• 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
Trang 1Figure 245 The complex machining of either a sculptured, or die and mould surfaces, will usually necessitate both
multifarious and sophisticated programming techniques
.
Trang 2• 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
( cmmin−)
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.
Trang 3erations 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]
.
Trang 4effect 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)
Trang 5Figure 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]
.
Trang 69.8.3 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)
Trang 7Figure 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
Trang 8have 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) = ( t−Ki ) Ni, k − (t)
Ki + k − −Xi + (Ki + k −t ) Ni + , k − (t)
Ki + k−Ki+ 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)
Trang 9When 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
Trang 10Figure 249 By utilising a sophisticated cutter and part simulation technique, any potential and very costly
ma-chining mistakes can be avoided
.