Pinhole Position Errors Research Articles

Mesh Load Factor Uncertainty Analysis in a 5‐MW Wind Turbine Planetary Gearbox Affected by Inherent Manufacturing Errors

ABSTRACTThe current work focuses on the study of the uncertainty related to the manufacturing process of gears for 5‐MW planetary transmissions aimed to the wind generator industry. With this objective, the Monte Carlo method is the employed tool to analyse the influence that selected manufacturing errors have in the performance of these planetary transmissions, more precisely in its mesh load factor. In more detail, the selected manufacturing errors are tangential pinhole position and tooth thickness errors, following the tolerances set by the DIN 3967. This study provides the probability distributions of mesh load factor values related to the size of the manufacturing errors in the transmission. Moreover, both kinds of errors are included together in numerous different planetary transmissions, and the probability distribution functions are also obtained for these. The results lead to relevant conclusions related to the influence of these errors in the performance of these transmissions and their durability and cost‐effectiveness.

INFLUENCE OF MANUFACTURING ERRORS ON THE BEHAVIOUR OF A TWO-STAGE PLANETARY GEAR TRAIN

Planetary gear train is widely used in large heavy-duty machineries such as helicopters and ships due to its large transmission ratio, strong bearing capacity, and small size. In this paper, and the load sharing ratio (LSR) and overall transmission error (TE) of a two-stage double-helical planetary gear train are studied. Firstly, the static balance equations of the double-helical planetary gear train are established. Then, the LSR under different mesh phasing and the overall TE are obtained by solving the equations. Finally, different errors such as pinhole position and eccentricity error are taken into consideration and the influence of errors on load sharing ratio and transmission error are analyzed. The results show that the excitation frequency of transmission error is related to the number of planet gears and mesh phasing and the LSR is related to the mesh phasing, especially to the sequentially phased transmission. It is also concluded that the excitation frequency of the output element of the two stages can be seen as the superposition of the mesh frequencies of each stage and that the studied errors have a significant impact on the LSR and the TE. Keywords: Double-helical planetary gear; Meshing phase; Load Sharing Ratio, Transmission Error.

Dynamic modeling and vibration analysis of planetary gear sets concerning mesh phasing modulation

This paper studies the changes in behavior, in terms of mesh phasing modulation, of planetary gear transmissions (PGTs) due to various gear pinhole position errors. An advanced model of the spur PGT is established to explore the effects of the position errors on mesh phasing relations and an analytical determination of the relative mesh phasing variation is derived. Furthermore, the vibration performance of planetary gears is investigated by developing a novel dynamic model and components of the vibration signals are clarified using the proposed model. Additionally, we further perform several experiments to measure the mesh phasing variations using strain gauges and collect the gear vibration signals using accelerometers. Finally, simulation and experimental results are compared to verify the proposed models, and the results indicate that the presented models provide the opportunity for the researchers to quantify the mesh phasing relations relative to the gear position errors as well as clarify the frequency modulation mechanism of gear vibrations in PGTs.

Use of sun gear orbits to obtain the load sharing in planetary transmissions and its impact in the tooth load

The present work assesses the possibility of using the orbits described by the sun gear in order to analyse the load sharing ratio in planetary gear transmissions. Furthermore, the current work is extended to observe the impact of the floatability and different tangential pinhole position errors in the load borne in a single contact between a pair of teeth in comparison to the load per planet. Therefore, it highlights the inaccuracy of the load sharing ratio (LSR) as an indicator of the overload in one tooth of the planet. Moreover, the use of the orbits represented with respect to a rotating reference provides helpful information to determine the overloads and underloads in the planets due to the existence of a tangential error in sequentially phased transmissions. Therefore, this proposal provides a simpler solution to the measurement of the LSR in planetary transmissions with different numbers of planets than the use of strain gauges.

Influence of errors in planetary transmissions load sharing under different mesh phasing

This work studies the changes in behaviour, in terms of load sharing, of planetary transmissions due to the incidence of different factors. Amongst those, mesh phasing and various errors, such as tooth thickness and pinhole position errors, are taken into consideration. As far as mesh phasing is concerned, the geometry of the transmission is studied and how this mesh phasing together with errors affects the transmission performance, especially for sequentially phased configurations given the imbalance in the load sharing ratio. All these are analysed for common configurations with odd number of planets given the interest behind the lack of diametrically opposed planets. Fruit of this work it is proved the non-negligible impact of radial errors in planetary transmissions, especially for sequentially phased transmissions. Furthermore, it was observed that a higher number of planets sharpens the effect of errors on the load sharing ratio.

Modeling, Analysis and Testing of Load Distribution for Planetary Gear Trains with 3D Carrier Pinhole Position Errors

A discrete model to study the load distribution behavior of helical planetary gear trains (PGTs) is developed, in which 3D planet position errors, induced by carrier pinhole position errors and tooth modifications, are duly considered. The model adopts a discrete approach with which the planetary gear train is discretized into a series of slice-units in order to ease the problem of gear meshing in 3D cases. In the modelling, compatibility conditions and discrete equilibrium are developed for the coupling among 3D planet position errors, tooth modifications, instantaneous meshing situations, elastic deformations and rigid body spatial motions. Upon the discrete model, a method for analysis of the load distribution is further developed. The influence of 3D planet position errors and tooth modifications on the load distribution was simulated for a helical PGT having three and four planets. Tests on the actual wind turbine PGTs were conducted with results agreed with the simulations obtained, which validate the proposed method.

Effects of Non-torque Loads and Carrier Pinhole Position Errors on Planet Load Sharing of Wind Turbine Gearbox

The effects of carrier pinhole position errors and non-torque loads on the load sharing of planet gears in a conventional-type three-point suspension wind turbine gearbox were investigated. A 1/4 scale-down model of a 2-MW class wind turbine gearbox was used, and a parametric study was conducted using a three-dimensional analysis model capable of performing system-level analysis. Axial force, radial force, and bending moment were used as non-torque loads, and the mesh load factor was used as an index representing the load sharing characteristics of the planet gears. The results of the analysis showed that the radial force and the moment were major non-torque load elements that affect the load sharing of the planet gears. The magnitudes, positions, and phases of pinhole position errors also made a significant impact on the load sharing characteristics of the planet gears. When non-torque loads and pinhole position errors acted together, the influence of pinhole position errors was greater than that of the non-torque loads. Their combination effect will be different according to the characteristics of drive train system. Therefore, the analysis that reflects actual specifications and operating conditions of all the drive train system components is necessary to derive the planet load sharing characteristics accurately.

Experimental Study on the Carrier Pinhole Position Error Affecting Dynamic Load Sharing of Planetary Gearboxes

In gearbox design, small size, light weight, and long service life are important factors that must be considered. The planetary gear train structure has been widely used to realize these characteristics. In this study, the effects of increasing the torque on and changing the rotation direction of a planetary gearbox on the dynamic load sharing among the planet gears were analyzed experimentally using a planet carrier manufactured at an industrial site. When the number of planet gears was even, one pair of planet gears exhibited higher load sharing than the other two pairs among the three pairs of planet gears, where the two gears in each pair faced each other directly, regardless of the rotation direction of the gearbox. In addition, increasing the torque of the planetary gearbox improved the mesh load factor. The mesh load factor varied significantly as to the rotation direction changed, due to the phase change of the carrier pinhole position error.

Influence of the Carrier Pinhole Position Errors on the Load Sharing of a Planetary Gear Train

Load sharing among planetary gears, one of the design variables, has a significant influence on the performance and service life of a gearbox. This study involved simulating and testing the design parameters related to load sharing among planetary gears. In this regard, the influence of errors in the carrier pinhole position on the load sharing among the planetary gears was analyzed. The results showed that the difference between the simulation results using the model and the laboratory test results was less than 10%. Furthermore, similar tendencies were observed according to the magnitude of the load applied to the planetary gears. As for the design parameters affecting load sharing, the service life of a gearbox containing planetary gears can be extended by using a floating system as opposed to a non-floating system. In addition, reduced planetary pin diameter and increased planetary bearing clearance leads to appropriate load sharing among the planetary gears and increases the service life and floating effect of the gearbox.

A Load Distribution Model for Planetary Gear Sets

A load distribution model of planetary gear sets presented is capable of simulating planetary gear sets having component- and system-level design variations such as component supporting conditions, different kinds of gear modifications and planetary gear sets with different numbers of equally or unequally spaced planets as well as different gear set kinematic configurations while considering gear mesh phasing. It also accounts for classes of planetary gear set manufacturing and assembly related errors associated with the carrier or gears, i.e., pinhole position errors, run-out errors, and tooth thickness errors. Example analyses are provided to indicate the need for a model of this type when studying load distribution of planetary gear sets due to unique loading of the gear meshes associated with planetary gear sets. Comparisons to measurements existing in the literature are provided.

유성기어박스의 캐리어 핀홀 위치 오차의 위상에 따른 유성기어의 하중 분할 연구

The planetary geartrain can be reduced in size and weight, and has excellent durability since the input torque is divided by the number of planet gears when the power is transmitted. In order to improve its durability, the load sharing among planet gears must be even. However, of the various manufacturing errors possible, the carrier pinhole position error has the greatest influence on load sharing. This study compared and analyzed the load sharing and the gear safety of planetary gears, according to the phase of the carrier pinhole position error. We confirmed that load sharing among the planet gears varied, depending on the phase of the carrier pinhole position error. The mesh load factor is inversely related to the gear safety factor for bending and contact, and affects the durability of the planetary geartrain. Also, in the design of the planetary geartrain, the load sharing among planet gears is directly affected by the carrier pinhole position error and its phase. Therefore, the geometric tolerance must be managed efficiently, which needs to be reflected in the production drawings.

A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional (3D) formulation of N planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all the three types of manufacturing errors, namely, constant errors such as carrier pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation, and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

캐리어의 핀홀 위치 오차에 따른 유성기어의 하중 분할 및 하중 분포 영향 분석

Gearboxes are mechanical components that transmit power by adjusting input and output speed and torque. Their design requirements include small size, light weight, and long lifespan. We have investigated the effects of carrier pinhole position error on the load sharing and load distribution characteristics of a planetary gear set with four planet gears. The simulation model for a simple planetary gear set was developed and verified by comparing analytical results with a putative model. Then, we derived the load sharing and load distribution characteristics under various pinhole position error conditions using the prototypical simulation model. The results showed that the mesh load factor and face load factor increased with the pinhole position error, which then influenced the safety factor for tooth bending strength and surface durability.

An experimental study on the effect of carrier pinhole position errors on planet gear load sharing

In this study, the test was conducted to verify the effect of carrier pinhole position errors on planetary gearbox load sharing. A 3D measurement was conducted to check the pinhole position errors of a carrier that was produced at an actual industrial site. A strain gauge was attached to the planet pin. The effect of planet pin manufacturing errors and the difference in errors according to the installation position of the strain gauge were examined. The effect of carrier pinhole position errors on planetary gearbox load sharing was examined for different input torques. As the input torque increased, load sharing was improved. When the test torque rate was 100%, the load sharing factor was 1.42 for the strain gauge under compression and 1.34 for the strain gauge under tension. These results were similar to the load sharing factor indicated in the design standards for wind turbine gearbox designs.

Characteristic Analysis of Planetary Gear Set of Hydromechanical Transmission System of Agricultural Tractors

Purpose: This study aims to establish the effect of pinhole position errors in the planet carrier of a planetary gear set (PGS) on load sharing among the planet gears in the hydromechanical transmission (HMT) system of an agricultural tractor. Methods: A simulation model of a PGS with five planet gears was developed to analyze load sharing among the planet gears. The simulation model was verified by comparing its results with those of a model developed in a previous study. The verified simulation model was used to analyze the load-sharing characteristics of the planet gears with respect to the pinhole position error and the input torque to the PGS. Results: Both simulation models had identical load magnitude sequences for the five planet gears. However, the load magnitudes on the corresponding planet gears differed between the models because of the different stiffnesses of the PGS components and the input torques to the PGS. The verified simulation model demonstrated that the evenness of load sharing among the planet gears increases with decreasing pinhole position error and increasing input torque. Conclusions: The geometrical tolerance of the pinhole position should be properly considered during the design of the planet carrier to improve the service life of the PGS and load sharing among the planet gears.

캐리어의 핀홀 위치 오차가 유성기어의 하중 분할에 미치는 영향 분석

캐리어의 핀홀 위치 오차가 유성기어의 하중 분할에 미치는 영향 분석

LOAD SHARING ANALYSIS OF PLANETARY GEAR BOX

One of the advantages of epicyclic transmissions is that the input torque is divided in a number of parallel paths. For n planet epicyclic system, each sun–planet–ring path is to transmit 1/n of the input torque. However, this is only true in the ideal case when there is equal load sharing between all the planets in the epicyclic system. Because of manufacturing errors, equal load sharing is not possible and the degree of inequality in load sharing has major role for gear system sizing, tolerancing schemes, and torque ratings. Therefore it is important to understand the fundamental cause of the unequal load sharing behavior in epicyclic gear sets. Load sharing behavior is associated with positional errors causing one or more planets to lead or lag the other planets. When the error is positive the planet with error lead the other planet while when the error is negative planet with error lags the other planet. Several manufacturing errors can introduce positional errors. Some of the common contributors are carrier pinhole position error, planet size variation, and run out of the gears. A set of precision planetary gear set is selected with the objectives of experimental and theoretical investigation of the load sharing behavior by introducing the position errors for the planets, the load shared by each planet is estimated by maximum stresses induced in each pin. The results of the experimentation are then validated with the FEM (Finite Element method) results.

Analytical study of floating effects on load sharing characteristics of planetary gearbox for off-road vehicle

Uneven load sharing of a planetary gear set is the main cause of preventing the miniaturization and weight reduction of a planetary gearbox. Non-torque loads and carrier pinhole position errors are the main factors that worsen the load-sharing characteristics. However, their effects are seldom analyzed at a system level especially for an off-road vehicle. To make up this gap, some simulation models are proposed to investigate the effects of floating members on the load-sharing characteristics and the strength of a planetary gear set with non-torque load and carrier pinhole position error. When the error is not considered, the mesh load factor converges to unity irrespective of the type and number of floating members and the safety factors for pitting and bending are increased slightly. When the carrier pinhole position error is considered, the mesh load factor dramatically worsens. Although it is improved using the floating members, it does not converge to unity. However, the bending safety factor of the planet gear with the error is increased by 26%. This indicates that the design modification for the original planetary gearbox is needed to satisfy the safety factor requirement, but the problem is solved using only floating members.

Pinion Assembly Strategies for Planetary Gear Sets

Previous works illustrate that the orientation of pinion run-out errors has strong effect on the load sharing behavior of floating planetary gear sets. To minimize the inequality of load sharing, an in-phase rule for assembling pinions is recommended by other researchers, while a theoretical proof is still lacking. In this paper, not only the orientation but also the assembly sequence of the pinions is under scrutiny. A generalized mathematical model is developed in order to study the best load sharing conditions and floating gear sets with 4-6 pinions are specially treated. Through statistical calculation, several pinion sequence rules and orientation rules are extracted. By numerical simulation, four different pinion assembly strategies, which originate from the combinations of the existing rules and methods, are compared with each other. The most effective assembly strategies for systems with 4-6 pinions are proposed. The statistical analysis indicates that the proposed strategies significantly improve the load sharing behavior if only pinion run-out errors are considered and retain their effectiveness when pinhole position errors and tooth thickness errors are introduced as interference factors.

Planet position errors in planetary transmission: Effect on load sharing and transmission error

In this paper an advanced model of spur gear transmissions developed by the authors is used to study the influence of carrier planet pin hole position errors on the behaviour of the transmission. The model, initially conceived for external gear modeling, has been extended with internal meshing features, and thus increasing its capabilities to include planetary transmission modeling. The new features are presented, along with the summary of the model general approach. The parameters and characteristics of the planetary transmission used in the paper are introduced. The influence of carrier planet pin hole position errors on the planet load sharing is studied, and several static cases are given as examples in order to show the ability of the model. Tangential and radial planet pin hole position errors are considered independently, and the effect of the load level is also taken into account. It is also given attention to the effect on the transmission error of the transmission. Two different configurations for the planetary transmission are used, attending to the fixed or floating condition of the sun, and the differences in terms of load sharing ratio are shown.