MECHANICAL MEASUREMENTS

M O T O R R O T A T I O N - S P E E D M E A S U R E M E N T S

W I T H H I G H D Y N A M I C P R E C I S I O N

V. V. K l i m o v UDC 531.77 : 681/626

In analyzing the dynamics of motors by means of an analog computer it is necessary to measure their rotation speed continuously with a high dynamic precision. For feeding the computer it is necessary to convert the rotation speed into an analog voltage.

The following methods are known for converting rotation speed into voltage.

1. Conversion into an analog vol tage whose magnitude is d i rect ly proportional to the rotation speed.

2. Conversion into a sinusoidal voltage whose ampl i tude and frequency are direct ly proportional to the speed of rotation.

3. Conversion into cons tant -ampl i tude rectangular vol tage pulses whose frequency is proportional to the speed of rotation.

The first two methods are at ta ined by means of a taehogenerator coupled to the motor axle [ 1]. Their draw-

back consists in the large pulsations of the output vol tage and the low dynamic precision.

In cases when it is not advisable to couple the tachogenerator to the motor axle, a method is used for con- vert ing the rotat ion speed into rectangular vol tage pulses whose frequency is direct ly proportional to the rotation

speed of the motor. For this purpose the motor axle is connected to a shaf t - to -d ig i t transducer which contains a given number of conducting and insulated It.minas. The rectangular pulses are then converted into an analog vol t - age [2-4]. Certain models of such devices [3] have a stat ic error in measuring the speed of rotation not exceeding

0.2%. They serve to obtain a vokage whose magnitude is d i rect ly proportional to the rotation speed of the motor. Their circuits are very simple. However, owing to their large dynamic error, they are unsuitable for a continuous measurement of the rota t ion-speed instantaneous values.

Below we examine devices for converting rotation speed into voltage whose value is inversely proportional to the speed. They have low output vol tage pulsations and a high dynamic precision.

A block schemat ic of the device for continuous measurements of the rotation speed is shown in Fig. 1. The

device comprises the negator NE, the electronic switches Sr-S 3, and capacitors. Rectangular pulses are fed from a sha f t - to -d ig i t a l converter to Input 1 of the device (Fig. 2a). They are inverted (Fig. 2b) by the negator NE and

fed to the control inputs of the e lect ronic switches S 1 and S z. The leading edge of the rectangular pulse energizes the switch S 1. The capaci tor C 2 discharges through the switch $1 whose internal resistance in a conducting state ap- proaches zero. As soon as the capaci tor had discharged, the switch S 1 blocks spontaneously. The switch S 2 remains energized for the duration of the rectangular pu re at the output of the negator. The capaci tor C 2 is charged from the vol tage source E. The t ime constant of the charge is determined by the value of this capaci tor and the inter-

nal resistance of the switch S z. The charging of the capaci tor C 2 is discontinued at the end of the rectangular pulse. Its charge is stored for the duration of the spacing between pulses. The voltage shape across the capaci tor C 2 is shown in Fig. 2d.

The switch $2, whose conducting internal resistance approaches zero, remains energized for the duration of the rectangular p u r e at the Input 1 (Fig. 2a). The capaci tor C 3 is thus connected to the capaci tor C 2 and receives a part of its charge. The switch S 3 blocks at the end of the Input 1 rectangular pulse, and the capaci tor C 3 stores the charge which it has received from the capaci tor C 2. During the interval between the pulses (Fig. 2a) a certain leakage of the charge from the capaci tor C 3 is possible. In order to compensate this l eakage ,a resistance R is pro- vided. The vol tage shape across the capaci tor C 3 and at the output of the circuit is shown in Fig. 2f.

The ci rcui t of the device is shown in Fig. 3. The negator NE (see Fig. 1) comprises the common emmi t t e r

transistor T 1. The electronic switches S 1 and S 2 (see Fig. 1) use transistors T 3, T 4 and T 2, Ts respect ively, whereas

Translated from Izmer i t e l ' naya Tekhnika, No. 1, pp. 26-28, January, 1969. Original ar t ic le submitted Octo- ber 7, 1966.

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I n 1

a

,, o b

,# c

Out f d 0

:gj e

f

L

3J3 NnflP I3Z-3 l-q nnfln n ,q [-1

. . . . . t Z t__--, t

I ' r - - ' t

Fig. 1 Fig. g

the e lectronic switch S a (see Fig. 1) uses direct ly transistor T 6, with transistors T7 and Ts serving to control transistor T6. The transistor Ts remains conducting for the duration of the rectangular pulse at the circuit input, thus energiz-

ing the b locking-osc i l la tor transistor T 7 which generates high-frequency oscillations. These oscil lations are trans- mit ted to the transistor T 6, thus energizing it for the duration of one of the half periods of each oscil lat ion. It is then necessary to meet condition fb >> fp, where f b and fp are the frequencies of the blocking osci l lator and the

rectangular pulses, respectively. In order to raise the re l iab i l i ty of the switch S 1 (the transistors T 3 and T4), the l im i t - ing resistance I~ is connected between it and the capaci tor C 2. For a value of 10 ijF the capaci tor C2 discharges in

7-10 Nec and the switch blocks in ~0.4 msec. The to ta l t ime of the capaci tor ' s discharge and the blocking of the switch can be taken as 0.4 msec. The use of a l imi t ing resistance increases insignificantly a capaci tor ' s discharge t ime but raises the re l iab i l i ty of switching.

In designing the circuit of Fig. 3 the following components were used. The transistors T 1, T z, T 4, T6, and T 8

of typeMP103, T s o f t y p e M p l 6 B , a n d T 3, TT of type B416; the capacitors C 1=430 pF, C 2 = 10 ~F ,C a =910 pF, a n d C 4 = 1 ~F; the resistorsR1, R4, andRll =5 .1k fa , R2andRtz = 2 k f ~ , R a a n d R a = l ka , l q - - 1 0 Z?,R~ a n d l ~ = 9 1 0

k a ~ = 2 . ~ l k g ~ a n d R l 0 =2 .2kfa ; the transformer Tr 1 uses a f e r r i t e c o r e o f l 0 x 6 x 4.S mm with 40 turns in the winding connected to the collectors of the transistors T 7 and T 8 and 15 turns in the remaining windings; a supply vol tage of E = +16 V; and rectangular pulses t ransmit ted from the shaf t - to -d ig i ta t converter with an ampli tude of

Uin : +16 V.

The above device is suitable for obtaining an analog vol tage whose value is inversely proportional to the rota-

tion speed.

It has a high dynamic precision. Any rotation speed variations are registered in 1 / m of a rotor revolution, provided that the sha f t - to -d ig i t a l transducer contains m conduct ing and m insulated laminas. The capaci tor con- verters [2, 3] provide a dynamic delay of tens of revolutions in registering rotat ion speed variations. This makes

them unsuitable for investigating the dynamics of an e lec t r ic drive.

Despite its high dynamic precision the above device has a lower stat ic precision than that of RC- network de- vices [2-4]. The stat ic precision of the device under consideration is affected by the precision of the shaf t - to- d igi ta l converter, the instabi l i ty of the supply voltage, the residual vol tage across the capagitor C 4 when the capac i - tor C a is connected to it, as wel l as the fact that the capaci tor C 4 is charged and discharged during the operation of

a single rectangular pulse.

A sha f t - to -d ig i t a l converter with a single conducting lamina does not contribute errors to the operation of the circuit in Fig. 3. For m conducting laminas the sha f t - to -d ig i t a l converter error can be expressed either in terms of

pulse durations rmax and rmin

esd.max = 2ran (~max-- "~min), (1)

where n is the speed of the shaft rotation, or in terms of the lamina lengths

m ( / m a x - lmin) (2) r ~ Im

m

34

. . . . l ~ T r

J'>o, __a

Fig. 3 Fig. 4

L O

Out I

Owing tO the error of the sha f t - to -d ig i t a l converter, the output voltage of the device in Fig. 3 has a pulsation

of

kUmax = Uch (~max- - ~min)' (3)

where Uch is the rate of charge of the capaci tor C z.

On the basis of (1) and (3) it is possible to wr~te the error which is due to the inaccuracy of the sha f t - to -d ig i - ta l converter:

Uch ~sd.max (4) /-lout 2ran

Therefore, it is advisable to use a sha f t - to -d ig i t a l converter with a single lamina.

The error due to the supply vokage instabi l i ty can be ca lcu la ted from the formula

eeUch ( . 5 )

2mnUout

where eE is the supply vol tage error.

It wi l l be seen from (5) that the error of the device depends to a considerable extent on the supply voltage in-

stabil i ty. In this connection the device shown in Fig. 3 should be supplied from a s tabi l ized vol tage source.

The error due to the residual vol tage across the capaci tor C4 when its is connected to the capaci tor C 2 can be ca lcu la ted from the formula

C~ (Uc, -~ Uc2 ) e~ = , ( 6 )

de , (C2 -~- C4)

where UC2 and Uc4 are the voltages across the capacitors C 2 and C 4.

It wil l be seen from (6) that the necessary condit ion for a static precision is C a >>C 4.

The error due to the charging and discharging of the capaci tor during the operation of a single pulse is deter - mined by the expression

~, = U c h - - , (7) Udis

where Udi s is the discharge rate of the capaci tor C 2.

When this device is used with analog computers, its stat ic systematic error determined by (7) can be e l i - minated by means of functional units.

The device is ca l ibra ted in a stat ic condition. One of the output voltages (in the middle of the range) is se lected as the true value:

1 Uou t = k - - ,

n

where k is a constant factor.

(8)

35

The remaining values of the output vokage are checked by means of this expression.

Yet another version of the device for converting the rotation speed into vol tage can be proposed (Fig. 4). It

wi l l be seen from its schemat ic in Fig. 1 that the part containing the switches S I and S z is doubled. In this case addit ional capacitors can be dispensed with. The capacitors C 2 and C 4 can be connected to the circuit output through rect ifying diodes. The vol tage shape across the capacitors C 2 and C 4 is shown in Fig. 2c and Fig. 2d respec- t ively. The voltage shape at the output of the circuit is shown in Fig. 2e. A comparison of the curves in Fig. 2e and Fig. 2f shows that the schemat ic in Fig. 4 converts more precisely. However, it requires a greater number of components, thus reducing operat ional reI iabi l i ty . The s ta t ic errors of the device Shown in Fig. 3 are determined

from (4), (5), and (7). In this case ~'max in (3) is the max imum duration of a pulse (spacing), whereas ~-min is the duration of a spacing (pulse) which follows pulse rmax. The device of Fig. 4 is free from the error determined by (6).

The above devices are intended for continuous measurements of angular veloci ty and its feeding to an analog computer. These devices are connected to the resoIving units of the computer by means of negators whose input re -

sistance amounts to 1 M~.

1~ 2. 3.

4.

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

Zh, A. Yampol'skii, Priborostroenie, No, 1 (1966). V. I. Turchenkov, Priborostroenie, No. 3 (19G6).

Smi th-Sav i l l e and Ness, Electronics, No. 3 (1966). V, I. Safonov, I, N. Ivanov, and V. N. Komlssarov, I zmer i t e l ' . Tekh., No. 5 (1963).

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