Computer aided design of NC machine tool gear boxes.

Predincea, Nicolae ; Constantin, George ; Ghionea, Adrian 等

Abstract: In the main kinematic chain structure of NC machine tools the utilization of combined adjusting mechanisms consisted of an DC or AC electric drive and a gear box with a reduced number of steps (m = 2 ... 4) has a large spread. On the basis of an algorithm for the kinematic computation of the adjusting mechanism of NC machine tool main kinematic chain structure a program was elaborated that has on the basis a bank of kinematic schemes that offers the designer the possibility to make his option for a variant depending on a certain kinematic and constructive criteria.

Key words: gearbox, spindle speed range, continuity, superposition, discontinuity.

1. INTRODUCTION

In CNC machine tools, the adjusting function of the main kinematic chain is achieved by an DC or AC electric motor with adjustable speed, combined with a gear box (GB) with a step number m = 2 ... 4. Some advantages of kinematic, constructive and economic nature are obtained [Weck, 2006].

Knowing the diversity of NC machine tools and cutting conditions the necessity of definition of a method of kinematic and element design with a general character appeared. The first preoccupations in the field were materialized through graphical solutions as basis for gear box design taking in consideration the speed range of the spindle and kinematic characteristics of the electric motor [Ispas et al., 1997, Perovic, 1993]. The innovation brought by this paper consists of elaboration of a calculation algorithm [Predincea et al., 1997] which sets up the computer aided design of NC machine tools gear boxes. On its basis a computing program was achieved that has a set of procedures that helps the kinematic and elemental design of the kinematic chain structure that supplies the revolution motion of the main spindle.

2. CALCULATION ALGORITHM

The structure of main kinematic chain in NC machine tools is determined by the speed variation ratio of the main spindle ([R.sub.n] = [n.sub.max] / [n.sub.min] = 20 ... 500), speed variation ration of the electric motor at constant torque M = const. ([R.sub.n M] = [n.sb.rated] / [n.sub.min]) and constant power P = const. ([R.sub.n P] = [n.sub.max] / [n.sub.rated] that has the values [R.sub.n P] = 3 ... 7 for DC electric motor or [R.sub.n P] = 3 ... 16 for AC electric motor), and for other functional criteria. The kinematic structure of the gear box (kinematic variant, step number m) depends on its adjusting capacity.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [i.sub.a max] = 2/1 and [i.sub.a min] = 1/3 are maximum and minimum transfer ratios of the gear box; [R.sub.nk]--spindle speed variation ratio depending on its speed range arranging mode at P = const. The signs [+ or -] correspond to the arrangement of the spindle ranges, namely with discontinuity (Fig. 1) or superposition. For continuity arrangement (Fig. 3,c), [R.sub.nk] = 1. If the speed adjustment of electric motor is necessary only at Prated = const, in equation (1) [R.sub.n M] = 1.

[FIGURE 1 OMITTED]

For the kinematic calculation of the gear box (Fig. 1), the next stages have to be followed [Predincea, et al., 1993]:

* Establishing the variation range of spindle ([q.sub.min] ... [q.sub.max]) depending on the production characteristics of the NC machine tool, geometric (workpiece or cutting tool: [D.sub.wp min] ... [D.sub.wp max]) and technological ones (feed: [f.sub.min] ... [f.sub.max], cutting speed: [v.sub.c] min ... [v.sub.c max]) of the workpiece.

* Determination of the rated power Prated of the electric motor in a cutting regime of roughing that loads maximally the main spindle [SIEMENS Catalog].

* Selection of the electric motor and its characteristics ([P.sub.rated], [n.sub.rated], [I.sub.rated], [n.sub.max], [T.sub.th], J, etc.), taking in consideration the ratio [R.sub.n P] and [R.sub.n M], keeping the functional characteristics, size, acquisition, exploitation and maintaining costs.

* Establishing the gear box step number m, pre-establishing the values for [R.sub.n M] and [R.sub.n k] (speed variation ratio with continuity--Fig. 3,c--or discontinuity--Fig. 1--at P = const), namely [R.sub.n M] < [R.sub.n]/4, if [R.sub.n] < 100 and [R.sub.n k] = 1.12 ... 1.25 (or k = 2 ... 3, depending on ration [phi]), admitting that power drop [DELTA]P = (5 ... 10)/100 from [P.sub.N]. The step number m of the gear box is given by relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

with the same hints connected to relation (1).

* Calculation of the ratio [R.sub.n M] and speed [n.sub.min 1] depending on the number m, which becomes an integer (decreased or increased in regard with the calculated value).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3,a,b)

* Determination of ration .M of the main spindle speeds obtained through gear box (the same hints for signs as for (3)):

[[PHI].sub.M] = [r.sub.n P][R.sup. [+ or -] 1.sub.nk]. (4)

[FIGURE 2 OMITTED]

* Representation of the speed diagram (Fig 3,c) and of the speed sub-ranges of the machine tools depending on the given, chosen, and calculated values and kinematic and functional constraints imposed to the gear box ([i.sub.R max] = 2/1; [i.sub.R min] [greater than or equal to] 1/3, etc., [i.sub.R]--variable adjusting ratio of a gearing).

* Determination of the characteristics (not included in paper) P = f (n) and M = f (n) for different services (S1, S6, etc.).

* Determination of the constant [i.sub.1], [i.sub.2], ... transmission ratios ... [i.sub.R] (Fig. 3,a) for the mechanisms of the main kinematic structure, using the speed diagram and specific calculation methods.

* Determination of the reference geometric elements of the gearings and belt transmissions.

3. PROGRAM STRUCTURE

The program has on the basis the structure presented in Fig. 2, the input data being the farthest speeds of the main spindle--minimum [q.sub.min] and maximum [q.sub.max] and the characteristic speeds of the electric motor--minimum [n.sub.min], rated [n.sub.rated], and maximum [n.sub.max]. Further, considering the presented calculation algorithm, the number of steps of the gear box is determined. This, being generally a decimal number, is chosen as an integer by approximation with minus or plus.

Therefore, the user has as options two kinematic variants resulted form arranging the electric motor speed ranges with discontinuity and with continuity, as the number m was ap proximated with minus or plus respectively. For the two cases the values [R.sub.n M] and [n.sub.min] are recalculated, keeping unchanged the variation ratio [R.sub.q].

[FIGURE 3 OMITTED]

As regards the kinematic particularities of the gear box (m = 2 ... 4, 1/3 = [i.sub.R] = 2/1) imposed by the characteristics of the machine tool ([R.sub.q]) and electric motor ([R.sub.n M], [R.sub.n P]), a kinematic scheme library was developed for main kinematic chain in NC machine tools. For each kinematic scheme the user gets output data such as: P = f (n), speed diagram, kinematic error diagram. For this purpose, the program has a set of procedures.

4. CONCLUSIONS

The program flexibility is remarked through the dialog user-computer, extension of the kinematic structure variants of gear box, selection of an optimum structure of main kinematic chain using the minimum size and adjusting range of the electric motor at P = const., increase the number of output data with element calculation and access to the CAD.

5. REFERENCES

Ispas, C.; Predincea, N.; Ghionea, A. & Constantin, G. (1997). Masini-unelte. Mecanisme de reglare (Machine Tools. Adjusting Mechanisms), Politehnica University of Bucharest, ISBN 973-31-1112-0, Bucharest.

Perovic, B. (1993). Arbeitsmappe fur den Konstrukteur. Fertigungsverfahren, Werkzeuge, Spanvorrictungen, Werkzeugmaschinen (Working Folder for Technical Designer. Manufacturing, Tools, Cutting, Machine Tools), VDI Verlag GmbH, Dusseldorf.

Predincea, N., Aurite, T., Ghionea, A. & Constantin, G. (1993). Gear Box Design of NC Machine Tools, Science Conference Advanced Manufacturing Technology, Th. University of Rousse, pp. 45-52, Rousse, Bulgaria.

Predincea, N., Constantin, G., Bratu, I. & Antofe, A. (1994). Computer Aided Design of Adjusting Mechanisms, Scientific Bulletin of Brasov University, pp. 149-156, Brasov, Romania.

Weck, M. & Brecher, C. (2006). Werkzeugmaschinen 2, Konstruktion und Berechnung (Machine Tools 2, Construction and Computation), Springer Verlag, ISBN 978-3-54022502-7, Berlin.