Mechanical behaviors of cross roller bearings with raceway roundness error

Taking the raceway roundness error into account,mechanical characteristics of cross roller bearings(CRBs)were investigated.A static analysis model of CRBs considering the raceway roundness error was established.Based on this model,the rotational accuracy and load distribution of CRBs under constraints of geometry and external loads were derived.The fatigue life of CRBs with roundness error was calculated by applying Palmgren-Miner linear cumulative damage theory.The influence of inner and outer raceway roundness error on the performance of the CRBs,such as rotational accuracy,load distribution,and fatigue life,was studied through the analysis of examples.The results indicate that the influence of roundness error on the rotating inner raceway is more significant than that of roundness error on the nonrotating outer raceway.The roundness error on the rotating inner raceway always degrades the performance of CRBs.However,a proper roundness error on the nonrotating outer raceway can reduce the loads acting on the rollers and thus improve the fatigue life of CRBs.The effect of the roundness error amplitude on the bearing performance is ordinal,whereas the effect of the roundness order on the bearing performance is not in order.

Roundness error evaluation by minimum zone circle via microscope inspection

Utilizing the convex hull theory, a novel minimum zone circle （MZC） method, named im- proved minimum zone circle （IMZC） was developed in this paper. There were three steps for IMZC to evaluate the roundness error. Firstly, with the convex hull algorithm, data points on the circle contour were categorized into two sets to determine two concentric circles which contained all points of the contour. Secondly, vertexes of the minimum circumscribed circle and the maximum inscribed circle were found out from the previously determined two sets, and then four tangent points for de- termining the two concentric circles were also found out. Lastly, according to the evaluation using the MZC method, the roundness error was figured out. In this paper l IMZC was used to evaluate roundness errors of some micro parts. The evaluation results showed that the measurement precision using the IMZC method was higher than the least squared circle （LSC） method for the same set of data points, and IMZC had the same accuracy as the traditional MZC but dramatically shortened com- putation time. The computation time of IMZC was 6. 89% of the traditional MZC.

On-Line Measurement Method for Diameter and Roundness Error of Balls

This paper presents an on-line measurement method for the diameter and roundness error of balls.An easy-installation rotary scanning system,which integrates the principles of the diameter and the roundness measurements,is constructed.The rotary scanning system consists of a rotary stage,a linear stage,and two sensors with a什at probe.Two sensors are initially installed on the linear stage and contact each other.The outputs of two sensors are reset to zero at first.The ball is then mounted on the rotary stage and positioned between two flat probes.The variations of the diameter and the roundness error of the ball at each angular position can be directly recorded by two sensors when the ball is rotated by the rotary stage.Substituting the outputs of two sensors into the proposed mathematical models,the diameter and roundness error can be evaluated.The effects of the alignment error induced by the spindle error of the rotary stage and the titling error and the eccentric error of the ball on the measurement accuracy can be self-separated in the proposed on-line measurement method.A series of experiments are carried out to verify the effectiveness and the capability of the proposed on-line measurement method and the designed rotary scanning system.The designed system is easy to construct both in the laboratory environment and the factory field.

Vibration analysis of a single row angular contact ball bearing with the coupling errors including the surface roundness and waviness

Roundness and surface waviness are main manufacturing errors on the components of single row angular contact ball bearings(ACBBs).An analytical study for vibrations of the ACBBs with coupling errors including the roundness and waviness can be useful for the vibration control of the rotating machinery.However,most previous works only focused on the single error modelling method.In this paper,an improved time dependent displacement excitation(TDDE)model is proposed to consider the coupling errors including the roundness and waviness on the inner and outer races of an ACBB.The TDDE model for the roundness and waviness is established by using a combination of several sinusoidal functions.A dynamic model in the previous study is improved to consider the influences of coupling errors including the roundness and waviness.The Hertzian contact theory and Dowson’s method are adopted to calculate the bearing contact stiffness.The time-and frequency-domain vibrations for the experimental and simulation results are compared to show some model validation.The influences of roundness orders and waviness amplitudes on the vibrations of the ACBB are analysed.The obtained results show that the coupling errors including the roundness and waviness have some influence on the time-domain impulse waveform and frequency-domain spectrum characteristics of the bearing accelerations.The differences of the vibrations between the coupling errors and sing error are from 4%to 42%.This paper can provide a useful guidance for the accurate diagnosis of surface imperfections in the ACBBs.

Rounded Data Analysis Based on Multi-Layer Ranked Set Sampling

Observations of sampling are often subject to rounding, but are modeled as though they were unrounded. This paper examines the impact of rounding errors on parameter estimation with multi-layer ranked set sampling. It shows that the rounding errors seriously distort the behavior of covariance matrix estimate, and lead to inconsistent estimation. Taking this into account, we present a new approach to implement the estimation for this model, and further establish the strong consistency and asymptotic normality of the proposed estimators. Simulation experiments show that our estimates based on rounded multi-layer ranked set sampling are always more efficient than those based on rounded simple random sampling.