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Procedia Engineering 206 (2017) 1029-1033

Procedia

Engineering

www.elsevier.com/loeate/proeedia

International Conference on Industrial Engineering, ICIE 2017

The Influence if Dynamical Parameter; on Surface Quality during

Ball-End Milling

A.V. Vybiishchik*

South Ural State University, 76, Lenin Avenue, Chelyabinsk, 454080, The Russian Federation

Abstract

The manufacturing of parts with freeform surfaces, viz. dies, moulds, blades, etc. presently is one of the most complex and diffi cult machining processes.Various strategies and technologi es of ball-end and chamfered-end milling at either a constant tool ditch for evcn and oblique surfaces or a variable tool pitcn for ffeeform surfaces ace required to improve the surface quality, viz. surface roughness, size tolerance ano form shbpe before finf machining steps. One of the key parametees influencing the syrface qualicy is the value s and ohe directions of mhe cuttine eorce normal and tangentialcomponenke, which aire described in tha pauer. A qifferential equation ntating the interrelation between the normal component oc the cutting force and the deeed of form with soneideration for different typieal shapes of the machined surfaces is given. The solution for the diffesential equation allows for che mathematical modeling of the surface qumlity after the penultimete machining step, whichf ennsequently, will allow predicting of the obtaining surface accuracy.

©2017 The Autoes. Pfalished by Elsevier Ltd.

Peer-review Andhr responsibility of the scientific conlineittee of" the IntematioIial Conference on Industrial Engineering Keywords: Ball-end milling; freeform surface; cutting force component; form defect; surface quality.

1. Introduction

Fieesofm surfaces have broad implementation in nowaday^ inslustllal plS)euction. The branches of industry which produce parts with such surfaces are aerospace [^3], automotive [1-3], die mould [1-4], eiomtaical [1,3] parts, sensors for micro-elecfro-mechanical sestema [5] and also turbine elesles in power engineering [6,77]. To produce freeform surfaces, 3 tm 5 INC milling machines are used [1-3]. The tools used to proauce freefonm surfaces are ball-end mills [1-3]. The manufacturing process is difficult and complex. The tool path generation is chiefly

* Corresponding author. Tel.: +73512679267. E-mail address: alex_vyb@li;t.ra

1877-7058 © 2017 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering. 10.1016/j.proeng.2017.10.589

based on tool path computation, so tool path consecutiveness is not optimum. The sequence is, the CAM preparation for complex surfaces requires up to 50-fold time of the manufacturing itself. The main problem is, as usual, that the shape of the final surface does not match the shape of the initial one, so big amount of bulk material is to be removed [7]. Hence, many factors as tool deflection [8,9], surface shape[10,11], etc. must be taken into account. Many researchers investigated manufacturing freeform surfaces with respect to speed parameters [12], tool deflection [8,9], machined surface geometry [10,11], tool geometry [13-15], surface roughness [8,16], machining strategy [17-20], chip formation [21], even tool wear [22], etc. whereas no analytical research investigating the combination of the rigidity of the machine-tool-work-piece complex and the cutting force with consideration for transient machining process, have been conducted so far. It is, however, mentioned by many researchers that the cutting force components varying during the machining process, on the one hand, and the deflections of the tool, on the other, influence the generation of form defects [14,22].

The purpose of rough machining passes at three-axis milling is the most productive removal of a metal surplus and the approximation of a blank's shape to a finished part's shape.

In actual practice, the final machining of freeform surfaces with the use of "across the trace" strategy is affected by variable cutting depth which, alongside with dynamical processes in the course of machining, influence the surface quality of the obtained surface. In view of the wide (approximately in 70 % out of all machined surfaces) usage of the strategy "across the trace", the need of the investigation of power factors at the strategy "across the trace" became particularly urgent.

2. Process description

Parts with freeform surfaces contain conjugate sections of surfaces having various geometrical shapes and combination. Each section has its own geometrical parameters, which, in turn, influence shape and size errors. Shape error is the deviation between the actual and the nominal surfaces. Nominal surface is an ideal surface used as a reference point for deviations. The value of the deviation is the maximum distance from points of the actual surface to the points of the superimposed surface.

Superimposed surface is a surface shaped like a nominal one, tangential to the actual surface and located outside the part. For a convex surface area with a certain radius, the superimposed surface is an arc of circle having the minimum radius and circumscribed around the actual profile of the part. For a concave surface area with a certain radius, the superimposed surface is an arc of circle having the maximum radius and inscribed into the actual profile of the part. Regardless of the shape of the surface section, the form defect is measured from the superimposed surface.

3. Modeling of form defect

One-sign deviations for the sake of machining convenience are usually specified as minus deviations. A typical machining strategy is the machining strategy "across the stroke" of an oblique surface with a ball-end mill (see Fig.1).

Primarily (over 80% in total), the total form defect after milling consists of flexible deflections of the tool from the machined surface. The value of flexible deflections also influences the form defect n of the actual machined surface from the nominal one. Another parameter influencing surface quality is the normal component of the cutting force Pn. Both the direction and the value of the normal component Pn are variable depending on the so-called "contact pattern" of the ball-end mill's spherical section and the machined surface, which, in turn, depends on inclination angle ra of the machined surface to horizontal plane. Variable values of the cutting force and variable rigidity of the machine-tool-work-piece complex while machining causes the deviation of the mill's centre and, as a consequence, the mill's cutting edges from the nominal direction. Hence, form defect ni on the machined is generated which is determined in the following way:

Where Pn is the variation of the normal component of the cutting force caused by the tool depth variation; jMTWn is the rigidity of the machine-tool-workpiece complex complying with the normal component of the cutting force.

The admittance of the machine-tool-workpiece complex, which is reciprocal of rigidity, is obtained as follows:

x cos® + y sin®

JMTWn Px c0s®+ Py sin®

Fig. 1. Form defect generation under the process of machining freeform surfaces.

Where Px, Py are the cutting force components along the direct and transversal axes respectively, x and y are the deflections of the tool along the direct and transversal axes respectively.

The interrelation between the normal component and the cutting depth in process of time can be described by a differential equation:

n(t) = Wp (T) t(T)

x cos® + y sin® Px cos® + P sin®

Where Wp(t) is a transfer function depending on response time Tp, also on the inclination angle m, the traversal rigidity of the machine-tool-work-piece complex jMTWy, the axial rigidity of the mill jj/x.

When a surface is machined by the "across the trace" strategy, the trace of the penultimate pass is a rectilinear or curvilinear triangle. The most influencing parameter is the height of the step and the corresponding maximum cutting depth tmax, other parameters having minor influence. Hence, all machining patterns can be traced to the simplest pattern, i.e. machining oblique surface with a constant inclination angle m (see Fig.2).

Therefore, the current cutting depth in process of time can be described:

Where r is a current machining time (from the beginning of machining to the present moment);

Fig. 2. The parameters of form defect generation under the process of machining "across the trace" strategy

(a) with ball-end mill; (b) with cylindrical end mill.

t0 - machining time of one triangle remained from the penultimate pass.

The non-homogeneous differential equation obtained from (3) with the substitution of (4) has a partial solution, which allows us to calculate the time tmax of the maximum form defect:

t (Tt = Tp ln

'T + T ^

'o T 1 p T

As a result, the .axi.u. for. defect nmax is obtained:

,(t) =

( ■ \ x cos® + y sin®

Px cos® + Py sin®

T0 + Tp

--p- ln To

't + T ^ 1 p

The above-stated dependency (6) is the partial solution of the differential equation (3). The expression (6) can be used for any machining pattern of "across the trace" strategy. The substitution of r0=1...3 s and Tp=0.1...0.6 s gives us the variation of cutting depth under actual machining conditions.

4. Conclusions

The above calculated dependences calculating the variation of form defect at the machining of freeform surfaces by "across the trace" strategy in course of time, depend on such parameters as response time Tp, inclination angle m, machining time t0 , cutting force components Px, Py, deflections of the tool along the direct and transversal axes x, y. The substitution of actual process parameters allows obtaining the maximum form defect which, in turn, will allow mathematical modelling of accuracy prediction. The practical outcome of the mathematical model will result in determining optimal cutting conditions under finishing freeform surfaces.

Acknowledgements

The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011 References

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