On Limiting Pneumatic Governors of Carburetor Automobile Engines

V. K. Nechaev

Modern carburetor engines of trucks are usually equipped with special pneumatic limiting governors, in which a flap rotating on an axis, installed in the engine intake system, simultaneously performs the functions of the sensing and actuating elements of the control system.¹)

Such governors, often called maximum engine-speed limiters, are installed, for example, on the engines of domestic trucks GAZ-51 and ZIS-150. These governors limit the maximum number of engine revolutions in cases when it operates under small loads or at idle with a large opening of the carburetor throttle. The governor does not interfere with the operation of the engine at engine-shaft speeds lower than the limiting permissible number of revolutions \(n_A\).

Throttle-governors are considerably simpler and cheaper than centrifugal governors, take up little space, do not require the installation of additional drives and transmissions, and do not need special maintenance. Recently, throttle-governors have become an integral element in the design of carburetors for truck engines (for example, in carburetors K-49, K-49A, K-80).

As practice shows, limiting the maximum number of revolutions of a carburetor engine by means of a limiting throttle-governor leads to an increase in engine service life and to improved economy in the operation of a truck.

The features of operation, theory, and methods of analysis and calculation of pneumatic governors of the throttle type are almost not covered in the literature²). The purpose of the present article is to partially fill this gap.

1. The Simplest Pneumatic Governor of the Throttle Type

Figure 1 shows a simplified diagram of such a governor. The governor is installed between the carburetor and the engine intake manifold. The main element of the governor is flap I, freely seated on an axis fastened at its ends in the walls of the governor housing. This axis is somewhat displaced from the axis of the governor branch pipe in the direction shown in Fig. 1.

Control of the engine is carried out here in the usual manner, by means of throttle valve II of the carburetor, connected with the accelerator pedal in the driver’s cab of the automobile.

¹) Such governors, in contrast to the known diaphragm-type pneumatic governors, should expediently, in our opinion, be called throttle-governors.

²) The only article known to the author—S. Akopyan, “Automatic Vacuum Governors,” American Technology, 1945, No. 9—by no means exhausts the question.

The governor throttle can rotate about its axis within certain limits: from a position slightly inclined to the axis of the governor branch pipe, characterized by the initial or “setting” angle \(\beta_o\), to the position \(\beta=\beta_{max}\), corresponding to complete closure of the throttle. A definite value of the initial angle \(\beta_o\) is ensured by special limiters or stops located on the throttle or on its axis.

The aerodynamic action of the flow of the working mixture entering the engine from the carburetor on throttle I, situated obliquely to the direction of flow, gives rise on this throttle to a certain torque \(M_c\), directed toward closure of the throttle. The torque \(M_c\) is opposed by the torque \(M_p\), developed on the throttle by the force of the governor spring, installed with a certain initial tension \(F_o\).

Fig. 1

Fig. 2

With the positions of both throttles unchanged (Fig. 1), the torque \(M_c\) on the governor throttle increases as the engine speed \(n\) increases. At normal rotational speeds of the engine shaft \((n<n_A)\), the torque \(M_c\) is less than the initial torque \(M_{no}\), produced on the throttle by the governor spring, and the governor throttle retains its position of maximum opening. In the case of engine acceleration with a large opening of the carburetor throttle, i.e., at \(n>n_A\), the torque \(M_c\) will exceed the initial spring torque \(M_{no}\), and the governor throttle will begin to close, thereby reducing (apart from the driver’s will) the filling of the engine and thus limiting any further increase in the rotational speed of the crankshaft.

The governor characteristic \(AB\) of an engine with a throttle-governor may have, for example, the form shown in Fig. 2 (in coordinates \(N_e\)—effective engine power, \(n\)—number of revolutions of the crankshaft per minute).

Its initial point \(A\) lies on the external characteristic of the engine; its final point \(B\) corresponds to idling of the engine.

The degree of nonuniformity of the governor is

\[ \delta=\frac{n_B-n_A}{n_{cp}}, \]

where

\[ n_{cp}=\frac{n_B+n_A}{2} \]

is not a particularly indicative characteristic for limiting governors. Here the directly absolute quantities \(n_A\) and \(n_B\) are more important, that is, those rotation speeds in the interval between which the governor is engaged and the maximum speed of the engine is limited.

The specific values of the limiting engine speeds \(n_A\) and \(n_B\) are determined primarily by the magnitudes of the moments \(M_c\) and \(M_n\) acting on the governor throttle. These moments vary as the rotational speed of the shaft increases (the moment \(M_c\)) and as the throttle and governor shutters are closed.

The moment \(M_n\) does not depend on \(\beta'\) and \(n\), and increases as the governor shutter is closed, that is, as the angle \(\beta\) increases. (Fig. 3).

Fig. 3

The moment \(M_c\) is a complex function of the shape and dimensions of the shutter, its angle of rotation \(\beta'\), and the characteristics of the working-mixture flow passing through the governor. It can be shown that the magnitude of this moment (in the case where the shutter has the usual elliptical or rectangular shape and small thickness) is determined by the approximate expression:

\[ M_c=k_1 q+k_2 \Delta p_{12}, \tag{1} \]

where

\[ k_1=BF_3\left(c_2+c_1\frac{e}{B}\right), \]

\[ k_2=F_3\cdot e. \]

Here \(F_3\) is the area of the shutter;
\(B\) is the major axis of the shutter ellipse or, for a rectangular shutter, the length of its side perpendicular to the axis of rotation;
\(e\) is the eccentricity of the shutter (the distance of the center of gravity of the shutter area from the axis of rotation of the latter);

$c_1$ and $c_2$ are coefficients depending on the shape of the throttle, its angle of rotation $\beta$, and the angle $\beta_{max}$ corresponding to complete closing of the throttle (the quantities $c_1$ and $c_2$ can be determined by blowing the throttle on a special test stand);

$\Delta p_{12}$ is the static pressure drop across the governor throttle, equal to the difference of the static pressures of the flow of the working mixture before the throttle $(p_1)$ and after the throttle $(p_2)$;

\[ q=\frac{\gamma_1 V^2}{2g} \]

is the dynamic pressure of the mixture flow before the throttle;

$V$, $\gamma_1$ are, respectively, the velocity and specific weight of the working-mixture flow before the throttle.

Formula (1) may be represented in a more general form:

\[ M_c = c_m B F_3 \cdot \Delta p, \tag{2} \]

where $\Delta p$ is the absolute static vacuum under the governor throttle, measured at some distance from the throttle;

$c_m$ is the total moment coefficient, determined, according to formula (1), by the expression:

\[ c_m = c_2 \frac{q}{\Delta p} + \frac{e}{B}\left(\frac{\Delta p_{12}}{\Delta p} + c_1 \frac{q}{\Delta p}\right). \tag{3} \]

The ratios $\dfrac{q}{\Delta p}$ and $\dfrac{\Delta p_{12}}{\Delta p}$ depend on the hydraulic characteristics of the engine intake system from the air cleaner to the intake manifold and on the absolute magnitude of the vacuum $\Delta p$ under the governor throttle. This vacuum changes with changes in the number of revolutions of the engine shaft and in the position of the governor throttle $\beta$. Thus, in each particular motor installation, under constant external atmospheric conditions and unchanged $\beta'$, the moment $M_c$ on the governor throttle is a function of two variables: the rotational speed of the engine shaft $n$ and the angle $\beta$ (Fig. 4). But for a given external load on the engine and a constant position of the carburetor throttle valve ($\beta'=\mathrm{const}$), the rotational speed of the engine shaft is determined by the magnitude of the flow area opened by the governor throttle, that is, ultimately, also by the magnitude of the angle $\beta$. In turn, the equilibrium position of the governor throttle is determined by the laws of variation of the moment $M_c$ with $n$ and $\beta$ and of the moment $M_n$ with $\beta$.

Fig. 4

Thus, in the control system under consideration with a throttle governor there is a circular dependence of a number of variables, schematically represented in Fig. 5. A change in any of the variables in this loop leads to a change in all the other variables.¹ Here the vacuum \(\Delta p\) under the governor valve is, as it were, the connecting link between the engine and the governor. This connection can be acted upon from the outside—by changing the characteristics of the governor spring and by changing the position of the carburetor throttle valve, i.e., the angle \(\beta'\).

A change in the position of the carburetor valve, quite common under operating conditions of an automobile engine, has a very substantial and, as will be shown below, predominantly undesirable effect on the characteristics of the governor according to Fig. 1.

Hence follows the need to investigate the operation of the throttle governor specifically for different values of the angle \(\beta'\), from \(\beta' = 0\) (complete opening of the carburetor throttle) up to that limiting value at which an excessive increase in engine speed \((n > n_B)\) is still possible in the event that the entire external load is removed from the engine. In this investigation, the use of a number of empirical relationships is unavoidable; these are represented not by equations, but by graphs and, as a rule, are nonlinear in character. Therefore an analytical investigation of throttle governors proves to be very difficult.

Fig. 5

Below a graphical method is set forth for analyzing the operation of throttle governors, which can be used both in calculating governors and in their adjustment and tuning.

2. Graphical investigation of the simplest throttle governor

(at \(\beta' = 0\), full throttle)

The combined accounting of the principal factors affecting the operation of a throttle governor can be carried out on the diagram described below (Fig. 6). Here, along four coordinate axes, the quantities \(N_e\), \(M_c\), \(M_n\), \(n\), \(h\), \(F\), \(\beta\) are plotted in the corresponding scales.² The scales for the torque quantities \(M_c\) and \(M_n\),

¹ A circular dependence is usual for systems of automatic engine control. Here, an accidental change in some variable may, after passing around the entire loop, turn out to be diminished or amplified. In the latter case the control system will be unstable.

² The quantities \(h\) and \(F\), omitted in Fig. 6, are plotted along the vertical coordinate axis of quadrant II.

plotted along one axis must be the same. The scales of all the other quantities are chosen arbitrarily, according to the desired dimensions of the entire diagram.

In quadrant I of the diagram (Fig. 6) are shown the external and partial characteristics of the engine \(N_e=f_1(n)\) with respect to the governor throttle (with the carburetor throttle kept unchanged at full opening, \(\beta'=0\)) for a series of different fixed positions \(\beta_0, \beta_1, \beta_2,\ldots\) of the governor throttle, within the limits from \(\beta=\beta_0\) to those greatest values of the angle \(\beta\) at which engine operation at idle \((N_e=0)\) is still possible at sufficiently high engine speeds. Each partial characteristic corresponds to a definite constant value of the angle \(\beta\), indicated in Fig. 6 near each curve \(N_e\). The external characteristic corresponds to the value \(\beta=\beta_0\).

In quadrant IV are shown the curves of variation of torque

\[ M_c=f_2(n) \]

on the governor throttle at \(\beta'=0\), for the same fixed values of the angle \(\beta\) that were chosen earlier for the partial engine characteristics shown in quadrant I.

Fig. 6

Each curve \(M_c\) is bounded on the right (in Fig. 6) by the limiting value of \(n\) corresponding to idle operation \((N_e=0)\) of the engine at the given fixed position of the governor throttle \(\beta=\mathrm{const}\). These end points of the curves \(M_c\) lie on verticals drawn through the terminal points (lying on the abscissa axis \(n\)) of the partial engine characteristics in quadrant I. The locus of the end points of the curves \(M_c\) is a certain curve \(Z\), which may be called the engine idle-speed curve.

In quadrant III of the diagram is shown the curve of variation of the spring moment

\[ M_p=f_3(\beta). \]

In quadrant II are shown the curves of variation of the force \(F\) of the governor spring and of the arm \(h\) of this force relative to the axis of rotation of the governor throttle.

For each given particular engine with a given governor and carburetor, the curves \(N_e=f_1(n)\) and \(M_c=f_2(n)\) can be obtained experimentally (plotted point by point): the external and partial characteristics \(N_e\) (at \(\beta'=0\))—by the usual methods adopted in bench tests of an engine; the curves \(M_c\)—there as well, with the aid of a special device that makes it possible to measure the moment \(M_c\) on the governor throttle during engine operation.

The curve \(M_n=f_3(\beta)\) is plotted from the calibration data of the governor spring on a non-operating engine, by applying to the governor throttle various external torques of known magnitude and measuring the corresponding angles of rotation \(\beta\) of the governor throttle. The initial point \(a\) of the curve \(M_n\) is determined by the setting angle \(\beta_0\) of the governor throttle, the force \(F_0\) of the initial tightening of the governor spring, and the initial value of the arm \(h\): \(M_{n0}=F_0h\).

In investigating or adjusting the governor, an analytical method of determining the moment \(M_n\) from the expression

\[ M_n=Fh, \]

where \(F\) and \(h\) are functions of the angle \(\beta\) (quadrant II in Fig. 6), may prove more appropriate. The values of \(F\) and \(h\) entering here are determined analytically or graphically from the known characteristic of the spring and the geometrical relations of the linkage mechanism between the governor throttle and the spring. In the case of experimental determination of the moments \(M_n\) (calibration), the curves \(F\) and \(h\) in quadrant II are not necessary.

The family of curves \(N_e=f_1(n)\) in quadrant I of the diagram in Fig. 6 represents the characteristic of the engine together with its intake system, carburetor, and governor throttle; the family of curves \(M_c=f_2(n)\) (quadrant IV) represents the combined characteristic of the governor and of the engine intake system with the carburetor; finally, the curve \(M_n=f_3(\beta)\) in quadrant III represents the characteristic of the elastic elements of the governor. With the aid of all these curves one can construct the governing characteristic \(AB\) of the engine, which may be regarded as a certain resultant static characteristic of the governing system as a whole.

The initial point \(A\) of the governing characteristic is determined as follows. Through the initial point \(a\) of the curve \(M_n\) (quadrant III) we draw the horizontal \(a\)—1 until it intersects, at point 1 (quadrant IV), the curve \(M_c\) plotted for the case \(\beta=\beta_0\).

It is evident that the abscissa of point 1, corresponding to the equality

\[ M_c=M_{n0}\quad \text{at}\quad \beta=\beta_0, \]

determines the engine speed \(n_A\) at which the governor will come into action and its throttle will begin to close (we neglect friction on the axis of the governor throttle, which may be the cause of a certain insensitivity of the governor).

The vertical drawn through point 1 intersects the external characteristic of the engine (the curve \(N_e=f_1(n)\) for \(\beta'=0\) and \(\beta=\beta_0\)) at the sought point \(A\). At \(\beta=\beta_0\) and \(n<n_A\), the governor throttle retains its initial position \((\beta=\beta_0)\), since here

\[ M_c<M_{n0}. \]

In the same way, other, intermediate, points of the governing characteristic can also be constructed. Thus, for example, at \(\beta=\beta_1\) the moment \(M_n\) of the spring is determined by the ordinate of point 2 on the curve \(M_n=f_3(\beta)\). The horizontal through point 2 intersects the curve \(M_c\) (for \(\beta=\beta_1\)) at a certain point 3. The vertical drawn through point 3 intersects the corresponding \((\beta=\beta_1)\)

the partial characteristic of the engine at point 4, which obviously belongs to the governor characteristic \(AB\).

The position of the final point \(B\) of the governor characteristic is found by means of a special construction. For this purpose the curve \(Z\) of limiting values of the torque \(M_c\) is transferred into quadrant III (Fig. 6), by projecting the points of this curve from quadrant IV along horizontals into quadrant III, onto the verticals corresponding to the same values of the angle \(\beta\) to which each given point of the curve \(Z\) corresponds. We obtain the curve \(Z_1\).

The final point \(B\) of the governor characteristic satisfies the condition \(N_e = 0\), that is, point \(B\) in quadrant I lies on the abscissa axis \(n\). Moreover, here

\[ M_c = M_n, \]

that is, point \(B\) corresponds to point \(b\), the intersection of the curves \(M_n\) and \(Z_1\) in quadrant III. Transferring point \(b\) horizontally to the curve \(Z\) (quadrant IV), we obtain point \(b_0\). The intersection of the vertical through point \(b_0\) with the abscissa axis \(n\) gives on the latter the required extreme point \(B\) of the governor characteristic and the corresponding limiting engine speed \(n_B\).

3. Operation of the simplest throttle governor with the carburetor throttle partially closed \((\beta' > 0)\)

With partial closing of the carburetor throttle valve, that is, when it is turned through a certain angle \(\beta' = \beta'_1\) from the axis of the carburetor diffuser and with the engine speed unchanged (which may occur, for example, with a corresponding decrease in the external load on the engine), the rarefaction \(\Delta p\) under the governor valve increases, while the mass flow rate per second of the working mixture entering the engine decreases.

At the same time, naturally, the dynamic pressure \(q\) in front of the governor valve decreases and, with the position of the governor valve unchanged \((\beta = \mathrm{const})\), so does the static pressure drop \(\Delta p_{12}\) across it.

But, according to formula (1), the decrease in the pressures \(q\) and \(\Delta p_{12}\) leads to a decrease (at the previous \(\beta\) and \(n\)) in the magnitude of the torque \(M_c\) on the governor valve, as compared with its value that occurred with the carburetor throttle fully open \((\beta' = 0)\).

Now the curves of the torque on the valve \(M'_c\) (constructed for the case \(\beta' = \beta'_1\) and shown in Fig. 7 by dashed lines) are located closer to the abscissa axis than the curves \(M_c\) of the torque on the valve for \(\beta' = 0\). Similarly, as a result of the decrease in the filling of the engine, the external and partial characteristics \(N'_e\) of the engine will also be lowered (constructed, as before, for different values of the angle \(\beta\), but at a fixed position of the carburetor throttle \(\beta' = \beta'_1\)) as compared with the external and partial characteristics for the case \(\beta' = 0\), which we used earlier in Fig. 6.

Each particular value of the angle \(\beta'\) will correspond to definite families of curves \(N_e\) and \(M_c\). The curve \(M_n\), however, obviously remains unchanged for any values of the angle \(\beta\). (The solid curves \(N_e\) and \(M_c\) in Fig. 7 are the same as in Fig. 6, that is, they refer to the case \(\beta' = 0\).)

From the curves \(M'_c\), \(M_n\), and \(N'_e\), by the method described above, the governor characteristic \(A'B'\) for the case of engine operation with the carburetor throttle partially closed \((\beta' = \beta_1)\) is constructed in Fig. 7.

It follows from the diagram in Fig. 7 that, as the carburetor throttle is closed in the arrangement of Fig. 1:

a) the initial point \(A\) of the governor characteristic shifts to the right, toward higher values of \(n\);

b) the no-load curve \(Z\) (in quadrant IV) shifts to the left, toward smaller values of \(n\), while the curve \(Z_1\) (in quadrant III) approaches the axis

abscissas; in this case the points \(b'_0\) and \(b'\) move toward smaller maximum values of the angle \(\beta\);

c) the end point \(B\) of the governor characteristic is also displaced to the right, toward higher values of \(n\); this displacement of point \(B\) is less than the displacement of point \(A\), that is, closing the carburetor throttle valve leads to a decrease in the degree of nonuniformity \(\delta\) of the governor.

With a sufficiently large closing of the carburetor throttle (but not yet so considerable as to eliminate the danger of an excessive increase in engine speed when the load is suddenly removed from it), the horizontal line drawn through point \(a\) (Fig. 7) intersects the curve \(M_c'\) (for \(\beta=\beta_0\) and \(\beta'>0\)) very far to the right. The governor in fact ceases to perform its function as a limiter of the engine’s maximum speed.

Fig. 7

Thus, here, in the simplest pneumatic governor of the type under consideration (Fig. 1), the engine’s limiting speed regime (the engine speed \(n_A\), at which the governor begins to operate) continuously increases as the carburetor throttle valve is closed.

The governor begins, as it were, to lag in its operation.

This lag will in fact be still more significant because of the presence in the governor of friction forces and the insensitivity of the governor caused by them. Finally, with a sufficiently large closing of the carburetor throttle, the limiting governor will come into operation at impermissibly high engine speeds, or will even fail completely to operate.

All this occurs for reasons fundamentally connected with the physical principles of operation of the throttle-governor, which responds to changes in the dynamic pressure \(q\) of the flow of working mixture impinging on the governor valve and to changes in the static pressure drop \(\Delta p_{12}\) on the same valve. As the upper valve (in Fig. 1) is closed and the engine speed remains unchanged (\(n=\mathrm{const}\)), an ever larger portion of the total vacuum \(\Delta p\) under the governor valve is created at the carburetor valve, while the quantities \(q\) and \(\Delta p_{12}\) continuously decrease; the result is a decreas—

the action of “driving” moments $M_c$ on the governor throttle valve and a reduction in the operability of the governor.

4. Improved Schemes of Throttle Governors

The substantial shortcomings noted above of the simplest governor according to Fig. 1 can be partially or completely eliminated by a number of measures:

1) by varying, depending on the position of the carburetor throttle valve, the stiffness $c$ and the force $F_0$ of the initial tension of the governor spring (reducing this tension as the angle $\beta'$ increases), by means of arranging an appropriate mechanical linkage between the governor spring and the carburetor throttle valve;

2) by using a special pneumatic device (a vacuum corrector) that ensures forced closing of the governor throttle valve in those cases when the governor’s own operability proves insufficient;

3) by an appropriate change (increase) in the initial (setting) angle $\beta_0$ of the governor throttle valve as the carburetor throttle valve is closed.

The first way of improving the characteristics of a throttle governor by using a special device for automatically changing the characteristics of the governor spring as the carburetor throttle valve is closed is associated with considerable design difficulties.

The second way (the vacuum-corrector device) is used, for example, in the Handy limiting governor installed on some Chevrolet truck engines. Unlike the governor throttle valve, which responds to the dynamic pressure $q$ of the working-mixture flow and to the pressure drop $\Delta p_{12}$ across the valve, the vacuum corrector responds to changes in the absolute (static) vacuum $\Delta p_1$ between the carburetor and the governor. At $n = \mathrm{const}$, this vacuum $\Delta p_1$, in contrast to the decreasing dynamic pressure $q$ and drop $\Delta p_{12}$, continuously increases as the carburetor throttle is closed.

In the Handy governor¹ the piston of the vacuum corrector is, on one side, under the action of atmospheric pressure, and on the other—of the vacuum $\Delta p_1$. The piston is loaded by a weak spring installed with a certain initial tension. At large angles $\beta'$ of closing of the carburetor throttle valve and sufficiently high engine speeds, the force produced on the vacuum-corrector piston by the pressure difference $\Delta p_1$ on its two sides overcomes the initial tension of this spring and causes the piston to move. In doing so, the end of the piston rod, acting on a projection on the governor throttle valve, closes the latter. By suitably selecting the piston diameter and the characteristics of the vacuum-corrector spring, it is possible to ensure satisfactory operation of the limiting throttle governor at large angles $\beta'$ of closing of the carburetor throttle valve.

But the use of a vacuum corrector leads to complication of the governor design and to a decrease in the reliability of its operation.

However, the use of a vacuum corrector can be avoided. For this it is necessary only to provide an appropriate increase in the setting angle $\beta_0$ of the governor throttle valve as the carburetor throttle valve is closed (the third of the methods listed above for improving the characteristics of pneumatic governors). In this way, with proper selection of the governor parameters, it is possible to compensate for the undesirable influence (with respect to the effectiveness of the throttle governor as a limiter of maximum engine speeds)—

...of the closing of the carburetor throttle valve on the magnitude of the moment \(M_c\) on the regulating valve.

But under these conditions one more step remains to be taken—to combine the functions of the carburetor throttle valve and the functions of the regulating valve in a single element, as has been done, for example, in the domestic carburetors K-49, K-49A, MKZ-14, K-80. Here the throttle valve, which is also the regulating valve, sits freely on its axis and is held at all times in the initial position (at an angle \(\beta_0\) to the axis of the diffuser) by the force of the governor spring, unless special cams \(K\), connected with the accelerator pedal, prevent this (Fig. 8). When the accelerator pedal is raised, these cams turn and close the throttle valve, overcoming the resistance of the governor spring. The valve will likewise close under the action of the moment \(M_c\), if the magnitude of this moment proves sufficient to overcome the moment \(M_n\) of the governor spring (the cams have a one-sided action and do not limit the motion of the valve in the direction of its closing).

Fig. 8

Fig. 9

Now in the intake system of the engine there is only one valve, if the air valve with its special functions is not also counted. Such a combination of the throttle and regulating valves is advantageous not only from the standpoint of a certain simplification of the carburetor and governor design. The main point is that here, when the engine is shifted to operation along partial characteristics (by the driver closing the valve through the accelerator pedal), the operating conditions of this same valve as the principal element of the governor prove to be considerably more favorable than in the simplest governor considered above in Fig. 1.

Here, in the device with the “combined” valve, as the angle \(\beta\) increases and the engine speed remains unchanged (\(n=\mathrm{const}\)), the dynamic pressure \(q\) in front of the valve decreases, while the static pressure drop \(\Delta p_{12}\) across the valve increases (Fig. 9). With a sufficiently large value of the positive eccentricity \(e\) of the valve, this increase of the pressure drop \(\Delta p_{12}\) with increasing angle \(\beta\) will have a decisive influence on the magnitude of the moment \(M_c\) and will completely compen-

will have a negative effect of reducing the dynamic pressure $q$ in formula (1).¹

On the whole, the combined governor (for example, of the K—49 type) is obtained as sufficiently simple and compact. It lacks the above-noted shortcomings of the simplest governor in Fig. 1—the considerable delay in the governor’s coming into action when the engine is operating with the throttle partly closed. In the combined governor, the shortcomings inherent in a governor with a vacuum corrector (possible sticking of the governor elements) are also eliminated, since the governing flap, which is also the throttle flap, is in motion almost all the time during engine operation. The occurrence of excessive friction, or of sticking of the flap on its axis, will immediately be detected by the driver through a sharp deterioration of the vehicle’s tractive properties.

5. Governing characteristic of a combined throttle-governor (K—49 type)

For investigating combined throttle-governors one may use the graphical method set forth above. The basis for the investigation is the same diagram in Fig. 6, which was constructed earlier when considering the operation of the simplest governor in Fig. 1, for the case $\beta' = 0$.

Now the curves $N_e = f_1(n)$ for $\beta = \mathrm{const}$ (with $\beta > \beta_0$) are, in the full sense, partial characteristics of the engine. The curve $N_e = f_1(n)$ for the “setting” position of the flap ($\beta = \beta_0$) should be regarded as the external characteristic of the engine, since it defines the maximum values of the effective power $N_e$ that can be obtained from this engine with the combined throttle-governor installed on it and having a fixed value of the angle $\beta_0$.

The transition of an engine with a combined throttle-governor to operation along partial characteristics does not lead to any change or displacement of the curves $M_c = f_2(n)$ in the fourth quadrant of the diagram. These curves remain the same as for the governor in Fig. 1, for the case of full opening of the carburetor throttle, provided, of course, that the aerodynamic characteristics of the governor flaps in the combined governor under consideration and in the governor of Fig. 1 are identical.

The limiting points $A$ and $B$ of the governing characteristic of an engine with a combined governor are determined (Fig. 6) in exactly the same way as before, when investigating the simplest governor with $\beta' = 0$. In a similar manner, any intermediate points of the governing characteristic may also be found.

In the combined governor under consideration, the position of the flap (angle $\beta$) is determined by the position of the accelerator pedal (which limits the maximum opening of the flap, that is, the minimum value of $\beta$), by the force of the governor spring (which reduces $\beta$), and by the moment $M_c$, directed toward increasing the angle $\beta$. Suppose that, through the corresponding action of the driver on the accelerator pedal, the flap is now set in some intermediate position $\beta = \beta_1$. In this case the spring moment $M_n$ acts on the flap, determined by the ordinate of point 2 on the curve $M_n$. The horizontal through point 2 intersects the curve $M_c$ corresponding to the angle $\beta = \beta_1$ at a certain point 3.

The intersection of the vertical line through point 3 with the partial characteristic \(\Lambda_c\) of the engine, corresponding to the same angle \(\beta_1\), gives point 4, which evidently lies on the governing characteristic \(AB\).

For \(\beta=\beta_1\) and \(n<n_4\), where \(n_4\) is the abscissa of point 4 of the governing characteristic, the governor does not operate and the throttle valve retains its angular position \(\beta=\beta_1\), being pressed against the stops controlled by the accelerator pedal by the difference of the moments \(M_n\) and \(M_c\). Equilibrium between \(M_n\) and \(M_c\) will occur only at \(n=n_4\). With a further increase in the engine speed \((n>n_4)\), an excess moment \(M_c-M_n\) will appear and the valve will begin to close.

Fig. 10

Thus, the engine speed corresponding to the beginning of operation of the combined governor increases somewhat as the engine is transferred to operation with progressively more closed throttles. However, the limiting engine speed \(n_B\) at idle remains here always the same (with unchanged atmospheric conditions, of course), regardless of the position of the accelerator pedal. The beginning of governor engagement is in each case determined by the abscissa of the point of intersection of the corresponding partial characteristic of the engine \(N_e\) with the governing characteristic \(AB\) (Fig. 10a). In Fig. 10b, for comparison, the governing characteristics of the engine with the governor in Fig. 1 are shown.

6. Influence of the characteristics of the governor spring on the operation of the throttle governor

It follows from the diagram in Fig. 6 that the position of the extreme points of the governing characteristic \(AB\) in the coordinates \(N_e\) and \(n\) depends decisively on the laws governing the variation of the moment \(M_n\) of the governor spring with respect to

the angle of rotation of the governor throttle $\beta$, that is, on the form and position of the curve $M_n$ in quadrant III of the diagram. In turn, the position and form of the curve $M_n=f_3(\beta)$ are determined by the elastic characteristics of the governor spring, its stiffness $c$ and initial tension $F_0$, and by the geometrical parameters of the mechanism linking the spring with the throttle. These parameters of the mechanism determine the laws of variation of the arm $h$ and of the deformation—elongation—of the spring $z$ with the angle $\beta$.¹)

For a given mechanism linking the spring with the throttle, the position of the curve $M_n=f_3(\beta)$ in the coordinates $M_n$ and $\beta$ depends only on the stiffness of the spring and on the force $F_0$ of its initial tension.

An increase in the force $F_0$ leads to a displacement of the curve $M_n$ in quadrant III of the diagram farther from the abscissa axis, usually without a substantial change in its form (for example, the curve $M'_n$ in Fig. 11). In this case the governor characteristic $AB$ shifts to the right, toward higher engine speeds $n$, and assumes a certain new position $A'B'$. The governor now comes into action at a higher engine speed $n'_A$ and has a smaller degree of nonuniformity $\delta'$.

An increase in the stiffness of the spring—for example, by cutting out part of its active coils—while maintaining an unchanged initial tension $F_0$, leads, as it were, to a rotation of the curve $M_n=f_3(\beta)$ in quadrant III about its initial point $a$ and, probably, to some change in the form of the curve. The curve $M''_n$ rises now more steeply along the ordinate axis. In this case the initial point $A$ of the governor characteristic remains in place, while the terminal point $B''$ shifts toward higher values of $n_B$. The degree of nonuniformity of the governor $\delta$ increases.

Fig. 11

¹) In Fig. 8 the mechanism linking the spring with the throttle is shown schematically, in the most simplified form. In reality this mechanism, for a number of reasons, is made according to somewhat more complex schemes.

Thus, by selecting the appropriate stiffness and initial tension of the governor spring, it is usually possible to ensure that the required values—set, for example, by specifying the limiting rotational speeds \(n_A\) and \(n_B\) and the degree of nonuniformity \(\delta\)—are obtained.

However, the quality of operation of the governor depends not only on the position of the extreme points \(A\) and \(B\) of the governor characteristic in the coordinates \(N_e\) and \(n\), but also on the shape of the curve \(AB\) between these points (see below).

The desired or acceptable form of the governor characteristic \(AB\) can be obtained only as the result of proper calculation and selection of the characteristics of the governor spring, the correct choice of the dimensions and shape of the governor throttle valve (the quantities \(e\), \(\beta_0\), \(\beta_{max}\), etc.), and also of the layout and geometrical parameters of the mechanism connecting the spring with the valve.

Questions concerning the method of selecting the optimum parameters of the mechanism and calculating the limiting throttle governor deserve separate consideration and will be dealt with in the author’s subsequent articles. Here we confine ourselves to the general indication of the fundamental possibility of realizing a governor characteristic \(AB\) of a prescribed form and with a prescribed, but not excessively small, value of the degree of nonuniformity \(\delta\). The conditions for this are the selection of appropriate characteristics of the governor throttle valve (its shape, dimensions, eccentricity) and the proper calculation and design provision of the necessary curve of spring moment \(M_n = f_3(\beta)\).

7. The form of the governor characteristic and the static stability of the throttle governor

As follows from the preceding, a change in the elastic characteristics of the governor spring has a very strong effect on the position (in the coordinates \(N_e\) and \(n\)) and on the form of the governor characteristic \(AB\), as well as on the magnitude of the degree of nonuniformity \(\delta\).

But the static stability or instability of the regulating system is determined by the form of the governor characteristic and by the magnitude of \(\delta\).

Instability of the governor may prove not especially undesirable, and sometimes even useful, in a limiting throttle governor which performs only the function of limiting the maximum engine speed and in fact operates only outside the range of the engine’s service speeds. But this instability will be wholly unacceptable if the throttle governor is assigned the duties of a single-mode governor of engine speed in the zone of the latter’s service speeds. Here the instability of the governor will manifest itself in large and continuous oscillations of the speed of the regulated engine.

In analytical form, the condition for the static stability of the throttle governor is expressed by the elementary relation:

\[ \frac{\partial M_c}{\partial \beta} < \frac{\partial M_n}{\partial \beta}, \tag{4} \]

which must be satisfied for any values of the angle \(\beta\) and any (at least in the interval from \(n_A\) to \(n_B\)) values of the engine speed.

Let us draw through the initial point \(A\) of the governor characteristic \(AB\) a vertical line (Fig. 12). It will intersect the curves \(M_c\), constructed for various fixed values of the angle \(\beta\), in quadrant IV at points 1, 2, 3... We transfer these points along horizontals into quadrant III onto the verticals corresponding to the same values of the angle \(\beta\). We obtain a curve representing the dependence \(M_c = f_4(\beta)\) at a constant engine speed \(n = n_A = \mathrm{const}\). In an analogous manner one can construct a family of curves \(M_c = f_4(\beta)\) for a series of values of \(n\) in the interval of those engine speeds at which the governor must operate.

Condition (4) for the static stability of the governor requires that, at the points of intersection of the curve \(M_n\) with each of the curves \(M_c=f_4(\beta)\), the curve of the spring torque \(M_n\) should rise more steeply with respect to the ordinate axis \((M_n, M_c)\) than the curve \(M_c\). For this, the curve of the spring torque \(M_n=f_3(\beta)\) must have a sufficiently steep rise along the ordinate axis.

Point \(D\) of the governor characteristic \(ADB\) corresponds to point \(d\) of intersection of the curves \(M_n=f_3(\beta)\) and \(M_c=f_4(\beta)\) at \(n=n_D=\mathrm{const}\) in quadrant III. It is obvious that point \(d\) satisfies condition (4), that is, the governor throttle at \(\beta=\beta_1\) and \(n=n_D\) (point \(D\) on the characteristic \(ADB\)) is in stable equilibrium. Condition (4) is also satisfied by all the other points of the governor characteristic \(ADB\) (Fig. 12), whose ordinates decrease continuously as the engine speed \(n\) increases. Here, as the governor throttle is closed, that is, as point \(D\) moves along the characteristic \(ADB\) toward point \(B\), point \(d\) moves continuously along the curve \(M_n=f_3(\beta)\) in the direction of increasing values of the spring torque \(M_n\).

Fig. 12

Some new curve of the spring torque \(M'_n\), however, passing through the former points \(a\) and \(b\), also corresponds to a new governor characteristic \(AHEB\) (Fig. 12). Now the vertical line drawn, for example, through point \(B\) intersects the curve \(AHEB\) at a second point \(H\). This means that the curve \(M'_n\) intersects the curve \(M_c=f(\beta)\), constructed for \(n=n_B\), at two points \(b\) and \(h\). But it is easy to see that both points \(b\) and \(h\) cannot simultaneously satisfy condition (4): this condition is fulfilled at point \(h\) and is violated at point \(b\).

Consequently, point \(H\) of the governor characteristic \(AHEB\) corresponds to stable equilibrium of the governor throttle, while point \(B\) corresponds to unstable equilibrium.

Let \(E\) be the rightmost (in Fig. 12) point of the governor characteristic \(AHEB\). It is obvious that the governor throttle is stable only on the segment \(AE\) of the characteristic and unstable on the segment \(EB\). Moreover,

one may say that only the segment \(AH\), corresponding to the interval of engine speeds from \(n_A\) to \(n_B\), is fully stable. On the segment \(HE\), however, the governor throttle valve has only limited stability: with large random oscillations of the valve—for example, near the equilibrium point \(h\)—a “jump” of it to the point \(b\) of a new, but already unstable, equilibrium is possible.

Thus, in order to ensure the static stability of the throttle governor over the entire governor characteristic, it is necessary that:

a) the entire governor characteristic \(AB\) in the coordinates \(N_e\) and \(n\) be located to the right of the vertical line drawn through the initial point \(A\) of the characteristic; that is, that the condition \(n_B > n_A\) be satisfied; and, in addition,

b) for each value of the engine speed \(n\) within the limits covered by the governor characteristic, there correspond only one point of intersection of the curves \(M_c\) and \(M_n\) in quadrant III in Fig. 12.

An unstable governor characteristic of the throttle governor can be corrected by a corresponding change in the characteristics of the spring (its stiffness) and by changing the parameters of the mechanism linking the spring with the valve. In particular cases, increasing the eccentricity \(e\) of the governor valve will be useful.

1. By positive eccentricity we mean the magnitude of the displacement of the center of gravity of the mean plane of the flap from the axis of rotation of the flap, toward the oncoming flow of the working mixture.

   It can be shown that a governing flap without eccentricity ($e = 0$), or with negative eccentricity ($e < 0$), does not ensure a continuous increase in the moment $M_c$ (at $\Delta p = \mathrm{const}$) with respect to the angle of rotation of the flap $\beta$, and therefore is unsuitable as the working element of a throttle-governor. ↩↩