Dun Lu

Effects of Rolling Bearing Type and Size on the Maximum Eccentricity Ratio of Hydrodynamic Rolling Hybrid Bearings

A hydrodynamic rolling hybrid bearing (HRHB) composed of a rolling bearing with a fixed clearance and a hydrodynamic bearing is developed to solve the wear problem in hydrodynamic bearings. In this study, the maximum eccentricity ratio is developed to assess the protection of the rolling bearing offers to the hydrodynamic bearing. An analytic model for the maximum eccentricity ratio is presented. The effects of the size of the ball bearing and cylindrical roller bearing on the maximum eccentricity ratio are investigated. The results show that the maximum eccentricity ratio is affected by the clearance constraint and contact deformation of the rolling bearing. The maximum eccentricity ratio presents itself at zero speed, at which the rolling bearing reaction is equal to the external load. The results also show that the type of rolling bearing has significant effects on the maximum eccentricity ratio. The increment of the maximum eccentricity ratio due to elastic deformation of ball bearings is about 8.6 times the increment due to elastic deformation of cylindrical roller bearings. In comparison, the size of the rolling bearing of the same type has a slight influence on the maximum eccentricity ratio. The maximum eccentricity ratio is a key parameter related to antiwear. When the maximum eccentricity ratio is smaller than the allowable value of the hydrodynamic bearing, direct contact between the hydrodynamic bearing and rotor can be avoided and the wear in the hydrodynamic bearing can thus be prevented by the rolling bearing.

Cage Speed of Hydrodynamic Rolling Hybrid Bearings

Hydrodynamic bearings are subjected to wear during starts and stops due to the absence of sufficient film pressure to effect complete separation of the sliding surfaces. In an earlier publication, our group reported the development of a new hydrodynamic rolling hybrid bearing (HRHB) to overcome the wear problem in hydrodynamic bearings. In the configuration, the transition of operation modes between the rolling bearing supporting state and the hydrodynamic bearing supporting state was realized by the clearance of the rolling bearing. Here we report on the development of a method to identify the operation modes for HRHBs based on monitoring the cage speed of the rolling bearing. The variation of cage speed with the shaft speed is measured. The effects of external load and starting time on the cage speed are also investigated experimentally. The results show that variation in the cage speed reflects changes in the load on the rolling bearing, as well as the operation modes of the HRHBs. With increases in the shaft speed, the variation in the cage speed presents three stages: the increasing stage, the decreasing stage, and the stationary stage. In the first two stages, the HRHB works at the rolling bearing supporting state while in stationary stage, the HRHB works at the hydrodynamic bearing supporting state. In additions to its property of no wear sufferance during starts and stops, compared to hydrodynamic bearings there is little risk of catastrophic failure with HRHBs during any interruption to the lubricant supply and compared to rolling bearings there is no fatigue failure. Therefore this hybrid design is useful at very high speeds.

Effect of the screw–nut joint stiffness on the position-dependent dynamics of a vertical ball screw feed system without counterweight

The study on the position-dependent dynamic characteristics of a vertical ball screw feed system without counterweight is an important step in the enhancement of the structural performance of mini-type vertical milling machines. The ball screw is generally driven by a servomotor, which converts a rotary motion into a linear motion through a screw–nut pair. To assess the position-dependent dynamic characteristics of a vertical ball screw feed system subjected to the influence of the screw–nut joint stiffness, a variable-coefficient lumped parameter model of the system is developed. This model is established taking into account the screw–nut joint stiffness under three different strategies: (1) considering the preload and the weight of the spindle system, (2) considering the elastic deformation but ignoring the effect of the weight, and (3) a perfectly rigid model. The differences between the three models in predicting the position-dependent dynamic characteristics of the system are compared, revealing that the stiffness of screw–nut joint greatly affects the vibratory behavior of the spindle system in the transmission direction. A set of conducted experimental results demonstrate that the stiffness model under the preload and the weight of the spindle system is the most accurate model for the prediction of the position-dependent natural frequency and displacement response of the system with the spindle system position. Therefore, it is more suitable for structure design, performance simulation, and evaluation of a vertical ball screw feed system without counterweight.

A parametric modeling method for the pose-dependent dynamics of bi-rotary milling head

Bi-rotary milling head is one of the core components of five-axis machining center, and its dynamic characteristics directly affect the machining stability and accuracy. During the sculptured surface machining, the bi-rotary milling head exhibits varying dynamics in various machining postures. To facilitate rapid evaluation of the dynamic behavior of the bi-rotary milling head within the whole workspace, this article presents a method for parametrically establishing dynamic equation at different postures. The rotating and swing shafts are treated as rigid bodies. The varying stiffness of the flexible joints (such as bearings and hirth coupling) affected by gravity and cutting force at different swing angles is analyzed and then a multi-rigid-body dynamic model of the bi-rotary milling head considering the pose-varying joint stiffness is established. The Lagrangian method is employed to deduce the parametric dynamic equation with posture parameters. The static stiffness, natural frequencies and frequency response functions at different postures are simulated using the parametric equation and verified by the impact testing experiments. The theoretical and experimental results show that the dynamics of the bi-rotary milling head vary with the machining postures, and the proposed method can be used for efficient and accurate evaluation of the pose-dependent dynamics at the design stage.

Effect of tilting angle on the dynamics of tilting table driven by worm and worm wheel

The dynamics of tilting table behaves differently during five-axis machining due to the constant changes of the position of its center of mass which leads to different forces acting on parts of the transmission system. In this research, the lumped parameter method is used to model the dynamics of tilting table driven by worm and worm wheel in the tilting direction, where the varying stiffness of the transmission system at different tilting angles is considered. The impact testing experiments of tilting table system with tilting angles from 0° to 90° are also performed to verify the analytical model. The results from sensitivity analysis show that the three stiffnesses have a great effect on the variation of system natural frequency in the tilting direction, including the equivalent tangential meshing stiffness of worm and worm wheel, the torsional stiffness of worm wheel shaft, and the axial stiffness of worm supporting bearings. Moreover, the variations of system natural frequency with the three stiffnesses at different tilting angles are further investigated.

Analysis on steady-state vibration induced by backlash in machine tool rotary table

This paper presents a mathematical model of a machine tool rotary table with backlash to describe the dynamic behavior of the mechanical system and the motion controller. The accuracy of this model is verified by experiments. The steady-state vibration under different conditions is simulated to investigate its mechanism and change rule. The results show that the steady-state vibration is attributed to the alternate impact of transmission components. Based on the different performances of the steady-state vibration for different control gains and different motion directions, the concept of stability region in the plane of control gains is presented. In the critical region, the steady-state vibration only occurs when the table moves toward backlash. The complex contact regimes may lead to a significant increase in the amplitude of the steady-state vibration. Besides, the influences of the load and the magnitude of backlash on the steady-state vibration and the stability region are also discussed.

The maximum dynamic eccentricity ratio of hydrodynamic rolling hybrid bearings

Hydrodynamic Rolling Hybrid Bearing (HRHB) is dual bearings combination where a hydrodynamic bearing and a rolling bearing with a clearance are assembled coaxially and side by side. The clearance of rolling bearing is a significant parameter for HRHBs. This paper aims to investigate the vibration characteristics of rotor supported by HRHBs to determine the permissible value of clearance of rolling bearing. The maximum dynamic eccentricity ratio is proposed based on the noninterference conditions of rolling bearing and rotor. Then an evaluation method of the maximum dynamic eccentricity ratio is developed. This paper also investigates the effects of the operation parameters such as rotational speed, perturbed force and structure parameters such as bearing span, diameter of rotor, and overhanging length on the maximum dynamic eccentricity ratio. The maximum dynamic eccentricity ratio on the front rolling bearing section is obviously larger than that on the back rolling bearing section. Moreover, the maximum dynamic eccentricity ratio reduces with the increase of the rotational speed and diameter of rotor, but increases with the augmentation of the perturbed force, bearing span, and overhanging length. When the maximum dynamic eccentricity does not go beyond the bound of the radius of the rolling bearing’s clearance circle, the rolling bearing does not interfere with the rotor. The paper provides theoretical basis for design of the minimum value of the rolling bearing’s clearance in HRHBs.

The Maximum Allowable Misalignment in Hydrodynamic Rolling Hybrid Bearings

A hydrodynamic rolling hybrid bearing (HRHB) assembled coaxially by a rolling bearing and hydrodynamic bearing is developed to achieve two functions at low and high speeds. At low speeds, the rolling bearing of the HRHB can be utilized to avoid wear in the hydrodynamic bearing. While at high speeds, the rotor is entirely supported by the hydrodynamic bearing, keeping away the interference of the rolling bearing. However, because the HRHB is mounted coaxially by two bearings, a misalignment cannot be avoided. This can lead two unexpected consequences: either the malfunction of the rolling bearing at low speeds or the interference of rolling bearing applied on the rotor. In this paper, a computational method to calculate the maximum allowable misalignment based on the noninterference conditions of the locus of the shaft center and rolling bearing at high speeds is proposed, and the influence of the rotating speed, the spindle, and bearing structural parameters on the maximum allowable misalignment is also analyzed. The results show that the locus of the maximum allowable misalignment forms a circle along the circumferential direction. The noninterference conditions are satisfied when the maximum allowable misalignment is inside the circle.

Effects of Parallel Misalignment on Performance of Hydrodynamic-Rolling Hybrid Bearing

A hydrodynamic-rolling hybrid bearing (HRHB) arranged in parallel is introduced, in which the radial clearance of rolling bearing is used to prevent the rotor and hydrodynamic bearing from contacting during starts and stops. The aim of this study is to investigate the effects of rolling bearing misalignment on performance of HRHB for providing a design guide of machining and assembling tolerance. An analytic model is developed to predict the static performance of HRHBs with a misalignment. The misalignment is represented as an offset and an include angle. Taking the misalignment into account, a force balance equation about oil film force, rolling bearing reaction and external load is derived. The effects of the misalignment on the locus of equilibrium position, the maximum eccentricity, and the transition speed are investigated. The results show that misalignment has significant influences on performance of HRHBs, but there are regions of included angle which are insensitive to the performance of HRHBs; according to the insensitive regions, requirement of alignment errors, machining and concentricity tolerance can be determined; distinct from conventional hydrodynamic bearings, the locus of equilibrium positions of misaligned HRHBs have three variation modes of monotone decreasing, monotone increasing, and increasing first and decreasing afterwards; the monotone decreasing mode of conventional hydrodynamic is not suitable for HRHBs below transition speed; and before the maximum eccentricity ratio, the variation mode of equilibrium positions locus should be determined.Copyright