Gear Body Research Articles

Numerical and experimental analysis of the progressive gear body with the use of finite-element method

Numerical and experimental analysis of the progressive gear body with the use of finite-element method

Coupled multi-DOF dynamic contact analysis model for the simulation of intermittent gear tooth contacts, impacts and rattling considering backlash and variable torque

Variable torque conditions in geared powertrain applications are known to lead to tooth contact loss, contact reversal, tooth impacts, rattling vibration and noise. Displacements/ deflections dominate the low-torque high-vibration responses and, besides backlash, the real-time dynamic lateral deflections of the gear bodies and the occurrence of simultaneous double-sided tooth contact influence the instantaneous mesh excitation strongly. The faster deterministic and stochastic analytical models do not consider this coupling, whereas the numerical models that do so implicitly by simulating the contact of discretised tooth surfaces/ volumes are significantly limited by the accuracy and computational overhead of their discrete meshes. To provide a both fast and accurate solution of the contact problem, especially in displacement-dominated operating conditions, this work analyses the dynamic contact of gears starting from basic principles and derives an accurate analytical model for the coupling between the compliance, contact geometry, the backlash, and the torsional and lateral displacements and deflections in the general three-dimensional multi-DOF system. This serves as a foundation for a series of dynamical simulations of a single-stage spur gear transmission under different variable-torque excitations to predict tooth contact loss and contact reversal and the basic interactions that lead to impacts and rattling vibration. This approach can be used to predict critical torque fluctuation levels, beyond which these phenomena emerge.

Study on modular modeling and performance evaluation of a conical gear for marine transmission system

Conical involute gears, which are also known as beveloid gears, are the involute gears with cone-shape gear body rather than cylindrical gear body. Generally, conical gears are used in anti-backlash transmission systems and marine transmission systems. In marine transmission system, in order to obtain optimal propulsive force, 7–14 degree inclination angle was needed. In this paper, a 7 degree cone angle conical gear used in 375 kW class marine power transmission system was selected as research objective. And in order to establish the design theory of conical gear, a design system named conical gear modular modeling system was developed. The prototype conical gear was developed by the above design system to be used to simulate in a certain condition. The simulated and optimized prototype conical gear was manufactured which is as a specimen to complete a series of performance tests which contains gear tooth profile test and contact rate test. As the results, the developed conical gear can well meet the performance requirements of the 375 kW class marine power transmission system.

Analytical Investigations on the Mesh Stiffness Function of Solid Spur and Helical Gears

Approximate formulae are presented which give the time-varying mesh stiffness function for ideal solid spur and helical gears. The corresponding results compare very well with those obtained by using two-dimensional (2D) finite element (FE) models and specific benchmark software codes thus validating the proposed analytical approach. More deviations are reported on average mesh stiffness which, to a large extent, are due to the modeling of gear body deflections.

Advanced model for the calculation of meshing forces in spur gear planetary transmissions

This paper presents a planar spur gear planetary transmission model, describing in great detail aspects such as the geometric definition of geometric overlaps and the contact forces calculation, thus facilitating the reproducibility of results by fellow researchers. The planetary model is based on a mesh model already used by the authors in the study of external gear ordinary transmissions. The model has been improved and extended to allow for the internal meshing simulation, taking into consideration three possible contact scenarios: involute–involute contact, and two types of involute-tip rounding arc contact. The 6 degrees of freedom system solved for a single couple of gears has been expanded to 6 + 3n degrees of freedom for a planetary transmission with n planets. Furthermore, the coupling of deformations through the gear bodies’ flexibility has been also implemented and assessed. A step-by-step integration of the planetary is presented, using two typical configurations, demonstrating the model capability for transmission simulation of a planetary with distinct pressure angles on each mesh. The model is also put to the test with the simulation of the transmission error of a real transmission system, including the effect of different levels of external torque. The model is assessed by means of quasi-static analyses, and the meshing stiffness values are compared with those provided by the literature.

Effects of gear crack propagation paths on vibration responses of the perforated gear system

This paper investigates the dynamic behaviors of a perforated gear system considering effects of the gear crack propagation paths and this study focuses on the effects of a crack propagating through the rim on the time-varying mesh stiffness (TVMS) and vibration responses. Considering the effects of the extended tooth contact, a finite element (FE) model of a gear pair is established based on ANSYS software. TVMS of the perforated gear with crack propagating through tooth and rim are calculated by using the FE model. Furthermore, a lumped mass model is adopted to investigate the vibration responses of the perforated gear system. The results show that there exist three periods related to slots of the gear body in a rotating period of the perforated gear. Gear cracks propagating through tooth and rim both reduce the gear body stiffness and lead to reduction of TVMS besides the crack tooth contact moment, and the TVMS weakening for the former is less than that for the latter. Moreover, the results also show that the gear crack propagating through the rim (CPR) has a greater effect on vibration responses than the gear crack propagating through the tooth (CPT) under the same crack level. Vibration level increases with the increasing crack depth, especially for the gear with CPR.

Modeling and monitoring of tooth fillet crack growth in dynamic simulation of spur gear set

This study integrates a linear elastic fracture mechanics analysis of the tooth fillet crack propagation into a nonlinear dynamic model of spur gear sets. An original formulation establishes the rigidity of sound and damaged teeth. The formula incorporates the contribution of the flexible gear body and real crack trajectories in the fillet zone. The work also develops a KI prediction formula. A validation of the equation estimates shows that the predicted KI are in close agreement with published numerical and experimental values. The representation also relies on the Paris–Erdogan equation completed with crack closure effects. The analysis considers that during dN fatigue cycles, a harmonic mean of ΔK assures optimal evaluations. The paper evaluates the influence of the mesh frequency distance from the resonances of the system. The obtained results indicate that while the dependence may demonstrate obvious nonlinearities, the crack progression rate increases with a mesh frequency augmentation. The study develops a tooth fillet crack propagation detection procedure based on residual signals (RS) prepared in the frequency domain. The proposed approach accepts any gear conditions as reference signature. The standard deviation and mean values of the RS are evaluated as gear condition descriptors. A trend tracking of their responses obtained from a moving linear regression completes the analysis. Globally, the results show that, regardless of the reference signal, both descriptors are sensitive to the tooth fillet crack and sharply react to tooth breakage. On average, the mean value detected the crack propagation after a size increase of 3.69 percent as compared to the reference condition, whereas the standard deviation required crack progressions of 12.24 percent. Moreover, the mean descriptor shows evolutions closer to the crack size progression.

Influence of propeller shaft bending vibration on drivetrain gear dynamics

A new multi-coordinate dynamic model of a hypoid geared rotor system considering the propeller shaft bending effect is formulated. The bending flexibility of propeller shaft is modeled as a lumped parameter set applying the component mode synthesis. The pinion and gear are modeled as flexibly coupled rigid bodies with backlash nonlinearity and time-varying mesh coupling. The kinematic transmission error is assumed to be the main excitation. The solution is obtained by employing the explicit Runge-Kutta integration method with adaptive time step, which yields the dynamic mesh force and also the vibratory response of the gear bodies in time domain. The frequency response functions are then determined by computing the root-mean-square of the time domain solutions at each frequency point. The analyses show that the effect of propeller shaft bending flexibility and damping on the geared rotor system dynamics are found to be mode shape dependent. It is further observed that increasing the damping of propeller shaft can effectively reduce the dynamic mesh force. This indicates that the damping treatment on propeller shaft can be a potential application to reduce the gearbox vibration and noise response.

Simulation Based on Trivariate Nurbs and Isogeometric Analysis of a Spur Gear

The approach provides simulation of the gear design with high-precision profile configuration parameters to accurately predict its load capacity and stress state, which requires incessant efforts, as gear failure modes depend largely on its profile representation. The finite element analysis (FEA) is a well-known effective computational method, which many authors used to estimate the gear tooth strength against the primary failure modes of gears. This method is not only known to be time-consuming but often expensive, it employs approximate geometry that resulted in a coarse mesh. The tooth strength and deformation modes were obtained from a three-dimensional gear model based on the trivariate nonuniform rational B-splines (NURBS) under loading and investigated using the isogeometric analysis (IGA) for simulation. The results produced with the IGA simulation are compared with the corresponding values derived from the classical estimation method with the Lewis equation and FEM analysis using ANSYS. Both results are in good agreement and confirm that the IGA model is more accurate than the FEM one. This study demonstrated that IGA was practically applicable, providing an alternative means of using high-precision geometry of 3D models to estimate the behavior of gear bodies under loading and modify their strength calculations.

Fault features analysis of cracked gear considering the effects of the extended tooth contact

Owing to the effect of gear flexibility, the extended tooth contact occurs, which is a phenomenon that the incoming tooth pair enters contact earlier than the theoretical start of contact, and the outgoing tooth pair leaves contact later than the theoretical end of contact. Considering the effects of the extended tooth contact and tooth root crack on the time-varying mesh stiffness (TVMS), a finite element (FE) model of a spur gear pair in mesh is established by ANSYS software. TVMS under different crack depths at constant rated torque (60Nm) are calculated based on the FE model. Then, a FE model of a geared rotor system is developed by MATLAB software. Frequency-domain features, statistical features (Kurtosis and RMS) and instantaneous energies based on empirical mode decomposition (EMD) under different crack depths are calculated at 1000rev/min and the corresponding measured results are also performed by model experiment. The results show that considering the effect of extended tooth contact, TVMS of crack gear pair becomes smooth from double-tooth engagement to single-tooth engagement; the gear crack has reduced the gear body rigidity, which leads to the reduction of stiffness of the healthy teeth and has little effect on the vibration response. The instantaneous energy can be chosen as a distinguishing indicator to qualitatively diagnose the gear cracks with different levels.

Application of Finite Element to Spur Gear Stress Reduction Using Stress Relieving Feature

The aim of this study was to create stress relieving features to reduce the root fillet stress in spur gear. A pilot model was established to predict von Mises stress at the root fillet of the gear without holes and was used as a reference model. Finite element modeling was adopted using Abaqus® package. The predicted stresses were compared with stresses obtained by AGMA analytical solution. A good agreement was found in the comparison between the calculated and predicted stresses. Then, another model, namely hole model, was built to investigate the effect of various hole parameters (number, diameter, location, angle). The hole model was performed by creating hole/holes in the gear body. The results obtained showed that increasing the diameter size of hole/holes resulted in higher percentage of stress reductions compared to the pilot case. Furthermore, increasing the number of holes resulted in higher percentage of stress reductions compared to the pilot case, but gear rigidity in this case was highly affected.

Study on Optimization Design Technique of Aviation Gear Body

In this paper, a kind of advanced gear body form is proposed, which has the structure characteristics of no weight reducing wholethin spoke platesthick rim and large fillet. The optimization effect is confirmated by comparative analyzing the structure before and after optimization on strengthstiffnessweight and frequency adjustment performance of gear. The results show that the kind of optimization gear body is suitable for application in aviation, for which has the features of high strength, good stiffness and light weight and which is easy to adjust gear frequency.

Strength and Stiffness Optimization of Heavy-Duty Gear

In this paper, a kind of advanced gear body form is proposed, which has the structure characteristics of no weight reducing whole, thin spoke platesthick rim and large fillet. The optimization effect is confirmated by comparative analyzing the structure before and after optimization on strengthstiffnessweight and frequency adjustment performance of gear. The results show that the kind of optimization gear body is suitable for application in aviation, for which has the features of high strengthgood stiffness and light weight and which is easy to adjust gear frequency.

Time-Domain Dynamic Analysis of Helical Gears with Reduced Housing Model

In this paper we present a time-domain dynamic analysis of a helical gear box with different housing models using a unique finite element-contact mechanics solver. The analysis includes detail contact modeling between gear pairs along with the dynamics of gear bodies, shafts, bearings, etc. Inclusion of the housing in the dynamic analysis not only increases the fidelity of the model but also helps estimate important NVH metrics, such as dynamic load and vibration transmission to the base, sound radiation by the gearbox, etc. Two different housing models are considered. In the first, the housing is represented by a full FE mesh, and in the second, the housing is replaced by a reduced model of condensed stiffness and mass matrices. Component Mode Synthesis (CMS) methods are employed to obtain the reduced housing model. Results from both the models are successfully compared to justify the use of reduced housing model for further studies. Steady state sound radiation by the gear box housing is then studied in the frequency domain using a boundary element solver. The housing frequency response, which is the boundary condition for the acoustic analysis, is estimated using two different methods. In one method, the response is computed from the generalized coordinates and component modes using modal superposition, in the other the bearing dynamic loads are used to perform forced response analysis on the full FE mesh of the housing. Thus, a template for end-to-end solution to predict radiated noise from a gear box is established.

Influence of cracks on dynamic characteristics and stress intensity factor of gears

Dynamic and three-dimensional finite element analytical models of cracked gears are established, and the dynamic characteristics (natural frequency and vibration shape) of the gear body are investigated when tooth cracks in the gear appear. Further, the influence of crack position and length on the dynamic characteristics of the gear structure are simulated and discussed. From this it was possible to determine that the crack position and crack length had an influence on the gear’s natural frequency and vibration shape. When the crack appears, the natural frequencies of the gear drop, and the vibration shapes also change. The influence of crack position on natural frequency and vibration shape are bigger than that of crack length. The natural frequencies’ decreases are bigger when the crack in the gear occurs at the tooth root rather than at the top of the tooth. Moreover, when the crack appears, the vibration shapes of the gear body are obviously different from without the crack, and the dynamic stresses of the gear body also change. On this basis, using the theory of fracture mechanics and the finite element method by ANSYS, the stress intensity factors were analyzed when the gear crack appeared. The variations in stress intensity factors are discussed related to changes in crack length, gear module, number of teeth, and load, when gear cracks occur at the pitch circle and tooth root. The pragmatic expressions of stress intensity factors are given by combining with the results obtained from the finite element method and the influence laws of multiple parameters on stress intensity factors are gained. These establish a good foundation for the fracture analysis and fault diagnosis of gears.

Multibody element for spur and helical gear meshing based on detailed three-dimensional contact calculations

The dynamic behavior of geared systems is highly affected by operating conditions which are different from the theoretical case and by deviations of the tooth surface from the perfect involute. This paper presents a contact element for global dynamic simulations of gear assemblies using multibody modeling that enables to take into account real-case parameters in a scalable way. The element is discussed for the purpose of gear whine simulation. To achieve high calculation efficiency, the gear bodies are considered rigid and the gears are connected by spring-damper elements with a variable stiffness. This equivalent mesh stiffness depends on the gear geometry and material, the instantaneous conditions of transmitted load and relative misalignments of the gears. This mesh stiffness is calculated in a pre-processing step by solving a three-dimensional tooth contact problem. It is then stored in multivariate lookup tables, which are interpolated during the multibody simulation. Results are presented for a reference helical gear pair.

Dynamic characteristics of cracked gear and three-dimensional crack propagation analysis

The dynamic model and three-dimensional finite element analytical model of cracked gear structure are established respectively according to the cracked beam theory, and the dynamic characteristics (natural frequency, vibration shape) of cracked gear body are investigated. Further the influences of crack position and crack length on the dynamic characteristics of gear structure are simulated and discussed. On this basis, the fracture and damage of gear structure are investigated according to the theory of fracture mechanics. Using FRANC3D software, the three-dimensional (3D) propagation of crack at tooth root for involute gear is simulated, and stress intensity factor (SIF)s of semi-circular crack at tooth root including three types are analyzed, their variation laws are gained, then the expressions of SIFs are obtained by numerical fitting FEM results. Based on this, the 3D crack propagation path at tooth root is simulated and discussed, then, it is verified by comparing to experimental results, according to the mutation of the maximum SIF at crack tip, the fracture and damage of gear tooth are judged, and its work life also is predicted. These have very important value for damage monitoring and diagnosis of gear.

Multi-tooth contact behavior of helical gear applying modified meshing equation

In tooth contact analysis, the numerical process of searching for true contact lines or points is always a daunting task. The true contact lines for ideal helical gear transmission can be easily obtained through the helical gear meshing theory; however, in practice, this approach does not work well due to effect of tooth elasticity that shifts the contact lines from their ideal position. To address this problem, an approximate method to seek the true contact positions is proposed applying a modified meshing equation for a pair of helical gear with error free and no shaft deformation. First, the helical gear tooth deformation is calculated with the combination of contact mechanics and finite element method. Second, the deformed tooth flanks are fitted with Chebyshev polynomials. Third, the modified meshing equation is formulated by accounting for the influence of not only gear rigid body movement but also the gear deformation on the meshing process. Finally, the true contact points are determined by solving the correlated tooth flank equations, meshing equations, and force balance equations. The deformations of the gear and pinion teeth within the meshing plane are analyzed, and the contact load distributions along with the Von Mises stresses over a mesh cycle are examined. The study indicates that the proposed numerical method can yield true contact lines quickly while avoiding costly computational time in the traditional true contact line searching process that searches iteratively in the whole meshed tooth flank.

Dynamic Analysis of Three-Dimensional Flexibility of Gear Structure Based on Finite Element Method

The paper established a three-dimensional flexibility dynamical model of gear structure based on the theory of finite element method. It presented the natural frequency of the gear elastomer and the analytical expression of natural functions and the simulative results. The results showed good agreement. This provided a study method for the vibration analysis of the gear structure body, and established the basis for studying the characteristics of acoustic radiation and the dynamic design of gears.

The Selection, Designing and Analysis of Heavy Duty Tractor Gearbox (ITM8200)

In recent years, ITM 399 series tractor has been manufactured in Iran Tractor Manufacturing Company (ITM), which can be suitable for small farms operations. For big farms operations, minimizing energy consumption, decreasing the time losses and increasing work efficiency, a heavy duty tractor of ITM 8200 series was started to design in the same Company. The gearbox selection, design and analysis for this tractor with the engine power of 154 horse power is studied in this research. The mechanical gearbox equipped with mechanical-hydraulic dynashift system was used in ITM 8200 power transmission system. The dynashift system produces four cases (A, B, C and D) with 8 speeds that produced by main gearbox, which altogether produces 32 forward speeds and 32 reverse speeds for this new tractor. To design the gearbox, with recommended speeds, gearbox ratios and gears ratios was calculated. Then by using the engine torque and slip torque on tractor gearbox, the exerted loads on gears were calculated. After this, by using of American Gear Manufacturing Association (AGMA) method and computer programming design, the gears have been designed. Finally one of the gears in ANSYS software analyzed. The results of this analysis show that: The gears have been designed for tractor gearbox can endure loading and transfer the power requirement of new tractor. The design safety factor of gears has been obtained by ANSYS software approximately equals with safety factor of AGMA methodology. In gear analysis, for applying load to one of gear tooth (unit contact ratio), stress distribution will produce in gear body and especially on neighboring teeth body. For tractor gearbox design, it would be necessary to include slip torque, which will decrease the gear width and gearbox volume.