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    mass was studied for these modes.
    Based on this analysis, the first mode is mainly axial, with a strong displacement of carriage position, whereas the second and third modes are mainly torsional.
    However, as the screw lead increases, the axial– torsional coupling increases accordingly and it is not suitable to consider each mode as pure axial or torsional.
    As the axial–torsional coupling varies, the frequency sensitivity of each mode to operating conditions varies. A strong axial–torsional coupling makes the
    frequency value of the first mode to be less sensitive to load mass variations. However, a low axial–torsional coupling may be preferred to minimize frequency variations of the second mode for variable carriage positions.
    The transmission ratio is a key design parameter with direct influence on the degree of axial–torsional coupling, which dominates the modes frequency shift.
    Therefore, it has a significant effect on the robustness of the control strategies used for position control.
    References

    1. Hecker RL, Flores GM, Xie Q, Haran RA (2008) A review of machine-tools servocontrol level. Lat Am Appl Res (Int J) 38(1):85–94
    2. Smith DA (1999) Wide bandwidth control of high-speed milling machine of feed drives. PhD dissertation, University of Florida
    3. Varanasi KK, Nayfeh SA (2004) The dynamics of lead-screw drives: low-order modeling and experiments. J Dyn Syst Meas Control (ASME) 126:388–396
    4. Kamalzadeh A, Erkorkmaz K (2007) Compensation of axial vibrations in ball screw drives. Ann CIRP 56(1):373–378
    5. Okwudire CE, Altintas Y (2009) Minimum tracking error control of flexible ball screw drives using a discrete-time sliding mode controller. J Dyn Syst Meas Control (ASME) 131:051006
    6. Erkorkmaz K, Kamalzadeh A (2006) High bandwidth control of ball screw drives. Ann CIRP 55(1):393–398
    7. Altintas Y, Brecher C, Weck M, Witt S (2005) Virtual machine tool. Ann CIRP 54(2):115–138
    8. Chen JS, Huang YK, Cheng CC (2004) Mechanical model and contouring analysis of high-speed ball-screw drive systems with compliance effect. Int J Adv Manuf Technol 24:241–250
    9. Zaeh MF, Oertli T, Milberg J (2004) Finite element modeling of ball screw feed drive systems. Ann CIRP 53(1):289–294
    10. Okwudire CE, Altintas Y (2009) Hybrid modeling of ball screw drives with coupled axial, torsional, and lateral dynamics. J Mech Des (ASME) 13(7):071002
    11. Ginsberg JH (2001) Mechanical and structural vibrations theory and applications. Wiley, New York
    12. Wei Ch Ch, Lin JF (2003) Kinematic analysis of the ball screw mechanism considering variable contact angles and elastic
    deformation. J Mech Des 125:717–733
    13. Varanasi KK (2002) On the design of a precision machine for closed-loop performance. MS thesis, Massachusetts Institute of Technology, Cambridge, MA
    14. Vicente DA, Hecker RL, Flores G (2007) Dynamic modeling of lead screw drives using Ritz series. In: XII RPIC, Río Gallegos, Santa Cruz, Argentina
    15. Vicente DA, Hecker RL, Flores G (2008) Vibration modes characterization in a lead screw drive. In: Proceedings of MUSME, the international symposium on multibody systems and mechatronics, San Juan, Argentina, Paper n. 23MUSME08
    建模和振动模态分析滚珠丝杠传动        
    Diego A. Vicente • Rogelio L. Hecker •
    Fernando J. Villegas • Gustavo M. Flores    

    摘要:机床的定位系统一般由滚珠丝杠驱使是因为其刚度高和外部扰动的灵敏度低。然而,现代机床需要增加他们的速度和定位加速度,这些系统的共振模式可以激发和降低轨迹跟踪精度。因此,动态模型包括振动模式所需的机器设计以及控制器的选择与调整。这项工作提出了一种高频动态模型滚珠丝杠传动。分析公式如下面的方法,在螺旋模型作为一个连续的子系统,利用里茲系列近似去获得一个近似的n个自由度的自由模型。基于这个模型,每种模式的轴向和角分量功能,研究了他们之间不同传动比确定的耦合度。在那之后,每个频率的变化模式研究了不同的车厢位置,不同的移动质量。最后,这些分析结果为应用控制器的设计与参数给出了估值。论文网
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