PERFORMANCE INDICATORS OF CONCHOIDAL STRAIGHT SPUR GEARS WITH INCREASED LOADING CAPACITY. THE THEORY

The article is devoted to the actual problem of increasing the performance indicators of machine gear drives. To solve this problem, in the article proposed to use a conchoidal engagement made with a shifting of the reference profile and special contact conditions. A feature of the proposed engagement is that it is less sensitive to manufacturing and assembly errors compared to conventional conchoidal engagement. As a result of theoretical studies, the performance indicators of such an engagement were determined. This made it possible to determine the level of load during further experimental tests of new gears. Contact strength and meshing losses were selected as performance indicators subject to further experimental verification. The ratios of these indicators, calculated for conchoidal spur gears with convex-convex contact, made with a shifting of the reference profile, with similar involute ones, are theoretically determined. Comparative analysis of performance indicators was carried out for gears of involute and conchoidal engagement with the same parameters and shifting of the reference profile. It was found that for experimental conchoidal drives with shifting, the maximum load is 1.2 times higher than that of a similar involute drive with shifting, and the loss in engagement is 21% less. A rational area of application of the new gearing is machine drives for high power transmissions. Keywords: spur gears, conchoidal gearing, profile shift, convex-convex contact, meshing characteristics, teeth surface strength, gearing power loss

The Mathematical Model of Curve-Face Gear and Time-Varying Meshing Characteristics of Compound Transmission

The curve-face gear pair is a new type of gear pair with variable transmission ratio for spatial finite helical motion. In this paper, mathematical models of a new developed curve-face gear were simplified and obtained directly by the standard shaper. The subsequent studies on the curve-face gear compound transmission characteristics were further analyzed by the combinations of the principle of space gearing and screw theory. Firstly, the conjugate tooth surface geometry as well the point contact traces of curve-face gears were derived. Secondly, the geometric relationships between gear pair and the corresponding meshing characteristics were evaluated by several basic geometric elements, including instantaneous screw, axodes, striction curve, and conjugate pitch surface. Based on that analysis, it was found that the tooth contact normal was reciprocal to the instantaneous twist, which demonstrated that the conjugate motion with the desired transmission ratio could be realized in current curve-face gear compound transmission. Moreover, the time-varying slip characteristics of the curve-face gear pair were also revealed, that is, rolling and sliding action coexist at all contact on the tooth surfaces. In brief, this work provided the theoretical basis for following researches on machining curve-face gear with standard shaper.

An Analysis of the Gear Meshing Characteristics of the Main Planetary Gear Trains of Helicopters Undergoing Shafting Position Changes

The complex three-shaft three-reducer structural designs of helicopter transmission systems are prone to changes in the relative positions of shafting under the conditions of main rotor and tail rotor loads. These changes will affect the transmission characteristics of the entire transmission system. In this study, the planetary gear trains of helicopters were examined. Due to the fact that these structures are considered to be the most representative structures of the main reducers of helicopters, they were selected as the study objects for the purpose of examining the meshing characteristics of planetary gear trains when the relative positions of the shafting changed due to the position changes of the main rotor shafts under variable load conditions. It was found that by embedding the comprehensive time-varying meshing stiffness values of the main rotor shafts at different positions, a dynamic model of the relative position changes of the planetary gear trains could be established. Then, combined with the multibody dynamics software, the meshing characteristics of the sun gears, and the planetary gears, the planetary gears and the inner ring gears were simulated and analyzed under different inclinations and offsets of the shafting. The results obtained in this study revealed the following: (1) the average meshing force of the gears increased with the increases in the angle inclinations, and the meshing force between the sun gears and the planetary gears increased faster than the meshing force between the planetary gears and the inner ring gears. It was observed that during the changes in the shafting tilt positions, obvious side frequency signals had appeared around the peak of the meshing frequency in the spectrum. Then, with the continuous increases in the tilt position, the peak was gradually submerged; (2) the average meshing force of the gears increased with the increases in the offset, and the increasing trend of the meshing force between the sun gears and the planetary gears was similar to that observed between the planetary gears and the inner ring gears. It was found that when the shafting offset position changed, there were obvious first and second frequency doubling in the spectrum; (3) the mass center orbit radii of the sun gears increased with the increases in the shafting position changes, and the changes in the angular tilt position were found to have greater influencing effects on the mass center orbit radii of the sun gears than the changes in the offset positions. This study’s research findings will provide a theoretical basis for future operational status monitoring of the main transmission systems of helicopters and are of major significance for improvements in the operational stability of helicopter transmission systems, which will potentially ensure safe and efficient operations.

Double-circular-arc tooth profile design and parametric analysis on the comprehensive performance of the harmonic drive

A tooth profile is of significant importance to the performance of a harmonic drive. Available studies about designing a tooth profile only consider the influence of the tooth profile on the meshing characteristics from a macro perspective. However, the effects of the surface roughness and contact geometry of the tooth on the lubrication characteristics from the micro perspective are rarely reported. In the present study, a double-circular-arc tooth profile is used as the basic tooth profile of the flexspline. Based on the modified kinematic method, a conjugate profile is calculated and the tooth profile of the circular spline is obtained. On this basis, the mathematical model for the mixed lubrication of the harmonic drive with a double-circular-arc tooth profile is established by considering the factors of the normal load of meshing point, relative velocity, contact geometry, and surface roughness. The comprehensive performance under different double-circular-arc tooth profile parameters (tooth face radius, tooth flank radius, and common inclination) is analyzed. To verify the correctness of the research, four sets of harmonic drives are designed and machined for testing their basic performance. The results show that the parameters of the double-circular-arc tooth profile have multiple influences on the comprehensive performance. The meshing performance and lubrication performance are restricted. Parameter control can effectively improve comprehensive performance and different tooth profile parameters should be designed for different applications.

Vibration Characteristics of Spur Gear Under Tooth Fatigue Wear

Tooth surface wear is one of the most common faults of gearboxes which increases the fatigue load on the gearbox and endangers its stable output characteristics and service life. Gear meshing characteristics vary significantly with the wear location and severity. Thus, the wear fault model considering tooth profile deviation, friction and time varying mesh stiffness (TVMS) was established in order to quantitatively study the vibration characteristics of tooth fatigue wear (TFW). Tooth profile modification and friction coefficient coupling were applied to characterize TFW, and the maximum wear depth was introduced to characterize TFW severity. The gear-pair simulation models under multiple wear severities were established and imported to a single-stage parallel gearbox whose dynamic differential equation was established under multiple torque conditions. The dynamic simulation results showed good agreement with the experimental data, which validated the method’s effectiveness. The vibration characteristics under different wear severities and simulation conditions were then obtained and compared.

Characteristics analysis of the new flexible ring gear for helicopter reducer

As a key component of the vibration generation and transmission of planetary transmission system, the design of ring gear will directly affect the vibration of the system. After considering the advantages and disadvantages of the traditional ring gear structure, the new flexible ring gear was designed by scholars and applied to helicopter reducer. There is a dearth of reported analysis in the meshing characteristics of the new flexible ring gear, which leads to the blind selection of the ring gear. By building an accurate parametric finite element model, the meshing characteristics of the new flexible ring gear and the difference in dynamic characteristics between the new flexible ring gear and the traditional ring gear are obtained. The analysis shows that the new ring gear is superior to the traditional ring gear in many aspects, but it also has the characteristic of unbalance loading on the tooth surface. In addition, a test method is proposed to accurately measure the load sharing coefficient and dynamic load factor of planetary transmission and the simulation results of flexible ring gear are verified by comparison.