A Physically Consistent Model for Forced Torsional Vibrations of Automotive Driveshafts

The aim of this research was to design a physically consistent model for the forced torsional vibrations of automotive driveshafts that considered aspects of the following phenomena: excitation due to the transmission of the combustion engine through the gearbox, excitation due to the road geometry, the quasi-isometry of the automotive driveshaft, the effect of nonuniformity of the inertial moment with respect to the longitudinal axis of the tulip–tripod joint and of the bowl–balls–inner race joint, the torsional rigidity, and the torsional damping of each joint. To resolve the equations of motion describing the forced torsional nonlinear parametric vibrations of automotive driveshafts, a variational approach that involves Hamilton’s principle was used, which considers the isometric nonuniformity, where it is known that the joints of automotive driveshafts are quasi-isometric in terms of the twist angle, even if, in general, they are considered CVJs (constant velocity joints). This effect realizes the link between the terms for the torsional vibrations between the elements of the driveshaft: tripode–tulip, midshaft, and bowl–balls–inner race joint elements. The induced torsional loads (as gearbox torsional moments that enter the driveshaft through the tulip axis) can be of harmonic type, while the reactive torsional loads (as reactive torsional moments that enter the driveshaft through the bowl axis) are impulsive. These effects induce the resulting nonlinear dynamic behavior. Also considered was the effect of nonuniformity on the axial moment of inertia of the tripod–tulip element as well as on the axial moment of inertia of the bowl–balls–inner race joint element, that vary with the twist angle of each element. This effect induces parametric dynamic behavior. Moreover, the torsional rigidity was taken into consideration, as was the torsional damping for each joint of the driveshaft: tripod–joint and bowl–balls–inner race joint. This approach was used to obtain a system of equations of nonlinear partial derivatives that describes the torsional vibrations of the driveshaft as nonlinear parametric dynamic behavior. This model was used to compute variation in the natural frequencies of torsion in the global tulip (a given imposed geometry) using the angle between the tulip–midshaft for an automotive driveshaft designed for heavy-duty SUVs as well as the characteristic amplitude frequency in the region of principal parametric resonance together the method of harmonic balance for the steady-state forced torsional nonlinear vibration of the driveshaft. This model of dynamic behavior for the driveshaft can be used during the early stages of design as well in predicting the durability of automotive driveshafts. In addition, it is important that this model be added in the design algorithm for predicting the comfort elements of the automotive environment to adequately account for this kind of dynamic behavior that induces excitations in the car structure.

Analytical Investigation of Roller Skew and Tilt in a Spherical Roller Bearing

The objective of this investigation was to analytically investigate the performance of a spherical roller bearing operating under various loading and speed combinations. In order to achieve the objective, a full six degree of freedom spherical roller bearing dynamic model was developed. The model was corroborated with results in open literature. An adaptive slicing method was developed to optimize the accuracy and computational effort of the roller force, skew, and tilt calculations. A comprehensive roller-race contact analysis in terms of slip velocity and contact area was then carried out to identify how bearing load and inner race speed variations change slip velocity and skew at the roller-race contact. The results from this investigation demonstrate that roller skew increases with inner race speed, while the roller tilt remains relatively constant. The inner race speed and roller slip velocity correlate well, which causes the traction force to increase and therefore produce greater skew. Skew and tilt angles also increase with applied axial load. However, at a certain load the skew angle begins to decrease.

Vibration Characteristics Diagnosis and Estimation of Fault Sizes in Rolling Contact Bearings: A Model Based Approach

A novel model based technique is presented in this paper for the estimation of the fault size in different components of rolling contact bearings. A detailed dimensional analysis of the problem is carried out and experimental methodology using Box-Behnken design is applied to generate the experimental data set. First, analysis of the vibration acceleration amplitude at the fault frequency, its dependence on the bearing operating and fault parameters using the obtained vibration data set is carried out by statistical analysis of variance. Numerical equations are developed then using the experimental data set for the correlation of the vibration acceleration amplitude in frequency domain with the fault sizes based on the developed dimensionless terms. A hybrid Back propagation neural network integrating genetic algorithms is also developed so as to check the computational performance of the developed model equations. Validation of the proposed method is carried experimentally also for three seeded defect sizes on outer race, inner race and rolling element. The maximum model accuracy observed is for inner race defect case with predictive accuracy of 99.44 percentage and for the roller defect case it is 98.77 percentage. The deviance observed for the model predictive performance is maximum for outer race defect case with least accuracy of 90.47 percentage amongst all.

Numerical investigation of the oil–air distribution inside ball bearings with under-race lubrication

Oil distribution inside the under-race lubricated bearing is crucial for lubrication and cooling of high-speed ball bearings. An under-race lubricated ball bearing is modeled to numerically investigate the effects of operating parameters and feed hole configuration on the distribution behavior of lubricant oil. The results of the numerical simulation indicate that the average oil volume fraction changes with a convex trend as the outer race rotating speed increases, while it changes monotonically with the inner race rotating speed, oil volume flow rate, and oil temperature. The extent of oil spreading on the outer race, cage, ball, and inner race decreases successively. Optimizing the feed hole configuration according to the average oil volume fraction is helpful to achieve precise lubrication of the under-race lubricated ball bearing.

An exploration of frictional and vibrational behaviors of textured deep groove ball bearing in the vicinity of requisite minimum load

In case of lightly loaded radial ball bearings, failure mechanisms other than fatigue such as smearing of raceways due to increased frictional torque and vibrations often prevail. Hence, attempts have been made herein for reducing the frictional torque and minimizing the vibrations of a radial deep groove ball bearing employing surface textures at the inner race. Nanosecond pulsed laser was used to create texture (involving micro-dimples having different dimple area density) on the inner race of test bearings. Using an in-house developed test rig, frictional torque and vibrational parameters were measured at different speeds and light loads (i.e. in vicinity of 0.01C, where C is dynamic load capacity of radial ball bearing). Significant reduction in frictional torque and overall vibrations were found in the presence of micro-dimples on inner race at light loads irrespective of operating speeds. Even without satisfying the minimum load needed criteria for the satisfactory operation, substantial reduction in smearing marks was found on the races of textured ball bearings in comparison to conventional cases.

A comparative study of the vibration characteristics of railway vehicle axlebox bearings with inner/outer race faults

Increasing service time makes the axlebox bearing of railway vehicle vulnerable to develop a fault in inner or outer races, which can cause some serious adverse effects on a railway vehicle’s safe operation. To tackle this problem, we established a railway vehicle vertical-longitudinal dynamic model with inner/outer races faults of axlebox bearing and validated it by experimental data. We utilized the time-synchronous average (TSA) technology to filter the raw signals and studied their vibration features. The results show that the longitudinal vibration features are more sensitive for inner race fault identification, while the vertical vibration features are more suitable for outer race fault identification. For inner race fault identification, the indicator peak-to-peak value (PPV) that increases 1056% relative to the healthy state at the most severe fault performs the best sensitivity. For outer race fault identification, the indicator skewness value (SV) that increases 518% relative to the healthy state at the most severe fault exhibits the best performance. The research work can provide meaningful guidance for accurate diagnosis of axlebox bearing faults of railway vehicles.