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A computer based tool for the design and manufacture of automatic lathe cams
ELSEWIER
Computers
in Industry 34 (1997) 1l-26
A computer based tool for the design and manufacture of automatic lathe cams Jonathan Borg *, Philip Bonello, Christopher Ciantar Department of Manufacturing Engineering, University of Malta, Msida MSD-06, Malta
Abstract The tool tip motion characteristics required for machining turned components on automatic lathes is a typical example where the compound movements generated by more than one cam plate are practically employed. Achieving problem specific tool tip motion characteristic requires considerable expertise and time in designing two separate planar cams, which when synchronized result in the desired turned component geometric shape. The objective of this paper is to present the analytical models adopted in the design, development and implementation of a computer based prototype tool for supporting the design and manufacture of such planar cams employed by automatic lathes. Evaluation of this prototype reveals that the use of cam profile blending models and edge vector based cam milling path approach, are a beneficial way of employing computers in industry to support the generation of cam plates that cater for profile blending problems inherent with synchronized cams. (3 1997 Elsevier Science B.V. Keywords: Planar cam design; Compound
motion; Profile blending;
1. Introduction The profile of any cam depends on the required follower motion characteristics [l] normally stated in terms of displacement and velocity attributes. In the case of an automatic lathe, primitive curves forming the shape of planar cams such as dwell-rise-dwell are governed by the tool tip motion characteristics required for turning a component having the desired dimensions and geometric attributes such as a spherical profile. The automatic lathe [2] employed as a case-study in this cam design project makes use of two independent spindles each with its own independently controlled double slide compound.
Auto-lathes;
Edge vectors
As with most lathes, each compound consists of two slides: a bottom slide which is constrained to move radially, that is, normal to the axis of rotation of the spindle along the machine bed together with an upper slide which is mounted on the lower slide which is constrained to move axially, that is, along the axis of rotation of the spindle. The tool posts, in this particular case, up to four, are rigidly mounted on the upper slide and are therefore capable of providing compound motion, as schematically illustrated in Fig. 1. The independent motions of the two slides of the compound are controlled by a pair of planar cams [3] consisting of a radial cam controlling toolpost movement in the radial direction and an axial
* Corresponding auth,Dr. 0166-3615/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SOl66-3615(97)00004-3
cam
controlling
movement
tion. The slide compound
motion
in the axial resulting
direc-
from
the
J. Borg et al. / Computers in Industry 34 (1997) II-26
12 Table 1 Relationship
between component
and cam profile
-(Iw
*-
c-
-
-
-+
+
-01
mw
?!zElmi EP -_-_-_E&I
vlvl ;4
r,rbbrrCnlr
azz EP -_-_-_f&J
r ’
c!J
LL r,r-ndCr
,
.I. Borg et al. / Computers in Industry 34 (1997) 1 I-26
13
trated in Fig. 1 has a linear relationship between the displacement of the cam follower and the tool slide. It is evident from Table 1 that there exists a strong relationship between a turned component’s geometric profile and the cam design shape, this due to the automatic lathe’s slide compound motion characteristics required when machining the part. These relationships can be basically stated as: component’s requires +
compound requires +
primitive profile
a specific compound
slide motion
(i)
slide motion synchronized
radial and cam profile curves (ii)
Fig. 1. Principle of compound
tool slide motion.
synchronized radial and axial planar cam movements is traditionally generated by a time-consuming and knowledge intensivle cam design process for each and every batch of components to be turned on such an automatic lathe, resulting in a number of problems highlighted in the next section.
2. Problem background Each primitive geometric profile of a turned component requires a compound slide motion as indicated in Table 1, these in turn requiring the primitive cam profile curves illustrated, from which the radial and axial planar cams can be synthesized. For instance, a cylindrical face primitive of a turned component requires a compound slide motion as illustrated in Table 1, this dictating a concentric contour on the radial cam to provide a dwell motion and a spiral contour on the axial cam for providing a rise motion. The actual type of cam profile used depends on the specific mechanism linking the cam follower to the tool slide of the particular lathe employed. For instance, the simple mechanism schematically illus-
where the term synchronized cam profiles in Eq. (ii) denotes that the resulting compound slide motion characteristic is the effect of the combination of the radial and axial cams profiles. Eq. (i> means that by breaking down a turned component into a number of generic primitives such as a taper profile the related tool post compound slide motion characteristics can be identified. Hence, relative generic cam profile analytical equations for the radial and axial cams can be employed to accurately and quickly design the required curves. Also, relationships (i) and (ii) imply that the cam profile can be synthesized from generic curves such as spiral or concentric, these related to the turned component’s geometric primitive profiles. Component primitive profiles such as taper are analogous to geometric features [4], the difference being that unlike the latter, they are two-dimensional profiles. This concept of 2-dimensional profiles, termed by Kalta et al. [5] as turned features lends itself well to the synthesis design [6] of a turned component by means of primitive profiles; in the case of automatic lathe cam design, the semantics of primitive profiles can include information indicating the type of compound tool post slide motion required and hence the type of radial and cam profile curves (e.g., dwellrise-dwell) for each motion. 2.1. Knowledge
and time intensive process
From the foregoing discussion and Table 1, it is evident that for every new batch of turned compo-
J. Borg et al. /Computers
14
in Industry 34 (1997) 11-26
substantially improved, the fact that the cam design and manufacture process is time consuming and knowledge intensive, makes it unattractive to employ machine tools making use of cams (such as automatic lathes) in today’s manufacturing industry where fast response to market needs demand efficient flexibility. 2.2. Cam projile error sources
I
l*Ic-’ Fig. 2. Typical operation layout sheet.
nents having a different combination of geometric profile curves, a new ‘pair’ of cams is required. Traditionally, these cams have to be either ordered from machine tool suppliers, this at very high cost and with undesirable time delays or else designed and manufactured within the company itself. Adopting the latter approach involves three major steps: (1) Process planning of the component to be machined on the automatic lathe and hence the preparation of what are termed as operation layout sheets of the required cams; operation layout sheets basically describe the amount of radial and axial displacement (in terms of cam radius) required at different cam intervals for each tool tip motion to generate the required tool slide compound motion; a sample operation layout sheet [7] is illustrated in Fig. 2. (2) The geometric design of me radial and axial cam profiles from their layout sheets. (3) Process planning and part programming for the manufacture of the cams on a computer numerically controlled (CNC) milling machine. From research carried out in this project, it was established that the latter two steps and especially the cam profile design process are the most knowledge intensive and time consuming of the whole cam development process because of the calculations involved and the details that have to be taken into consideration such as the blending of the primitive cam profiles to avoid the cam follower roller from jamming up under certain profile situations. Unless
The design of a planar cam involves the computation of points of the various elementary contours (e.g., rise) of which it is made up, each such contour being associated with a particular operation to be controlled by the cam for eventual machining of the turned component. As a consequence, a manual cam profile design approach, results in a wide margin of error. This is because designers commonly employ analytical methods [S-10] (basically making use of algebra and calculus) supplemented by graphical methods [ll] where the former become too complex to handle. Thus, the wide margin of error in the manual design process is attributed both to the limits of manual analytical calculation (such as the determination of sufficiently closely spread points) and to the inevitable errors introduced with graphical construction. For instance, an initial step in the cam design process is the location of the turning operation end points on the cam profile, these implicitly given in operation layout sheets. These specify for each turning operation, the initial and final cam radii and the respective initial and final angular positions. The operation end-contact points are given by the points of intersection of the initial and final cam radii of each operation with the arcs representing the initial and final angular positions of the cam for that operation. These arcs represent the loci of the geometric points of contact of the cam-follower roller with the cam. The automatic lathe employed as a case-study in this research project, does not make use of design charts with straight lines (see Fig. 3) passing through the origin due to an extra degree of motion of the follower. As a result, this lathe and similar machine tools employing followers with extra degrees of motion, introduce a more complex problem for determining exactly the location of the necessary point on the cam contour, requiring a more complex analytical model.
J. Borg et al. / Computers in Industry 34 (1997) I1 -26
Following all th’ese calculations, a CNC part program has to be tediously generated by a part programmer for the milling of the cam plate. The CNC programming task itself is a source of error due to tool path calculation inaccuracies and manual data entry mistakes introduced whilst typing on the CNC controller. All the,re tasks are schematically illustrated in Fig. 4. From the case study encountered, it can be stated that in such an approach, trial and error methods are the norm: The initial designs being invariably inaccurate and corrected after the corresponding cams are milled, tested on the automatic lathe and the resulting turned component examined for defects and dimensional inaccuracies. This procedure is repeated as many times as rrecessary until the resulting turned component turns out satisfactory. Only then are the cam profile designs finalised. The points and contours obtained in the profile design of cams have to be precise not only to ensure accuracy of the component to be machined on the automatic lathe but also to enable the cams to be milled on the CNC milling machine. The latter type of machines work to a high degree of accuracy and readily record runtime errors due to any geometric inconsistency arising from approximations. Hence, additional time is wasted in detecting and rectifying errors recorded by the CNC controller by recalculating all the points on the cam
15
COMPONENT GEOMETRY
DESIGN AND
Performed bY
GENERATION
MANUAL ENTRY OF PART PROGRAM AND CNC MILLING
Fig. 4. Cam development process.
contour. Needless to say, all this has a consequent loss in production and material wastage. 2.3. Problems related to cam profile blending
Fig. 3. Case-study cam design chart.
Using such a generic profile based cam design process introduces another problem which is critical when the motion characteristics of such cams is being used to turn components to a high degree of
16
f, Borg et al. / Computers in industry 34 f 1997) 11-26
3. Analytical models of primitive
Fig. 5. Cam profile blending problem.
cam profiles
It is necessary to first establish an analytical model for locating the end contact points in Cartesian form, of the follower’s roller. For each machining operation, these points relate to what are being termed the primitive cam contour end contact points. As described earlier, these points are implicitly specified in non-Cartesian form in the operation layout sheet. The objective of this analytical model is therefore to determine the Cartesian coordinates x and y of a point P, lying at a radius r on the 0” locus as schematically illustrated in Fig. 6. In general, it can be stated that: x=rcos[90-(8+68)]
accuracy and surface finish. This problem arises with the transition taking place from one generic profile (e.g., idle drop) to another (e.g., spiral). Industrial tests carried out in this project reveal that this transition part in the cam profile has to be blended in such a way so as to avoid potential motion characteristic problems resulting from the cam’s follower roller momentarily jamming up or loosing contact with the cam plate under certain profile situations such as that illustrated in Fig. 5. 2.4. Emerging research problem The foregoing arguments suggest that speeding up the design and manufacture of cams is beneficial to today’s firms still utilizing cam-driven machine tools. In an effort to efficiently design and manufacture the cam plates, computer based assistance becomes an attractive route as it not only helps in speeding up the cam design and manufacture process but also ensures that cam design expertise is available when and where required even if the human cam designer is not available or is busy with more demanding tasks. The emergent problem in achieving this objective is therefore the formulation of computational feasible analytical models for the different primitive cam profile curves which however automatically take into consideration the highlighted profile blending requirement for the different profile combinations so as to enable a generic profile based cam design approach to be adopted.
(1)
y=rsin[90-(8+68)] where 80 = 88 ( r camtype)
(2)
that is, SO is a function of radius r and the type of cam being designed (in the case-study, camtype = 1 assigned to an axial cam and camtype = 2 assigned to a radial cam). This is necessary since the exact geometry of the loci of the geometric points of contact of the follower roller on a cam depends on the specific linkage mechanism in a machine tool for which the cams are being developed, in this casestudy that linking the follower and the toolpost, being different for the axial and radial cam follow-
Y t
e’ Division Line
Fig. 6. Locating end-contact
points.
J. Borg et al. / Computers in Industry 34 (1997) 11-26
17
ers. Similar expres:sions have been developed for SO for the axial and radial cams employed in this casestudy and can be found in the work by Bone110 et al.
ml. A computer procedure nicknamed Endpoints0 employing Eqs. (1) and (2) were developed and implemented in the prototype computer based tool to locate the end contact points of all the different primitive contours making up a planar cam. After end contact points are determined through the above approach, they are joined by primitive contours, resulting in the necessary cam profile.
kentm of
mtatlcm) Fig. 7. Generating point on spiral.
3.1. Spiral primitiue contour analytical
model
The function of a spiral contour is to provide a steady rate of increase to the planar cam radius with the cam rotation, and hence a constant component of the tool tip motion characteristic in the direction controlled by that particular cam. As illustrated in Table 1, such a motion characteristic and hence contour is used for generating a radial face, a cylindrical face, a chamfer or taper primitive profile on the turned component. The latter turned component profiles require a synchronized motion in both the axial and radial directions, thereby making the precision and surface finish quality of component chamfers highly sensitive to errors generated in the determination of the spiral contours. This again highlights the benefits of computer based profile generation over a manual and graphical approach since it becomes easier to efficiently generate a large number of highly accurate points. The general equation of a spiral contour, employed in the definition of this analytical model, is of the form: R=R,+k@
(3) where: R = radius at the 0” locus, R, = starting radius, k = constant. R and 0 are not polar coordinates and the spiral contour is not an ordinary Archimedean spiral [ 131. Fig. 7 illustrates the principle method of generating successive points with coordinates u[j], u[ j] (j = 1, 2,. . . ) on the spiral contour, (these separated by a 1’) of cam rotation, given the initial and final cam radii together with the initial and final angular positions. It should. be stated that the 1” interval has been empirically determined as it was found highly adequate for machining of the contour.
If Sangle = (endaugle - stangle) and Srad = (endrad - &ad), then, the rate of increase in the cam radius is given by: Grad radrate = Sangle Hence, if rad[ j] is the radius at point number the spiral contour (see Fig. 7), then: rad[ j]: = strad + 0.2( j - 1) X radrate and the angular position of point number by:
‘j’ on
(5) ‘j’ is given
O[j]:=stangle+0.2(j-1)
(6)
Hence, u[ j]: = rad[ j] X cos[90 - {@[j} + @J(rad[jl,camtype))l
(7)
u[j]:=rad[j]Xsin[90-{O[j] +~@(rad[jl,camtype)j]
(8)
using a similar approach to that used in the preceding paragraphs. The expressions can be employed from j= 1 to k where kissuchthatpoint{u[k],v[k]) does not lie on an angular position clockwise to the final angular position endangle. A computer based version of this analytical model, called Spiral0 has been implemented in the prototype system for evaluation purposes. 3.2. Modet for the blending of spiral contours As highlighted earlier, a major problem in generating planar cam profiles is, that unless preceded by
J. Borg et al./Computers rfolloner
roller
El Wy2)
wa32)
0
X Fig. 8. Special blending.
an invariably steeper idle rise primitive contour a spiral contour needs to be blended with the preceding curve by giving it a small starting radius so as to prevent the cam follower from momentarily loosing contact with the cam. If this condition is not catered for in the cam profile, it would result in serious dimensional and surface finish defects during taper turning and chamfering operations due to the loss of synchronicity between the compound motions of the radial and axial cams. As an example of how cam profile blending can be achieved, this section describes the equations developed for blending spiral contours forming part of the Blending0 model. In Fig. 8, A-B are the end contact points of the primitive spiral contour computed as described in the previous section. (R,a), (r,,O,) and (r2,02) are all polar coordinates relative to the initial line OX. In order to provide suitable blending, the problem becomes one of locating the point of tangency P of a spiral drawn from B, tangent to the follower’s roller. Having located P, a spiral contour can then be generated from P to B using the procedure Spiral0
in Industry 34 (1997) 11-26
defined earlier. The complete primitive contour will therefore consist of a radiused portion AP providing the necessary blending and a spiral contour PB providing the required tool motion characteristics. The analytical solution derived for this blending problem is one based on approximation for the purpose of determining the coordinates of P only. This assumes that spiral PB is an Archimedean spiral of the type r = (r. + k@) where r and 0 are now polar coordinates, (as distinct from equation 3) measure relative to axis OX. Testing out of cam profiles generated using this method revealed that this approximation is an acceptable one with respect to the dimensional accuracy manifested in the turned components. From Fig. 9, it can be seen that:
r=r,+(e-8,)-
R - r2
(Y- 8,
From which it can be found that:
[COS(Y-(a-
(10) Also, P lies on the roller’s circle equation,
(11)
(x-p)2+(y-4)2=r; Hence, (RCOS(Y-R)2+(Rsina-q)2=r~ A2
/\repositioning
rounded
No maneouvre
B,)sincr]
off
Manoeuvre Fig. 9. Tool manoeuvring.
at sharp
edge
J. Borg et al. / Computers in Industry 34 (1997) 11-26
from which, on expansion ing is obtained: R=pcosa+qsintr-
and solution,
the follow-
(pcoso+qsina)’ 1
-(p2+q2-r$
(12)
Also, from Eq. (111, one can find that,
(fJP=-(g-)
(13)
From Eqs. (10) and (13), -(
19
completed by generating a spiral from P to B using the procedure Spiralo. Analytical models employing similar methods have been generated for the other cam profile primitive contours listed in Table 1, individually explained in the work by Bone110 et al. [12]. The provision of these analytical models supports the complete profile design process for planar cams. The design solution generated through these models has to be converted into machine instructions for the machining of the cam plates on a CNC machine tool, a conversion process achieved as described in the following section.
“,f;::;) 4. CNC process planning and part progrartming
[cosa - ((Y - B,)sino]
(14) Now, from Eq. (1.2), it can be seen that R is a function of (Y, anjd that therefore Eq. (14) can be written in the form: f(a)
=0
(15) where, (Y will be the only unknown variable. This equation was solved for (Y to a high degree of accuracy using the Newton Raphson’s Method [14] taking 0, as the initial approximation for (Y as A is sufficiently close to P. After R and cx are determined, (Y‘, the angular position of P is established by considering that CY ’ = 90 - cx - 6@( R, camtype) thereby converting (Y from radians to degrees. A procedure Startradius() based on these derived equations has been imlplemented in the prototype computer based system for evaluation purposes of the profile blending approach. The centre of the cam follower roller, (p,q) is given by: p = (r, + r,)sin8, 4=(r,+r,)cos8,
(16)
where r,, is the design value of the follower roller radius, which is however taken larger by up to 1 mm than the actual value so as to give adequate clearance of fit of the roller in the cam contour valleys. Once r and a1 are determined, the primitive contour is
Once the contour of the cam has been generated the implemented system has to perform the necessary process planning and part programming for the machining of cams on a CNC milling machine. The cams are milled from steel discs of thickness 10 mm and radius 65-70 mm. The prototype system developed first ‘plans’ the path to be taken by the milling cutter and therefore examines the overall profile of the cam contour. This is achieved by making use of the primitive curves established during design. The most suitable point on the contour from where to start milling has to be determined for such an exercise. Practical experience translates itself to a point that should be a sharp comer since the tool will be cutting the two sides forming the comer not sequentially but towards the beginning and end of the milling operation. Moreover, the entry of the tool into the profile at the start of the milling process should be tangential to the side of the comer to be cut first. This means that the analytical model (on which a computer system is to be based) has to be capable of identifying all the sharp comers of the contour (a comer or edge is said to be formed where the ends of the two adjacent primitive profiles meet). In addition, sharp comers necessitate special manoeuvring of the tool as shown in Fig. 9. Experience gained in the project shows that the loss of accuracy in the resulting turned component due to the rounding off of a sharp edge is highly significant and should therefore be catered for during the cam profile process planning procedure. Moreover, the runoffs and re-entries of the tool during
20
J. Borg et al./Computers
such a manoeuvre shoArchuld preferably be tangential. Also, a circular repositioning movement is suitable as it maintains the tool at a constant distance from the comer; if the repositioning was defined as linear, the shortest distance of the tool from the comer would depend on the comer angle, resulting in cam profile chipping off for small angles if the distance is less than the tool radius. Thus the milling cutter requires guidance from the beginning to the end of its path, provided by what are being termed edge vectors. This concept ensures that the system generates a precise, effective and safe milling cutter path for any given cam profile design. Edge vectors are vectors that point tangentially outwards from the ends of each elementary contour. An example for the radiused spiral contour is given in Fig. 10. Analytical models employing suitable mathematical formulae are thus implemented in the prototype system to ensure that these vectors point in the correct direction under all cam profile conditions. Referring to Fig. 11, the angle a[ i] between the edge vectors x,[i]i + yJi]j and x,[i + l]i + y,[i + llj is an indication of the sharpness of the comer formed at the point where the contours for the operations numbers i and i + 1 meet (the smaller the L![i], the sharper the comer). This analytical model, nicknamed Sharp0 will consider a comer sharp if the corresponding value for n[i] is less than a certain predefined constant sharpmin (defined as 140” in this project). Hence after computing all the edge vectors x,[ i]i + yl[i]j and x,[i]i + y2[i]j (from i: = 1 to noops), the angle O[i] between any two adjacent edge vec-
in Industry 34 (1997) 11-26
\ yl[i
+
Fig. 11. Determination
OF OPERATION
No.
i
:
SPIRAL
(risetype[i]
=
I
I
RADIUSED
SPIRAL
(risetype[i
-
1]
Fig. 10. Edge vectors example.
=
1)
2)
of sharp corners
tors is calculated. The least LZ[i] is then determined so as to find the sharpest comer. The start point S of the cam milling process is hence established. The model then uses the appropriate edge vector to find point S, such that
is tangential to the cam contour (S, will be the point of immersion of the tool into the material and
represents to be cut; TYPE
+ llj
the approach of the cutter to the contour
I@ is a constant controlled by the user called startdistance. Hence, the entry into the contour will be tangential. It should be stated that l2[i] is defined as the comer angle at the end of operation number i when moving clockwise round the cam. Referring to Fig. 12, to determine S,,, the analytical model takes the edge vector indicated, normalises
J. Borg et al. / Computers in Industry 34 (1997) 11-26
Operation
21
no. (start-l)
i+
IPart
Fig. 12. Determination
it (that is, reduces it to unit magnitude) scalar multiplication to obtain vector
and performs
of initial cutting point.
cams, making use of analytical for tool manoeuvring.
models such as those
5.1. Cam profile design module
Having previously calculated the coordinates of S (in the cam design stage) SO will then be located, this allowing the tool path CNC program to be initiated and calculated. This Sharp0 model has been embedded within the CNC part programming module of the prototype system developed, described in the following section.
5. The CAMCAM
prototype system
A prototype computer based system (nicknamed CAMCAM) employing the analytical models developed, has been implemented on an IBMTM compatible personal computer, using the programming environment provided by Turbo PascalTM. This programming language was selected as it provided adequate mathematical and graphical functions besides the fact that it was readily available. The CAMCAM system consists bastcally of two modules, (1) Generating the cam profile design making use of analytical mode1.s such as those for spiral curves and for profile blending, (2) Another module for the generation of the CNC part program, necessary for machining the planar
The generation of the component’s process plan and the preparation of the operation layout sheets of the required cams require a great deal of personal judgement and were therefore left to the designer, this resulting in a computer based assistance approach rather than complete design and manufacturing automation [151. As a consequence, when using the cam profile design module, the user inputs the manually generated operation layout sheet. During entry of the related information the system assigns relevant values to variables such as integer values to two array components risetype[ i] and droptype[il from i: = 1 to No._of_operations according to the type (e.g., facing) of operation number i. This integer value enables the system to subsequently recognise the type of each operation (e.g., chamfering) defined by the user. By means of model Endpointso, the system is capable of performing the first step in the cam design process: the location of the end points of the cam contour required for each operation to be controlled by the cam. After all the operation end points have been located the system ‘visits’ each operation No. i (i: = 1 to no_of_operations) of the layout sheet, examines its type according to its values of risetype[il and droptype[i] and employs the appro-
22
J. Borg et d/Computers
in Industry 34 (1997) 11-26
priate analytical model (convexsphere, concavesphere, ideldrop, etc.) to generate the required cam profile for that operation. In addition, the CAMCAM system employs the related Blending0 model for blending the primitive curves. Blending becomes necessary whenever the previous primitive contour is less steep than the following one. Once the cam profile is completely designed, it’s resultant geometry is automatically employed by the part programming module to generate the necessary tool path and hence machine instructions. Fig. 13 is a flowchart illustrating how the analytical models developed have
been implemented module.
5.2. CNC part programming
OPERATION
LAYOUT
GENERATE
ENDPOINTS
-
SHEET
DATA
I
CHECK
SAVE
II
FOR TYPE
CAM GEOMETRIC
‘_
profile design
module
By retrieving the cam profile generated, this module first determines the initial (sharp) cutting point using the model Sharp() described earlier. The system then ‘visits’ each elementary contour making up the cam profile, examines its type (e.g., by considering risetype[ i] and generates the appropriate CNC blocks for machining the contour. Since only linear
INPUT
by
in the CAMCAM
using
ENDPOINTS<
>
OF OPERATION
PROFILE
DATA
Fig. 13. Flow chart for cam profile design module.
23
J. Borg et al. / Computers in Industry 34 (1997) 1 l-26
and circular interpolations are possible on the milling machines used in this case study, curves such as spiral are machined either by linear or circular interpolation from point to point as chosen by the user. Following evaluation experiments, only points separated by 1” of arc are considered when milling such
curves. In the case of spiral milling by circular interpolation the system takes three consecutive points at a time, locates the centre of the circular arc that fits them and writes the CNC block for the milling of each such small arc. After writing the CNC block(s) for the generation of the contour of an
EXAHNTYRQCERATIONNfJ.IAM WWIE GLOCKSTO GaauTE
WRITE GLOCKS TO mmmi WNOEWREATAWPWESE UsIts -0 I
RRITE SLOC%STO TEMNAlE I
P!ACHlNMG PWCEG3
Fig. 14. Flow chart for cam profile design module.
ITS CCMTOU?
24
J. Borg et al./Computers
operation No. i, the procedure examines its value of L?[i] to see if there is a sharp corner at the end of that contour (a[ i] < sharpmin). If so, then the additional blocks to enable the tool to perform a manoeuvre, as indicated earlier in Fig. 9 are generated, using the Manoeuvreo model which makes use of edge vectors previously computed, to guide the tool safely around the sharp comer. The method used to locate A, and A, is similar to that previously indicated to obtain point S, at the start of the milling process. In the CAMCAM system, an option for the graphical simulation of the milling cutter path is also provided; this was found particularly helpful by the operator of the CNC milling machine when determining the clamping points for the cam blank. In addition, the CAMCAM system allows the automatic transfer of the generated CNC code from the PC to the CNC machine’s controller thereby eliminating the laborious, time consuming and error prone, manual data entry task. Fig. 14 illustrates how the cam machining process plan and CNC code are generated in the CAMCAhil part programming module. 5.3. System evaluation The CAMCAM prototype system provided a suitable testbed for evaluating the different analytical models developed. Axial and radial cams were generated for testing on a Kummer K20 lathe. The CAMCAM system was interfaced and tested on two CNC controllers, one utilising a SiemensTM [16] controller whilst the other utilising a HeidenhainTM [17] controller. It has been tested on a total of twenty-four layout sheets producing successfully the cam design and part program in each case. The criteria used for measuring this success was attributed to the fact that the cam plates designed and machined generated the required turned component on the Kummer automatic lathe without the need of any modification to their profile. Also, the resulting components using the CAMCAM system had dimensional tolerance and surface finish superior to those previously machined from manually designed cams. This was evident for instance from the accuracy of tapers and chamfers verified by measurements on an optical comparator. Plate 1 illustrates one of a pair of cams designed and machined via the CAMCAM system.
in Industry 34 (1997) II-26
Plate 1. Planar cam designed CAM system.
and manufactured
through
CAM-
As a consequence the evaluation of the CAMCAM prototype system employing the analytical models developed, besides demonstrating that the models developed are computational feasible, reveals that: . Errors due to the lack of accuracy associated with manually designed cams and traditional profile blending problems are eliminated. . There is a significant reduction in the time required to design the cams and the time required to program the CNC controller, with a consequent reduction in the costs of cams. . It becomes feasible to re-utilize cam-driven machinery such as automatic lathes in markets demanding efficient and flexible manufacturing operations. However, as implemented, the system provides no means of supporting or automating the generation of the cam profile design directly from the turned component’s geometry. A future direction for research in automatic lathe cam design is one related towards supporting the generation of cam profiles by a turned component feature-based-approach, thereby eliminating the need of manually generating operation layout sheets.
6. Conclusions The research work carried out reveals that it is not sufficient to implement analytical models for the generation of cam profile primitive curves. This is because the synthesis of these individual curves commonly results in profiles having transition points that are the source of erratic follower movement, due
J. Borg et al. /Computers
to the follower’s roller momentarily sticking or losing contact with the cam plates. The CAMCAM prototype system demonstrates that a superior approach to planar cam profile design is the combined implementation of the analytical models established in this paper which generate the required primitive profile curves and which automatically take into consideration the necessary profile blending requirements. Besides resulting in an approach that provides a generic framework that can be equally applied to other machine tools or applications, the resultant cam profile is a superior starting point for the generation of the required cam milling process plan and the CNC part programming exercise. From a practical point of view, the case study fum is “extremely satisfied with the results” obtained and is now making use of the prototype system. This demonstrates how the computational feasible analytical models established and presented in this paper can help today’s industry efficiently utilise machine tools employing motion characteristics generated through one or more planar cam.
Acknowledgements: This project received considerable support from the Department of Manufacturing Engineering of the Faculty of Engineering, University of Malta. The authors would like to thank Mr. F.E. Farrugia, Head of the Manufacturing Engineering Department, and Mr. M.P. Scibetras, then Manager at Beacon Precision Limited, for their professional advice and for the latter in providing frequent access to the company’s facilities where the implemented computer based cam profile design system was installed and evaluated.
References [l] D.M. Tsay, B.J. Lin, Improving the geometry design of cylindrical cams using nonparametric rational B-splines, Computer-Aided Design 28 (11 (1996) 5-15. [2] M. Haslehurst, Auto lathes, In: Manufacturing Technology, 3d Edn. Hodder and Stoughton, London, 1985, pp. 109-125. [3] .I. Hannah, R.C. Stephens, Mechanics of Machines, Elementary Theory and Examples, 4th Edn., Edward Arnold, London, 1984, pp. 1244137.
in Industry 34 (1997) 11-26
25
[4] L.S. Wierda, Linking design, process planning and cost information by feature-based modelling, .I. Eng. Des. 2 (1) (1991) 3-19. [5] M. Kalta, B.J. Davies, CADEXCAP: Integration of 2D CAD models of turned components with CAPP, Int. J. Mamtfact. Technol. 8 (1993) 145-159. [6] G. Pahl, W. Beitz, Engineering Design, The Design Council, Springer-Verlag, London, 1984. 171 K. Freres, Instructions for the Preparation of Operation Layouts. Calculation of Machining Time, Cam Design for Kummer - Two Spindle Chucking Automatics K20, Kummer Freres, Tramelan, Suisse. [8] S.G. Dhande, B.S. Bhadoria, J. Chakraborty, A unified approach to the analytical design of three-dimensional cam mechanisms, ASME J. Eng. Indust. 97B (1) (1975) 327-333. [9] R.L. Jordan, A general approach to CAM surface definition, Design For Manufacturability., ASME 52 (1993) 159-162. [lo] D.M. Tsay, C.O. Huey Jr., Application of rational B-splines to the synthesis of cam-follower motion programs, ASME J. Mech. Des. 115 (3) (1993) 621-626. [ll] W. Abbott, Practical geometry and engineering graphics, Blackie, London, 1972, pp. 62. [12] P. Bonello, C. Ciantar, Computer Aided Design and Manufacture of Cams, Dissertation, Department of Mechanical Engineering, University of Malta, May 1994. [13] A.E. Avallone, T. Baumeister III, Mark’s Standard Handbook for Mechanical Engineers, 9th Edn., McGraw-Hill, New York, pp. 2-26. [I41 A.E. Avallone, T. Baumeistem III, Mark’s Standard Handbook for Mechanical Engineers, 9th Edn., McGraw-Hill, New York, pp. 2-16, 2-44. [15] K.J. MacCallum, Does intelligent CAD exist?, Artificial Intell. Eng. 5 (2) (1990) 1. [16] Huller Hille, Instructions for Programming, Huller Hille, 1984. [ 171 Heidenhain, Heidenhain TNC145, TNCl50, TNC15 1, TNC155 Contouring Control-Issue No. 12/85, Dr. Johannes Heidenhain, GMBH. Jonathan Borg graduated in Mechancal Engineering from the University of Malta in 1989, after which he worked for 3 years with a Water Authority responsible for CAD systems employed for designing desalination plants. During this period, he also formed part of a team responsible in designing and implementing a computer based mathematical model of a water aquifer. In 1992 he joined the University of Malta, responsible for lecturing and carrying out research in CAD/CAM. In 1993, he graduated with an MSc in Computer Aided Engineering Design from the University of Strathclyde, Glasgow, with whom he is currently a PhD candidate. He is a member of the Institute of Engineering Designers (UK), the Institute of Mechanical Engineers (UK) and the Society of Manufacturing Engineers (USA).
26
J. Borg et al. / Computers in Industry 34 (1997) I1 -26
Philip Bonello graduated in Mechanical Engineering from the University of Malta in 1994. He has since been employed as an engineer with Enemalta Corporation, the island’s energy producer, where he is in charge of a team of maintenance workshop personnel who carry out maintenance work on power plant components at a major power station. His current research interest is the development of a computerised modelbased fault diagnosis system as applied to power-plant components encompassing material failure and vibration problems in rotating machinery. Since 1995, Mr.Bonello has been a part-time lecturer in the Department of Mechanical Engineering of the University of Malta.
Christopher Ciantar has studied Mechanical Engineering at the University of Malta and later moved to Brunei University London where he completed studies in the building services industry leading to an MSc degree. He is currently employed as a building services engineer with particular responsibilities for managing the computer-aided system design of commercial and industrial environments. His areas of interest are focused on computer-based techniques used to design and optimise processes used in the building services industry.
Computers
in Industry 34 (1997) 1l-26
A computer based tool for the design and manufacture of automatic lathe cams Jonathan Borg *, Philip Bonello, Christopher Ciantar Department of Manufacturing Engineering, University of Malta, Msida MSD-06, Malta
Abstract The tool tip motion characteristics required for machining turned components on automatic lathes is a typical example where the compound movements generated by more than one cam plate are practically employed. Achieving problem specific tool tip motion characteristic requires considerable expertise and time in designing two separate planar cams, which when synchronized result in the desired turned component geometric shape. The objective of this paper is to present the analytical models adopted in the design, development and implementation of a computer based prototype tool for supporting the design and manufacture of such planar cams employed by automatic lathes. Evaluation of this prototype reveals that the use of cam profile blending models and edge vector based cam milling path approach, are a beneficial way of employing computers in industry to support the generation of cam plates that cater for profile blending problems inherent with synchronized cams. (3 1997 Elsevier Science B.V. Keywords: Planar cam design; Compound
motion; Profile blending;
1. Introduction The profile of any cam depends on the required follower motion characteristics [l] normally stated in terms of displacement and velocity attributes. In the case of an automatic lathe, primitive curves forming the shape of planar cams such as dwell-rise-dwell are governed by the tool tip motion characteristics required for turning a component having the desired dimensions and geometric attributes such as a spherical profile. The automatic lathe [2] employed as a case-study in this cam design project makes use of two independent spindles each with its own independently controlled double slide compound.
Auto-lathes;
Edge vectors
As with most lathes, each compound consists of two slides: a bottom slide which is constrained to move radially, that is, normal to the axis of rotation of the spindle along the machine bed together with an upper slide which is mounted on the lower slide which is constrained to move axially, that is, along the axis of rotation of the spindle. The tool posts, in this particular case, up to four, are rigidly mounted on the upper slide and are therefore capable of providing compound motion, as schematically illustrated in Fig. 1. The independent motions of the two slides of the compound are controlled by a pair of planar cams [3] consisting of a radial cam controlling toolpost movement in the radial direction and an axial
* Corresponding auth,Dr. 0166-3615/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SOl66-3615(97)00004-3
cam
controlling
movement
tion. The slide compound
motion
in the axial resulting
direc-
from
the
J. Borg et al. / Computers in Industry 34 (1997) II-26
12 Table 1 Relationship
between component
and cam profile
-(Iw
*-
c-
-
-
-+
+
-01
mw
?!zElmi EP -_-_-_E&I
vlvl ;4
r,rbbrrCnlr
azz EP -_-_-_f&J
r ’
c!J
LL r,r-ndCr
,
.I. Borg et al. / Computers in Industry 34 (1997) 1 I-26
13
trated in Fig. 1 has a linear relationship between the displacement of the cam follower and the tool slide. It is evident from Table 1 that there exists a strong relationship between a turned component’s geometric profile and the cam design shape, this due to the automatic lathe’s slide compound motion characteristics required when machining the part. These relationships can be basically stated as: component’s requires +
compound requires +
primitive profile
a specific compound
slide motion
(i)
slide motion synchronized
radial and cam profile curves (ii)
Fig. 1. Principle of compound
tool slide motion.
synchronized radial and axial planar cam movements is traditionally generated by a time-consuming and knowledge intensivle cam design process for each and every batch of components to be turned on such an automatic lathe, resulting in a number of problems highlighted in the next section.
2. Problem background Each primitive geometric profile of a turned component requires a compound slide motion as indicated in Table 1, these in turn requiring the primitive cam profile curves illustrated, from which the radial and axial planar cams can be synthesized. For instance, a cylindrical face primitive of a turned component requires a compound slide motion as illustrated in Table 1, this dictating a concentric contour on the radial cam to provide a dwell motion and a spiral contour on the axial cam for providing a rise motion. The actual type of cam profile used depends on the specific mechanism linking the cam follower to the tool slide of the particular lathe employed. For instance, the simple mechanism schematically illus-
where the term synchronized cam profiles in Eq. (ii) denotes that the resulting compound slide motion characteristic is the effect of the combination of the radial and axial cams profiles. Eq. (i> means that by breaking down a turned component into a number of generic primitives such as a taper profile the related tool post compound slide motion characteristics can be identified. Hence, relative generic cam profile analytical equations for the radial and axial cams can be employed to accurately and quickly design the required curves. Also, relationships (i) and (ii) imply that the cam profile can be synthesized from generic curves such as spiral or concentric, these related to the turned component’s geometric primitive profiles. Component primitive profiles such as taper are analogous to geometric features [4], the difference being that unlike the latter, they are two-dimensional profiles. This concept of 2-dimensional profiles, termed by Kalta et al. [5] as turned features lends itself well to the synthesis design [6] of a turned component by means of primitive profiles; in the case of automatic lathe cam design, the semantics of primitive profiles can include information indicating the type of compound tool post slide motion required and hence the type of radial and cam profile curves (e.g., dwellrise-dwell) for each motion. 2.1. Knowledge
and time intensive process
From the foregoing discussion and Table 1, it is evident that for every new batch of turned compo-
J. Borg et al. /Computers
14
in Industry 34 (1997) 11-26
substantially improved, the fact that the cam design and manufacture process is time consuming and knowledge intensive, makes it unattractive to employ machine tools making use of cams (such as automatic lathes) in today’s manufacturing industry where fast response to market needs demand efficient flexibility. 2.2. Cam projile error sources
I
l*Ic-’ Fig. 2. Typical operation layout sheet.
nents having a different combination of geometric profile curves, a new ‘pair’ of cams is required. Traditionally, these cams have to be either ordered from machine tool suppliers, this at very high cost and with undesirable time delays or else designed and manufactured within the company itself. Adopting the latter approach involves three major steps: (1) Process planning of the component to be machined on the automatic lathe and hence the preparation of what are termed as operation layout sheets of the required cams; operation layout sheets basically describe the amount of radial and axial displacement (in terms of cam radius) required at different cam intervals for each tool tip motion to generate the required tool slide compound motion; a sample operation layout sheet [7] is illustrated in Fig. 2. (2) The geometric design of me radial and axial cam profiles from their layout sheets. (3) Process planning and part programming for the manufacture of the cams on a computer numerically controlled (CNC) milling machine. From research carried out in this project, it was established that the latter two steps and especially the cam profile design process are the most knowledge intensive and time consuming of the whole cam development process because of the calculations involved and the details that have to be taken into consideration such as the blending of the primitive cam profiles to avoid the cam follower roller from jamming up under certain profile situations. Unless
The design of a planar cam involves the computation of points of the various elementary contours (e.g., rise) of which it is made up, each such contour being associated with a particular operation to be controlled by the cam for eventual machining of the turned component. As a consequence, a manual cam profile design approach, results in a wide margin of error. This is because designers commonly employ analytical methods [S-10] (basically making use of algebra and calculus) supplemented by graphical methods [ll] where the former become too complex to handle. Thus, the wide margin of error in the manual design process is attributed both to the limits of manual analytical calculation (such as the determination of sufficiently closely spread points) and to the inevitable errors introduced with graphical construction. For instance, an initial step in the cam design process is the location of the turning operation end points on the cam profile, these implicitly given in operation layout sheets. These specify for each turning operation, the initial and final cam radii and the respective initial and final angular positions. The operation end-contact points are given by the points of intersection of the initial and final cam radii of each operation with the arcs representing the initial and final angular positions of the cam for that operation. These arcs represent the loci of the geometric points of contact of the cam-follower roller with the cam. The automatic lathe employed as a case-study in this research project, does not make use of design charts with straight lines (see Fig. 3) passing through the origin due to an extra degree of motion of the follower. As a result, this lathe and similar machine tools employing followers with extra degrees of motion, introduce a more complex problem for determining exactly the location of the necessary point on the cam contour, requiring a more complex analytical model.
J. Borg et al. / Computers in Industry 34 (1997) I1 -26
Following all th’ese calculations, a CNC part program has to be tediously generated by a part programmer for the milling of the cam plate. The CNC programming task itself is a source of error due to tool path calculation inaccuracies and manual data entry mistakes introduced whilst typing on the CNC controller. All the,re tasks are schematically illustrated in Fig. 4. From the case study encountered, it can be stated that in such an approach, trial and error methods are the norm: The initial designs being invariably inaccurate and corrected after the corresponding cams are milled, tested on the automatic lathe and the resulting turned component examined for defects and dimensional inaccuracies. This procedure is repeated as many times as rrecessary until the resulting turned component turns out satisfactory. Only then are the cam profile designs finalised. The points and contours obtained in the profile design of cams have to be precise not only to ensure accuracy of the component to be machined on the automatic lathe but also to enable the cams to be milled on the CNC milling machine. The latter type of machines work to a high degree of accuracy and readily record runtime errors due to any geometric inconsistency arising from approximations. Hence, additional time is wasted in detecting and rectifying errors recorded by the CNC controller by recalculating all the points on the cam
15
COMPONENT GEOMETRY
DESIGN AND
Performed bY
GENERATION
MANUAL ENTRY OF PART PROGRAM AND CNC MILLING
Fig. 4. Cam development process.
contour. Needless to say, all this has a consequent loss in production and material wastage. 2.3. Problems related to cam profile blending
Fig. 3. Case-study cam design chart.
Using such a generic profile based cam design process introduces another problem which is critical when the motion characteristics of such cams is being used to turn components to a high degree of
16
f, Borg et al. / Computers in industry 34 f 1997) 11-26
3. Analytical models of primitive
Fig. 5. Cam profile blending problem.
cam profiles
It is necessary to first establish an analytical model for locating the end contact points in Cartesian form, of the follower’s roller. For each machining operation, these points relate to what are being termed the primitive cam contour end contact points. As described earlier, these points are implicitly specified in non-Cartesian form in the operation layout sheet. The objective of this analytical model is therefore to determine the Cartesian coordinates x and y of a point P, lying at a radius r on the 0” locus as schematically illustrated in Fig. 6. In general, it can be stated that: x=rcos[90-(8+68)]
accuracy and surface finish. This problem arises with the transition taking place from one generic profile (e.g., idle drop) to another (e.g., spiral). Industrial tests carried out in this project reveal that this transition part in the cam profile has to be blended in such a way so as to avoid potential motion characteristic problems resulting from the cam’s follower roller momentarily jamming up or loosing contact with the cam plate under certain profile situations such as that illustrated in Fig. 5. 2.4. Emerging research problem The foregoing arguments suggest that speeding up the design and manufacture of cams is beneficial to today’s firms still utilizing cam-driven machine tools. In an effort to efficiently design and manufacture the cam plates, computer based assistance becomes an attractive route as it not only helps in speeding up the cam design and manufacture process but also ensures that cam design expertise is available when and where required even if the human cam designer is not available or is busy with more demanding tasks. The emergent problem in achieving this objective is therefore the formulation of computational feasible analytical models for the different primitive cam profile curves which however automatically take into consideration the highlighted profile blending requirement for the different profile combinations so as to enable a generic profile based cam design approach to be adopted.
(1)
y=rsin[90-(8+68)] where 80 = 88 ( r camtype)
(2)
that is, SO is a function of radius r and the type of cam being designed (in the case-study, camtype = 1 assigned to an axial cam and camtype = 2 assigned to a radial cam). This is necessary since the exact geometry of the loci of the geometric points of contact of the follower roller on a cam depends on the specific linkage mechanism in a machine tool for which the cams are being developed, in this casestudy that linking the follower and the toolpost, being different for the axial and radial cam follow-
Y t
e’ Division Line
Fig. 6. Locating end-contact
points.
J. Borg et al. / Computers in Industry 34 (1997) 11-26
17
ers. Similar expres:sions have been developed for SO for the axial and radial cams employed in this casestudy and can be found in the work by Bone110 et al.
ml. A computer procedure nicknamed Endpoints0 employing Eqs. (1) and (2) were developed and implemented in the prototype computer based tool to locate the end contact points of all the different primitive contours making up a planar cam. After end contact points are determined through the above approach, they are joined by primitive contours, resulting in the necessary cam profile.
kentm of
mtatlcm) Fig. 7. Generating point on spiral.
3.1. Spiral primitiue contour analytical
model
The function of a spiral contour is to provide a steady rate of increase to the planar cam radius with the cam rotation, and hence a constant component of the tool tip motion characteristic in the direction controlled by that particular cam. As illustrated in Table 1, such a motion characteristic and hence contour is used for generating a radial face, a cylindrical face, a chamfer or taper primitive profile on the turned component. The latter turned component profiles require a synchronized motion in both the axial and radial directions, thereby making the precision and surface finish quality of component chamfers highly sensitive to errors generated in the determination of the spiral contours. This again highlights the benefits of computer based profile generation over a manual and graphical approach since it becomes easier to efficiently generate a large number of highly accurate points. The general equation of a spiral contour, employed in the definition of this analytical model, is of the form: R=R,+k@
(3) where: R = radius at the 0” locus, R, = starting radius, k = constant. R and 0 are not polar coordinates and the spiral contour is not an ordinary Archimedean spiral [ 131. Fig. 7 illustrates the principle method of generating successive points with coordinates u[j], u[ j] (j = 1, 2,. . . ) on the spiral contour, (these separated by a 1’) of cam rotation, given the initial and final cam radii together with the initial and final angular positions. It should. be stated that the 1” interval has been empirically determined as it was found highly adequate for machining of the contour.
If Sangle = (endaugle - stangle) and Srad = (endrad - &ad), then, the rate of increase in the cam radius is given by: Grad radrate = Sangle Hence, if rad[ j] is the radius at point number the spiral contour (see Fig. 7), then: rad[ j]: = strad + 0.2( j - 1) X radrate and the angular position of point number by:
‘j’ on
(5) ‘j’ is given
O[j]:=stangle+0.2(j-1)
(6)
Hence, u[ j]: = rad[ j] X cos[90 - {@[j} + @J(rad[jl,camtype))l
(7)
u[j]:=rad[j]Xsin[90-{O[j] +~@(rad[jl,camtype)j]
(8)
using a similar approach to that used in the preceding paragraphs. The expressions can be employed from j= 1 to k where kissuchthatpoint{u[k],v[k]) does not lie on an angular position clockwise to the final angular position endangle. A computer based version of this analytical model, called Spiral0 has been implemented in the prototype system for evaluation purposes. 3.2. Modet for the blending of spiral contours As highlighted earlier, a major problem in generating planar cam profiles is, that unless preceded by
J. Borg et al./Computers rfolloner
roller
El Wy2)
wa32)
0
X Fig. 8. Special blending.
an invariably steeper idle rise primitive contour a spiral contour needs to be blended with the preceding curve by giving it a small starting radius so as to prevent the cam follower from momentarily loosing contact with the cam. If this condition is not catered for in the cam profile, it would result in serious dimensional and surface finish defects during taper turning and chamfering operations due to the loss of synchronicity between the compound motions of the radial and axial cams. As an example of how cam profile blending can be achieved, this section describes the equations developed for blending spiral contours forming part of the Blending0 model. In Fig. 8, A-B are the end contact points of the primitive spiral contour computed as described in the previous section. (R,a), (r,,O,) and (r2,02) are all polar coordinates relative to the initial line OX. In order to provide suitable blending, the problem becomes one of locating the point of tangency P of a spiral drawn from B, tangent to the follower’s roller. Having located P, a spiral contour can then be generated from P to B using the procedure Spiral0
in Industry 34 (1997) 11-26
defined earlier. The complete primitive contour will therefore consist of a radiused portion AP providing the necessary blending and a spiral contour PB providing the required tool motion characteristics. The analytical solution derived for this blending problem is one based on approximation for the purpose of determining the coordinates of P only. This assumes that spiral PB is an Archimedean spiral of the type r = (r. + k@) where r and 0 are now polar coordinates, (as distinct from equation 3) measure relative to axis OX. Testing out of cam profiles generated using this method revealed that this approximation is an acceptable one with respect to the dimensional accuracy manifested in the turned components. From Fig. 9, it can be seen that:
r=r,+(e-8,)-
R - r2
(Y- 8,
From which it can be found that:
[COS(Y-(a-
(10) Also, P lies on the roller’s circle equation,
(11)
(x-p)2+(y-4)2=r; Hence, (RCOS(Y-R)2+(Rsina-q)2=r~ A2
/\repositioning
rounded
No maneouvre
B,)sincr]
off
Manoeuvre Fig. 9. Tool manoeuvring.
at sharp
edge
J. Borg et al. / Computers in Industry 34 (1997) 11-26
from which, on expansion ing is obtained: R=pcosa+qsintr-
and solution,
the follow-
(pcoso+qsina)’ 1
-(p2+q2-r$
(12)
Also, from Eq. (111, one can find that,
(fJP=-(g-)
(13)
From Eqs. (10) and (13), -(
19
completed by generating a spiral from P to B using the procedure Spiralo. Analytical models employing similar methods have been generated for the other cam profile primitive contours listed in Table 1, individually explained in the work by Bone110 et al. [12]. The provision of these analytical models supports the complete profile design process for planar cams. The design solution generated through these models has to be converted into machine instructions for the machining of the cam plates on a CNC machine tool, a conversion process achieved as described in the following section.
“,f;::;) 4. CNC process planning and part progrartming
[cosa - ((Y - B,)sino]
(14) Now, from Eq. (1.2), it can be seen that R is a function of (Y, anjd that therefore Eq. (14) can be written in the form: f(a)
=0
(15) where, (Y will be the only unknown variable. This equation was solved for (Y to a high degree of accuracy using the Newton Raphson’s Method [14] taking 0, as the initial approximation for (Y as A is sufficiently close to P. After R and cx are determined, (Y‘, the angular position of P is established by considering that CY ’ = 90 - cx - 6@( R, camtype) thereby converting (Y from radians to degrees. A procedure Startradius() based on these derived equations has been imlplemented in the prototype computer based system for evaluation purposes of the profile blending approach. The centre of the cam follower roller, (p,q) is given by: p = (r, + r,)sin8, 4=(r,+r,)cos8,
(16)
where r,, is the design value of the follower roller radius, which is however taken larger by up to 1 mm than the actual value so as to give adequate clearance of fit of the roller in the cam contour valleys. Once r and a1 are determined, the primitive contour is
Once the contour of the cam has been generated the implemented system has to perform the necessary process planning and part programming for the machining of cams on a CNC milling machine. The cams are milled from steel discs of thickness 10 mm and radius 65-70 mm. The prototype system developed first ‘plans’ the path to be taken by the milling cutter and therefore examines the overall profile of the cam contour. This is achieved by making use of the primitive curves established during design. The most suitable point on the contour from where to start milling has to be determined for such an exercise. Practical experience translates itself to a point that should be a sharp comer since the tool will be cutting the two sides forming the comer not sequentially but towards the beginning and end of the milling operation. Moreover, the entry of the tool into the profile at the start of the milling process should be tangential to the side of the comer to be cut first. This means that the analytical model (on which a computer system is to be based) has to be capable of identifying all the sharp comers of the contour (a comer or edge is said to be formed where the ends of the two adjacent primitive profiles meet). In addition, sharp comers necessitate special manoeuvring of the tool as shown in Fig. 9. Experience gained in the project shows that the loss of accuracy in the resulting turned component due to the rounding off of a sharp edge is highly significant and should therefore be catered for during the cam profile process planning procedure. Moreover, the runoffs and re-entries of the tool during
20
J. Borg et al./Computers
such a manoeuvre shoArchuld preferably be tangential. Also, a circular repositioning movement is suitable as it maintains the tool at a constant distance from the comer; if the repositioning was defined as linear, the shortest distance of the tool from the comer would depend on the comer angle, resulting in cam profile chipping off for small angles if the distance is less than the tool radius. Thus the milling cutter requires guidance from the beginning to the end of its path, provided by what are being termed edge vectors. This concept ensures that the system generates a precise, effective and safe milling cutter path for any given cam profile design. Edge vectors are vectors that point tangentially outwards from the ends of each elementary contour. An example for the radiused spiral contour is given in Fig. 10. Analytical models employing suitable mathematical formulae are thus implemented in the prototype system to ensure that these vectors point in the correct direction under all cam profile conditions. Referring to Fig. 11, the angle a[ i] between the edge vectors x,[i]i + yJi]j and x,[i + l]i + y,[i + llj is an indication of the sharpness of the comer formed at the point where the contours for the operations numbers i and i + 1 meet (the smaller the L![i], the sharper the comer). This analytical model, nicknamed Sharp0 will consider a comer sharp if the corresponding value for n[i] is less than a certain predefined constant sharpmin (defined as 140” in this project). Hence after computing all the edge vectors x,[ i]i + yl[i]j and x,[i]i + y2[i]j (from i: = 1 to noops), the angle O[i] between any two adjacent edge vec-
in Industry 34 (1997) 11-26
\ yl[i
+
Fig. 11. Determination
OF OPERATION
No.
i
:
SPIRAL
(risetype[i]
=
I
I
RADIUSED
SPIRAL
(risetype[i
-
1]
Fig. 10. Edge vectors example.
=
1)
2)
of sharp corners
tors is calculated. The least LZ[i] is then determined so as to find the sharpest comer. The start point S of the cam milling process is hence established. The model then uses the appropriate edge vector to find point S, such that
is tangential to the cam contour (S, will be the point of immersion of the tool into the material and
represents to be cut; TYPE
+ llj
the approach of the cutter to the contour
I@ is a constant controlled by the user called startdistance. Hence, the entry into the contour will be tangential. It should be stated that l2[i] is defined as the comer angle at the end of operation number i when moving clockwise round the cam. Referring to Fig. 12, to determine S,,, the analytical model takes the edge vector indicated, normalises
J. Borg et al. / Computers in Industry 34 (1997) 11-26
Operation
21
no. (start-l)
i+
IPart
Fig. 12. Determination
it (that is, reduces it to unit magnitude) scalar multiplication to obtain vector
and performs
of initial cutting point.
cams, making use of analytical for tool manoeuvring.
models such as those
5.1. Cam profile design module
Having previously calculated the coordinates of S (in the cam design stage) SO will then be located, this allowing the tool path CNC program to be initiated and calculated. This Sharp0 model has been embedded within the CNC part programming module of the prototype system developed, described in the following section.
5. The CAMCAM
prototype system
A prototype computer based system (nicknamed CAMCAM) employing the analytical models developed, has been implemented on an IBMTM compatible personal computer, using the programming environment provided by Turbo PascalTM. This programming language was selected as it provided adequate mathematical and graphical functions besides the fact that it was readily available. The CAMCAM system consists bastcally of two modules, (1) Generating the cam profile design making use of analytical mode1.s such as those for spiral curves and for profile blending, (2) Another module for the generation of the CNC part program, necessary for machining the planar
The generation of the component’s process plan and the preparation of the operation layout sheets of the required cams require a great deal of personal judgement and were therefore left to the designer, this resulting in a computer based assistance approach rather than complete design and manufacturing automation [151. As a consequence, when using the cam profile design module, the user inputs the manually generated operation layout sheet. During entry of the related information the system assigns relevant values to variables such as integer values to two array components risetype[ i] and droptype[il from i: = 1 to No._of_operations according to the type (e.g., facing) of operation number i. This integer value enables the system to subsequently recognise the type of each operation (e.g., chamfering) defined by the user. By means of model Endpointso, the system is capable of performing the first step in the cam design process: the location of the end points of the cam contour required for each operation to be controlled by the cam. After all the operation end points have been located the system ‘visits’ each operation No. i (i: = 1 to no_of_operations) of the layout sheet, examines its type according to its values of risetype[il and droptype[i] and employs the appro-
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priate analytical model (convexsphere, concavesphere, ideldrop, etc.) to generate the required cam profile for that operation. In addition, the CAMCAM system employs the related Blending0 model for blending the primitive curves. Blending becomes necessary whenever the previous primitive contour is less steep than the following one. Once the cam profile is completely designed, it’s resultant geometry is automatically employed by the part programming module to generate the necessary tool path and hence machine instructions. Fig. 13 is a flowchart illustrating how the analytical models developed have
been implemented module.
5.2. CNC part programming
OPERATION
LAYOUT
GENERATE
ENDPOINTS
-
SHEET
DATA
I
CHECK
SAVE
II
FOR TYPE
CAM GEOMETRIC
‘_
profile design
module
By retrieving the cam profile generated, this module first determines the initial (sharp) cutting point using the model Sharp() described earlier. The system then ‘visits’ each elementary contour making up the cam profile, examines its type (e.g., by considering risetype[ i] and generates the appropriate CNC blocks for machining the contour. Since only linear
INPUT
by
in the CAMCAM
using
ENDPOINTS<
>
OF OPERATION
PROFILE
DATA
Fig. 13. Flow chart for cam profile design module.
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J. Borg et al. / Computers in Industry 34 (1997) 1 l-26
and circular interpolations are possible on the milling machines used in this case study, curves such as spiral are machined either by linear or circular interpolation from point to point as chosen by the user. Following evaluation experiments, only points separated by 1” of arc are considered when milling such
curves. In the case of spiral milling by circular interpolation the system takes three consecutive points at a time, locates the centre of the circular arc that fits them and writes the CNC block for the milling of each such small arc. After writing the CNC block(s) for the generation of the contour of an
EXAHNTYRQCERATIONNfJ.IAM WWIE GLOCKSTO GaauTE
WRITE GLOCKS TO mmmi WNOEWREATAWPWESE UsIts -0 I
RRITE SLOC%STO TEMNAlE I
P!ACHlNMG PWCEG3
Fig. 14. Flow chart for cam profile design module.
ITS CCMTOU?
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operation No. i, the procedure examines its value of L?[i] to see if there is a sharp corner at the end of that contour (a[ i] < sharpmin). If so, then the additional blocks to enable the tool to perform a manoeuvre, as indicated earlier in Fig. 9 are generated, using the Manoeuvreo model which makes use of edge vectors previously computed, to guide the tool safely around the sharp comer. The method used to locate A, and A, is similar to that previously indicated to obtain point S, at the start of the milling process. In the CAMCAM system, an option for the graphical simulation of the milling cutter path is also provided; this was found particularly helpful by the operator of the CNC milling machine when determining the clamping points for the cam blank. In addition, the CAMCAM system allows the automatic transfer of the generated CNC code from the PC to the CNC machine’s controller thereby eliminating the laborious, time consuming and error prone, manual data entry task. Fig. 14 illustrates how the cam machining process plan and CNC code are generated in the CAMCAhil part programming module. 5.3. System evaluation The CAMCAM prototype system provided a suitable testbed for evaluating the different analytical models developed. Axial and radial cams were generated for testing on a Kummer K20 lathe. The CAMCAM system was interfaced and tested on two CNC controllers, one utilising a SiemensTM [16] controller whilst the other utilising a HeidenhainTM [17] controller. It has been tested on a total of twenty-four layout sheets producing successfully the cam design and part program in each case. The criteria used for measuring this success was attributed to the fact that the cam plates designed and machined generated the required turned component on the Kummer automatic lathe without the need of any modification to their profile. Also, the resulting components using the CAMCAM system had dimensional tolerance and surface finish superior to those previously machined from manually designed cams. This was evident for instance from the accuracy of tapers and chamfers verified by measurements on an optical comparator. Plate 1 illustrates one of a pair of cams designed and machined via the CAMCAM system.
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Plate 1. Planar cam designed CAM system.
and manufactured
through
CAM-
As a consequence the evaluation of the CAMCAM prototype system employing the analytical models developed, besides demonstrating that the models developed are computational feasible, reveals that: . Errors due to the lack of accuracy associated with manually designed cams and traditional profile blending problems are eliminated. . There is a significant reduction in the time required to design the cams and the time required to program the CNC controller, with a consequent reduction in the costs of cams. . It becomes feasible to re-utilize cam-driven machinery such as automatic lathes in markets demanding efficient and flexible manufacturing operations. However, as implemented, the system provides no means of supporting or automating the generation of the cam profile design directly from the turned component’s geometry. A future direction for research in automatic lathe cam design is one related towards supporting the generation of cam profiles by a turned component feature-based-approach, thereby eliminating the need of manually generating operation layout sheets.
6. Conclusions The research work carried out reveals that it is not sufficient to implement analytical models for the generation of cam profile primitive curves. This is because the synthesis of these individual curves commonly results in profiles having transition points that are the source of erratic follower movement, due
J. Borg et al. /Computers
to the follower’s roller momentarily sticking or losing contact with the cam plates. The CAMCAM prototype system demonstrates that a superior approach to planar cam profile design is the combined implementation of the analytical models established in this paper which generate the required primitive profile curves and which automatically take into consideration the necessary profile blending requirements. Besides resulting in an approach that provides a generic framework that can be equally applied to other machine tools or applications, the resultant cam profile is a superior starting point for the generation of the required cam milling process plan and the CNC part programming exercise. From a practical point of view, the case study fum is “extremely satisfied with the results” obtained and is now making use of the prototype system. This demonstrates how the computational feasible analytical models established and presented in this paper can help today’s industry efficiently utilise machine tools employing motion characteristics generated through one or more planar cam.
Acknowledgements: This project received considerable support from the Department of Manufacturing Engineering of the Faculty of Engineering, University of Malta. The authors would like to thank Mr. F.E. Farrugia, Head of the Manufacturing Engineering Department, and Mr. M.P. Scibetras, then Manager at Beacon Precision Limited, for their professional advice and for the latter in providing frequent access to the company’s facilities where the implemented computer based cam profile design system was installed and evaluated.
References [l] D.M. Tsay, B.J. Lin, Improving the geometry design of cylindrical cams using nonparametric rational B-splines, Computer-Aided Design 28 (11 (1996) 5-15. [2] M. Haslehurst, Auto lathes, In: Manufacturing Technology, 3d Edn. Hodder and Stoughton, London, 1985, pp. 109-125. [3] .I. Hannah, R.C. Stephens, Mechanics of Machines, Elementary Theory and Examples, 4th Edn., Edward Arnold, London, 1984, pp. 1244137.
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[4] L.S. Wierda, Linking design, process planning and cost information by feature-based modelling, .I. Eng. Des. 2 (1) (1991) 3-19. [5] M. Kalta, B.J. Davies, CADEXCAP: Integration of 2D CAD models of turned components with CAPP, Int. J. Mamtfact. Technol. 8 (1993) 145-159. [6] G. Pahl, W. Beitz, Engineering Design, The Design Council, Springer-Verlag, London, 1984. 171 K. Freres, Instructions for the Preparation of Operation Layouts. Calculation of Machining Time, Cam Design for Kummer - Two Spindle Chucking Automatics K20, Kummer Freres, Tramelan, Suisse. [8] S.G. Dhande, B.S. Bhadoria, J. Chakraborty, A unified approach to the analytical design of three-dimensional cam mechanisms, ASME J. Eng. Indust. 97B (1) (1975) 327-333. [9] R.L. Jordan, A general approach to CAM surface definition, Design For Manufacturability., ASME 52 (1993) 159-162. [lo] D.M. Tsay, C.O. Huey Jr., Application of rational B-splines to the synthesis of cam-follower motion programs, ASME J. Mech. Des. 115 (3) (1993) 621-626. [ll] W. Abbott, Practical geometry and engineering graphics, Blackie, London, 1972, pp. 62. [12] P. Bonello, C. Ciantar, Computer Aided Design and Manufacture of Cams, Dissertation, Department of Mechanical Engineering, University of Malta, May 1994. [13] A.E. Avallone, T. Baumeister III, Mark’s Standard Handbook for Mechanical Engineers, 9th Edn., McGraw-Hill, New York, pp. 2-26. [I41 A.E. Avallone, T. Baumeistem III, Mark’s Standard Handbook for Mechanical Engineers, 9th Edn., McGraw-Hill, New York, pp. 2-16, 2-44. [15] K.J. MacCallum, Does intelligent CAD exist?, Artificial Intell. Eng. 5 (2) (1990) 1. [16] Huller Hille, Instructions for Programming, Huller Hille, 1984. [ 171 Heidenhain, Heidenhain TNC145, TNCl50, TNC15 1, TNC155 Contouring Control-Issue No. 12/85, Dr. Johannes Heidenhain, GMBH. Jonathan Borg graduated in Mechancal Engineering from the University of Malta in 1989, after which he worked for 3 years with a Water Authority responsible for CAD systems employed for designing desalination plants. During this period, he also formed part of a team responsible in designing and implementing a computer based mathematical model of a water aquifer. In 1992 he joined the University of Malta, responsible for lecturing and carrying out research in CAD/CAM. In 1993, he graduated with an MSc in Computer Aided Engineering Design from the University of Strathclyde, Glasgow, with whom he is currently a PhD candidate. He is a member of the Institute of Engineering Designers (UK), the Institute of Mechanical Engineers (UK) and the Society of Manufacturing Engineers (USA).
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Philip Bonello graduated in Mechanical Engineering from the University of Malta in 1994. He has since been employed as an engineer with Enemalta Corporation, the island’s energy producer, where he is in charge of a team of maintenance workshop personnel who carry out maintenance work on power plant components at a major power station. His current research interest is the development of a computerised modelbased fault diagnosis system as applied to power-plant components encompassing material failure and vibration problems in rotating machinery. Since 1995, Mr.Bonello has been a part-time lecturer in the Department of Mechanical Engineering of the University of Malta.
Christopher Ciantar has studied Mechanical Engineering at the University of Malta and later moved to Brunei University London where he completed studies in the building services industry leading to an MSc degree. He is currently employed as a building services engineer with particular responsibilities for managing the computer-aided system design of commercial and industrial environments. His areas of interest are focused on computer-based techniques used to design and optimise processes used in the building services industry.