Helical Gears Research Articles

PERENCANAAN ULANG RODA GIGI PINION PADA GARDAN BELAKANG KENDARAAN JEEP BJ-212

Gears function to transmit high power and precise rotation through interlocking teeth. Gears are superior to other transmission systems as they are more compact, capable of transmitting large power with high efficiency, and have a minimal risk of slipping. Additionally, gears can withstand higher loads and allow for speed variations as needed. One commonly used type is the bevel gear, where the pitch surface forms a cone with its apex at the intersection of the shaft axes. Straight bevel gears are the easiest to manufacture and frequently used, although they produce significant noise due to their low contact ratio. Other types of bevel gears include spiral bevel gears, helical bevel gears, and hypoid gears, each with unique characteristics and advantages in transmission systems.

Meshing Performance Analysis of a Topologically Modified and Formed Internal Helical Gear Pair

Internal helical gear pairs are sensitive to manufacturing and assembly errors, loading deformation, which can result in vibration and noise. Three-dimensional topological modification of tooth surfaces is available to reduce this sensitivity. A 3D topological modification method is proposed by means of an internal helical gear form grinding method. The modified tooth surface model was constructed using spatial meshing theory and matrix transformations. Loaded tooth contact analysis (LTCA) was established to investigate the effect law of modification parameters on gear loading performance. Simulation results indicated that the contact area appeared at the middle area of the tooth surface under design loading conditions, with little edge contact existing. Transmission error decreased by up to 28.4% compared to the tooth without modification. The dynamic meshing performance of the internal helical gear pair was enhanced significantly. A transmission experiment was conducted to verify the effectiveness and validity of the simulation results.

The Investigation of the Working Conditions on 3D Printed Helical Gears

The Investigation of the Working Conditions on 3D Printed Helical Gears

Research on Multi-Objective Optimization of Helical Gear Shaping Based on an Improved Genetic Algorithm

Traditional design and shaping methods of helical gears may have difficulties in meeting the requirements of multiple performance indicators simultaneously, such as tooth surface accuracy, load-carrying capacity, and transmission efficiency. This study attempts to overcome these limitations through a multi-objective optimization method and achieve the comprehensive optimization of multiple performance indicators. This paper aims to boost gear system power transmission and cut vibration and noise. It assesses gear shaping impacts via normal load per unit length of the helical gear surface and gear vibration amplitude. Traditional gear shaping schemes were first determined using classic theories and formulas. Then, an improved genetic algorithm was applied to seek optimal helical gear shaping parameters. An eight-degree-of-freedom lumped mass model of the helical gear transmission system, considering bending–torsion–axial coupling, was developed based on Newton’s second law and solved via the fourth-order Runge–Kutta method. Comparisons showed that the traditional shaping scheme reduced the maximum normal load per unit length by 20.6% and the system’s vibration amplitude by 18.3%. In contrast, the improved genetic algorithm achieved greater reductions of 26.34% and 27.2%, respectively. Both methods effectively decreased the maximum normal load per unit length and system vibration amplitude, with the improved genetic algorithm yielding superior results. This work offers a key theoretical basis and reference for enhancing load transmission, reducing costs, and mitigating vibration and noise in gear transmission systems.

Study on the Design of the Gear Pair and Flow Characteristics of Circular-Arc Gear Pumps

Compared with traditional gear pumps, circular-arc gear pumps have the advantages of silence and small flow pulsation, but the theory of design is underdeveloped. This paper presents a design method for gear pumps with circular-arc helical gear pairs, and the influence mechanism of flow characteristics is studied. First, a model of the gear pair is established, and a design method for the gear pair is proposed. Second, a CFD model is demonstrated, and the influences of the tooth profile parameters (tooth number, modules, and pressure angle) on the flow characteristics are analyzed. Finally, the significance of the influencing factors is analyzed. The results show that when the stagger angle of the two ends of the arc helical gear pair is an integral multiple of π/Z, there is no flow pulsation, and there is little noise. The tooth number and modules are positively correlated with the flow rate and flow pulsation, among which the modules have the most significant influence. The flow rate of the gear pump increases by 4–5 L/min for every 0.2 increase in the modules. The pressure angle and flow rate show a negative correlation trend, but the influence is insignificant. The flow rate is less than 1 L/min for every 2° change in the pressure angle. This paper provides a theoretical basis and reference value for the gear pair design of gear pumps.

Improved Nonlinear Dynamic Model of Helical Gears Considering Frictional Excitation and Fractal Effects in Backlash

Surface roughness and sliding friction are pivotal in determining the dynamic meshing performance of helical gears, especially under conditions of flexible support. In addition, the meshing parameters influenced by gear vibrations exhibit time-varying characteristics under flexible support stiffness, which is disregarded by many scholars. Based on this, a nonlinear dynamic model of a helical cylindrical gear system under flexible support conditions is developed, considering the coupling effects of dynamic friction and backlash influenced by fractal surface roughness. The motion differential equations of the system are derived using the Lagrange method, and numerical solutions are obtained through the Runge–Kutta method. The effect of several control parameters (driving speed, surface roughness and fractal dimension) on the dynamic response of gear system is studied, and the proposed dynamic model is compared with the traditional model under different support stiffness to demonstrate its adaptability to highly flexible support scenarios. The results indicate that the proposed dynamic model is better suited for flexible support structures. Moreover, the coupling effects of sliding friction and fractal backlash amplify the dynamic response of the gear system and introduce complex spectrum characteristics. This study provides theoretical guidance for the optimization of vibration and noise reduction designs in helical gear systems.

Dynamic Characteristics Analysis and Optimization Design of Two-Stage Helix Planetary Reducer for Robots

The dynamic characteristics of high-precision planetary reducers in terms of vibration response and dynamic transmission error have a significant impact on positioning accuracy and service life. However, the dynamics of high-precision two-stage helical planetary reducers have not been studied extensively enough and must be studied in depth. In this paper, the dynamic characteristics of the high-precision two-stage helical planetary reducer are investigated in combination with simulation tests, and the microscopic modification of the gears is optimized by the helix modification with drums, with the objective of reducing the vibration response and dynamic transmission error. Considering the time-varying meshing stiffness of gears and transmission errors, a translation–torsion coupled dynamics model of a two-stage helical planetary gear drive is established based on the Lagrange equations by using the centralized parameter method for analyzing the dynamic characteristics of the reducer. The differential equations of the system were derived by analyzing the relative displacement relationship between the components. On this basis, a finite element model of a certain type of high-precision reducer was established, and factors such as rotate speed and load were investigated through simulation and experimental comparison to quantify or characterize their effects on the dynamic behavior and transmission accuracy. Based on the combined modification method of helix modification with drum shape, the optimized design of this type of reducer is carried out, and the dynamic characteristics of the reducer before and after modification are compared and analyzed. The results show that the adopted modification optimization method is effective in reducing the vibration amplitude and transmission error amplitude of the reducer. The peak-to-peak value of transmission error of the reducer is reduced by 19.87%; the peak value of vibration acceleration is reduced by 14.29%; and the RMS value is reduced by 21.05% under the input speed of 500 r/min and the load of 50 N·m. The research results can provide a theoretical basis for the study of dynamic characteristics, fault diagnosis, optimization of meshing parameters, and structural optimization of planetary reducers.

Numerical and experimental study of windage power loss in high-speed double helical gears considering the influence of oil-air volume ratio

Numerical and experimental study of windage power loss in high-speed double helical gears considering the influence of oil-air volume ratio

Tooth surface design of double-pressure-angle helical face gear considering non-orthogonality, offset, and modification

Tooth surface design of double-pressure-angle helical face gear considering non-orthogonality, offset, and modification

Generation and Stress Analysis of Helical Gear Tooth Combining Involute with Epicycloidal and Hypocycloidal Profiles

This paper examines the helical gear that combines the involute with epicycloidal-hypocycloidal profiles. The tooth profile was produced through the shaper-cutting process, which was conducted using an appropriate rack cutter with a Cartesian coordinate system. A computer program was developed using Microsoft Visual Basic and subsequently integrated into SolidWorks using the application programming interface. This numerical investigation aims to analyze the impact of tool parameters on the produced gear tooth profile, with the goal of enhancing the dynamic performance and deformation resistance of the proposed helical gear model. Additionally, this study assesses the effect of teeth thickness on the helical gear model. The results indicate a highly accurate approximation of the involute, cycloidal, and modified gear tooth profiles, which were programmed according to the module, teeth number, and rolling angle. The use of a combination of curves (epicycloidal, involute, and hypocycloidal) in a single tooth resulted in a larger contact area, thereby improving the ability of the gears to withstand greater pressures and extending their lifespan. The modified non-parallel helical gear drive outperformed other non-parallel helical gear drives. The best enhancements in maximum contact stress and teeth bending stress achieved approximately 33.169% and 26.08% compared to the standard involute profile and about 17.69% and 0.67% when compared to the cycloidal profile.

Analysis of gear transmission error in helical gear using enhanced tooth contact analysis model considering measured tooth profile errors

A loaded tooth contact analysis model was developed to assess transmission error by incorporating profile errors in a helical gear pair. Profile errors for all teeth of both the pinion and wheel were measured, and the mean profile error was computed and integrated into the model. To validate the model, static transmission error (STE) was measured experimentally. The experimental results, particularly the peak-to-peak static transmission error (PPSTE) in relation to torque and tooth-meshing harmonics, demonstrated consistency with the simulation outcomes. Subsequently, the model was employed to investigate the impact of surface waviness (SW) on the STE, focusing on SW amplitude, spatial frequency, and initial phase. It was observed that both the amplitude and spatial frequency of the SW influenced the PPSTE and the harmonic characteristics of the transmission error, while the initial phase of the waviness had no significant effect.

Phenomenological analysis of the electrical behavior of helical gears to identify sensory utilizable effects for condition monitoring approaches

In this contribution the electrical behavior of helical gear contacts is investigated. The investigation is based on impedance measurements obtained on an industrial gearbox test bench. The results are analyzed to identify the qualitative influence of rotation speed, load, rotation direction, load direction and surface alterations. Furthermore, potentials and limitations of utilizing the electrical behavior of helical gear contacts for condition monitoring applications are discussed. The investigations show that the lubrication condition can be qualitatively identified based on the characteristics of the electrical behavior of the gear contact. Important influencing factors for the lubrication film thickness and consequently the impedance of the gear contact can be determined to be rotation speed and load but also rotation and load direction. Surface alterations like damages but also tooth pitch deviations in the region of single digit micrometers can be seen to have a measurable influence on the impedance signal of the gear contact. These effects can potentially be used for condition monitoring approaches. However, the ambiguity of the impedance signal due to the high number of influencing factors remains a limitation of this new measurement method. Another factor for the ambiguity of the impedance signal is the simultaneous contact of multiple teeth which are not distinguishable in the impedance signal. This contribution shows the potentials and limitations for the sensory utilization of the electrical behavior of helical gear contacts and highlights novel research gaps.

Design and Pressure Pulsation Analysis of Pure Rolling External Helical Gear Pumps with Different Tooth Profiles

This paper investigates the design methodologies of pure rolling helical gear pumps with various tooth profiles, based on the active design of meshing lines. The transverse active tooth profile of a pure rolling helical gear end face is composed of various function curves at key control points. The entire transverse tooth profile consists of the active tooth profile and the Hermite curve as the tooth root transition, seamlessly connecting at the designated control points. The tooth surface is created by sweeping the entire transverse tooth profile along the pure rolling contact curves. The fundamental design parameters, tooth profile equations, tooth surface equations, and a two-dimensional fluid model for pure rolling helical gears were established. The pressure pulsation characteristics of pure rolling helical gear pumps and CBB-40 involute spur gear pumps, each with different tooth profiles, were compared under specific working pressures. This comparison encompassed the maximum effective positive and negative pressures within the meshing region, pressure fluctuations at the midpoints of both inlet and outlet pressures, and pressure fluctuations at the rear sections of the inlet and outlet pressures. The results indicated that the proposed pure rolling helical gear pump with a parabolic tooth profile exhibited 42.81% lower effective positive pressure in the meshing region compared to the involute spur gear pump, while the maximum effective negative pressure was approximately 27 times smaller than that of the involute gear pump. Specifically, the pressure pulsations in the middle and rear regions of the inlet and outlet pressure zones were reduced by 33.1%, 6.33%, 57.27%, and 69.61%, respectively, compared to the involute spur gear pump.

Improved Analytical model for mesh stiffness of helical gears considering the relationship of friction and flash temperature under steady temperature field

Abstract In the transmission process, thermal deformation of gears due to external factors, coupled with the thermal expansion of the tooth profile induced by flash temperature from surface friction, significantly impacts the time-varying mesh stiffness (TVMS) characteristics. Therefore, this paper proposes a novel analytical model for the TVMS of helical gears that considers these factors. In this model, the thermal deformation of gear foundation under a bulk temperature field is first determined using the displacement method. Blok's theory is then applied to establish the relationship between tooth surface friction and flash temperature, leading to the derivation of the actual tooth profile expansion equation under steady-state conditions. After that, based on this equation and considering the friction force in tangential, radial, and axial directions, the gear tooth and foundation stiffness of helical gear in transverse and axial directions under steady-state temperature field are accurately established. Finally, the proposed model is obtained by coupling each stiffness. By comparing with the FE result, the model is validated, and the influence of friction coefficient, bulk temperature, and gear parameters on TVMS is studied. The analytical model and findings provide valuable insights for optimizing gear parameter design.

Research on failure mechanism of final drive gears of a passenger car based on multi-condition varying-speed accelerated test

To standardize the reliability test evaluation schedule of passenger cars powertrain, a multi-condition varying-speed accelerated test criteria correlated with the statistical data of target vehicles is developed. With this test criteria, a real-vehicle test is conducted to evaluate a trial-manufacture car equipped with a newly developed transmission. Regarding the fracture failure of the driving and driven gears of the final drive, a heat treatment quality inspection is conducted on the fractured gears. From the meshing state of the gears, it is observed that machining precision errors caused an excessively large bearing clearance of the helical gear in the differential housing, with the meshing area of the driving gear tilting to one side and generating eccentric loads under uneven stress. The fatigue damage of the gears is calculated by the rainflow cycle matrix of the gears obtained with the rotating rainflow counting method. The calculation results show that largest loads transmitted by the final drive gears in varying-speed test condition 2, which was the main condition for fractures of the driven gear. Under this condition, the driving gear also produced bending fatigue failure due to the significant-amplitude cyclic loading caused by the eccentric loads.

The Modularized Development of a Wheel-Side Electric Drive System Using the Process of Hobbing and Form Grinding

The wheel-side electric drive system is a melding of a vehicle powertrain and suspension system, which saves chassis space and can adapt to different models. To achieve the goal of highly modularized development, the system is supposed to meet the requirements of various working conditions without changing the interface state. The electric motor drives the wheel through two-stage fixed axis helical gears, so the transmission is short in path and acts as the suspension arm at the same time. As a result, the gears are critical to output robustness and NVH performance. The modeling accuracy is decisive for simulations and tests, so it is necessary to build a precise geometric model instead of the data-fitting estimation. The gears are manufactured by a hobbing and form grinding process, which is described functionally along with the relationship between the tooling parameters and tooth profile curves. Based on the rain flow methodology and extrapolation theory, a comprehensive load spectrum with nine stages is formulated, which can cover the working conditions of a basic version, a NVH version, and a durability version. According to the Miner cumulative damage hypothesis, the equivalent durability mileage of 150,000 km is converted. The prototype machine is simulated and verified on the test bench, and the test results show that the wheel-side electric drive system has a reliable output performance. The equivalent damage of the comprehensive load spectrum is 63.27%, where the 2# stage driving gear is the most vulnerable component of the whole system. The research in this paper can provide data support for damage calculation and lightweight optimization with modularized development and applications in the future.

Effect of Multifunction Cavitation Treatment on Helical Gear Surface

Abstract This study proposes using multifunction cavitation (MFC) to strengthen the surface of helical gears used in transmissions. In addition, because the steel used for helical gears exhibits poor corrosion resistance in water, samples plated with electroless nickel and iron tetroxide were also investigated. In addition to using samples with modified surfaces, we used samples strengthened by carburizing and nitriding. The noncoated and plated samples showed a slight increase in surface roughness and increased compressive residual stress and hardness. The plating method that did not cause red rust during the MFC treatment was iron tetroxide plating. In the samples strengthened by carburizing and nitriding, red rust did not occur on the surface after MFC treatment, the surface roughness was suppressed, and compressive residual stress and hardness increased. The results show that the MFC treatment effectively improved the fatigue properties of gear surfaces with complex shapes.

Catastrophic Failure Analysis of a Wind Turbine Gearbox by the Finite Element Method and Fracture Analysis

The wind turbine gearbox, used as a multiplier, is one of the main components directly related to a wind turbine’s efficiency and lifespan. Therefore, strict control of the gearbox and its manufacturing processes and even minor improvements in this component strongly and positively impact energy production/generation over time. Since only some papers in the literature analyze the mechanical aspect of wind turbines, focusing on some parts in depth, this paper fills the gap by offering an analysis of the gearbox component under the highest amount of stress, namely relating to the sun shaft, as well as a more holistic analysis of the main gear drives, its components, and the lubrification system. Thus, this work diagnoses the fracture mechanics of a 1600 kW gearbox to identify the main reason for the fracture and how the chain of events took place, leading to catastrophic failure. The diagnoses involved numerical simulation (finite element analysis—FEA) and further analysis of the lubrication system, bearings, planetary stage gears, helical stage gears, and the high-speed shaft. In conclusion, although the numerical simulation showed high contact stresses on the sun shaft teeth, the region with the unexpectedly nucleated crack was the tip of the tooth. The most likely factors that led to premature failure were the missed lubrication for the planetary bearings, a lack of cleanliness in regard to the raw materials of the gears (voids found), and problems with the sun shaft heat treatment. With the sun gear’s shaft, planet bearings, and planet gears broken into pieces, those small and large pieces dropped into the oil, between the gears, and into the tooth ring, causing the premature and catastrophic gearbox failure.

Differential helical planetary gear transmission simulation and fatigue life analysis

Abstract In drivetrains widely used in large automobiles, agricultural machinery, and tanks, the differential system is a key part of the system that allows the left and right drive wheels to rotate at different speeds, thereby enabling the vehicle to perform operations such as steering in place. Among them, the bevel gear is one of the important components of the differential system. During the bevel gear transmission process, the stresses on the gear are mainly bending and contact stresses. The bend should be applied with force in the direction of the width of the tooth. Contact stress is the stress generated by friction between two teeth when the gear is operating. Uneven load distribution on the gear flanks, stresses on the bent gear teeth and contact stresses during meshing are caused by deformation and friction of the gear flanks during meshing, and thermal effects and other factors are generated when the gears are meshed. The design process requires us to consider the effects of these loads and calibrate the strength of the gears through finite element analysis. At the same time, in order to ensure foolproof operation in the event of dry friction of the helical bevel gear sub due to oil loss in the differential system, wear analysis of the helical bevel gears is required to ensure that the helical bevel gear sub can work normally for a certain period of time even under complicated working conditions. This paper takes a kind of helical bevel gear as an example and elaborates in detail the process of simulation analysis, strength check, and wear life analysis of a helical bevel gear pair using finite element software.

A Cross-Timescale Prediction Method for Vibration and Stiffness Degradation of Helical Gear Drive

A Cross-Timescale Prediction Method for Vibration and Stiffness Degradation of Helical Gear Drive