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• Defining the minimum radii requirements and the maximum depth of the cavity, needs consideration, ensuring selected tooling can cope with these part geometries, • Approximately estima

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Figure 245 The complex machining of either a sculptured, or die and mould surfaces, will usually necessitate both

multifarious and sophisticated programming techniques

.

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Defining the minimum radii requirements and the

maximum depth of the cavity, needs consideration,

ensuring selected tooling can cope with these part

geometries,

Approximately estimate the amount of excess stock

material from the die, or mould that needs to be

removed by milling operations1,

NB Establishing what is roughing-out and

semi-finishing operations, will for a large die-set often

mean that roughing-out is both more efficient and

productive on conventional-speed machining

cen-tres, with any semi-finishing undertaken by HSM

• In preparation and prior to milling, ensure that the

workpiece fixturing is both accurate and precise as

well as very robust and rigid, otherwise this latter

factor in particular, is a classic source for any

resul-tant vibrations and will significantly influence the

tool’s life together with degradation of the die and

mould surfaces,

NB HSM requires a totally rigid fixturing, if

vibra-tional tendencies are to be minimised, as it proves

disastrous for any long length-to-diameter tool

ratios, that are often utilised for high-speed milling

operations

• For the machining processes, they should

ide-ally be divided into at least three types of milling

 ‘Material removal rate’ for HSM milling is generally

consider-ably smaller than in conventional machining (i.e except when

aluminium and non-ferrous machining occurs) Formula for

material removal rate

Q=ap� ae� vf

 ( cmmin−)

Where: ap = axial DOC (mm); ae = radial DOC (mm); vf = feed per

minute (mm min–1).

 ‘Die and mould milled surface texture’ , by HSM milling

op-erations dramatically reduces the manual polishing

require-ment – by reducing the resultant milled surface ‘cusp-heights’

Often conventional milling operations produce relatively large

‘cusps’ (i.e see Fig 245a – resulting from the large width of the

‘pick-feed’) For example, when a large automobile bonnet (i.e

‘hood’ – in the USA) die-set has been produced by

conven-tional milling practices, any manual polishing activities range

between: 350–400 man-hours!

NB This order of manual polishing will affect the geometrical

accuracy of the die-set (Source: Sandvik Coromant, 2000)

operations, namely: roughing-out; semi-finishing; finishing

NB ‘Restmilling operations’  are normally

under-taken during any semi-finishing, or finishing op-erations

9.8.2 Die-Cavity Machining –

Retained Stock

Whenever a rough-milling operation is undertaken with a square-shouldered cutter, this creates the

well-known ‘stair-case profile’  (i.e see Figs 246 a and b) of

remaining stock that must now be removed by a semi-finishing milling operation The die-cavity’s cross-sec-tional profile will significantly influence the amount

of stock remaining against the cavity wall, which will create a variation in the cutting forces and have an in-fluence on tool deflection The consequence of this un-even stock will be that when semi-finishing the profile,

it could affect the geometrical accuracy and precision

of the die, or mould Clearly, in the schematic diagram shown in Fig 246a – left, the large chamfered die fea-ture when being roughed-out for a given DOC, will leave significant material here for subsequent semi-finish-ing Likewise, in the cavity of the convex-to-concave profile illustrated in Fig 246 – right, it has significant stock material remaining at the lower regions of the concave feature, obviously necessitating a following machining removal operation (i.e semi-finishing) When a square-shouldered cutter is utilised with a triangular geometry insert, it will have relatively weak corner cross-sections (i.e by way of illustrating this effect of insert shape strength, see Fig 155 – bottom), creating a somewhat unpredictable machining behav-iour Triangular, or rhombic insert geometries, will also create large radial cutting forces and as a result of number of cutting edges, they are unexpectedly, less economical than some other counterparts for such

op- ‘Restmilling operations’ , are those milling operations where

any Ball-nosed: Slot-drills; Endmills; or in some cases,

toroi-dal-geometry inserted cutters; are employed

 ‘Stair-case profile’ , is so-called, because it resembles an actual

stair-case when taken in cross-section (i.e see Fig 246) The height and width of the remaining stock for each step, is de-pendent upon a proportion of the actual ‘step-size’ (pick-feed) and the DOC previously selected Obviously requiring a semi-finishing operation at the very least, to remove this unwanted material.

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erations On the contrary, round cutting inserts that

allow milling paths to be undertaken in any direction,

are often specified because they provide a smooth

transition between successive tool passes, while also leaving behind the twin benefits of less and more even stock, for later removal in semi-finishing This residual

Figure 246 Die-sinking sculptured profiles with a 90° square-shouldered milling cutter, introduces a ‘staircase effect’ on the

machined profile [Courtesy of Sandvik Coromant]

.

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effect of less additional stock produced by round

in-sert’s on the workpiece profile, is shown schematically

in both Figs 247ai and aii and, should be compared to

Fig 246a – this latter effect being the result of utilising

square-shouldered cutting inserts, in terms of stock to

be removed later in semi-finishing operations

Amongst the notable benefits of using round inserts,

are that they produce a variable chip thickness, which

allows for higher feedrates if compared to other

insert-shaped geometries Round cutting inserts provide a

very smooth cutting action (i.e see Fig 246 – bottom

right: inset), because the entering angle changes from

almost zero – in the case of very shallow DOC’s, to that

of 90° – under certain conditions with the larger DOC’s

Thus, at the maximum DOC, the entering angle is 45°

and when copying with the periphery, the angle is 90°

This DOC variability using round inserts, also goes some

way in explaining why these inserts are so strong in

comparison to other insert shapes Namely, round

in-serts with their actual ‘work-loading’ – at the cut’s

ini-tial progression – is successively built-up, rather than

almost immediately with inserts having greater

enter-ing angles, usually provided by their less-than-robust

geometry counterparts Consequently, round inserts

should always be regarded as the primary choice in

cutter selection when either roughing, or for

medium-roughing operations When 5-axis machining, the use

of round cutting inserts can be usefully exploited, as

they have virtually no limitations when machining

sculptured surfaces Therefore, with optimum CNC

programming, either round inserts, or toroid-shaped

milling cutters can normally be substituted for

ball-nosed end mills (Fig 79b), as they can offer: superior

cutting performance; improved chip-breaking

effi-ciencies; as well as better chip evacuation; this latter

point is important when deep cavities might otherwise

retain work-hardened swarf Typically, the increases

in productivity range between 5-to-10 times better,

if compared to that of previously utilising ball-nosed

end mills Round insert tooling is very rigid so as a

re-sult, they only produce a small amount of run-out and,

when combined with ground, positive and light

cut-ting geometries, may be used for semi-finishing and

occasionally some finishing operations (Fig 246 –

bot-tom right: inset)

Some of the main questions to be answered

re-garding the correct application of technology is

con-cerned with optimising: the cutting data; likely insert

grades; together with their geometries; in relation to

the: specific workpiece material to be machined; actual

machining operations to be undertaken; anticipated

productivity requirements; and the likely workhold-ing restaint/security issues Die and mould work in-variably involves complex sculptured male and female surfaces, with any calculations of the effective cutting speed being based upon either the ‘true’ , or effective diameter in-cut (‘De’ – see Fig 247b) So, if the DOC is

very shallow – as is the case when semi-finishing

op-erations are being carried out, then the ‘true’ cutting

speed will be much lower (Fig 247b) If the original

cutter diameter was chosen for the cutting data calcu-lations, then for a shallow cut – due to ‘De’ being the effective diameter, this drastic reduction in actual cut-ting speed will not have been anticipated, causing the feedrate utilised to be severely compromised, as it is dependent on the calculated cutter’s rotational speed This will not only severely impede component produc-tivity, but will increase the tool’s potential wear-rate significantly, this being the case for all round insert cutters, ball-nosed end mills, plus end mills having large corner radii Due to the adverse and miscalcu-lated cutting data, there is a likelihood for premature cutting edge frittering and chipping – created by too low a cutting speed and localised heat in the cutting zone When undertaking either finishing, or super-fin-ishing of the die and mould sculptured surfaces (Fig 246biii) on hardened tool steel, it is vitally important

to choose tool materials and coatings with ‘hot hard-ness’ capabilities

A major factor to consider when milling for either finishing, or super-finishing hardened steel sculptured surfaces by HSM, is to take shallow cuts Notably, the

DOC should not exceed 0.2/0.2 mm (ae/ap – Fig 247b) This strategic machining decision should be made, so that excessive deflection of the cutting tool assembly is avoided, enabling a high tolerance level and geometric accuracy to be held on the die, or mould Accordingly, very stiff tool assemblies are essential, usually utilising solid cemented carbide: due to its inherent stiffness; coupled with the maximum core diameter possible; that the die, or mould part features will allow

 ‘Tool materials for: hardened steel milling’ , they are usually

coated cemented carbide, with the micro-grain structural matrix (i.e typical grain size being <1 µm), providing good wear resistance and transverse rupture strength (i.e this be-ing ‘related’ to its toughness) Coatbe-ings can include: titanium aluminium nitride (TiAlN); titanium carbonitride (TiCN); having multiple coatings of between 2 to 12 µm thick, applied

by Plasma Vapour deposition (PVD) Diamond-like coatings (DLC) are also utilised (Source: Dewes and Aspinwall, 1996)

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Figure 247 By utilising a ball-nosed cutter geometry for die-sinking sculptured surfaces, this reduces finishing stock needed to

be subsequently removed [Courtesy of Sandvik Coromant]

.

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9.8.3 Sculptured Surface Machining –

with NURBS

Prior to a discussion on the application

‘curve-fit-ting’ with ‘Non-Uniform Rational Bezier-Splines’

– ‘NURBS’ for short, it is worth a brief review into

the background as to why there has been a

wide-ac-ceptance of them for machining operations involving

sculptured surfaces The technique of curve fitting is

not new, it was devised in the 1960’s, where indirect

methods were found making it relatively easy to

ma-nipulate these curves – without recourse to

modify-ing the different equation parameters that defined

the sculptured surface In a typical system, a complex

curve geometry would be comprised of several discrete

curves – termed a ‘spline’ , equally, a surface is simply

a curve with an extra dimension Thus, for

‘curve-fit-ting’ the cubic method is particularly suited, although

a modified cubic approach that can accommodate the

uneven spacing of ‘nodes’ – the start and end points –

has particular benefits when digitising surfaces

In France, Bezier who at that time was working for

the automotive company Renault, was intrigued by car

body design and found the ‘point-and-slope technique’

for curve-fitting rather crude and inconvenient for

accurate and precise curve design (i.e see Fig 248a)

Hence, Bezier’s philosophy was to find a way of

manip-ulating the individual parameters contained within the

curve’s basic equation, but in a more easy and in-direct

manner Bezier utilised an ‘open polygon’ (i.e a plane

figure of many angles and straight sides), by which a

curve that approximates to passing through the start

and end points of the open polygon: results in a

de-signer having the ability to change the polygon and as

such, achieving different results By having more

de-fined points in the polygon, this produces additional

flexible control for surface manipulation Further, the

curves generated are formed by equations comprised

of parameters raised to higher powers than that of the

cubic varieties, thereby having longer and more

com-plex mathematical expressions Such a curve, is a

dis-crete segment in a complex curve and these segments

must be joined together

In the Bezier ‘curve-fitting’ technique, the transition

between the curve segments, or ‘patches’ – the surface

equivalent to a line segment, requires close study by the

designer A further refinement, but not one developed

by Bezier although incorporating his mathematical

ex-pressions, was that of the ‘B-Splines’, which ensure

 ‘B-Splines’ , were originally introduced by Cops De Bore.

a smooth transition between segments/patches While yet another and improved refinement to the Bezier equations, was the development of non-uniform B-Splines – which could tolerate an uneven spacing of the nodes Terminology which is not usually perceived, but is associated with the term ‘NURBS’ , includes the

‘rational’ and ‘non-rational’ parametric surfaces So,

a ‘rational’ parametric surface may be represented in many forms, with mathematical precision While the cubic non-rational variety cannot express an 90° arc with mathematical precision, although it has adequate accuracy for machining requirements The amalga-mation of the two ‘curve-fitting’ approaches, namely, that of the ‘rational’ parametric surfaces together with

their ‘non-rational’ counterparts, results in Non-Uni-form Rational B-Splines – ‘NURBS’ Hence, ‘NURBS’

in its simplest form, is a data compression algorithm that reduces the data necessary to define curved sur-faces

In order to successfully utilise ‘NURBS’ impressive

‘curve-fitting’ abilities, the term ‘NURBS-interpolation’

was coined by Siemens Energy and Automation – when they first introduced its capabilities onto the market With its ability to reduce data in defining complex curves, ‘NURBS’ offers significant benefits, such as: ties

up less CNC memory producing shorter programs; al-lows higher feedrates to be exploited; produces shorter cycle-times; reduces tool vibrations – hence enhances tool wear rates; improves machined surface geometric definition and finishes; coupled to increased part pro-file accuracy and precision

Today’s CNC controllers have large memories with very high block processing speeds that can

ap-ply sophisticated ‘look-ahead capabilities’ that can scan

the anticipated programmed cutter path for abrupt changes So, these ‘real-time algorithms’ can not only

‘see’ the expected turns coming, but will slow down the feedrate to keep the cutter on its confirmed path and

avoid potentially inconvenient moments of ‘data-star-vation’ Moreover, even these enhanced CNC features

will struggle when a dense cluster of data points gen-erated by linear interpolation possibly causing block processing problems, having the affect of significantly reducing the feedrate as it ‘corners’ from each line seg-ment to the next Consequently, ‘NURBS’ tool paths will undoubtedly alleviate data starvation and feedrate troubles by being more efficient, but like point-to-point toolpaths (Fig 248b), they are not exact representa-tions of the surface The ‘NURBS’ toolpath must be calculated which involves some approximation –

simi-lar to the ‘chordal deviation parameter’ used in many

CAM systems (Fig 248c)

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Figure 248 CNT tool cutter path control

while contouring sculptured surfaces – utilis-ing nurbs [Courtesy of Sandvik Coromant]

Until about a decade ago, there existed only one

practical way to represent free-flowing curves in a

cutter path This was despite the fact that CAD/CAM

systems could mathematically define virtually any geometric shape with smooth curves These CAD/ CAM systems generated pristine forms which would

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have to be converted into a recognisable

program-ming structure that the machine tool’s servo-drives

could understand and apply This ‘translation’ took

the form of representing complex curves as a series of

straight lines, or linear segments, being joined

end-to-end within a user-defined tolerance band (Fig 248a)

Thus, the length of each linear segment was governed

by the curvature of the profile and the tolerance band

previously set Any tight precision radii on the

work-piece, requires very small tolerance bands, creating a

large number of segments needing considerable

pro-grammed-blocks of toolpath data This technique is

acceptable in many respects, but its hardly very

effi-cient because complex 3-D surfaces need large

quan-tities of data to accurately represent their geometric

profiles This conflict between ‘CAD shape-defining

data’ to that of the machine tool’s motional

kinemat-ics necessary to produce the profile, means that

trans-mission rates and corresponding feedrates suffer, as

each line segment corresponds to a ‘bottleneck’ in the

part program, this being data point expressed as an

X-Y-Z co-ordinate To minimise these problems and

more specifically, now that HSM capabilities are

com-monplace, CNC builders are incorporating ‘complex

curve interpolation’ capabilities into their controllers,

enabling tool paths to be machined utilising the same

mathematical terms that CAD/CAM systems use to

generate them In other words, ‘NURBS’ , which in

practice largely means that for the same quantity of

data, the controller can achieve faster, smoother and

more accurate machining

A ‘NURBS’ is constructed from three discrete

pa-rameters: Poles; Weights; and Knots As a result of

‘NURBS’ being defined by non-linear motions, the

tool paths will have continuous transitions, enabling

significantly higher: acceleration; deceleration; plus

enhanced interpolation speeds; than was previously

 ‘NURBS’: The rational equation, can be expressed, as follows:

P (t) =

i=

n Ni,  (t) GiPi

i=

n Ni,  (t) Gi

The Non-Uniform B-Splines can be expressed, as follows:

Ni,  (t) =����

����

(Ki � t � Ki + )

< Ki, Ki+ < t)

Ni, k (t) = ( tKi ) Ni, k − (t)

Ki + k − Xi + (Ki + k −t ) Ni + , k − (t)

Ki + kKi+  Where: Pi = Control point; Gi = Weight; Ki = Knot

vec-tor (Source: Oakham, 1998)

available by CNC controllers without the ‘complex curve interpolation’ capabilities As ‘NURBS’ have the ability to describe any free-form curve, or surface pre-cisely and efficiently, they became immensely popular with CAD Software-developers, because it allowed Design Engineers more freedom to manipulate 3-D data, than had been available utilising simple ‘line-segments’ and ‘primitives’ The logical extension for the application of ‘NURBS’ was followed-up by CAM

developers, as many systems were integrated into one

by the same company that developed the CAD system This CAD/CAM integration, enabled these companies

to supply post-processors that supported all the major digital controller manufacturers offering a ‘NURBS-capability’

In order to more fully comprehend just how

‘NURBS’ works, it is worth a slight digression to briefly discuss the techniques utilised to represent curved surfaces By way of illustration, the CAD equivalent

of the Draughtsman’s ‘Flexi-curve’ used to create

free-from curves, is termed a ‘spline’  The alternative ‘B-Splines’  differ from that of ‘Splines’ , instead, they

function somewhat like a ‘gravitational pull’ acting on them, pulling and distorting the curve, but in the con-trol point’s direction While, ‘NURBS’ are essentially a more controllable version of ‘B-Splines’ The resulting output from ‘NURBS’ is very efficient, as it describes the curve’s geometry with a fraction of the data output necessary for linear interpolation One disadvantage is that the calculation of ‘NURBS’ are much more com-plex, necessitating considerable amounts of comput-ing power to compute them The ‘Non-Uniform’ term

in ‘NURBS’ , refers to what is called its ‘knot vector’ ,

which indicates the portion of a curve that is affected

by an individual control point, but where it does not have to be ‘uniform’ By ‘dissecting’ the ‘NURBS’ term still further, the portion of it affected by the ‘Ratio-nal’ part of the formula, means that the weight of the control points’ pull (weighting) – which can be speci-fied This ‘weighting’ allows conic sections to be repre-sented, without having to slice them up to determine their geometric aspect

 ‘Splines’ , can simply be defined as follows: As a series of

equally spaced control points which the computer connects to create a smooth flowing curve’.

 ‘B-Splines’ , may be defined in a slightly differing manner to

that of ‘Splines’ , such that: Utilising the end and control points

that do not necessarily intersect the curve, thereby they can dis-tort the curve’ (Source: Oakham, 1998)

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When applying ‘NURBS’ to a complex part’s

curva-ture, it is important to recognise that it defines the entire

curve, not just a series of facets, enabling it to express

any curve geometry, utilising less data than for other

‘curve-fitting techniques’ Data transmission times are

significantly improved as a result, this is because one

does not have to transfer all of the curve data, just the:

control points; the order of the polynomial; the knot

vector; and its weighting; as defined by the CAD

sys-tem Once this has been achieved, the machine tool’s

CNC controller then decodes this information, in

or-der to control its servos While a single ‘NURBS’

ex-pression can describe a simple curve, complex curves

(e.g Fig 248c) are described by moving ‘weighting’ on

the control points, running the calculation, then

mov-ing the ‘weightmov-ing’ again and re-calculatmov-ing and so on,

in a recursive manner Thus, each point moved has

an influence on the others, but the more the control

points utilised, the less their influence becomes – in a

similar manner to the so-called: ‘law of diminishing

returns’ ‘NURBS’ is comparable to linear interpolation

in that the greater the accuracy the more the number

of points needed, although it requires less data in

to-tal – with a figure of 60% data-reduction, with an

as-sociated 40% improvement in time, has been claimed

Although the solution to virtually every curve-fitting

geometry can be undertaken by ‘NURBS’ , it cannot

partake in all ‘surface-describing miracles’ If the CAD

system outputs poor data, this will end up with a

simi-larly pitiable ‘curve-fitting routine’ , so as the old saying

goes, it’s the equivalent of: ‘Garbage in, garbage out!’ In

time, these ‘NURBS’ will have even more refinements

added to enhance the already powerful ‘curve-fitting

processes’

9.8.4 Sculptured Surface Machining –

Cutter Simulation

Once the free-flowing curves for the sculptured

sur-faces have been generated and the actual workpiece

is about to be machined, many companies embark on

a ‘cutter simulation routine’ prior to undertaking any

surface machining Many of the sophisticated surface

machining software packages, can provide several

variations of complex surface machining routines

Typical of such routines, is that shown for a particular

leading company’s product for the multi-axis

sequen-tial machining, depicted in Fig 249a This specific

‘sequential surface machining’ routine (Fig 249a), is

an interactive, graphic implementation of

‘drive-part-check’ surface machining, as defined in the:

Automati-cally Programmed Tool (APT) Standard This routine

is greatly enhanced when utilised in combination with

two other machining software packages, namely: ‘Se-quential machining’; and ‘Drive curve mill’ While an

enhanced function incorporated into the machining

package is termed ‘looping’ , which enables the user to

generate multiple passes on a surface, by defining the inner and outer tool paths, allowing the system to then generate the intermediate stock-clearance tool path steps

A typical modular-package might offer: surface con-touring; parameter line machining; rough-to-depth; and zig-zag tool paths; having any design modifica-tions, or changes being automatically handled through

what is termed ‘associativity’ , thereby significantly

re-ducing any attendant costly, but otherwise necessary prove-outs By utilising cutter simulation, parameters such as: feedrate; spindle speed; and part clearance; are instantly accessible and, being ‘modal’ they remain un-changed, unless the user modifies these values While

at any time during the development of the simulation,

a user can test a setting by generating a tool path with its accompanying high-resolution graphic display (Fig 249a) Surface machining will automatically simulate the cutter’s tool path, being displayed on a graphics

screen and generate textural output into a ‘cutter lo-cation source file’ (CLSF) After simulation, the user

may either choose to accept the tool path simulation and then save these parameters, or reject it and modify whatever parameters are necessary to correct for any attendant problems encountered It should be stated

that if a problem had occurred when actually cutting

the complex geometric component’s surface – such as

‘surface gouging’ 0, this would have probably scrapped

the otherwise expensive stock of workpiece material, that has also added significant value to it, by the time-consuming process of machining this part’s intrinsic geometric characteristics

So the application of cutter simulation is not only economic and fiscally important, it offers many other significant production benefits Therefore, with such enhanced cutter simulation, a range of important fea-tures can be addressed ‘off-line’ , such as:

• Supporting typical CAD ‘Surfaces and Solids’ pack-ages,

• Providing both 3- and 5-axis contouring motion – including tool orientations that may be offset from

0 ‘Surface gouging’ , is if a cutter unintentionally removes

mater-ial (gouges-out) a portion of surface

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Figure 249 By utilising a sophisticated cutter and part simulation technique, any potential and very costly

ma-chining mistakes can be avoided

.

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