EFFECT OF M A N U F A C T U R I N G ERRORS ON THE I N S T A N T A N E O U S

C H A R A C T E R I S T I C S OF C O U N T I N G M E C H A N I S M S

G. A. T a l a l a e v UDC 621.317.785.084.088

Rising requirements for the precision and durability of electricity meters make it necessary to improve all the units of their measuring mechanisms, includingthe register. The quality of a register is determined by the value and fluctuations of the opposing moment, which are produced by it on the axle of the register's moving part owing to fric- tion in the bearings and gearing, unbalance of the components' masses and links with respect to the geometrical ro- tation axis, the moment of inertia of links, etc. The opposing moment Mop and its fluctuations AMop depend on the friction coefficient in gears and bearings, geometrical parameters of gears and bearings, radial and axial loading of bearings, efforts in gears, torque ratios [1], as well as manufacturing and assembly errors. The effect of manufac- turing and assembly errors [2, 3] on the characteristics of moments can be accounted for theoretically only partially; therefore, the author carried out experimental investigations for finding the effect on Mop and AMop of the unbal- ance of the rotating links' masses, errors of distances between centers, and the displacement of the mean plane of the gear with respect to the worm in the first worm transmission of the register.

We investigated the mechanism of an electricity meter type SO=2M2, class 2.5. Since the majority of modern registers are similar in their kinematic, structural, and other designs, the investigation results can be applied to other types of registers.

The opposing moments were measured on a high-precision rotating dynamometer developed by the author [4].

The particular feature of electricity meters' registers as compared with other small geared mechanisms, for in- stance, those of watches, consists of the absence in them of a useful load, and as a result of this the presence of only

/5

z

5

O./~r g2~ O.Jz G,4z gSz /,Ox ZSx 2,g~ 9, tad

/4 rad

Fig. 1. 1) M u = 2 . 3 5 m N . m m ; 2 ) M u = 6 . 0 m N - m m ; 3 ) M u = 1 1 . 0 raN. ram.

Translated from Izmeritel 'naya Tekhnika, No. 2, pp. 56-58, February, 1973.

@1973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West ]Tth Street, New

York, N. Y. lOOll. All rights reserved. This article cannot be reproduced for any purpose whatsoever

without permission of the publisher. A copy of this article is available from the publisher for $15.00.

247

M op

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300 - J00

200 -

100 - too

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4 8 Mu, mN �9

AMop~

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:2,~ -1,8 .-t2 -#,6 o g6 t2 tO e,~rn dg

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0 O,2rn o,a o,5 o,8 tom dA

Fig. 2 Fig. 13

Fig. 2. Relationship of the first link's opposing moment and its oscillations to the unbalance mo- ment for repeated measurements. 1, 4) Register No. 1; 2, 5) register No. 2; 3, 6) register No. 8.

Fig. 3. Relationship of the first link's opposing moment and its oscillations to the error AA in the distance between centers of aworm transmission and the error Ag in the displacement of the gear mean plane with respect to the worm; 1) ~ o p / M g p = jez(A A); 2) ~op /M~p = fz(Ag); 3) n M o p / MOp = f3(Ag).

small efforts and moments in the bearings of their transmissions. Therefore, such small effects as changes in the axles' points of contact in bearings, variations of gear profiles, presence of minute dust particles in beazings and on gears, etc. produce noticeable changes in the opposing moments of registers and their separate links. In view of the above, in order to obtain trustworthy and comparable experimental relationships, the number of measurements of in- stantaneous Mop values made with the rotating dynamometer for each type of testing was set at as high a value as possible which was equal for all the measuring cycles. Since the effect of the majority of manufacturing errors on Mop and ZkMop is of a periodic nature, measurements were made for a complete rotation of the link whose errors were investigated. Therefore, the measuring cycle of the rotating dynamometer consisted of 400 continuous mea- surements of the instantaneous Mop values, which were carried out at every 0.005 rrrad in the rotation of the tested register's first link gear.

The unbalance of the rotating components' masses with respect to the geometrical rotation axes is due to the geometrical configuration of pointers, traces of waste metal on indicators, excessive radial beating of gears, curva- ture of rotating axles, etc. The effect of the unbalance of the first link's mass on the link's AMop was tested for the unbalance moment M u whose values were based on the actual possible values for various geometrical shapes and dimensions of the components. The value of M u was varied according to the equation M u = mpg by glueing to the pointer of the counting mechanism flat weights of mass m at different radii p of application. The mass m was mea- sured by repeated weighing on a microanalytical balance type SMD-1000. The radius p was evaluated on a projec- tor type ChP with a magnification of 50 x . Figure i shows the variations in Mop of one of the tested links with re- spect to the rotation angle ~ for various values of M u. The measurement results were processed by calculating the value of Mop and A Mop of the link for all the values of M u by the methods of mathematical statistics [5]. The value of AMop was determined as the difference between the dispersion ranges oftheinstantaneous values of Mop over one rotation of the link for Mu~ 0 and Mu = 0. The rise in/~lop and AMop for a rising M u was determined in percentages with respect to the value of M ~ for M u = 0. The relationships AMop/M~ = fz (Mu) and Mop/ MOp = f2 (Mu) shown in Fig. 2 indicate that ~ increased unbalance of the links' masses with respect to the geo- metrical rotation axes increases the value of Mop and increases considerably AMop. Therefore, a limitation of the unbalance moment of links, especially the Krst one, is an essential condition for stabilizing the counting meeha- nism's opposing moment.

Error in the distance between the geometrical axes of the gear rim and the worm in the grst worm transmission includes the radial clearance /~ of the axle in the bearing hole of the cylindrical support, the eccentricities eg and e w of the gear and the worm, and the error AA, in the distance between the geometrical axes of the bearing heles produced in assembly. The maximum error can be calculated from the formula

AA = AAz +_ [ a + e g + ewl.

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The radial clearance A in the register bearings which are manufactured at the present time attains 0.15 ram, which amounts to 0.3 m (module) for m = 0.5 ram. The permissible eccentricity for worms and gears amounts to 0.2 m (module). The errors in distances contributed in the assembly of the first transmission range from AA1 = 0.05 to /XA1 = 0.3 ram, which amounts to (0.1-0.6) m for m = 0.5 ram. For the register under investigation the distances between centers were set on a dynamometer so as to obtain various deviations (&A = 0, 0.1, 0.2 ram, etc. until the gear and worm were disconnected) by displacing the mechanism by means of a mobile support along the dynamome- ter's reading device [4]. The empirical curve l~op -- f I ( A A ) shorn in Fig. 3 was obtained from the measurement results. Variations of Mop are shown in percentages with respect to l~I~p for AA -= 0. It will be seen that a reduc- tion of l~Iop occurs rapidly in tile range of &A = 0 to &A = 0.5 m and less rapidly from &A = 0.5 to AA = 1.0 m (module). In order to reduce l~Iop, it is advisable to increase the distance between centers with respect to the nomi- nal one by 0.4 module in the worm gear which consists of a worm and a straight-tooth spur gear. This distance can be calculated from the formula

A = O.Sm (Zg+ Zw+ 0.8).

The displacement &g of the gear mean plane with respect to the worm in the worm transmission includes the displacement due to the assembly error Agl , axial displacement of the gear link Ax, end beating of the gear teeth &p, and the worm eccentr ici ty e w.

The maximum total error is

I A x + A p ! AE = Agl + - 2 ~ - -1- ew[ "

In testing the effect of the displacement Ag on Mop, the value of Ag was varied within the range encount- ered in practice in assembling counting mechanisms and amounted to - 1 . 0 to + 1.0 mm. The positive displace- ment was assumed to be in the direction of the worm's rotation. Variations of/Viop for various values of &g with respect to lvIgp for &g = 0 were calculated from the measurement results. The value of &Mop was determined as the difference between the dispersion range of the Mop instantaneous values per one rotation of the link for & g e 0 and &g = 0. Variations of &Mop for a rising &g were calculated in percentages with respect to the value of l~I~ for &g = 0. The relationships &Mop/M~ = )e 3 (&g) and I~iop/l~I~ p = fz(&g) are shown in Fig. 3. Their analysis shows that the displacement of the gear mean plane with respect to the worm produces reductions up to 10% in the moment I~Iop and rises up to 25% in &Mop, It is advisable to limit the total error Ag of a register to :~0.6 module.

Conclusions. Limitation of the unbalance moment of the first link is an indispensable condition for stabilizing the counting mechanism's opposing moment.

An optimum setting of the distance between centers in the first worm transmission leads to a reduction of the opposing moment down to 12%.

In order to raise the opposing moment 's stabilization, it is advisable to l imit the displacement of the gear mean plane with respect to the worm in the register worm transmission.

1. 2.

31

4. 5.

L I T E R A T U R E C I T E D

G. A. Talalaev, Mokslas ir Technika (Nauka i Tekhnika) [in Lithuanian], No. 1, AN IAtSSR (1971). G. A. Talalaev and I. P. Ablo~evic"jus, Materials of the 21st Republican Scientific and Technical Conference, Kaunas (1971)o G. A. Talalaev, Pribory i Sistemy Upravleniya, No. 12 (1971). G. A. Talalaev, Izmeri te l ' . Tekh., No. 4 (1971). RTM 44-62,"Method for statistical processing of empirical data," Standartgiz, Moscow (1963).

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