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Bearing preload significantly affects the running performance of a shaft-bearing system including the fatigue life, wear, and stiffness. Due to the mounting error, the bearing rings are often angularly misaligned. The effects of the combined bearing preload and angular misalignment on the fatigue life of ball bearings and a shaft-bearing system are analyzed in this paper. The contact force distribution of angular contact ball bearings in the shaft-bearing system is investigated based on the system model. The system model includes the bearing model, and the shaft model is verified by comparing with the manufacturer&rsquo, s manual and the results from other theoretical models, with the difference between the results from the present bearing model and manufacturer manual within 3%. The global optimization method is used to replace the Newton&ndash, Raphson algorithm to solve the ball elements&rsquo, displacements and friction coefficients, which improves the computation efficiency of the system model. The fatigue life of each bearing is evaluated with the consideration of the two preload methods and two angular misalignment cases. The fatigue life results show that the system life at the optimal angular misalignment is more than 1.5 times that without angular misalignment at the low preload value, and this ratio decreases as the preload value increases. The optimal angular misalignment of both the shaft-bearing system and the misaligned bearing is not always consistent, which depends on the preload value and bearing life. Both the constant-displacement preload and constant-force preload do not cause a significant difference in the highest system life. The different misaligned bearings can lead to different highest system lives as the preload value is low.

This study was aimed to investigate the machining stability of a spindle tool with different preloaded amount. To this end, the vibration tests were conducted on the spindle unit with different preload to assess the dynamic characteristics and machining stability of the milling machine. Current results demonstrate that the tool tip frequency response characteristics and the machining stabilities in X and Y direction are affected to change due to the different preload of spindle bearings. As found from the results, a high preloaded spindle tool shows higher limited cutting depth at mid position, while a spindle with low preload shows a higher limited depth. This indicates that the machining stability of a milling machine is affected to vary by the spindle unit when it was assembled with different bearing preload., {"references":["E. Abele, Y. Altintas, C. Brecher, \"Machine Tool Spindle Units,\" CIRP\nAnnals – Manufacturing Technology, vol. 59, no. 4, pp. 781–802, 2010.","M. Weck, A. Koch, \"Spindle-bearing systems for high-speed applications\nin machine tools,\" CIRP Annals-Manufacturing Technology, vol. 42, no.\n1, pp. 445–448, 1993.","S. P. Harsha, L. Sandeep, R. E. Prakash. \"Effects of Preload and Number\nof Balls on Nonlinear Dynamic Behaviors of Ball Bearing System,\"\nInternational Journal of Nonlinear Science and Numerical Simulation.\nvol. 4, no. 3, pp. 265-278, 2003.","Y. Cao, Y. Altintas, \"Modeling of Spindle-Bearing and Machine Tool\nSystems for Virtual Simulation of Milling Operations,\" International\nJournal of Machine Tools and Manufacturing. vol. 47, no. 9 pp.\n1342-1350, 2007.","M. A. Alfares, A. A. Elsharkawy. \"Effects of Axial Preloading of Angular\nContact Ball Bearings on the Dynamics of a Grinding Machine Spindle\nSystem,\" Journal of Materials Processing Technology. vol. 136, no. 3, pp.\n48-59, 2003.","S. A. Spiewak, T. Nickel. Vibration Based Preload Estimation in Machine\nTool Spindles, International Journal of Machine Tools & Manufacture.\nvol. 41, no. 4, pp. 567-588, 2001.","A. Gunduz, J. T. Dreyer, R. Singh. \"Effect of Bearing Preloads on the\nModal Characteristics of a Shaft-Bearing Assembly: Experiments on\nDouble Row Angular Contact Ball Bearings,\" Mechanical Systems and\nSignal Processing. vol. 31, pp. 176-195, 2012.","J. Tlusty, .M. Polacek. \"The Stability of Machine Tools Against\nSelf-Excited Vibrations in Machining,\" Trans. ASME, International\nresearch in production engineering. Pp. 465-474, 1963.","S. A.Tobias, W. Fishwick. \"The Chatter of Lathe Tools under Orthogonal\nCutting Conditions\", Trans. ASME, Journal of Engineering for Industry,\nvol. 80, pp. 1079-1088, 1958.\n[10] E. Ozturk, U. Kumar, S. Turner, T. Schmitz. \"Investigation of Spindle\nBearing Preload on Dynamics and Stability Limit in Milling,\" CIRP\nAnnals-Manufacturing Technology. vol. 61, no. 1, pp. 343-346, 2012.\n[11] C. W. Lin, J. F. Tu. \"Model-Based Design of Motorized Spindle Systems\nto Improve Dynamic Performance at High Speeds,\" Journal of\nManufacturing Processes. vol. 9, no. 2, pp. 94-108, 2007.\n[12] S. Jiang, H. Mao. \"Investigation of Variable Optimum Preload for a\nMachine Tool Spindle,\" International Journal of Machine Tools and\nManufacture. vol.50, no. 1, pp. 19-28, 2010.\n[13] S. Jiang, H. Mao. \"Investigation of Variable Optimum Preload for a\nMachine Tool Spindle,\" International Journal of Machine Tools and\nManufacture. vol.50, no. 1, pp. 19-28, 2010.\n[14] Y. Altintas, E. Budak. \"Analytical prediction of stability lobes in\nmilling,\" Annals of the CIRP Vol. 44, pp.357–362, 1995.\n[15] J. P. Hung, Y. S. Lai, T. L. Luo, K. D. Wu, Y. Z. Zhan, \" Effect of\nDrawbar Force on the Dynamic Characteristics of a Spindle-Tool Holder\nSystem,\" World Academy of Science, Engineering and Technology,\nInternational Journal of Mechanical, Industrial Science and Engineering\nvol. 8, no.5, pp. 970-975, 2014"]}

This paper presents the variation of the dynamic characteristics of a spindle with the change of bearing preload. The correlations between the variation of bearing preload and fundamental modal parameters were first examined by conducting vibration tests on physical spindle units. Experimental measurements show that the dynamic compliance and damping ratio associated with the dominating modes were affected to vary with variation of the bearing preload. When the bearing preload was slightly deviated from a standard value, the modal frequency and damping ability also vary to different extent, which further enable the spindle to perform with different compliance. For the spindle used in this study, a standard preload value set on bearings would enable the spindle to behave a higher stiffness as compared with others with a preload variation. This characteristic can be served as a reference to examine the variation of bearing preload of spindle in assemblage or operation., {"references":["E. Abele, Y. Altintas, C. Brecher, \"Machine Tool Spindle Units,\" CIRP\nAnnals – Manufacturing Technology, vol. 59, no. 4, pp. 781–802, 2010.","M. Weck, A. Koch, \"Spindle-bearing systems for high-speed applications\nin machine tools,\" CIRP Annals-Manufacturing Technology, vol. 42, no.\n1, pp. 445–448, 1993.","S. P. Harsha, L. Sandeep, R. E. Prakash. \"Effects of Preload and Number\nof Balls on Nonlinear Dynamic Behaviors of Ball Bearing System,\"\nInternational Journal of Nonlinear Science and Numerical Simulation.\nvol. 4, no. 3, pp. 265-278, 2003.","Y. Cao, Y. Altintas, \"Modeling of Spindle-Bearing and Machine Tool\nSystems for Virtual Simulation of Milling Operations,\" International\nJournal of Machine Tools and Manufacturing. vol. 47, no. 9 pp.\n1342-1350, 2007.","M. A. Alfares, A. A. Elsharkawy. \"Effects of Axial Preloading of Angular\nContact Ball Bearings on the Dynamics of a Grinding Machine Spindle\nSystem,\" Journal of Materials Processing Technology. vol. 136, no. 3, pp.\n48-59, 2003.","S. A. Spiewak, T. Nickel. Vibration Based Preload Estimation in Machine\nTool Spindles, International Journal of Machine Tools & Manufacture.\nvol. 41, no. 4, pp. 567-588, 2001.","A. Gunduz, J. T. Dreyer, R. Singh. \"Effect of Bearing Preloads on the\nModal Characteristics of a Shaft-Bearing Assembly: Experiments on\nDouble Row Angular Contact Ball Bearings,\" Mechanical Systems and\nSignal Processing. vol. 31, pp. 176-195, 2012.","J. Tlusty, .M. Polacek. \"The Stability of Machine Tools Against\nSelf-Excited Vibrations in Machining,\" Trans. ASME, International\nresearch in production engineering. Pp. 465-474, 1963.","S. A.Tobias, W. Fishwick. \"The Chatter of Lathe Tools under Orthogonal\nCutting Conditions\", Trans. ASME, Journal of Engineering for Industry,\nvol. 80, pp. 1079-1088, 1958.\n[10] NSK Technologies Company. \"NSK super precision bearings Part 5:\nTechnical guides,\" http://www.nsk.com/products/spb/, 2003.\n[11] E. Ozturk, U. Kumar, S. Turner, T. Schmitz. \"Investigation of Spindle\nBearing Preload on Dynamics and Stability Limit in Milling,\" CIRP\nAnnals-Manufacturing Technology. vol. 61, no. 1, pp. 343-346, 2012.\n[12] C. W. Lin, J. F. Tu. \"Model-Based Design of Motorized Spindle Systems\nto Improve Dynamic Performance at High Speeds,\" Journal of\nManufacturing Processes. vol. 9, no. 2, pp. 94-108, 2007.\n[13] S. Jiang, H. Mao. \"Investigation of Variable Optimum Preload for a\nMachine Tool Spindle,\" International Journal of Machine Tools and\nManufacture. vol.50, no. 1, pp. 19-28, 2010.\n[14] J. P. Hung, Y. S. Lai, T. L. Luo, K. D. Wu, Y. Z. Zhan, \" Effect of\nDrawbar Force on the Dynamic Characteristics of a Spindle-Tool Holder\nSystem,\" World Academy of Science, Engineering and Technology,\nInternational Journal of Mechanical, Industrial Science and Engineering\nvol. 8, no.5, pp. 970-975, 2014."]}

The machining performance is determined by the frequency characteristics of the machine-tool structure and the dynamics of the cutting process. Therefore, the prediction of dynamic vibration behavior of spindle tool system is of great importance for the design of a machine tool capable of high-precision and high-speed machining. The aim of this study is to develop a finite element model to predict the dynamic characteristics of milling machine tool and hence evaluate the influence of the preload of the spindle bearings. To this purpose, a three dimensional spindle bearing model of a high speed engraving spindle tool was created. In this model, the rolling interfaces with contact stiffness defined by Harris model were used to simulate the spindle bearing components. Then a full finite element model of a vertical milling machine was established by coupling the spindle tool unit with the machine frame structure. Using this model, the vibration mode that had a dominant influence on the dynamic stiffness was determined. The results of the finite element simulations reveal that spindle bearing with different preloads greatly affect the dynamic behavior of the spindle tool unit and hence the dynamic responses of the vertical column milling system. These results were validated by performing vibration on the individual spindle tool unit and the milling machine prototype, respectively. We conclude that preload of the spindle bearings is an important component affecting the dynamic characteristics and machining performance of the entire vertical column structure of the milling machine., {"references":["Yoshimi Ito, Modular design for machine tool, McGraw Hill Company,\n2008.","Y. Seo, D. P. Hong, I. Kim, T. Kim, D. Sheen, and G. B. Lee, Structure\nmodeling of machine tools and internet-based implementation,\nProceedings of the 2005 Winter Simulation Conference, December 2005,\nOrlando, Florida, USA.","J. Tlusty, M. Polacek, The stability of machine tools against self-excited\nvibrations in machining, 1963, in: Proceedings of the ASME\nInternational.","J. Tlusty, Dynamics of high-speed milling, Trans. ASME, Journal of\nEngineering for Industry 108 (2) (1986) 59-67.","F. Koenisberger, J. Tlusty, Machine tool structuresÔÇöVol. I: stability\nagainst chatter, Pergamon Press, Englewood Cliffs, NJ, 1967.","S.A. Tobias, W. Fishwick, The chatter of lathe tools under orthogonal\ncutting conditions, Trans. ASME, Journal of Engineering for Industry 80\n(1958) 1079-1088.","N. Akt├╝rk, M. Uneeb, M. R. Gohar, The effects of number of balls and\npreload on vibrations associated with ball bearings, Trans. ASME,\nJournal of Tribology 119 (4) (1997) 747-753.","S. P. Harsha, K. Sandeep, R. E. Prakash, Effects of preload and number of\nballs on nonlinear dynamic behaviors of ball bearing system,\nInternational Journal of Nonlinear Science and Numerical Simulation\n4(3) (2003 ) 265-278.","Y. Cao, Y. Altintas, Modeling of spindle-bearing and machine tool\nsystems for virtual simulation of milling operations, International Journal\nof Machine Tools and Manufacturing 47 (2007) 1342-1350.\n[10] M. A. Alfares, A. A. Elsharkawy, Effects of axial preloading of angular\ncontact ball bearings on the dynamics of a grinding machine spindle\nsystem, Journal of Materials Processing Technology 136(1-3) (2003)\n48-59.\n[11] N. Lynagh, H. Rahnejat, M. Ebrahimi, R. Aini, Bearing induced vibration\nin precision high speed routing spindles, International Journal of Machine\nTools and Manufacture 40(4) (2000) 561-577.\n[12] M.R. Movahhedy, P Mosaddegh, Prediction of chatter in high speed\nmilling including gyroscopic effects. International Journal of Machine\nTools and Manufacture, 46(9) (2006) 996-1001.\n[13] C. W Lin, J. F. Tu, and J. Kamman, An integrated thermo mechanical\ndynamic model to characterize motorized machine tool spindles during\nvery high speed rotation, International Journal of Machine Tools and\nManufacture, 43(2003)1035-1050.\n[14] S. Y. Jiang, S. F. Zheng, A modeling approach for analysis and\nimprovement of spindle-drawbar bearing assembly dynamics.\nInternational Journal of Machine Tools and Manufacture, 50(\n2010)131-142.\n[15] Y. Altintas and S. Park, Dynamic compensation of spindle-integrated\nforce sensors. CIRP Annals - Manufacturing Technology 53(1\n(2004)305-308.\n[16] Y. Altintas and Y. Cao, Virtual design and optimization of machine tool\nspindles. CIRP Annals Manufacturing Technology, 54(1)(2005) 379-382.\n[17] J. P. Hung, Load effect on the vibration characteristics of a stage with\nrolling guides, Journal of Mechanical Science and Technology 23(1)\n(2009) 92-102.\n[18] C. Y. Lin, J. P. Hung, and T. L. Lou, Effect of preload of linear guides on\ndynamic characteristics of a vertical column-spindle system,\nInternational Journal of Machine Tools and Manufacture 5(8) (2010)\n741-746.\n[19] K. J. Johnson, Contact mechanics, Cambridge University Press (1985).\n[20] T.A. Harris, in: Rolling Bearing Analysis, third ed., John Wiley and Sons,\nNew York, 1991.\n[21] D. E. Brewe, B. J. Hamrock, Simplified solution for elliptical-contact\ndeformation between two elastic solid, Trans. ASME, Journal of\nLubrication Technology 99 (1997) 485-487.\n[22] J. A. Greenwood, Analysis of elliptical Herztian contacts, Tribology\nInternational 30 (1997) 235-237.\n[23] J. P. Hung, Y.L. Lai, C. Y. Lin, and T. L. Lou, Modeling the machining\nstability of vertical milling machine under the influence of the preloaded\nlinear guide, International Journal of Machine Tools and Manufacture.\n51(9)(2011)731-739.\n[24] Hiwin Technologies Company. Hiwin linear guideway technical\ninformation. Taiwan: 2000. http://www.hiwin.com/online_cat\n[25] Hiwin Technologies Company. Hiwin ballscrews technical information.\nTaiwan:2000. http://www.hiwin.com/online_cat\n[26] THK Technologies Company. THK Ball screw technical information:\nball screw peripheral. http://www.thk.com/online_cat.\n[27] THK CO., LTD., Features of the LM Guide,\nhttp://www.thk.com/online_cat.\n[28] Y. Altintas, E. Budak, Analytical prediction of stability lobes in milling,\nAnnals of the CIRP 44 (1995) 357-362.\n[29] E. Budak, Y. Altintas, Analytical prediction of chatter stability in\nmillingÔÇöPart I: general formulation; Trans. ASME, Journal of Dynamic\nSystems, Measurement, and Control 120 (1998) 22-30."]}

The five appended papers all deal with gearbox noise and vibration. The first paper presents a review of previously published literature on gearbox noise and vibration. The second paper describes a test rig that was specially designed and built for noise testing of gears. Finite element analysis was used to predict the dynamic properties of the test rig, and experimental modal analysis of the gearbox housing was used to verify the theoretical predictions of natural frequencies. In the third paper, the influence of gear finishing method and gear deviations on gearbox noise is investigated in what is primarily an experimental study. Eleven test gear pairs were manufactured using three different finishing methods. Transmission error, which is considered to be an important excitation mechanism for gear noise, was measured as well as predicted. The test rig was used to measure gearbox noise and vibration for the different test gear pairs. The measured noise and vibration levels were compared with the predicted and measured transmission error. Most of the experimental results can be interpreted in terms of measured and predicted transmission error. However, it does not seem possible to identify one single parameter, such as measured peak-to-peak transmission error, that can be directly related to measured noise and vibration. The measurements also show that disassembly and reassembly of the gearbox with the same gear pair can change the levels of measured noise and vibration considerably. This finding indicates that other factors besides the gears affect gear noise. In the fourth paper, the influence of bearing endplay or preload on gearbox noise and vibration is investigated. Vibration measurements were carried out at torque levels of 140 Nm and 400 Nm, with 0.15 mm and 0 mm bearing endplay, and with 0.15 mm bearing preload. The results show that the bearing endplay and preload influence the gearbox vibrations. With preloaded bearings, the vibrations increase at speeds over 2000 rpm and decrease at speeds below 2000 rpm, compared with bearings with endplay. Finite element simulations show the same tendencies as the measurements. The fifth paper describes how gearbox noise is reduced by optimizing the gear geometry for decreased transmission error. Robustness with respect to gear deviations and varying torque is considered in order to find a gear geometry giving low noise in an appropriate torque range despite deviations from the nominal geometry due to manufacturing tolerances. Static and dynamic transmission error, noise, and housing vibrations were measured. The correlation between dynamic transmission error, housing vibrations and noise was investigated in speed sweeps from 500 to 2500 rpm at constant torque. No correlation was found between dynamic transmission error and noise. Static loaded transmission error seems to be correlated with the ability of the gear pair to excite vibration in the gearbox dynamic system. QC 20100923