Effects of axial preloading of angular contact ball bearings on the dynamics of a grinding machine spindle system

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Abstract

A mathematical model based on a five degrees of freedom dynamic system is utilized to study the effects of axial preloading of angular contact ball bearings on the vibration behavior of a grinding machine spindle. The grinding forces (as a function of grinding wheel wear rate percentage for five different workpiece materials) were used to simulate external loading on the grinding machine spindle. The results show that the initial axial preload applied on the bearings plays a significant role to reduce the vibration levels of the grinding machine spindle system and consequently results in better accuracy for the finished surfaces. The vibration levels of grinding machine spindle system increases as wheel wear rate percentage increases and/or the hardness of the workpiece material increase. This analysis can be used to calculate the optimum initial axial preload in order to obtain high accuracy for surface finish.

Introduction

The new generation of machine tools needs severe requirements concerning the main spindle design: better assembly, higher operating accuracy, and increased component reliability. It is also known that, the dimensional accuracy and surface finish of a machined part depend upon the dynamic characteristics of the machine tool spindle–bearing–workpiece system. Vibrations induced in the system due to the dynamic forces during metal cutting operations can cause low quality surface finish. A grinding machine spindle is one such system where vibration causes major problems in the grinding process since the depth of cut is small, so that even the slightest amplitude of vibration can have dramatically damaging effects on surface finish, wheel wear, and form-holding. Bearing systems can be one of the major sources of vibration within the grinding machine spindle systems. Ball bearings are used in grinding machine spindles where they involve high speeds, high temperatures, and heavy loadings. Therefore, it is important to fully understand their vibration characteristics when operating in different conditions.

The bearing contact force contains at least four intercoupled components: initial axial preload, thermal preload, external load, and inertial load (e.g., centrifugal forces). Initial axial preload of rolling element bearings is commonly used to obtain high stiffness of machine tool spindle [1], [2]. It is known that the preload appears when an axial (thrust) load is applied to a bearing at the assembly stage. This axial loading compresses the balls and races and one ring will be displaced with respect to the other. When the bearing is preloaded and an additional load is applied, then any additional axial movement of the shaft will be smaller than the case of without preloading. It is clear that a slight preload on the bearing raises the quality of the surface finish of the workpiece significantly, due to the higher grinding accuracy. In practice, the normal procedure for preloading is to adjust two bearings, or two rows of rolling elements against one another by the application of a permanent axial load. Generally, a higher preload would reduce the shaft deflection under the load, but might also decrease the bearing life. Therefore, as stated by Katter and Tu [3], preload should not be higher than necessary for the application but should be sufficient to avoid the preload being completely relieved from any bearing by action of external load. Therefore, a certain minimum preload is necessary to seat all of the balls and insure firm rolling contact. If this level of preload is not reached, balls will intermittently skid and roll and produce cage-ball instability. When this occurs, vibration levels may be one or even two orders of magnitude higher than that normally associated with the bearing [2]. Initial axial preload may also affect the damping characteristics of a spindle assembly, which can be considered critical to minimize chatter problems [4].

Fundamental studies on the effects of preloading bearings on the dynamics of machine tool spindles have received considerable interest in the literature. Harris [1] showed that proper preloading increases the bearings’ service life. Kim and Kim [5] showed experimentally that both initial axial preloading and thermal expansion due to high temperature have significant effect on roundness accuracy in a machining process. Tu and Stein [6] found that preload regulation could be achieved by carefully controlling the circulation of a cooling (or heating) flow around the spindle housing to manipulate the housing and the outer ring temperatures. Jorgensen and Shin [7] showed that thermal expansion increases the contact deformation, which leads to an increase in both contact load and bearing stiffness. Tu and Katter [8] examined the relative magnitudes of the main components of the race/roller contact force, e.g., the bearing initial preload, thermally induced preload and grinding load over an extended period of time. Their results showed that the bearing preload provides a consistent index for monitoring bearing condition with a view toward preventive maintenance. Stein and Tu [9] studied different factors related to monitoring thermally induced preload in anti-friction spindle bearing of high-speed machine tools. They showed that the induced preload is extremely sensitive to the initial value of preload. Furthermore, higher values of initial preload produces higher induced preload and eventually result in thermal instability.

The objective of the present paper is to study the effect of initial axial preload on the vibration behavior of the grinding machine spindle. A five degrees of freedom model is utilized to simulate the dynamical behavior of the grinding machine spindle. The numerical scheme presented by Aini et al. [10] and refined by Alfares and Elsharkawy [11] is implemented in the present study. Malkin’s [12] experimental measurements for the grinding forces as a function of grinding wheel wear rate percentage for five different workpiece materials are used to simulate external loading on the grinding machine spindle.

Section snippets

Mathematical formulation

Fig. 1 shows a schematic representation of a grinding machine spindle supported by a pair of angular contact ball bearings. The bearings are identical and in a back-to-back configuration. The degrees of freedom are three translations (x, y, z) and two rotations (Φ, φ) as shown in the figure. The external grinding forces are acting in the x and y directions. A five degrees of freedom model for the spindle system, which was developed by Aini et al. [10], and refined by Alfares and Elsharkawy [11]

Results and discussion

Table 1 shows the data used in the present study which were taken from [10], [15]. The experimental measurements by Malkin [12] for the grinding forces (Fx and Fy) as a function of grinding wheel wear rate percentage wr (percentage of wheel surface consisting of wear flats) for five different workpiece materials are displayed in Fig. 3. It is clear that as wr increases, the grinding forces increase. Furthermore, the workpiece material has significant effect on the grinding forces. These forces

Conclusions

A mathematical formulation to study the effect of initial axial preload on the vibration behavior of the grinding machine spindle has been presented. The numerical scheme for a five degrees of freedom model presented by Aini et al. [10] and refined by Alfares and Elsharkawy [11] was implemented in the present study. Malkin [12] experimental measurements for the grinding forces as a function of grinding wheel wear rate percentage for five different workpiece materials were used to simulate

Acknowledgements

The authors would like to acknowledge the support of Research Administration, Kuwait University for providing the sufficient funding to carry out the study presented in this paper under grant no. EM 02/01.

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