or when there was no release port, no distinct effect of direction of rotation on the total and volumetric efficiencies was observed. (4) Double-helical gear pumps operating under forward rotation showed total efficiencies higher than those of spur gear or single-helical gear pumps. (5) Double-helical gear pumps under backward rotation would have an efficiency equal to or worse than the efficiencies of spur gear or single-helical gear pumps.

The Effects of Direction of Rotation in Double-Helical Gear Pumps on Delivery Characteristics

The Effects of Direction of Rotation in Double-Helical Gear Pumps on Delivery Characteristics

Paper 13: Choice of Tooth Type for High-Speed Gearing

The paper considers the pros and cons of spur, single, and double helical gearing. A detailed geometric analysis of the basic load capacities of helical and spur gears, respectively, leads to non-dimensional optimum tooth numbers for each type, having a constant ratio to one another irrespective of size and material. Helical gears are shown to require the same volume as spurs but relatively coarser teeth. Consideration of the possible dynamic effects of characteristic errors leads to the conclusion that spur gears are potentially superior for very high speed applications.

Paper 6: Noise and Vibration from Ancillary Marine Equipment with Particular Reference to a 350-KW Turbo-Alternator

Experiments have been undertaken at selected electrical loads on a self-contained turbo-alternator set comprising a 350-kW 60-c/s alternator driven by means of double helical parallel shaft gearing by a high-speed (15 000 rev/min) steam turbine. The turbo-alternator was erected on flexible mountings with all steam, water, and other service connections arranged in such a manner that they placed no constraint on the machine. In addition to the turbine and alternator rotors several auxiliary drives each contribute to the total noise output. These include the d.c. exciter, pilot exciter, and metadyne unit which are driven directly, or by belts, from the alternator shaft and the oil pumps, governor, etc., which are driven from the turbine shaft by way of spur and bevel gears. The paper describes the manner in which the separate effects of each of the major sources of structural vibration and airborne noise were isolated and measured. In-place balancing techniques were employed to aid an investigation of the variation of vibration level with rotor out-of-balance. In the process experimental information was obtained about the damping effects of journal bearing oil films, vibration amplitudes of the bearing housing being as much as 25 dB below the equivalent shaft amplitudes.

Load Distribution in Marine Reduction Gears : (2nd Report, Double Helical Gears)

Load Distribution in Marine Reduction Gears : (2nd Report, Double Helical Gears)