Effect of the screw–nut joint stiffness on the position-dependent dynamics of a vertical ball screw feed system without counterweight

Abstract

The study on the position-dependent dynamic characteristics of a vertical ball screw feed system without counterweight is an important step in the enhancement of the structural performance of mini-type vertical milling machines. The ball screw is generally driven by a servomotor, which converts a rotary motion into a linear motion through a screw–nut pair. To assess the position-dependent dynamic characteristics of a vertical ball screw feed system subjected to the influence of the screw–nut joint stiffness, a variable-coefficient lumped parameter model of the system is developed. This model is established taking into account the screw–nut joint stiffness under three different strategies: (1) considering the preload and the weight of the spindle system, (2) considering the elastic deformation but ignoring the effect of the weight, and (3) a perfectly rigid model. The differences between the three models in predicting the position-dependent dynamic characteristics of the system are compared, revealing that the stiffness of screw–nut joint greatly affects the vibratory behavior of the spindle system in the transmission direction. A set of conducted experimental results demonstrate that the stiffness model under the preload and the weight of the spindle system is the most accurate model for the prediction of the position-dependent natural frequency and displacement response of the system with the spindle system position. Therefore, it is more suitable for structure design, performance simulation, and evaluation of a vertical ball screw feed system without counterweight.

Keywords

Screw–nut joint stiffness vertical feed system without counterweight variable-coefficient spindle system position-dependent dynamics

Get full access to this article

View all access options for this article.

References

Seo Y, Hong D P, Kim I, et al. Structure modeling of machine tools and internet-based implementation. In: Proceedings of the 2005 winter simulation conference, Orlando, FL, USA, 2005.

Ito

. Modular design for machine tools, New York: McGraw Hill Professional, 2008.

Zhang

Liu

et al.

Dynamic modeling and analysis of the high-speed ball screw feed system. Proc IMechE, Part B: J Engineering Manufacture 2015; 229: 870–877.

Aini

Rahnejat

Gohar

. An experimental investigation into bearing-induced spindle vibration. Proc IMechE, Part C: J Mechanical Engineering Science 1995; 209: 107–114.

Chen

Chiu

Cheng

. Dynamic analysis of disc spring effects on the contact pressure of the collet—spindle interface in a high-speed spindle system. Proc IMechE, Part C: J Mechanical Engineering Science 2009; 223: 1191–1201.

Zhang

et al.

Dynamics prediction of spindle system using joint models of spindle tool holder and bearings. Proc IMechE, Part C: J Mechanical Engineering Science 2015; 229: 3084–3095.

Zhang

et al.

A parametric modeling method for the pose-dependent dynamics of bi-rotary milling head. Proc IMechE, Part B: J Engineering Manufacture 2016, pp. 1–19.

Sulitka

Kolar

Janota

. Properties of the spindle and machine frame coupled system. Jpn Soc Mech Eng 2009; 5: 745–750.

Kolar

Matej

Janota

. Simulation of dynamic properties of a spindle and tool system coupled with a machine tool frame. Int J Adv Manuf Technol 2011; 54: 11–20.

10.

Beards

. Damping in structural joints. Shock Vib Digest 1992; 24: 3–7.

11.

Zhang

Zhao

et al.

Dynamic modeling and analysis for gantry-type machine tools considering the effect of axis coupling force on the slider – guide joints’stiffness. Proc IMechE, Part B: J Engineering Manufacture 2015; 230: 2036–2046.

12.

Yigit

Ulsoy

. Dynamic stiffness evaluation for reconfigurable machine tools including weakly non-linear joint characteristics. Proc IMechE, Part B: J Engineering Manufacture 2002; 216: 87–101.

13.

Law

Phani

Altintas

. Position-dependent multibody dynamic modeling of machine tools based on improved reduced order models. J Manuf Sci Eng 2013; 135: 021008–021008.

14.

Henninger

Eberhard

. Computation of stability diagrams for milling processes with parallel kinematic machine tools. Proc IMechE, Part I: J Systems and Control Engineering 2009; 223: 117–129.

15.

Okwudire CE and Altintas Y. Modeling of the screw-nut interface dynamics of ballscrew drives. In: International mechanical engineering congress and exposition. New York: American Society of Mechanical Engineers, 2007, pp.1875–1883.

16.

NSK Co. Ltd, Precision machine components. https://www.jp.nsk.com.

17.

Fleischer

Herder

. A daptronic ball screw for the enhancement of machine precision. Procedia CIRP 2012; 1: 621–626.

18.

Verl

Frey

Heinze

. Double nut ball screw with improved operating characteristics. CIRP Ann-Manuf Technol 2014; 63: 361–364.

19.

Feng

Pan

. Investigation of ball screw preload variation based on dynamic modeling of a preload adjustable feed-drive system and spectrum analysis of ball-nuts sensed vibration signals. Int J Mach Tools Manuf 2012; 52: 85–96.

20.

Luo

Pan

Cai

et al.

A method to predict position-dependent structural natural frequencies of machine tool. Int J Mach Tools Manuf 2015; 92: 72–84.

21.

Lin

Hung

. Effect of preload of linear guides on dynamic characteristics of a vertical column–spindle system. Int J Mach Tools Manuf 2010; 50: 741–746.

22.

Hung

Lai

Lin

et al.

Modeling the machining stability of a vertical milling machine under the influence of the preloaded linear guide. Int J Mach Tools Manuf 2011; 51: 731–739.

23.

Wang

Zhang

et al.

Effect of stiffness of rolling joints on the dynamic characteristic of ball screw feed systems in a milling machine. Shock Vib 2015; 2015: 1–11.

24.

Greenwood

. Analysis of elliptical Hertzian contacts. Tribol Int 1997; 30: 235–237.

25.

Harris

Kotzalas

. Essential concepts of bearing technology, Boca Raton, FL: CRC Press, 2006.

26.

Brewe

Hamrock

. Simplified solution for elliptical-contact deformation between two elastic solids. J Lubr Technol 1977; 99: 485–487.