US2753688A

US2753688A - Methods of and apparatus for driving a rotating load device

Info

Publication number: US2753688A
Application number: US333640A
Authority: US
Inventors: Tillman T Bunch
Original assignee: Western Electric Co Inc
Current assignee: AT&T Corp
Priority date: 1953-01-28
Filing date: 1953-01-28
Publication date: 1956-07-10
Anticipated expiration: 1973-07-10

Description

y 0, 1956 T. T. BUNCH 2,753,683

METHODS OF AND APPARATUS FOR DRIVING A ROTATING LOAD DEVICE Filed Jan. 28; 1955 2 Sheets-Sheet l m 1 A I Q a O u g k.

//v|//v TOR 7. T. BUNCH ATTORNEY T. T. BUNCH July 10, 1956 METHODS OF AND APPARATUS FOR DRIVING A ROTATING LOAD DEVICE Filed Jan. 28

2 Sheets-Sheet 2 E L H mm R '8 u wm m r M L "m E 17 I P R E a m A T M '6 R H E c T 0 m M 15 LP A ATS H m c n w T RR @M a W C -4 HmQ m TP .l N 3 A T S w m :2 C T Wm Wm T 0 {I A R A H c 0 0000000 00 0000000w00 m98765432 C ww: wmDmmmNE FLUID FLOW (G.P.M.)

FIG. 4

NOMINAL FLOW VERSUS R.P.M.

ROTATIONAL SPEED (RPM) FIG. 3

TORQU E VER SUS PRE SSURE LEAKAGE VERSUS PRE S SURE 400 PRESSURE (P. s. I)

FIG. 2

United States Patent i .METHODS OF AND APPARATUS FOR DRIVING A ROTATING LOAD DEVICE Tillman T. Bunch, near Ashland,.Md., assignor to Western Electric Company, Incorporated, New York, N. Y., a corporation of New York Application January 28, 1953, Serial No. 333,640

9 Claims. (Cl. 60- 51) This invention relates to methods of and apparatus for driving a rotating load device, and more particularly to methods of and apparatus for driving a rotating load device at speeds which are varied in response to changes in torque.

One of the most perplexing problems encountered in designing apparatus suitable for use in a coiling operation is the problem of maintaining a constant tension on a strand being wound on a coiling head. Assuming that it is desired to maintain a predetermined constant tension on a strand which is advanced to the coiling head at a predetermined constant linear speed, it is essential that the rotational speed of the coiling head at the start of a coiling operation be relatively high and decrease proportionally with the increase in the winding diameter as a coil builds up. Since at the start of the coiling operation the winding diameter is small, the required torque is likewise relatively small and as the winding diameter increases the torque must increase proportionally therewith in order to maintain the predetermined tension on the strand.

From the above-mentioned relationships between the torque and winding diameter and the rotational speed and winding diameter, it is manifest that in order to maintain a constant tension on the strand under these conditions the torque must vary inversely with respect to the rotational speed. Hence, it is necessary that a drive system designed to fulfill the foregoing requirements must be capable of delivering a substantially constant power output.

It is an object of this invention to provide new and improved methods of and apparatus for driving a rotating load device.

Another object of this invention is to provide new and improved methods of and apparatus for driving a rotating load device at speeds which are varied in response to changes in torque.

A method illustrating certain features of this invention, may include rotatably driving a coiling head by means of a constant displacement, hydraulic motor, maintaining a supply of hydraulic fluid at a predetermined constant pressure, and conducting the hydraulic fluid from the supply to the motor through a fluid resistance having resistance ,to the flow of the fluid such that the power output of the hydraulic motor is substantially constant, thereby maintaining a substantially constant tension on a filamentary article being wound on the coiling head.

An apparatus illustrating certain features of the invention, may include a constant displacement, hydraulic motor, means for containing a supply of hydraulic fluid and maintaining the hydraulic fluid discharged therefrom at a constant predetermined pressure, and a fluid resistor consisting of a tube of predetermined length and diameter such that the resistance to the flow of hydraulic fluid therethrough maintains the power output of the hydraulic motor substantially constant.

A complete understanding of the invention will be had rrom the following detailed description of certain em- 2,753,688 Patented July 10, 1956 bodiments thereof, when read in conjunction with the appended drawings, in which:

Fig. l is a schematic diagram of a hydraulic drive system for a coiling head, partly broken away for clarity;

Fig. 2 is a graph showing certain operating characteristics of a particular hydraulic motor forming a part of the system;

Fig. 3 is a graph showing another operating characteristic of the hydraulic motor;

Fig. 4 is a graph showing certain characteristics of the hydraulic system;

Fig. 5 is a schematic diagram of a portion of a by draulic system representing an alternative embodiment of the invention, and

Fig. 6 is a schematic diagram of a portion of a hydraulic system representing a second alternative embodiment of the invention.

Referring now to Fig. 1, there is shown a conventional coiling head 10 mounted on a shaft 11 which is rotatably driven by a constant displacement, hydraulic motor 14 through a flexible coupling 15. The coiling head 10 is designed to take up a strand 16 which is advanced at a predetermined constant linear speed by means of a conventional capstan (not shown). Positioned at a point intermediate of the coiling head 10 and the capstan is a distributor sheave 18 over which the strand 16 passes before being wound upon the reel of the coiling head 10. The distributor sheave 18 is reciprocated axially by conventional distributing means (not shown) to insure a uniform lay of the strand 16 upon the reel of the coiling head 10.

A hydraulic fluid supply system associated with the constant displacement, hydraulic motor 14 includes a reservoir 20 which receives the discharge of hydraulic fluid from the outlet of the hydraulic motor 14. The hydraulic fluid within the reservoir 20 is maintained at atmospheric pressure by means of a breather 21 com municating with the interior of the reservoir. Since the hydraulic fluid in the reservoir 20 is maintained at atmospheric pressure, the outlet pressure of the hydraulic motor may be considered to be substantially zero.

Hydraulic fluid is pumped from the reservoir 20 through a supply line 22 to an accumulator 24 by means of a suitable hydraulic pump, such as a constant displacement pump 26 driven by a conventional two speed electric motor 28. The accumulator 24 is of a conventional typedesigned to maintain the pressure at its outlet 30 substantially constant at a preselected value. The accumulator 24 includes a tank 32 for receiving hydraulic fluid pumped from the reservoir 20. In operation the tank is always partially filled with hydraulic fluid, while the remaining space within the tank 32 above the surface of the fluid contains entrapped air under a pressure which varies with the level of fluid in the tank. As the volume of the hydraulic fluid in the tank increases, the level thereof rises with a resulting increase in the pressure of the entrapped air. A flexible membrane 33 is provided within the accumulator to separate the hydraulic fluid .from the entrapped air, thereby preventing undesirable frothing of the hydraulic fluid.

Mounted on the Wall of the tank 32 is a conventional pressure-sensitive switch 35 having a pressure-sensitive diaphragm (not shown) which is in contact with the entrapped air within the tank. As long as the pressure of the entrapped air is greater than a predetermined maximum, the electric motor 28 is operated continuously at a low speed to supply .a small amount of fluid to the accumulator 24. When the pressure of the entrapped air within the tank 32 drops below the predetermined value, the pressure-sensitive switch 35 closes a circuit which causes the -electric motor 28 to operate at a substantially greater speed so as to cause the pump 26 to increase the supply of hydraulic fluid to the accumulator 24 until the level of the fluid within the tank is such that the pressure of the entrapped air is again at the predetermined value. The switch 35 is provided with an adjustable nut (not shown) for preselecting the predetermined pressure. In this manner, by maintaining the pressure of the entrapped air at a predetermined value, it is possible to maintain a substantially constant preselected hydraulic pressure at the outlet 39 of the accumulator 28.

Hydraulic fluid is supplied to the hydraulic motor 14 through a fluid resistor 69 communicating at one end with the outlet of the accumulator 24 and at the other end with the inlet port of the hydraulic motor. The fluid resistor 60 is designed to have characteristics such that for a predetermined constant accumulator outlet pressure the inlet pressures at the hydraulic motor at the full reel and empty reel conditions, respectively, are such that accompanying power outputs are substantially equal and variations from a constant power output at intermediate reel conditions are relatively small. The design of the fluid resistor 65) is determined by the given operating conditions and operating characteristics of the particular constant displacement, hydraulic motor 14 to be used in the system.

For illustrative purposes, it will be assumed that the strand 16 is advanced to a coiling head 10, having an empty reel diameter of 12 inches, at a constant linear speed of 1400 feet per minute, and that it is desired to maintain a substantially constant tension of pounds as the winding diameter increases from 12 inches to 24 inches for a full reel. The operating characteristics of a conventional constant displacement, hydraulic motor, suit able for these purposes, are shown in Figs. 2 and 3, namely, output torque versus pressure, nominal fluid floW versus rotational speed, and leakage fluid flow versus pressure. The particular hydraulic motor selected is a Gerotor Type MH-255 hydraulic motor manufactured by Gerotor May Corporation, Baltimore, Maryland, and described in their catalogue section designated 6-108, page 2.

From the assumed conditions, the output torque and rotational speed of the motor shaft required at both the full reel and empty reel conditions may be calculated in a conventional manner. At the full reel condition, in order to maintain a constant tension of 10 pounds, it is necessary that the torque be 120 inch pounds and that the rotational speed of the shaft 11 be 222.5 revolutions per minute. At the empty reel condition the necessary torque has decreased to 60 inch pounds, whereas the rotational speed of the shaft 11 must increase to 445 revolutions per minute.

Referring now to the operating characteristics of the hydraulic motor 14 (Figs. 2 and 3), the nominal flow, the leakage flow and the motor pressure for the above conditions may be obtained. The actual fluid flow required by the hydraulic motor 14 at a given rotational speed and pressure is the sum of the leakage flow at the given pressure plus the nominal fluid flow required at the given rotational speed. The actual flow represents the flow of fluid which must be supplied from the accumulator 2 through the fluid resistor 60 to the hydraulic motor 14 at a given shaft speed and output torque.

The data obtained from the previous calculations and the operating characteristics of the fluid motor 14 (Figs. 2 and 3) are set out in a summarized form below:

Full Reel Empty Reel Leakage Flow (G. P. 1\/ Nominal Flow Required (G. PMM

From the above data, graphs are made of pressure versus actual flow and pressure versus nominal flow" for the two operating conditions, namely the full reel condition and the empty reel condition (Fig. 4). A straight line is then drawn through each of the two sets of coordinates (Fig. 4). The plot of pressure versus actual flow has been designated input characteristic and may be represented by the equation:

wherein:

p=pressure,

P1=intercept on the pressure axis, Q=actual flow, and

C1=slope of the input characteristic curve.

From an analysis of the above linear equation, it was found that a substantially constant power output can be obtained from the hydraulic motor 14 by maintaining a pressure at the inlet port thereof which varies in accordance with the above relationship.

The above linear relationship may be approximated by supplying the hydraulic fluid from the accumulator 24 at a constant, predetermined pressure equal to P1, through the fluid resistor 60 having characteristics such that the pressure drop per unit length is substantially directly proportional to the rate of flow of the hydraulic fluid therethrough and having a coefficient of resistance to fluid flow equal to C1, the slope of the input characteristic curve. Under these conditions the power outputs at the full reel and empty reel conditions will be equal and variations from this constant power output value at intermediate reel conditions will be negligible. Hence, the tension on the strand may be considered to remain substantially constant at 10 pounds throughout the coiling operation.

In selecting a fluid resistor which would meet the above requirements, it was noted that for laminar fluid flow in a smooth pipe of any size, the relationship expressed by the Hagen-Poiseuille formula holds, that is, the pressure drop per unit length, ignoring the losses in kinetic energy which may be kept relatively insignificant by proper design, is directly proportional to the flow of fluid through the pipe. The Hagen-Poiseuille formula may be stated in the following form:

pl 64 AWL 2D VD V s iral wherein:

Ap=pressure drop,

K=a constant,

L=length of pipe, D=diameter of pipe, ,u=viscosity of fluid, s=specific gravity of fluid, =mass density of fluid, and V=the velocity of fluid.

Assuming a constant effective diameter and a given fluid under given conditions, this formula may be reduced the form:

A p CZQ wherein:

Cz=coetflcient of fluid resistance per unit length, Q=actual flow, and L=length of pipe From the above relationship, it will become apparent that by utilizing a length of conduit in the form of a pipe or tubing having a coefiicient of fluid resistance C2 per unit length equal to C1 Where L =the length. of the conduit) and by maintaining a constant accumulator outlet pressure of P1, the input characteristic curve may be obtained. Attention is directed to the fact that, in order for the proportional relationship expressed by Poiseuilles formula to hold, the diameter of the conduit, the visocity and density of the hydraulic fluid, and the fluid'velocities must be such that laminar flow conditions are maintained within the fluid resistor 60 throughout the operating range from the full reel condition to the empty reel condition.

It will be recalled that the Reynolds number, which is used as the criterion for determining whether or not laminar or turbulent flow conditions exist, depends upon prevailing velocities, viscosity and mass density of the hydraulic fluid and the pipe diameter, and may be expressed wherein:

=mass density, V=fluid velocity, D=pipe diameter, and =viscosity.

in the particular embodiment illustrated in Fig. 1, the fluid resistor 60 consists of a length L of tubing having a coelficient of fluid resistance per unit length equal to C1 108 Z F The value C1=l08 is determined graphically from the slope of the input characteristic curve (Fig. 4). The outlet pressure at the accumulator 24 is preselected. and maintained constant at a value of P1=795 pounds per square inch as determined from the intercept of the input characteristic curve. Hence, the pressure at'the inlet of the hydraulic motor may be expressed as:

wherein p=pressure at the inlet of the motor, Q==the actual flow,

P1=the constant pressure at the outlet of the ac'cum'ulator, and Li="the length of the tubing.

Substituting the data obtainedfrom the slope and inter cept of the input characteristic curve, the above equaon may be written as follows:

Referring now to Fig. 4, an output characteristic" curve has been plotted by subtracting the leakage flow from the actual flow at various pressures. From the latter curve it is possible to obtain the relative power output with respect to the power output at the full reel condition and the empty reel condition for various values of flow. The power output may be expressed by the following relationship:

Power output=pQn wherein p=pressure, and Qn=nominal flow.

In order to illustrate the relatively small amount of variation in the power output from a constant power out put equal tothat at the empty reel condition to the full reel condition, a theoretical constant power output curve has been plotted (Fig. 4). For a constant power output, the following relationship holds:

pQn=constant=Ca The constant C is obtained from the pressure and nominal. flow values at either the empty reel or full reel condition, since the power outputs at either of the conditions are equal due to the design of the fluid resistor 60.

The theoretical constant horsepower characteristic curve has been plotted as p Q. (Fig. 4). Since the latter curve is hyperbolic, it is manitest that when utilizing a fluid resistor having a linear characteristic, there can be only two points whichfall on the theoretical constant power output characteristic curve (i. e. at the full reel condition and at the empty reel condition). However, the variations at points intermediate the extreme reel conditions are manifestly small and the power output of the hydraulic'rnotor may be considered to be substantially constant from the empty reel condition to the full reel condition.

In order to illustrate the small amount of variation that occurs from the preselected theoretical constant power output at intermediate operating conditions, the maximum per cent variation may be calculated in the following manner:

The point of maximum variation from the theoretical constant power output characteristic curve may be obtained by setting theslope of. the output characteristic curve (i. e. pressure versus nominal flow) equal to the slope of the theoretical constant power output characteristic curve (Fig. 4). The slope of the former, which is a linear relationship, may be found graphically from Fig. 4 to be:

C4==slope of output characteristic, curve The expression for the slope of the'theoretical constant power output characteristic curve (pQn=C3=925) may-be obtained by difierentiating that expression to obtain the following:

Substituting the relationship P=C4Qn in the expression PQn=C3, the point of maximum variation may be found to be when:

Max. percent var. X 11.9

It is apparent that this small amount of variation in power output during a coiling operation would result 7 only in a maximum increase of approximately 1.2 pounds in strand tension from the theoretical constant strand tension of pounds.

Assuming that the particular hydraulic fluid used in the heretofore described system is an oil having a specific gravity of 0.90 and a Saybolt viscosity of 300 at an average temperature of 20 C. and that a fluid resistor comprising a length of /2 inch diameter stainless steel tubing is utilized, the calculated predetermined length L of tubing required to obtain an approximation of input characteristic curve (Fig. 4) is found to be 46.4 feet. As illustrated in Fig. 1, it has been found practical to utilize this length of tubing in the form of a coil due to the relatively large length involved.

An additional factor which must be considered is the dissipation of heat evolved due to the energy losses in the fluid resistor 60. This heat must be dissipated at a rate sufficient to prevent substantial changes in the temperature of the fluid resistor and the hydraulic fluid, which would effect the physical properties thereof. Hence, it is desirable to use a heat exchanger, such as a tubular cooling jacket 62, concentrically surrounding the coiled tubing comprising the fluid resistor 60. A cooling medium is continuously circulated through the outer tubular cooling jacket 62 at a predetermined rate sufiicient to maintain the hydraulic fluid within the resistor at a normal temperature.

First alternative embodiment In the embodiment of the invention described hereinabove, the tubing forming the fluid resistor 60 has been shown interposed between the accumulator 24 and the inlet port of the hydraulic motor 14. It is manifest that the same calculated length (L of tubing could be connected at one end to the outlet port of the hydraulic motor and arranged to discharge into the reservoir 20. The resulting pressure differential across the hydraulic motor would vary in the same manner as heretofore described in relation to the embodiment shown in Fig. 1.

As shown in Fig. 5, a fluid resistor 160 comprising a length (L of tubing in the form of a coil is connected to the outlet port of a hydraulic motor 114 identical with the hydraulic motor 14. The fluid resistor 160 is arranged to discharge into a reservoir 120 wherein the fluid is maintained at atmospheric pressure. The outlet of an accumulator 124 is connected directly to the inlet of the motor 114. A heat exchanger 162 similar to that described previously is utilized to dissipate the heat evolved from the fluid resistor 160 during operation of the hydraulic motor.

Second alternative embodiment As shown in Fig. 6, the fluid resistor may be separated into two parts. For example, a length of tubing 260 may be interposed between an accumulator 224 and the inlet of a hydraulic motor 214, and a second length of tubing 261 may be connected to the outlet of the hydraulic motor and arranged to discharge into a reservoir 220. Assuming that the equipment and conditions are identical with those described in the preferred embodiment, the only requirement would be that the combined lengths of the tubing 260 and the tubing 261 inust be equal to the calculated length L

Outer cooling jackets

263 and 264 are provided for dissipating heat due to energy losses in the fluid passing through the tubing 260 and 261.

The above-described arrangements are merely illustrative embodiments of the invention, and it is manifest that numerous other arrangements embodying the prin ciples of the invention and falling within the spirit and scope thereof may be provided by those skilled in the art.

What is claimed is:

' 1. The method of achieving a substantially constant power, variable speed output from a constant displacement hydraulic motor for driving a rotating member within a predetermined speed range, which comprises maintaining a supply of hydraulic fluid at a predetermined constant pressure, supplying the hydraulic fluid to the constant displacement motor through a fluid resistor having resistance characteristics such that the pressure differential across the hydraulic motor varies in accordance with the following relationship:

p=the pressure differential across the motor,

P1=the predetermined constant pressure at the supply,

Q=the actual flow of the hydraulic fluid through the conduit, and

C3=the coefficient of fluid resistance of the resistor,

the values of P1 and C3 being preselected so that the power output of the hydraulic motor remains substantially constant within the predetermined speed range.

2. The method of achieving a substantially constant power, variable speed output from a constant displacement hydraulic motor for driving a rotatable load member between predetermined maximum and minimum speeds, which comprises maintaining a supply of hydraulic fluid at a predetermined constant pressure, supplying the hydraulic fluid to the constant displacement motor through a fluid resistor having resistance characteristics such that the pressure ditferential across the hydraulic motor varies in accordance with the following relationship:

wherein:

p=the pressure differential across the motor,

Pr=the predetermined constant pressure at the supply,

Q=the actual flow of the hydraulic fluid through the conduit, and

C3=the coeflicient of fluid resistance of the resistor,

the values of P1 and C being preselected so that the power outputs of the hydraulic motor at the maximum speed and at the minimum speed are equal.

3. The method of achieving a predetermined variation in the power output of a constant displacement motor for driving a rotatable load member within a predetermined speed range from a maximum speed to a minimum speed, which comprises maintaining a supply of hydraulic fluid at a predetermined constant pressure, supplying the hydraulic fluid to the constant displacement motor through a fluid resistor having resistance characteristics such that the pressure differential across the hydraulic motor varies in accordance with the following relationship:

p=the pressure differential across the motor,

P1=the predetermined constant pressure at the supply,

Q=the actual flow of the hydraulic fluid through the conduit, and

Cs=the coefficient of fluid resistance of the resistor,

the values of P1 and Ca being preselected so that the power outputs of the hydraulic motor at a maximum speed condition and at a minimum speed condition, respectively, are such that the desired variation in power output of the motor is obtained.

4. A hydraulic power transmission for driving a rotating member at speeds which are varied in response to changes in torque, which comprises a constant displacement hydraulic motor, a supply of hydraulic fluid, means for maintaining the supply of hydraulic fluid at a preselected constant pressure, and a laminar flow fluid resistor for conducting the hydraulic fluid to the hydraulic motor from the supply thereof, said preselected and the resist ance to the flow of hydraulic fluid presented by the fluid resistor being such as to tend to maintain the power output of the hydraulic motor sul 'itantially constant within a redetermined speed range.

5. A hydraulic power transmission for driving a rotating load device at speeds which are varied in response to changes in torque, which comprises a constant displacement hydraulic motor, a constant pressure, variable volume fluid source, means for preselecting the value of the constant source pressure, and a fluid resistor consisting of a tube having a predetermined length and diameter and connecting the source to the hydraulic motor, said constant preselected pressure and the resistance to the flow of the hydraulic fluid through the fluid resistor being such as to tend to maintain the power output of the hydraulic motor substantially constant within a predetermined speed range.

6. A hydraulic power transmission for driving a rotating load device at speeds which are varied in response to changes in torque, which comprises a constant displacement hydraulic motor, a constant pressure, variable volume fluid source, means for preselecting the value of the constant source pressure, a fluid resistor consisting of a tube having a predetermined length and diameter and connecting the source to the hydraulic motor, said preselected pressure and the resistance to the flow of the hydraulic fluid through the fluid resistor being such as to tend to maintain the power output of the hydraulic motor substantially constant within a predetermined speed range, and means for dissipating the heat evolved from the fluid resistor so as to maintain the temperature of the fluid flowing therethrough substantially constant.

7. A hydraulic power transmission for driving a load device within a predetermined speed range at speeds which vary in response to changes in torque, which comprises a constant displacement hydraulic motor, an accumulator for containing a supply of hydraulic fluid, means for maintaining the pressure of hydraulic fluid discharged from the accumulator constant at a preselected value, a fluid resistor through which is conducted to the motor the hydraulic fluid discharged from the accumulator, said resistor comprising a predetermined length of tubing having a fluid resistance characteristic such that resulting pressure differential in a hydraulic fluid flowing therethrough varies directly with the volume rate of flow of said fluid, said preselected constant pressure and the coeflicient of fluid resistance per unit length of the fluid resistor being such that the power output of the hydraulic motor at the maximum speed and the minimum speed are substantially equal, and a heat exchanger for dissipating the heat evolved from the fluid resistor so as to maintain the temperature of the fluid passing therethrough substantially constant.

8. A hydraulic power transmission for driving a rotating load device within a predetermined speed range at speeds which vary in response to changes in torque,

which comprises a constant displacement hydraulic motor, an accumulator for containing a supply of hydraulic fluid, a fluid resistor through wh ch all of the fluid supplied from the accumulator and utilized by the hydraulic motor is conducted, said resistor comprising a length of tubing oi. a predetermined length and diameter, a reservoir for receiving the hydraulic fluid discharged by the motor, pump means for pumping fluid from the reservoir to the accumulator, and means for operating the pump so as to maintain the pressure of the fluid supply contained in the accumulator constant at a preselected value, the constant preselected pressure and the fluid resistance characteristic of the tubing being such that the power outputs of the motor at the predetermined maximum speed and at the predetermined minimum speed are substantially equal.

9. A hydraulic power transmission for driving a rotating load device within a predetermined speed range at speeds which vary in response to changes in torque, which comprises a constant displacement motor, an accumulator for containing a supply of hydraulic fluid, means for maintaining the pressure of the hydraulic fluid discharged from the accumulator constant at a predetermined value, and a fluid resistor through which is conducted the fiuid supplied by the accumulator to the motor, said fluid resitsor consisting of a tube of a predetermined length and diameter such that the pressure diflerential across the motor varies in accordance with the following relationship:

wherein:

=the pressure diflerential across the motor, P1=the predetermined constant discharge pressure at the accumulator, Q=the actual flow of hydraulic fluid through the fluid resistor, and C3=the coefficient of fluid resistance of the fluid resistor,

the values of P1 and C3 being preselected so that the power outputs of the hydraulic motor at the predetermined maximum speed and at the predetermined minimum speed are equal.

References Cited in the file of this patent UNITED STATES PATENTS 2,079,268 Wiedmann May 4, 1937 2,200,811 Thompson May 14, 1940 2,232,317 Douglas Feb. 18, 1941 2,283,321 Doe et a1 May 19, 1942 2,357,821 Harrington et al Sept. 12, 1944 2,398,265 Tyler Apr. 9, 1946 2,425,496 Tyler Aug. 12, 1947 2,447,406 George Aug. 17, 1948 2,447,441 Tweedale Aug. 17, 1948 2,447,442 Tweedale Aug. 17, 1948 2,487,520 Brown Nov. 8, 1949