Housing Stiffness Research Articles

Numerical analysis of stresses on angular contact ball bearing under the static loading with respect to race thickness and housing stiffness

A 3-dimensional model of the angular contact ball bearing (ACBB) was modeled using Abaqus/standard (Dassault systems- version 2017) to investigate the influence of race thickness on the bearing performance. It was found that the ability to support higher contact stress increased with race thickness. However, large deformations were found to occur on outer race with thickness of 3.3 mm and only small deformations were observed on outer race with a thickness of 9.9 mm. The large deformations induce higher shear stresses on thin races than on thick races. These stresses cause spall growth in bearings and propagate into a network of cracks. As a result of these findings, thin races are prone to failure compared with thick races.

Computational Method to Predict Three-Dimensional Chatter Vibration in Cold Rolling of Flat Metals

Abstract Introduced is a three-dimensional, physics-based mathematical model capable of efficiently predicting self-excited chatter vibration phenomena in the cold rolling of metal strip and sheet. The described nonlinear chatter model combines the 3D mill structural dynamics behavior with the elastic–plastic rolling process dynamics to predict conditions of instability in a single-stand 4-high mill that can lead to both third-octave and fifth-octave chatter. Formulation of the 3D chatter model is achieved by coupling the dynamic simplified-mixed finite element method with a nonlinear roll-bite process dynamics model to capture self-exciting feedback interactions. In contrast to prior approaches to model chatter in the cold rolling of flat metals, the presented method abandons several simplifying assumptions, including 1D or 2D linear lumped parameter analyses, vertical symmetry of the upper and lower halves of the roll-stack, and continuous contact between the rolls and strip. The model is demonstrated for a single-stand 4-high rolling mill considering the detrimental third-octave self-excited chatter condition. Detailed stability analyses that show time histories of the 3D mill behaviors are presented, respectively, for stable, marginally stable, and unstable rolling speeds, and for changes in the lower housing stiffness to reflect more realistic, asymmetric rolling mill conditions.

The Effect of Fit Clearance between Outer Race and Housing on Vibration Characteristics of a Cylindrical Roller Bearing with Localized Defects

Due to bolt looseness or operating ambient temperature, fit clearance can often be found between the outer ring and housing. The vibration characteristics of a cylindrical roller bearing with localized defects are greatly affected by the fit clearance and the accuracy of bearing fault diagnosis may be reduced. Thus, a mathematical model for a cylindrical roller bearing was constructed and the interaction between the outer ring and housing was described. The classical localized defects were modeled, such as the inner ring defect, outer ring defect and roller defect. The relative experiments were conducted to check the constructed model. Then, it was found that the RMS (Root Mean Square) of housing acceleration decreased with increasing housing stiffness and viscous damping. When the fit clearance and friction coefficient increased, the RMS values increased. Except for housing stiffness and viscous damping, there were no uniform change rules of defect frequency amplitudes for other conditions. In the bearing with an outer ring defect or roller defect, the shock times of housing acceleration and the contact force between outer ring and housing were delayed, while fit clearance decreased. However, contrary variation trends were found for the inner ring defect. If the phase difference between defect location and rotor unbalanced force increased, the RMS and acceleration fluctuation amplitudes for the inner ring defect decreased. When the location angle of the outer ring defect increased, RMS and frequency amplitudes increased and RMSy/RMS decreased. The calculated results may provide the theoretical foundation for condition monitoring rotating machinery systems.

Advanced method of including housing stiffness into calculation of gear systems

One of the central goals during the design of helical gear systems is the achievement of a well-distributed contact load in the gear mesh. An equal load distribution is a key factor for a high load carrying capacity, the economic use of materials and a long lifetime. Mesh misalignment can be caused by tooth deflections, manufacturing deviations or elastic deformation of the shaft-bearing system and the gearbox housing. Those deformations have to be taken into account during the design process of adequate tooth-flank geometry. Elastic deformations of gearbox housings can be significant, especially in the case of automotive applications with aluminium cases. This paper presents an advanced method of including housing stiffness into the calculation of gear systems. A validation of the approach is carried out by comparing the calculated deformations with measurements of a static test rig of a hypoid gearbox.Many calculation programs offer the opportunity to analyse the deformation behaviour of the shaft-bearing-housing system. Most of the components in these programs are described by analytic approaches. However, components that are geometrically more complex, like the housing or planet carriers cannot be represented as easily as that by analytic expressions. There are several alternatives to take into account the elasticity of those objects. One way is to model the stiffness of the bores using imported stiffness matrices. These matrices contain the elasticity of the bores itself as well as crossover influences between the bearings. The reduced stiffness matrices may be the result of a static reduction of the geometry using the finite element method (FEM). As state of the art, the reduction is mostly carried out at the centre points of the bearing bores. The proposed advanced method uses the static reduction of geometries on several points at the bores, distributed over the circumference. This approach offers a more detailed modelling of the elastic behaviour of complex geometries within the analytic deformation calculation of gear systems. To validate the advanced approach, the calculation results of the elastic deflections of the shaft-bearing-housing system is compared with measurements of a static test rig. In the course of these comparisons, the influence of different modelling methods of gearbox housings on the accuracy of the calculation results is discussed.

Detecting the 3D spatial varying crack evolution-induced vibration of gearbox through a system level rigid-flexible coupling model

Gear crack evolution is a complex process; therefore, fault diagnosis and monitoring can help to avoid catastrophic accidents. In view of the deficiency that the simple linear plane assumption is made in the conventional crack model, the 3D spatial varying crack evolution (propagating in the depth, tooth width and tooth profile directions simultaneously) is investigated based on the linear elastic fracture mechanics in this study. The acquired crack morphology is used to analyse the time-varying meshing stiffness variation. Then, a system level rigid-flexible coupling model consisting of a housing, gear, shaft, and bearing is utilized to predict the dynamic response, and the theoretical results are compared with the experimental results. Furthermore, crack evolution-induced vibration detection is carried out by the proposed model, and the frequency spectrum characteristic, statistical indicator and instantaneous energy are obtained. The results reveal that the vibration impact is less obvious at the initial stage of crack evolution, but the instantaneous energy can amplify and capture the fault feature. Decreasing the housing stiffness can decrease the vibration impact induced by crack evolution; nevertheless, it increases the difficulty of crack detection.

Rib Design for Improving the Local Stiffness of Gearbox Housing for Agricultural Electric Vehicles

In this work, a rib design process is proposed to improve the local stiffness of gearbox housing for agricultural electric vehicles. Unlike conventional engines, electric powertrain noise includes high frequency factors and pure tones. Considering these characteristics, local stiffness was evaluated in the frequency range of interest for the prediction of dynamic behavior. The local stiffness of the gearbox housing was evaluated using the finite element (FE) model. Experimental modal analysis and FE model update were conducted to ensure the reliability of the results. Using the results of local stiffness evaluations, the stiffness weak point was identified, and the rib design location was selected through a strain analysis. The shape of the ribs was parameterized by width, length, and height, and parameter studies were used to compare the local stiffness increase rate according to the rib design pattern. According to the results, the stiffness increase rate against the same mass was distributed differently according to the rib shape, and the most efficient rib shape was selected from a manufacturing perspective.

Influence of Housing Stiffness of the Slewing Reducer of a Tower Crane on the Load Distribution Pattern over the Gear Tooth Flank

To increase the life of slewing reducers, the reliability of their gearboxes is essential. They should be designed, simulated, and tested considering the installation environment and actual load conditions. Many studies have been conducted on the reliability improvement of gearboxes for reducers; however, a few studies have considered actual input load conditions. Furthermore, there is insufficient research on the effects of housing stiffness on gear misalignment, gear life, and load distribution and maximum contact load of the gear tooth flank. In this study, the effects of housing stiffness were analyzed using input torque measurements to investigate the causes of ring gear damage during durability tests on a slewing reducer. The contact pattern of the gear tooth flank was analyzed by applying dyes to all gears inside the reducer, and the results were compared with simulation results. A large edge contact in the first-stage ring gear of conventional slewing reducers was suggested as the cause of the ring gear damage. A new simulation model using a gearbox housing with an increased stiffness showed that edge contact was improved by the decreased gear misalignment. No abnormal wear and/or partial fracture of the ring gear occurred during the durability test on the improved model under the same conditions as those of the initial model. These results indicate that an increase in the stiffness of the housing reduced the gear misalignment, improved the load distribution, decreased the maximum load of the tooth flank, and increased the gear life.

Influence of the Foundation on the Threshold of Stability for Rotating Machines with Roller Bearings—A Theoretical Analysis

The paper presents a mathematical model for analyzing the threshold of stability for rotating machines, where the rotor is linked to the stator by roller bearings, bearing housings and end-shields and where the stator feet are mounted on a soft foundation. The internal (rotating) damping of the rotor is the only source of instability, which is considered in the paper. After the mathematical coherences of the multibody model are described, a procedure is presented for deriving the threshold of stability. Additionally, a numerical example is shown, where the threshold of stability is calculated for different boundary conditions. It could be demonstrated, that the stiffness of the foundation—even if the foundation stiffness is isotropic—can help stabilizing this kind of vibration system in the same way as orthotropic bearing stiffness or orthotropic bearing housing and end-shield stiffness for a rigid foundation.

Effect of the coupling strength on the nonlinear synchronization of a single-stage gear transmission

This paper discusses a study of the synchronization phenomenon of a single-stage gear transmission. The analysis is based on numerical and experimental data. Numerical data were obtained from a 4-DOF lumped-mass model which includes the housing stiffness as a linear spring. Experimental data were acquired from a gearbox with soft housing. Both numerical and experimental data were analyzed by different signal processing techniques: the continuous wavelet transform, the phase diagram, the synchronization error diagram, the Kuramoto’s order parameter, and statistical descriptors, such as the mean value, standard deviation, and kurtosis. Statistical descriptors were used to quantify the synchronization degree. It was found that the kurtosis increases as the system becomes more synchronized. The numerical results show that if the coupling strength is sufficiently weak, there is no synchronization; if it reaches a certain threshold, the mechanical elements synchronize; and if it is too stiff, the synchronization ceases. In the case of the experimental data, results indicate a high degree of synchronization. Finally, through analysis of the power spectral density, it was found that the cyclic loading increases 40 % due to synchronization.

Experimental Study of Four-Point Contact Ball Bearing with Deformable Rings

When a ball bearing is designed with thin rings or is mounted in a flexible housing, the assumption of rigid rings is not true anymore. In this article, an experimental study is presented and a comparison with a numerical model is performed. The numerical approach is based on the coupling between a semi-analytical code and a finite element (FE) model that computes the deformation of the rings and housings. The numerical model accounts for ring ovalization, raceway opening, change of conformity, and structural displacements of the whole assembly. The experimental setup allows investigation of the load–displacement behavior of a four-point contact ball bearing submitted to a static thrust loading. Displacements are measured by an optical method (stereo-correlation) that enables comparison of the surface deformation of the two tested bearings and computation of the rigid-body displacement of the inner ring with respect to the outer ring. A comparison between experimental results, numerical results, with and without consideration of ring and housing stiffness, is presented. The numerical results show the importance of the housing stiffness in the modeling, even with standard ball bearings with relatively large and thick rings. Good agreement between measured quantities and numerical results was found. This permits the prediction of the real nonlinear bearing stiffness (load–displacement curve) with a reasonable margin of error.

Additive manufacturing of active struts for piezoelectric shunt damping

One strategy to deal with unwanted vibrations of lightweight structures is to actively control systems using integrated actuators, such as piezoceramic multilayer actuators. In the presented research work, selective laser melting is used to manufacture active struts by integrating multilayer actuator into a metallic, monolithic housing. Besides the fulfilment of manufacturing constraints (e.g. low volume and individualization), a major objective of this study is to demonstrate the potential of selective laser melting for application tailored smart components. A truss structure is used as demonstration platform. Based on experimentally validated numerical models of the truss structure, a beneficial position of the active strut and the mode to be damped are determined. A model of the multilayer actuator and corresponding housing allows the dimensioning of the housing stiffness to maximize the electromechanical coupling. Thus, an efficient resistive resonant shunted system can be achieved. Numerically designed active struts with specific stiffnesses are manufactured and experimentally characterized. Measurements with connected RL-shunts using the active struts are performed and compared to the original system. Results indicate an efficient damping of the desired mode by means of application tailored active struts. The presented procedure allows rapid design of versatile actuator housings for an optimized electromechanical coupling.

수소 재순환 블로어 소음 진동 저감을 위한 설계 및 제어에 관한 연구

At the fuel processing system (FPS) of fuel cell vehicle, hydrogen recirculation blower (HRB) is used for the recirculation of remained hydrogen after reaction. In this paper, noise and vibration improvement of HRB is studied by changing design and control. It is checked the campbell diagram and critical speed for stability of rotor, and housing stiffness is improved using simulation of frequency response function (FRF). A method is suggested that can decrease the unbalance amount of the rotor and impeller which main source of noise and vibration. In order to reduce the noise during deceleration of blower, electrical braking is applied and tested the risk impact of durability. Founded the optimum switching frequency of the motor control, and reduced the idle rpm by increasing of aerodynamic performance. The superiority of paper is proved by measurement of the improved product's noise and vibration.

Optimal Design of Hot Rolling Strip Mill Housing with Improved GA

Mill housing vibration influents the strip thickness fluctuation. The longitudinal deformation of rolling mill will directly affect plate thickness difference. The longitudinal deformation should be reduced , improving the mill stiffness. Hot rolling mill is seen as is as subject investigated . The improved GA is used to optimize the mill housing parameters. The optimal result is analyzed. The housing stiffness improves. Low order natural frequency improves after optimization, avoiding resonance and improving the housing dynamic stability.

Design and Optimization of PSD Housing Using a MIGA-NLPQL Hybrid Strategy Based on a Surrogate Model

A new power-split device (PSD) is designed as the core component of the multi-power coupling system in a hybrid electric vehicle. It is important to consider the influence of the factors of weight and stiffness on performance of PSD when designing PSD housing. In this paper, the overall arrangement of the power distribution system and PSD housing are redesigned. The finite element analysis is conducted to test PSD housing stiffness. According to the results of the analysis, this study adopts a hybrid optimization strategy based on surrogate models to obtain the least weight under the constraint of PSD housing stiffness. The surrogate models are established using a responsive surface method based on the data obtained by the optimal Latin hypercube design (OLHD). The hybrid optimization strategy combines a multi-island genetic algorithm (MIGA) with a nonlinear programming quadratic line search (NLPQL), which ensures obtaining optimal design parameters for PSD housing. In comparison with optimization using a single MIGA, this hybrid optimization strategy is more efficient and feasible for optimizing housing.

Finite Element Analysis and Optimal Design of Commercial Vehicle Drive Axle Housing

In order to solve the heavy mass problem of the commercial vehicle drive axle housing, the structure of axle housing is optimized with finite element method. At first, the parametric finite element model of axle housing is built by using ANSYS software, and the dynamic response characteristics of axle housing are obtained with transient dynamics analysis. The dynamic analysis results show that strength and stiffness of axle housing can satisfy design criteria very well. Then the fatigue life of axle housing are predicted based on the dynamics analysis, and results show that the fatigue dangerous regions occur on the spring seats. Finally, the structure optimization of axle housing is done aimed at lightweight with goal drive optimization method, and the fatigue life of optimized axle housing are verified with FEA and bench test. The results of verification by both FEA and test show that the optimized axle housing has apparent lightweight effects with its fatigue life meeting design requirements.

The effect of nonlinear traveling waves on rotating machinery

The effect of the housing stiffness on nonlinear traveling waves is presented in this work. It was found that the housing controls the synchronization of nonlinear elements and it allows nonlinear waves to travel through the structure. This phenomenon was observed in a gearbox with a soft housing, and the phenomenon was reproduced with a lump-mass dynamic model. The model included a pair of gears, the rolling bearings and the housing. The model considered all the nonlinear effects. Numerical and experimental results were analyzed with a time–frequency method using the Morlet wavelet function. A compound effect was observed when the nonlinear waves travel between the gears and the bearings: the waves increased the dynamic load amplitude and add another periodic load.

Research on Mill Longitudinal Stiffness Calculation of Wide Hot Strip Mills

Mill is always weighed by its longitudinal stiffness. The prediction precision of longitudinal stiffness related strip geometric accuracy. Taking 1700mm hot strip line as research object, stiffness of housing, bearing wall and roll was calculated by finite elements method(FEM), hydraulic system stiffness was obtained by theoretical formula. Analyzing vertical system and structural symmetry of mill, functional relationship between longitudinal stiffness and its components stiffness was derived according to series or parallel connection with various components. Longitudinal stiffness was the basis on thickness set-up model. Calculation result was verified by practical test.

Finite Element Static Analysis on Heavy-Duty Truck Gearbox Housing

The heavy-duty truck’s gearbox housing is studied in this paper. The analysis model is built with finite element software. MPC (multipoint constraint) contact algorithm is used to simulate the connections between different gearbox housings. The strength and stiffness of gearbox housing is calculated at its low-speed load case in the first gear. The contour of the stress and displacement is obtained through the calculation results. The results show that the housing meets the design requirements and it provides a reference for optimization and improvement of the gearbox housing.

Theoretical Analysis of High-Speed Cylindrical Roller Bearing with Flexible Rings Mounted in a Squeeze Film Damper

For high-precision mechanical systems such as gas-turbine engines that operate under extreme conditions, it is particularly important to accurately predict the behavior of the mainshaft rolling bearings. This prediction includes, among others, the load distribution, stiffness, and power dissipation. Although the shaft speeds tends to increase, rings and shaft are becoming thinner due to size and weight constraints. Thus, the bearing behavior is now dependent on the housing and ring stiffness. Furthermore, the use of a squeeze film damper (SFD) is widespread in gas-turbine engines to significantly reduce the vibratory levels. In this case, a single thin ring provides the interface between the bearing rolling elements and the fluid film. Due to the flexibility of this ring, an elastic coupling occurs modifying the behavior of the bearing-SFD system. A global flexible bearing-SFD assembly model is proposed in this paper. Large deformations can occur, resulting in a contact between the ring common to the bearing and the SFD and its housing. To reproduce this interference, an effective mechanical stop model is also proposed. The behavior of an industrial bearing-SFD assembly is then investigated for different operating conditions. The presented results show that this coupling has a first-order influence on the behavior of the bearing-SFD system. It is also shown that such elastic coupling introduces a dissymmetry of the load distribution with respect to the applied load direction. Moreover, in certain cases, the position of the bearing in its housing can reach eccentricities larger than the radial clearance of the SFD.

Numerical analysis of lubrication in a journal bearing by a thermoelastohydrodynamic lubrication (TEHL) model

AbstractIn recent years, in high power, compact, and light weight automotive engines, the bearing load has been increasing and the housing stiffness has been decreasing. The engine bearing performance is significantly influenced by both an elastic deformation and an increase in temperature. Under these harsh operating conditions, an extreme temperature rise of the bearing is expected to occur in the thin oil-film region when the oil-film thickness is not kept thick enough within the bearing. Consequently, the high-temperature rise sometimes causes the bearing to have a seizure. Thus, it is necessary to predict accurately the bearing performance in a design stage. A thermoelastohydrodynamic lubrication (TEHL) analysis could theoretically predict the bearing performance under these harsh conditions with high reliability. In order to clarify the validity of the theoretical TEHL model, a rig test was conducted under dynamic load conditions. The test conditions simulated the connecting rod bearings in real aut...