23rd International Colloquium Tribology - January 2022 385 Investigation of the Ball Motion Behavior in Spindle Bearings under Dynamic Loads Hans-Martin Eckel Laboratory of Machine Tools and Production Engineering (WZL) of RWTH Aachen University, Aachen, Germany Corresponding author: h.eckel@wzl.rwth-aachen.de Christian Brecher Laboratory of Machine Tools and Production Engineering (WZL) of RWTH Aachen University, Aachen, Germany Stephan Neus Laboratory of Machine Tools and Production Engineering (WZL) of RWTH Aachen University, Aachen, Germany 1. Introduction In case of high-speed applications, bearings are subjected to a complex static and dynamic load conditions. Typical excitation sources are cutter edge engagements during machining or tooth engagements in gears. Under the influence of radial forces and moment loads, a modulation of the balls orbital velocity around the bearing axis occurs. The result is a leading and trailing motion of the balls in the cage pockets, the so-called ball advance and ball retardation (BaBr). If this value exceeds the clearance of the balls, formed by their clearances in the cage pockets and the cage guidance, significant contact forces arise between balls and cage. The risk of a cage and bearing failure increases. The motions of the balls cannot be described unambiguously with analytic kinematic formulas. It is subject to the load-dependent friction condition in the rolling contacts. Even under static loads, common calculation approaches show completely different ball kinematics. So far, experimentally validated results under dynamic load at high speeds are not available. 2. Ball kinematics A rolling and drilling motion occurs superimposed at the inner and outer rolling contact at high speeds and loads. The ratio of these motions influences the ball pitch angle with which the ball rotates around the bearing axis. In the influence of different kinematic hypotheses on the axial bearing stiffness and the pitch angle is calculated. The most common hypotheses are the innerand outer-race control (IRC/ ORC). At high speeds, the calculated pitch angles and thus the orbital velocity of the balls differ significantly between the hypotheses. In the operating behavior of rolling bearings under dynamic load is investigated. Calculations for a deep groove ball bearing (size 6220) at 1,000 rpm show that a significant change in ball rotational speed occurs only under axial load. In the stress of the cage caused by the BaBr under static loads is investigated for a deep groove ball bearing (size 6310) in the speed range up to 1,600 rpm. For higher speeds, presents a system for measuring the ball and cage motions by means of high-speed videography, results at radial load are not given. 3. Test Equipment and measuring method The metrological investigations under dynamic load are carried out on the test stand already presented in for the investigation of ball kinematics under static loads and high speeds (30,000 rpm), extended by a dynamic actuation system (Figure 1). The test bearing of size 7014 in hybrid design is elastically preloaded with a second spindle bearing with 1,000 N in an O-arrangement. The contact angle is 19°, the pitch circle diameter 90 mm and the ball diameter 11.906 mm. A photoelectric measuring system records the ball positions. For this purpose, the bearing is illuminated by 21 LED between the inner ring and the cage. Opposite to the LED mounted photodetectors detect the light signals that are intermittently blocked by the balls. 386 23rd International Colloquium Tribology - January 2022 Investigation of the Ball Motion Behavior in Spindle Bearings under Dynamic Loads Figure 1: Test bench for dynamic bearing excitation Two preloaded piezoelectric actuators with a relative angle of 90° generate the dynamic forces. The forces are applied via a load unit, which decouples the rotation of the spindle shaft with another bearing, into the shaft. The actuators are coupled to the load unit with specially developed solid-state joints with applied strain gauges, so that tensile and compressive forces can be applied with high amplitudes. 4. Results Measurements at stationary, static loads are the basis to understand the balls behavior under dynamic load. Figure 2 shows the measured deviations of a ball along the bearing circumference for different radial forces and speeds. The load acts in the direction of 0° and the ball position is equal to the direction of cage rotation. The modulation of the ball movement at 1,000 N is small and rises with increasing speed. A trailing deviation builds up after the load zone, which kinematically corresponds to an predominant ORC. At 2,000 N, a strong modulation occurs in the middle speed range, where the balls show a leading motion after the load zone. This behavior indicates a predominant IRC. Figure 2: Measured deviations of orbital ball motion The BaBr reaches significant values above a certain radial force at which a high deviation of the contact angles occurs between the inner and outer rolling contacts. Above this force, the BaBr increases progressively with increasing load. Under high dynamic loads, load conditions can arise within a force period, which, according to the results under static load, cause a slight and a strong increased modulation of the ball velocities. The interaction of dynamic and static force components is relevant for the formation of the BaBr. Figure 3 shows the measured BaBr values for four static load conditions with superimposed dynamic, stationary loading with harmonics of the shaft rotation frequency. In the purely alternating load case (F stat = 0 N), no significant BaBr appears at any load case. Figure 3: BaBr under dynamic load at 12,000 rpm The BaBr reaches higher values only under the influence of static force components. In the range of medium static force, the highest BaBr values are found with a dynamic excitation at the rotational frequency. A significant increase of the BaBr due to increased excitation frequencies does not occur. The BaBr is saturated at the load case with F stat = 2,000 N, where the dynamic loading has no influence. In the case of dynamic load, the relative position of the ball to the acting force determines the load and thus the kinematics. A recurring load on the ball over the bearing circumference, as in the static case, does not occur due to the odd cage speed. In the case of an unbalanced load, the balls experience a smaller change in load due to the rotating force over a larger angle of rotation of the cage. As an extreme example, Figure 4 shows the deviations of the ball motions with circulating forces of 250 N dynamic amplitude corresponding to the cage and shaft rotational frequencies. In the case of the cage rotational frequency, the load condition for a ball remains constant over a long period of time, so that individual balls build up a very high leading or trailing deviation. In contrast, the dynamic excitation at rotational frequency shows low BaBr values. 23rd International Colloquium Tribology - January 2022 387 Investigation of the Ball Motion Behavior in Spindle Bearings under Dynamic Loads Figure 4: BaBr with circulating forces 5. Conclusion The results show, that contrary to previous assumptions, high speeds and high load forces are not necessarily critical for high BaBr values. Dynamic forces with harmonics of the shaft rotational frequency do not cause a significant increase in BaBr. A purely unbalanced load does not lead to critical BaBr values. A dynamic load with the rotational frequency increases BaBr values only under the influence of a static force component. 6. Acknowledgement Supported by Federal Ministry for Economic Affairs and Energy on the basis of a decision by the German Bundestag. The authors would like to thank the German Federation of Industrial Research Associations (AiF) and the German Machine Tool Builders’ Association (VDW) for financial support of the project 21640 N/ 1. References [1] Noel, D.; Ritou, M.; Furet, B.; Le Loch, S.: Complete Analytical Expression of the Stiffness Matrix of Angular Contact Ball Bearings. In: Journal of Tribology. 135. Jg., 2013, Nr. 4 [2] FVA: Einfluss von Vibrationsanregung auf Wälzlager. Abschlussbericht zum Forschungsvorhaben Nr. 589 I, 2014. [3] Kakuta, K.: The Effects of Misalignment on the Forces Acting on the Retainer of Ball Bearings. In: Journal of Basis Engineering, 1964, Nr. 86. S. 449-456 [4] Holland, L.: Analyse des Bewegungsverhaltens der Komponenten in Spindellagern mittels Hochgeschwindigkeitsvideographie. Dissertation Technische Hochschule Darmstadt, 2018 [5] Brecher, C.; Eckel, H.-M.; Fey, M.; Neus, S.: Measuring the Kinematic Behavior of the Rolling Elements in a Spindle Bearing under Axial and Radial Loads. In: Bearing World Journal. 2020, S. 159- 167