Rolling bearings are important mechanical parts commonly used in complex mechanisms, such as aircraft gas turbines, precision machine tools, disks, and gyroscopes. The rotational accuracy of an assembled bearing directly impacts the working accuracy of the mechanical equipment1,2. In manufacturing, the dynamic action and accuracy of the machine tool spindle will always introduce some degree of error into the bearing components. This roundness error is a critical factor in the motion error3 and must be studied to further improve the rotational accuracy of roller bearings.

Previous research on the rotational accuracy of rolling bearings mainly focused on the radial run-out. Bhateja et al.4 proposed a method for calculating the run-out of hollow roller bearings and studied the resultant components of the run-out from the geometric and dimensional errors in the rollers and raceways. Chen et al.5,6 proposed a method for calculating the radial run-out and static load distribution of cylindrical roller bearings and analyzed the effects of the roundness errors in the raceways and diameter differences of the rollers on the radial run-out and load distribution.

In the previous research in this series, Yu et al.7,8 proposed a method for calculating the radial run-out of the inner ring and analyzed the effects of the form error in the inner raceway and roller number on the radial run-out of cylindrical roller bearings. Yu et al.9, Li et al.10, and Liu et al.11 proposed a method for calculating the radial run-out of the outer ring considering roundness error of the outer raceway and investigated the influences of the roundness error, roller number, and radial clearance on the radial run-out in cylindrical roller bearings. Yu et al.12 proposed and experimentally verified a method for calculating the orbit of the outer ring center considering the geometric errors of the bearing components.

Researchers have also studied the influence of the component geometric error on the non-repetitive run-out (NRRO) and shaft axis orbit. Noguchi et al.13,14,15,16,17developed a method for calculating the NRRO of ball bearings and theoretically investigated the effects of the ball number and element geometric error on the NRRO. Jang et al.18 analyzed the effect of viscoelastic damping on the NRRO of a ball bearing. Liu et al.19 and Tada et al.20 proposed prediction models for the NRRO of a ball bearing and analyzed the effect of the waviness of the inner groove, the outer groove, balls, and ball number on the NRRO. Ma et al.21 proposed a shaft center orbital method for spherical roller bearings and analyzed the influence of the roller diameter errors on the orbit of the shaft’s center. Okamoto et al.22 presented a calculation model for the ball bearing shaft axis orbit and investigated the influence of the form error, ball number, and ball diameter error on the shaft axis orbit.

Other researchers have investigated the influence of the waviness of the bearing components on the dynamic performance of roller bearings under different operating conditions. Wardle et al.23,24 and Ono et al.25,26 investigated the effect of element waviness on the dynamic performance of ball bearings. Talbot et al.27 investigated the influence of the macrogeometry of bearing components on the load intensities. Harsha et al.28, Wang et al.29, and Gunhee et al.30 analyzed the effect of the raceway and ball waviness on the dynamics of rigid rotor-bearing systems. Xu et al.31,32 and Kankar et al.33 analyzed the influence of waviness and localized defects on the dynamic performance of mechanisms. Shao et al.34 and Wang et al.35 investigated the effect of raceway localized defects on the bearing vibration. Tong et al.36 analyzed the influence of the form error on the tapered roller bearing performance. Petersen et al.37 investigated the influence of local defects and raceway roughness on the dynamics of a double row roller bearing. Podmasteriev38 analyzed the effect of the raceway geometric error on the probability of microcontacts in friction zones.

While there have been studies on the non-repetitive run-out and dynamic performance, there is relatively little research on the rotational accuracy of rolling bearings. Research on the rotational accuracy has mainly focused on the motion error of bearings derived from the combined action of the roller number and component roundness error in the process of rotation. The motion error of the bearing includes the run-out of the rotating ring in the horizontal and vertical directions of the radial plane.

In the current research on the rotational accuracy, many studies have investigated the effect of the component geometric error on the vertical run-out of the rotating ring. The vertical run-out of the rotating ring does not accurately reflect the run-out of the rotating ring in the radial plane, however, because it ignores the horizontal run-out of the rotating ring. We sought to identify the key contributing factors to the motion error of rolling bearings by studying both the influence of the coupling effect of the roller number and the influence of the component roundness errors on the run-out of the rotating ring in the radial plane. A motion error prediction model for cylindrical roller bearings was proposed in the previous paper of this series39 and is briefly described in “Prediction model for rotational accuracy of cylindrical roller bearings” section. The present study will experimentally verify the previously proposed model.