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TECHNICAL PAPERS

# Dynamic Hybrid Modeling of the Vertical $Z$ Axis in a High-Speed Machining Center: Towards Virtual Machining

[+] Author and Article Information
Giovanni Tani

DIEM: Department of Mechanical Construction Engineering, University of Bologna, viale Risorgimento 2, 40136 Bologna, Italygiovanni.tani@mail.ing.unibo.it

Raffaele Bedini

DMTI: Department of Mechanical and Industrial Technologies, University of Florence, via di Santa Marta 3, 50139 Firenze, Italyraffaele.bedini@unifi.it

Alessandro Fortunato

DIEM: Department of Mechanical Construction Engineering, University of Bologna, viale Risorgimento 2, 40136 Bologna, Italyalessandro.fortunato@mail.ing.unibo.it

Claudio Mantega

DIEM: Department of Mechanical Construction Engineering, University of Bologna, viale Risorgimento 2, 40136 Bologna, Italyclaudio.mantega@mail.ing.unibo.it

J. Manuf. Sci. Eng 129(4), 780-788 (Feb 13, 2007) (9 pages) doi:10.1115/1.2738097 History: Received November 28, 2005; Revised February 13, 2007

## Abstract

This paper describes the modeling and simulation of the $Z$ axis of a five axis machining center for high-speed milling. The axis consists of a mechanical structure: machine head and electro-mandrel, a CNC system interfaced with the feed drive, and a pneumatic system to compensate for the weight of the vertical machine head. These subsystems were studied and modeled by means of: (1) finite element method modeling of the mechanical structure; (2) a concentrated parameter model of the kinematics of the axis; (3) a set of algebraic and logical relations to represent the loop CNC-$Z$ feed drive; (4) an equation set to represent the functioning of the pneumatic system; and (5) a specific analytical model of the friction phenomena occurring between sliding and rotating mechanical components. These modeled subsystems were integrated to represent the dynamic behavior of the entire $Z$ axis. The model was translated in a computer simulation package and the validation of the model was made possible by comparing the outputs of simulation runs with the records of experimental tests on the machining center. The firm which promoted and financed the research now has a virtual tool to design improved machine-tool versions with respect to present models, designed by traditional tools.

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## Figures

Figure 1

(a) The BRETON MC; and (b) scheme of Z axis group

Figure 2

Integrated mechatronic model

Figure 3

Genesis of reduced finite element model of the Z axis

Figure 4

Simulink block architecture of integrated FEM model (on the left) and FEM model of MC head with master DOF (on the right)

Figure 5

Friction model (15)

Figure 6

(a) Layout of the pneumatic valve; and (b) pneumatic system model

Figure 7

Trajectory generation model

Figure 8

Cascade position, velocity, and current control loop

Figure 9

Comparison between the simulated and the real paths

Figure 10

Kv factor effect on the simulated step command

Figure 11

(a)Kv factor effect on the simulated ramp command; (b) zoom of the A zone of Fig. 1; and (c) zoom of the B zone of Fig. 1

Figure 12

(a) Comparison between the simulated and the real paths for a sine command; and (b) zoom of the C zone of Fig. 1

Figure 13

Influence of the variation of the σ1 on the reversal error

Figure 14

Balancing pneumatic force due to simulated response of the head

Figure 15

Effect of the pneumatic force on the simulated axis path

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