“…It also demonstrates that the fluctuation of wear rates decreases with the increasing axial load, which is probably due to the larger contact stiffness. 29 Figure 4.Ball-bearing wear characteristics for one ball against both raceways with different axial load ( F a = 500 N/1000 N, n i = 3600 r/min): (a) outer raceway wear under F a = 500 N, (b) inner raceway wear under F a = 500 N, (c) outer raceway wear under F a = 1000 N and (d) inner raceway wear under F a = 1000 N.…”
Section: Resultsmentioning
confidence: 99%
“…This fluctuation comparison is the same law as vibration and torque properties discussed before. 29 Figure 8(c) and (d) shows the wear characteristics for outer waviness order of 2, and inner waviness order of 1 with both waviness amplitude of 0.5 µm. It can be observed that the wear form is approximately coincident with that when outer waviness order equals 2 (Figure 7(a) and (b)), thus the effect of inner waviness order of 1 (usually from the rotor unbalance) on the raceway wear is tiny.…”
Section: Resultsmentioning
confidence: 99%
“…The wavy surface of both raceways can be assumed to waviness on YZ-plane which characterized as simple harmonic variation as shown in Figure 2(b). 29,30 Figure 2.Ball-bearing movements in the inertial system of O-XYZ: (a) 3D translational movements of the inner race centroid due to the applied loads and (b) raceway waviness model.…”
Section: Model and Methodsmentioning
confidence: 99%
“…These transient movements of the inner race and every ball are evaluated with suitable coordinate systems depending on the features. 26,29…”
Section: Model and Methodsmentioning
confidence: 99%
“…Subsequently, the variable step-size Runge–Kutta scheme of fourth-order is used for the solution of the differential equations. 26,29 Finally, once the iterative simulation is finished under the convergence criteria with an error limit of 10 −4 , the dynamic response characteristics and the dynamic wear of each bearing element can be obtained.…”
A dynamic contact wear model of ball bearings consisting of wear degree and position distribution is proposed by integrating the developed contact wear model, multi-body dynamics and raceway waviness or ball diameter differences. Subsequently, the dynamic wear characteristics, not only for the ideal bearing under different axial and radial loads, but also for the bearing with above defects are analysed. The influences of load, typical waviness orders and amplitude on the wear of each ball against both raceways are evaluated and qualitatively validated. Finally, the dynamic characteristics of ball bearings with one ball larger are discussed, and then vibration frequency and wear rates distinction are verified by the experiment with working-surface roughness measurement as a way for wear rate assessment.
“…It also demonstrates that the fluctuation of wear rates decreases with the increasing axial load, which is probably due to the larger contact stiffness. 29 Figure 4.Ball-bearing wear characteristics for one ball against both raceways with different axial load ( F a = 500 N/1000 N, n i = 3600 r/min): (a) outer raceway wear under F a = 500 N, (b) inner raceway wear under F a = 500 N, (c) outer raceway wear under F a = 1000 N and (d) inner raceway wear under F a = 1000 N.…”
Section: Resultsmentioning
confidence: 99%
“…This fluctuation comparison is the same law as vibration and torque properties discussed before. 29 Figure 8(c) and (d) shows the wear characteristics for outer waviness order of 2, and inner waviness order of 1 with both waviness amplitude of 0.5 µm. It can be observed that the wear form is approximately coincident with that when outer waviness order equals 2 (Figure 7(a) and (b)), thus the effect of inner waviness order of 1 (usually from the rotor unbalance) on the raceway wear is tiny.…”
Section: Resultsmentioning
confidence: 99%
“…The wavy surface of both raceways can be assumed to waviness on YZ-plane which characterized as simple harmonic variation as shown in Figure 2(b). 29,30 Figure 2.Ball-bearing movements in the inertial system of O-XYZ: (a) 3D translational movements of the inner race centroid due to the applied loads and (b) raceway waviness model.…”
Section: Model and Methodsmentioning
confidence: 99%
“…These transient movements of the inner race and every ball are evaluated with suitable coordinate systems depending on the features. 26,29…”
Section: Model and Methodsmentioning
confidence: 99%
“…Subsequently, the variable step-size Runge–Kutta scheme of fourth-order is used for the solution of the differential equations. 26,29 Finally, once the iterative simulation is finished under the convergence criteria with an error limit of 10 −4 , the dynamic response characteristics and the dynamic wear of each bearing element can be obtained.…”
A dynamic contact wear model of ball bearings consisting of wear degree and position distribution is proposed by integrating the developed contact wear model, multi-body dynamics and raceway waviness or ball diameter differences. Subsequently, the dynamic wear characteristics, not only for the ideal bearing under different axial and radial loads, but also for the bearing with above defects are analysed. The influences of load, typical waviness orders and amplitude on the wear of each ball against both raceways are evaluated and qualitatively validated. Finally, the dynamic characteristics of ball bearings with one ball larger are discussed, and then vibration frequency and wear rates distinction are verified by the experiment with working-surface roughness measurement as a way for wear rate assessment.
Forced cooling, as an efficient way of heat dissipation, significantly affects the spindle temperature. Although a full cooling passage was factored into the finite element analyses by some scholars, often only the model for the front or rear half of a spindle is need for the purpose of the thermal evaluation simplification and data overhead reduction in engineering applications. So far, how the coolant passage affects the heat dissipation of the front or rear half of a spindle has not been well characterized. This paper devotes to constructing a scaling factor to represent the coolant unit effect on the thermal growth of spindles. The experiments about the effect of coolant units on spindle temperature were first implemented, and then the qualitative conclusions were got with various coolant parameter settings. To further quantify these influences, the regressive analysis was carried out. As a result, the peak temperature area was found and the scaling factors were proposed to describe the effect of the cooling system on the front or rear half of spindle temperature. In this process, the thermal equivalent convection for coolant passage was modeled based on the thermal resistance theory. In the meantime, we planned a novel thermal network of a motored spindle for contrast and validation, in which the cooling mechanism was integrated, and the structural constraints were considered by the aid of the proposed scaling factors. The result is indicative of a better agreement with real values when employing the proposed model.
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