Algorithm and System for Automatic Camshaft Testing

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ALGORITHM AND SYSTEM FOR AUTOMATIC CAMSHAFT TESTING

T.C.IONESCU .... 8.M DASCALU

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1. INTRODUcnON Our research was directed towards developing a family of systems dedicated to the camshaft automatic inspection and testing (Dascalu, 1989). The staning point was characterised by a marked absence of information concerning technological aspects and, moreover, a perfect disagreement about the appropriate testing methods. We have used the general information obtained from the Italian company Samputensili Bologna (Anon., . 1982) and the preliminary results offered by Pitesti University (Anon., 1983). A first set of conclusions has been drawn in an early paper (Ionescu, 1984), in which the imponance of the proper camshaft testing for the operation of an engine is emphasised. It has been shown that the prOfile errors and the contour undulations of cams, resultingfrom inaccuratepl'OCCSSing,induce vibration pbenomena and loss of engine power. • The main objectives of the camshaft automatic iDapection and testing aim at deteiminlng the pometric parameters associated to the camshaft. These parameters are: - real positions of cam reference axes (eq>ressed in angular values); - relative positions of inlet and exhaust cams, i.e. the so called -angular offset-; - rising diagrams of tbe probe on the cams; - speed diagrams; - acceleration diagrams; - bearing journals -excentridty" (position errors of journals centres with respect to the rotation axis), expressed in polar coordinates; - the bearing journal average radius.

These measurements allow the computation of secondary data, such as the extent of the area of constant rising, the range of risings in the cam active zone and like. Since these computationsare trivial, they will be ignored in the sequel. All measurements mentioned above are compared against theoretical data and a a quality cenificate is issued. Moreover, coordination parameters for the machine tool used to process the camshaft can be produced. This information is of value in computeraided manufacturing,since it eliminates the buman intervention in adjusting the improperly operating system component. 2. 1HE TESTING ALGORITHM

2.1. Working Hypotheses The essential diagram in designing a cam is that of the tappet rising (TR) and, especially that of the tappet rising in the eactive zone- (TRAZ). All other diagrams derive directly from this one. At this po~t first decision bas to be taken in connection to the type of probe. We bave chosen the plane probe. Of course, this might not allow the determination of the cam prOfile, but the tappet movement profile, and we considered that this is by . far more important to know for the actual engine behaviour. The 1R is stipulated by the camshaft designers by a set of values (expressed in micrometres), corresponding to successive angular positions of the tappet in close contact to tbe cam. The term 'successive-sbould be considered in connection to the camshaft rotation movement. Therefore, the

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introduction of the notion of -angular stepW is appropriate , with the meaning of -angular interval between two successive rising values of the plane probe". Usually, tbe theoretical TR diagram (TRD) is expressed with an angular step of either 10 or 0.50• Consequently, the measurements will be effected with an angular step at most equal to that used in the theoretical . mo. A set of data oomposed of n values is associated to eacb of the N cams of the sbaft: X. , 0 ~ i ~ n-l, (1) in whicb n = 360 or an integer multiple of this value. The same notation can be used for the M bearing journals of the camshaft. Table 1 sbows an elWDple of a theoretical TR diagram. Table 1 Theoretical TRD Angle If]

Rising b[J.Lm]

-90

1 7 21

- 2 - 1 0 1 2

4978 4993 5001 4993 4976

-92

- 91

89

9

90

1

For a full cbaracterisation of the measurement space a system of cylindric ooordinates (x, y,8) is .used (Fig.l), related to the m~urement system and not to the camshaft itself.

:t! ... .

~. ~

I

Fig. 1. The cylindric ooordinates system in oonnection to the measurement system With the oonventions established above, the tappet speed will be expressed in micrometres/degree, and its acceleration - in micrometres/degree2• The errors induced by the electronic measuring system will be neglected in the algorithm description in oomparison witb that of the mecbanical pan of the system, the aa:uracy of the latter being a problem lying mostly with the mechanics designer. Anyway, tbe performance of .

the computer based measurement system exceeds by far tbat achievable by any mechanical system. Therefore, tbe contribution of the electronics and software is negligible in the total error figure of the system. Practical oonsiderations prompt the choice of internal data representation. Indeed, since the values of x do not exceed a few tens of thousands of micrometres, 16 bit ienght will be used for input data. . 2.2 Stages

It is obvious that data obtained from bearing journals are processed in a different manner as oompared witb data from cams. However, a testing algoritbm (Ionescu, 1984), makes use of the oomputed bearing journal -excentricities" to produce, by linear interpolation, a set of oorrection values for the data obtained by cam measurement. This correction takes into account the real camshaft behaviour, which is rather different from that of tbe camshaft in the testing system, due to tbe presence of bearing caps in the real life situation. Due to this, the following stages are required in the process of measurement and testing: a. measurement of bearing journals and parameter evaluation; b. evaluation of cam excentricity with the view of obtaining oorrection parameters to be used in a later stage; c. measurement of cams and evaluation of characteristic parameters. It is also possible (Ionescu, 1987) to establish from the cam passive zone (if it is extended over more than lSOO) the cam excentricity without making use of bearing journal data. One has to point out that he first two stages are optional,since they do not emphasise directly the cam parameters. By neglecting tbem, the test process tates mucb sboner time (the measurement of a bearing journal lasts as long as that of a cam, since the number of angular steps is the same and the angular speed is tbe same in both cases). However, it is difficult to give a final answer to the question concerning the optimal data processing, namely what sets of data should be used to fully cbaracterise the camshaft real life behaviour. This answer should came from the designers of mechanics, but we provided all facilities to tate into account any possible set of measurements and parameters.

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2.3 Processing of data associated to bearing journals The computation of data obtained from bearing journal measurements is of little complexity. The staninghypothesisassumes tbat a bearing journal can be assimilated, ideally, to a circle of radius R and centre 0, the latter being placed on the camshaft rotation axis. In reality, two types of errors can occur simultaneously: profile errors and, due to twisting and bending of the camshaft, excentridty errors (Fig.2).

!to'

.-0~ sin(21li/n)

v=(2/n) I:

(7)

2.4 Computation of cam excentricity According to the remarks made in 2.2, the results of the previous stage (a) can be used to determine the cam excentridty, useful for correcting the data obtained directly tbrough cam measurement. By using the linear interpolation, theexcentridtyvectorforthecam C, (1 < IS n) can be computec1. If Y'.j' Y.,j+' are the cam longitudinal distances from the closest bearing journals Pj and Pj +, (1 S j S M-I) the following formulae are derived: (8)

,s,=tan" - - - - - - - - - - Fig.2. Theoretical and real life positions of a bearing journal

The ·excentridty vector", expressed in polar coordinates (p,a), can be extracted from the set of measurements. The Fourier transform is used for this purpose (Stanasila, 1981). By using the notations (1) the following values are easily obtained:

0 .iflLl,lI~O , 1L"z~O k= { 1 if J.L~.
(9)

(10)

wbere: y"j+'

(11)

(12)

(i) Average bearing journal radius: (2)

J.L1,z= - - - - - - - - -

(ii) The excentridty vector:

- module

For the significance of notations refer to Fig.3. (3)

(4)

0 if u~O, v~O

t- 1 ifv
(13)

.r~---+------~x

(S)

2 ifu
wbere:

Fig.3. Significance of notations

!to'

u=(2/n) I: '" cos(27[i/n)

.-0

(6)

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2.S Processing of data associated to cams

A3 Table 1 shows, the theoretical1RD contains data with reference to the rf angle of the cam, corresponding to the so called 8reference axis w and usually (although not always so) to the cam peak (maximum raising point). Therefore, in order to compare the real 1RD against theoretical 1RD it is first nec::cssary to determine the cam reference axis. The method we suggest to determine the angular position of cam reference axis uses measurement information obtained in the zero acceleration zones of the cam profile. The iDlet and ezhaust laws require the ezistence on the cam profile of such zones. They bave various extensions, depending on the shaft type. Sometimes, these zones are symmetrical with respect to the cam peak. It is wonh noting that the zero acceleration zones are also characterised by the maximum speed along the cam profile. Given a set of data as in (1) associated to a panicular cam and the characterisation of the zero acceleration zone by measure angle 8. and the pair (I .. hJ and the raising X. one can determine that the actual cam position is rotated (relative to the theoretical position) with the angle (14)

eq>ected intervals [h.."h,) or [h.,hi . , ) (i.e. 148.1 >8,), a more accurate formulation for (14) is in order:

48 1 c

'" - h. (-

+ q) 8,

(15)

h.., - hi Usually, q is limited to values depending on the cam profile and imposed accuracy (as a rule: Iq I S 3). The overtake of this limit must be c:osidered as a serious error. The real cam prOfile being different from the ideal prOfile, it is necessary to consider several points in the constant speed zone. We consider the same number m of points on both zones. The estimation of the cam angular position error (relation (18» is derived by averaging the values of the angular errors for the ascending (relation (16» and the descending (relation (17» active zone of the cam: m

48 A-(lJm) E 48A-1!

,,-,

(16)

m

48 0 =(11m) E 48 0 0k

(17)

48 =

(18)

11-'

Here 8, is the angular step o(the measurement. In order to Simplify the treatment, 8, is considered equal to I, (the angular step between succesive theoretical values).

The number of chosen points depends on the c:nension of constant speed zones and, also, on the tolerance accepted for the cam rotation. The usual values for these numbers are 3, Sand 7.

ID Fig.4 the case X. > 11. is shown.

Once the value from (18) is obtained, interpolation is required in order to compared measured_gainst theoretical data:

1I•• 11IIIl

110•....••••..•.•.............••...••...•......•...••...••••••••••.~..

-x. - x. -(x. -z..,) - 48 --

(19)

8,

bo·

p •.

+-~:••..-.---:l.&~--:i --r.. --:;:+I.) ~ er jAi, ~

FigA. Interpolation acceleration zone

of x in the zero

Since it is possible for X. to rest outside one of the

If 1481 c:xc:eeds 8., a prior rotation of the data set is necessary. After the rotation, (17) is applied to the new set of values. Following that, the values of X; are compared to their theoretical correspondents, which permits to assess their position with respect to 8tolerance band- (Fig.S).

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computer. Under special circumstances, a dedicated equipment built along the general lines exposed above can be used. "-~---r

S. CONCLUSION

.~--

:~----

....

Fig.S. Behaviour within tolerance band

The essential cam parameters being determined, the other determinations follow suit: .'

-the angular offset between cams k and I: (20) - the real speeds: VI

-= Xt - Xt.,

for i corresponding to Wactive zone W

(21)

- the real tappet accelerations:

-a -= - -v~, = -Xt - 2x.., - +j

VI -

Ij,2

(22)

We emphasise that the suggested method takes into account the two essential elements in cam testing:

Aa and X.,

o ~ i ~ 3S9

4. THE TESTING SYSTEM

The testing system has been built around an IBM compatible pc, provided with an intelligent interface, the latter being able to provide the raw • results of required measurements. This electronic system is connected to the mechanical system which allows the camshaft rotation and .probe displacement. Obviously, the mechanical system has to be designed in aa:ordance to the type of camshaft under test, while the electronic system remains the same in all circumstances. Note that tbe test system can operate also in manual mode (tbe movements are controlled by a human operator); this facility is required during commissioning operations. The system easily allows its integration in a CIM scbeme, due to the versatility offered by the

The algorithm which constitutes the topiC of the paper has been tested through implementing it on four systems dedicated to engine manufacturers in Romania. The results are of good value with respect to accuracy and efficiency of testing. The accuracy is better by an order of magnitude in comparison to that of the mechanical system. A full test takes less than 10 mins for an 8 cam shaft. The performance is limited by tbe use of low cost inductosyn type transducers for position measurement. With this kind of performance the connection of the automatic camsahft inspection and testing system into a complex CIM systemis straightforward. 6. REFERENCES

Stanasila, 0., (1981). wAnaIiza matematica", Ed. Didactica si Pedagogica, Bucuresti. Anon., (1982). wSamputensili SU SOO/DAC User's Manual", Bologna. Anon., (1982). WStudii referitoare la comportare a dinamica a camelor", raport tehnic, Institutulde Invatamint Tehnic, Pitesti. Anon., (1983). WStudii referitoare la comportare a dinamica a camelor", raport tehnic, _ Institutulde Invatamint Tehnic, Pitesti. Ioncscu, T., Ceaparu, M. and Dascalu, S.,(1984). -Testarea automata a arborilor cu came de la autoturismele DACIA 1300", CNETAC S, Bucuresti. Carstoiu, D., Dascalu, S. and Moldovan, L, (1985). wAn Application of Computer Aided Testing in Automotive Industry", Conference on Control Systems and Computers Science VI, Bucuresti. Ioncscu, T. and Dascalu, S., (1987). "A method of measuring camshaft parameters implemented on ESMC", Conference on Control Systems and Computers Science VII, Bucuresti. Dascalu, S., (1989). •Aspecte constructive si functionale ale subsistemului de calcul, masura si comanda din componenta ESMC04·, AlII-lea simpozion de WStructuri, algoritmi si echipamente de conducere a proceselor industriale", lasi.