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| United States Patent |
3,561,329 |
|
Firth
, et al.
|
February 9, 1971
|
BALL PISTON HYDROSTATIC MACHINES
Abstract
A ball piston hydrostatic machine comprises a cylinder block in which are
formed a plurality of cylinders at a constant pitch. Ball pistons working
within the cylinders run on a cam track defining the stroke of each ball
piston in its cylinder and having fewer complete cam lobes lying between
the points of contact of the first and last balls with the cam than the
total number of balls multiplied by the ball pitch. Each cam lobe is so
profiled as to produce a ball stroke including a period of constant
acceleration and a period of constant deceleration with or without an
intermediate period of constant velocity. The duration of the latter, as a
proportion of the total ball stroke, is predetermined by the number (n )
of ball pistons and the number (m ) of cam lobes according to the
expression:
1-2l (x )/n
Where l = the highest common factor of m and n, and
x = an integer n /2l and is even when n /l is even.
| Inventors: |
Firth; Donald (East Kilbridge, SC), Cunningham; Sinclair (East Kilbridge, SC) |
| Assignee: |
National Research Development Corporation
(London,
EN)
|
| Appl. No.:
|
04/871,750 |
| Filed:
|
October 28, 1969 |
Foreign Application Priority Data
| | | | |
|
Aug 15, 1964
[GB] | | |
33412/64 |
|
|
| Current U.S. Class: |
91/498 ; 417/273 |
| Current International Class: |
F01B 1/06 (20060101); F01B 1/00 (20060101); F04b 027/00 (); F04b 027/08 () |
| Field of Search: |
103/161,174,162 91/205
|
References Cited [Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Primary Examiner: Freeh; William L.
Parent Case Text
This invention relates to ball piston hydrostatic machines which operate at
high hydrostatic pressures, and this application is a continuation of U.S.
Ser. No. 711,966, filed Mar. 11, 1968 and now abandoned, which was in
turn, a continuation-in-part of U.S. Ser. No. 479,192 filed Aug. 12, 1965;
U.S. Ser. No. 567,549 and U.S. Ser. No. 567,623, now abandoned, both filed
Jul. 25, 1966, all now abandoned.
Claims
We claim:
1. A cam controlled reciprocating piston hydrostatic machine having a piston pitch/cam pitch ratio less than unity and constant mechanical thrust characteristics throughout every cycle
of operation, comprising a cylinder block forming a housing for a plurality n of cylinders carrying pistons movable on a cam track having a plurality 2m of similarly contoured half-lobes each having a profile which determines, for each piston moving
thereover, a stroke having consecutive periods of constant acceleration, constant velocity and constant deceleration, the variations in thrust of any one piston during said acceleration and deceleration periods being compensated by respective oppositely
varying thrusts resulting from the simultaneous movement of at least one other piston over the appropriate segment of the cam track, and the proportion of the stroke occupied by the constant velocity period (excluding any extension to cover a dwell
period at inner dead center of each piston) being given by the expression l - 2lx/n, where l is the highest common factor of m and n; and x is an integer which must be an even number whenever the value n/l is even, and whose magnitude is not greater
than n/2l, x being chosen within the following limitations:
i. x must be a positive integer;
ii. x must be even when .sup.n is even;
iii. x must not exceed the value of .sub.21 and m and n being chosen so that the value of the expression .sup.21x does not exceed unity for the smallest permissible value for x.
2. A machine according to claim 1 having radial balance, at any position of the cylinder block relative to the pintle, of the working thrust forces acting on the piston, wherein the cylinders are radially disposed in a rotary cylinder block, and
all of the pistons which at any given instant are at the same positions in their respective strokes are grouped symmetrically about the shaft axis, each piston being at the same point on its coacting cam lobe as each other ball in the same symmetrical
group.
3. A machine according to claim 1 wherein the profile of each half-lobe of the cam produces a piston stroke having consecutive ideal periods of constant acceleration and constant deceleration, and the thrust variations during said acceleration
and deceleration periods are compensated by respective oppositely varying thrusts resulting from the movement of at least one other piston over the appropriate segment of the cam track, the value of x in the expression l - 2lx/n being such that the
expression reduces to zero.
4. A machine according to claim 1 wherein the cross-sectional shape of the cam track is modified locally at points of change of acceleration to reduce Hertzian stresses in the cam track.
5. A machine according to claim 4 wherein said pistons comprise pistons of circular profile in cross section, the cam track is grooved transversely of its length at a radius about 21/2 percent in excess of the radius of the pistons, and the
depth of the groove progressively increases from either side up to the crest of each lobe at the inner dead center position of a piston.
6. A machine according to claim 1 wherein the rigorously derived cam profile is modified at each junction between consecutive periods of deceleration in one sense and acceleration in the opposite sense to provide a short dwell period in which
the velocity of a piston axially of its cylinder is substantially zero, the said dwell period being of a duration sufficient only to permit the cylinder port connections to be reversed, and each rigorously derived period of constant velocity of a piston
being extended at each end to compensate for a corresponding half of a dwell period of another piston.
7. A machine according to claim 1 wherein said pistons comprise pistons of circular profile in cross section and wherein the cam has six lobes and the cylinder block has nine pistons, and the profile of each half-lobe of the cam is such that
each stroke of each piston conforms to the equations: ##SPC2##
where .theta. = the angle subtended at the axis of the machine by the locus of a piston center from its dead center position up to its instantaneous position; where
r.sub.o = radial distance from machine axis to center of a piston at inner dead center on the cam track;
r.sub.1 = radial distance from machine axis to center of a piston at outer dead center on the cam track;
r = instantaneous radial distance from machine axis to piston center at any given position of the cylinder block in relation to the cam track.
Description
Such machines may be either motors or
pumps, and the torque output of a motor or input of a pump, for substantially constant line pressure, usually varies over each complete revolution. This is not always desirable, especially in a servomotor system.
An hydrostatic machine is one in which the mechanical output (motor) or mechanical input (pump) is a function of the pressure or potential energy of the working fluid rather than its velocity or kinetic energy.
The present invention is concerned only with an hydrostatic machine in which more than one ball is in contact with any one complete cam lobe. The latter is defined as that part of the cam lying between corresponding points on its profile.
Points on the profile are said to correspond if the slopes of the profile thereat are equal in both magnitude and sign relative to a common datum. In a linear machine, the datum is a straight line tangential to all the crests, or a line parallel
thereto. In a rotary or segmental machine, the datum is an arc of a circle tangential to all the crests, or an arc described about the same center. Thus, a cam lobe is that part of the cam profile lying between adjacent crests or between adjacent
troughs, or between alternate points of intersection with intermediate parts of the profile by a line parallel to, or described about the same center as, a line tangential to the crests.
In a linear or a segmental machine according to the present invention, therefore, this means that there are always fewer complete cam lobes lying between the points of contact of the first and last balls with the cam than the number of balls
multiplied by the ball pitch. In a rotary machine, according to the present invention, there are always more balls than complete cam lobes. For convenience of terminology, this relationship between ball pistons and cam lobes will be expressed as a
ratio of ball pitch to cam pitch of less than unity which will be assumed to apply throughout the subsequent description and claims.
In the graphical analyses which appear later in this specification, certain profiles or profile modifications have been drawn in an exaggerated fashion for clarity of illustration.
It is an object of the present invention to provide a ball piston hydrostatic machine having a ball pitch to cam pitch ratio of less than unity in which the mechanical power output (motor) or input (pump) is constant over each working cycle of
the machine. For a rotary machine, a working cycle is a revolution of its shaft. For a linear or a segmental machine, a working cycle is the relative displacement of the cylinder block and the cam track equal to the ball pitch multiplied by the number
of balls.
To this end, it can be shown that if the cam track over which each ball moves during each complete outward or inward stroke is profiled so as to produce a ball motion having consecutive periods first of constant acceleration; then of constant
velocity; and finally of constant deceleration; and provided that the numbers of balls and of cam lobes is chosen so that the variation in thrust contributed by one ball during a period of acceleration or deceleration of that ball is compensated by an
oppositely varying thrust contributed by another ball during a complementary period of its stroke, or by the sum of appropriate parts of such thrust contributions by a plurality of other balls, then the total effect on the cylinder block will be one of
constant thrust. (For convenience of subsequent description herein, the machines will be assumed to be rotary--i.e. thrust = torque). Thus, a rising torque produced by one ball of a rotary machine during an acceleration period must be complemented by a
falling torque produced by at least one other ball during a coextensive deceleration period, these two torques adding up, at any given instant, to the same value of torque at any instant during each complete cycle of the machine. Furthermore, it can be
demonstrated that the period of constant ball velocity relative to its cylinder reduces to vanishing point for certain combinations of numbers of balls and cam lobes, or can, for certain such combinations, be of alternative determinate periods one of
which, in special cases, is zero. (It should be noted that the velocity of, the rate of fluid displacement by, and the thrust produced by a ball are directly proportional to one another). This arrangement has the advantage of ensuring substantially
constant rate of flow of working fluid in the high pressure line and ports, which promotes smooth running of the machine.
The generalized expression for the proportion of each stroke of a ball which is occupied by the component of constant velocity must not be less than the value of the expression 1 - 21 (x)/ n where: n = the number of balls;
l = the highest common factor of n and the number ( m) of cam lobes; and
x = an integer which must be even when n /l is even, and must not exceed n /2l.
Where a dwell is provided at the dead center regions of the cam profile, as hereinafter explained, the extent of the dwell is added to the period of constant velocity given by the above expression.
For a six lobe, nine ball machine where no dead center dwell is provided, therefore, (l =3, n/l is odd) the period of constant velocity of each ball on each half lobe of the cam track is one third of the stroke of the ball. In this case, x
cannot exceed unity because n/2l = 9/6 = 1.5.
Transient fluid pressures and thrust have been observed when the hydraulic circuit connections to a cylinder are reversed from high to low pressure or vice versa at the ports in the pintle. To combat these transients a ball piston hydrostatic
machine according to a feature of the present invention has its cam track profile modified in such a way as to produce a dwell period during which each ball is stationary in its cylinder between successive port events--i.e. during which a cylinder is not
connected to either an inlet or an outlet port in the pintle. The relative positions and dimensions of the lands on the pintle are not so critical when the cam profile is modified as described to give the dwell periods. In other words, the tolerances
to which the pintle ports and cylinder ports must be machined are increased.
The insertion of a dwell in this manner changes the timing of the commencement of the acceleration phase of the stroke and the end of the deceleration phase of the stroke. For constant torque these timings in respect of one ball are required to
coincide respectively with the end and the beginning of the constant velocity phase of the stroke of another ball and the latter therefore require to be correspondingly retimed. It thus becomes necessary to extend the constant velocity phase as given by
the said expression 1 - 21 (x)/ n by the addition thereto of a period equal to the dwell period.
The cases where, (in the absence of a dead center dwell period), the constant velocity period reduces to zero, or where alternative lengths for the constant velocity period include an alternative where the constant velocity period is zero, are
those cases where 1 - 21 ( x)/n = 0, and are confined to cases where n/l is an even number, (where x cannot be less than 2), and n/m is greater than 2.
The limitation previously stated that x must not exceed n/2l is the equivalent of a limitation that the term 2i( x)/ n must not exceed unity, for if it did, the length of the constant velocity phase would be a minus quantity, which is an
absurdity. The cases where there are alternative values for the length of the constant velocity phase are those where x can have a plurality of values without the term 21 ( x)/n exceeding unity. It can be shown that the term 2l (x)/ n can never
actually equal unity (to give a zero constant velocity phase) when n /l is an odd number because the numerator 2l(x) is inevitably an even number and the denominator n must be an odd number if n/l is odd; therefore the numerator and denominator of 2l
(x)/ n can never be equal to one another to give the term a value of unity.
Where n/l is even 2l( x)/n may be equal to unity for some value of x, bearing in mind that x must be an even number. Some combinations of ball to lobe number, for instance 12 balls/5 lobes, permit of more than one value for x which does not
exceed n/2l and some of these combinations give a value of unity for the term 2l(x)/n for the highest permissible value of x.
Other n/l = even combinations, for instance 8 balls/2 lobes, have only one permissible value for x, namely 2, and 2l(x)/n can only equal unity.
Where there is a choice of more than one value for the length of the constant velocity phase it is generally advantageous to choose the shortest as this choice provides the lowest acceleration and deceleration at the region of the cam lobe crest
where Herzian stresses are highest due to the mutual convexity of the interacting ball and cam surfaces in this region.
Another desirable characteristic of a ball piston rotary machine is that there should at all times be radial balance of the working thrust forces acting on the balls. The requirement for radial balance is met if there is a symmetry in the
arrangement of balls relative to the entire cam track. This condition of symmetry is satisfied if the number (m) of cam lobes and the number (n) of ball pistons have a highest common factor which is an integer greater than unity. Thus, for example, if
the number of lobes m is equal to 6 and the number of balls n is equal to 9, the highest common factor is 3, so that there are always balls spaced at 120.degree. around the shaft axis, each ball being at the same position of its stroke as its other two
counterparts on an equivalent segment of the track.
The balls in a machine according to the present invention may be arranged either internally or externally of the cam track, and either the cylinder block or the track may be arranged to rotate within a fixed housing. For a servomotor application
of the invention, however, the machine must have maximum "stiffness," defined in terms of possible positive and negative limits of displacement error of the follower motor relative to the desired position signalled by the input. Hence, for this
application of the invention, the volume of oil trapped in the machine between the balls and the servocontrol valve must be a minimum.
Where it is necessary to achieve radial balance of the thrust forces, the number of lobes and the number of balls are both restricted by the need for geometrical symmetry in the relative dispositions of the balls and the lobes. Taking, for
example, the case of a nine ball machine with a six lobe cam, the following equations define the shape of each half-lobe. ##SPC1##
where r.sub.o = radial distance from machine axis to center of a ball at inner dead center on the cam track,
r.sub.1 = radial distance from machine axis to center of a ball at outer dead center on the cam track,
r = instantaneous radial distance from machine axis to ball center at any given position of the cylinder block in relation to the cam track.
A graphical analysis of the behavior of the ball pistons of a machine according to the present
invention will now be given with reference to FIGS. 1--7 of the accompanying drawings in which:
FIG. 1 is a diagram for a nine ball, six lobe machine;
FIG. 2 is a diagram for a nine ball one lobe machine; the left-hand and right-hand halves of this FIG. showing alternative choices for the length of period of constant velocity;
FIG. 3 is a single triangle taken from a complete velocity/stroke diagram of a machine in which the ratio n/ l is odd, and illustrating four alternative choices for the length of period of constant velocity;
FIG. 4 is a diagram similar to FIG. 3 where n/ l is even;
FIG. 5 shows part of a single lobe cam diagram relating the velocity v of a single ball in a cylinder to the angular position .THETA. of the cylinder relative to the pintle and showing a profile modification introduced by the present invention
to provide a stationary or dwell period for the ball in the vicinity of inner dead center;
FIG. 6 is a schematic view of the profile of the cam track on either side of the inner dead center position of a ball showing the profile modification necessary to produce the curve of FIG. 5;
FIG. 7 is a velocity/stroke diagram similar to FIG. 1 for a six ball one lobe cam machine showing modifications to provide dwell periods at the dead center positions of the balls; and
FIGS. 8A--8D illustrate cam track modifications at the sections A-A to D-D in FIG. 1.
(For convenience, the remaining FIGS. 9--14 of the accompanying drawings are described hereinafter).
Referring first to FIGS. 1--4, each abscissa represents strokes of a ball piston and each ordinate represents ball piston velocity. In
FIGS. 1 and 2, each horizontal row of triangles represents, in the simplest form, the basic essentials of a stroke--that the ball must accelerate from rest at one dead center location on the cam to a certain peak velocity and decelerate from that peak
velocity to rest again at the opposite dead center location on the cam.
In FIG. 1, each line of triangles is numbered (1 to 9) to represent a respective ball of a nine ball six lobe machine, each triangle pertaining to a respective cam half-lobe. All the lines are of equal length representing the complete cam track
pitch or 360.degree. of cam track, and each line is divided into 12 equal intervals, each representing one half cam lobe, or one full stroke of the respective ball. These subdivisions of successive lines are mutually displaced horizontally (to the left
in the drawing) by one-ninth of the complete line length (representing 360.degree. as aforesaid), to represent the relative angular displacements of successive balls, the timed events proceeding from left to right and the balls being numbered in the
order in which the balls pass a given point on the cam track.
The triangles in each line are drawn alternately positive (above the line) and negative (below the line) to represent, respectively, alternate high and low pressure strokes of the ball concerned. For a motor having a rotary cylinder block
enclosed by a fixed annular cam track, a working stroke is outwards with respect to the shaft of the machine; for a similarly arranged pump, a working stroke is inwards. Every fourth line of triangles is geometrically identical.
Each complete triangle represents a basic condition of motion of the ball comprising a half stroke at constant acceleration followed by a half stroke at constant deceleration. A period of constant velocity is represented by cutting off the peak
of each triangle parallel with its base. It becomes necessary to do this to achieve constant torque except in circumstances where the apex of a triangle for one ball coincides in time with the zero crossing point of the triangle for another (conjugate)
ball so that each rising triangle side for one ball is coterminous with the falling side of a stroke triangle for a conjugate ball (comparing power stroke with power stroke and induction/exhaust or idle stroke with induction/exhaust stroke).
Subject to an exception described below in relation to FIG. 2, the criteria for determining the level at which the peak of a triangle is to be cut off to provide the appropriate constant velocity phase are:
a. that the start of each constant velocity period (i.e. the finish of a period of constant acceleration) of each ball must coincide with the finish of a period of constant deceleration of a conjugate ball;
b. the end of the constant velocity period of one ball must coincide with the beginning of the constant acceleration of a conjugate ball.
These criteria are satisfied in FIG. 1. For example, taking ball No. 1, let the top left trapezium 1A represent a working stroke of the ball No. 1 and the adjacent trapezium 1B represent an idle stroke thereof. Then the left flank of the
trapezium 1A coincides in time with the right flank of the first trapezium 3A (only partly shown) of ball No. 3. Similarly, the right flank of the first trapezium 1A coincides with the left flank of the first trapezium 2A of ball No. 2. Thus, the
constant velocity period of the trapezium 1A of ball No. 1 starts at the same instant as the first intersection 3x of the velocity/stroke curve for ball NO. 3 with the zero or base line for that ball, and finishes at the first intersection 2x of the
velocity/stroke curve of ball No. 2 with its zero or base line. To indicate this, the starts and finishes of the constant velocity periods of the trapezia 1A, 1C and 1D for ball No. 1 are marked by the bracketed numerals (3) and (2) respectively, which
identify the complementary curve which establishes the relevant point on the curve of ball No. 1. Similar identifications appear on other ball curves.
In the particular configuration of machine to which FIG. 1 relates, it so happens that there are more than one set of complementary conditions to establish the duration of each constant velocity period. Balls Nos. 1, 2 and 3 form one
complementary group, complete in itself, whilst balls Nos. 4, 5 and 6, and balls Nos. 7, 8 and 9 likewise form complementary groups each complete in itself. This arises from the relatively large value of l (=3) whereby the stroke diagrams,
successively displaced by the ball pitch, come into phase again every fourth ball.
Although only "positive" trapezia have been specifically considered in the foregoing analysis, it will be evident by the symmetry of the system that the constant velocity periods of "negative" trapezia for any one ball can be similarly
established in relation to the curves of conjugate balls.
A simple method for constructing diagrams of this type, for different combinations of ball number and lobe number, is to choose a convenient length for dividing up into basic triangle stroke diagrams corresponding to the number of lobes and to
construct separate stroke diagrams for the respective balls, one below another and each displaced laterally from the one above it by a distance equal to the said length divided by the ball number.
Vertical lines are then drawn, from top to bottom of the diagram, through every point where a stroke triangle for a ball intersects the zero line. A number of such vertical lines are shown at the right hand side of FIG. 1.
It will be found that these lines are separated by a distance being a proportion of the length of a stroke which is equal to l/ n where n/ l is odd and 2l/ n where n/ l is even. In a limited number of the latter cases these vertical lines will
pass through the apices of stroke triangles and these are the cases where constant torque can be obtained with a constant velocity period of zero. In all other cases it will be found that the apex of each stroke triangle is flanked by at least one pair
of such vertical lines which intersect the sides of the triangle, the lines of a pair being equidistant from the apex. The points of intersection of the lines of any such pair with the sides of the triangle mark the beginning and end of the constant
velocity period which, when inserted into the middle of the stroke, will provide the required constant torque characteristic.
FIG. 2 shows a graphical analysis, generally similar to FIG. 1, of ball velocities in a nine ball, one lobe machine, but for this ball/lobe combination, several pairs of vertical lines symmetrically flank the apex of each triangle, so that
alternative periods of constant velocity are obtainable for each curve. Obviously, only one alternative will be embodied in any one machine. In FIG. 2, the longer alternative constant velocity period is illustrated in the left hand half of the FIG. and
the shorter alternative period is illustrated in the right hand half.
For this particular configuration of machine, it so happens that there are in fact four alternative periods of constant velocity, the two actually drawn being the shortest (right hand side) and the longest but one (left hand side). The limits of
these are indicated, on the curve 5A for ball No. 5, by the pair of bracketed numerals (3) and (7) and, on the curve 1A for ball No. 1, by the pair of bracketed numerals (9) and (2). Verticals drawn through each of these points pass through the
intersections of the other identified ball curves with their respective zero lines when the said other curves are parallel to the flanks of the curve 1A or 5A. This condition is the exception to the criteria (a) and (b) previously referred to in
connection with FIG. 1, but is justified as follows:
Taking, for purposes of illustration, the curve 5A, each flank of the trapezium between its point of intersection with the zero line and the corresponding end of the constant velocity line at (3) or (7), respectively, can be subdivided into four
parts of equal length marked by arrowheads. Each lowermost subdivision is now seen to be exactly complementary to the corresponding subdivision of an oppositely inclined flank of a curve of a conjugate ball, that on the left flank of the curve 5A being
complemented by the lowermost subdivision of the curve for ball No. 9 and being marked 9, whilst that on the right flank is complemented by the curve for ball No. 2, and is marked 2. The complementary subdivisions are connected by dotted lines.
Similar complementary pairs for the curve 5A are also connected by dotted lines and marked with the appropriate numerals. Corresponding markings are shown on the curves 4A and 6A, and symmetry shows that the same analysis can be made for all the
ball velocity/stroke curves in the diagram. Consequently, this arrangement of machine provides constant torque.
In a 9/1 machine (FIG. 2). n1l is odd, so that the duration of a constant velocity period is 1 - 2l(x)/n. It can be shown that for the left hand side of FIG. 2, x = 2, and for the right hand side x = 4.
The other two alternative periods of constant velocity in FIG. 2 obey the criteria (a) and (b) mentioned above in connection with FIG. 1, and the value of x is 3 for the shortest but one, and 1 for the longest.
FIGS. 3 and 4 show the comparison between two similar trapezia, representing ball velocity/stroke curves, for machines where n/l is odd and even, respectively. The two FIGS. illustrate alternative lengths of the constant velocity period.
In a motor, the useful output is a mechanical force linear thrust for a linear machine and rotary torque for a rotary or oscillatory segmental machine. In a pump, the useful output is an hydraulic pressure. The foregoing analysis has concerned
itself with the behavior of a ball piston, but it will be appreciated that displacement of a ball is exactly proportional to displacement of a volume of hydraulic fluid (ignoring, as is justified in all normal working applications of the invention,
compressibility of the fluid). Hence, the ordinates of any of the curves of FIGS. 1--4 can be expressed in terms of volume of fluid displaced on each stroke of a ball piston.
A factor making it desirable to modify the ball stroke/velocity characteristics represented by FIGS. 1 to 4 is that a practical machine will always require a finite period of time for reversal of port connections to the cylinders. In a rotary
machine, these are customarily controlled by a pintle valve in the cylinder block, and although the rate of displacement of a ball in its cylinder is a minimum at the time of reversal of the port connections, and although also there will inevitably be
leakage of fluid between relatively moving components which will tend to reduce back pressures, it is nevertheless of advantage to be able to give a ball piston zero displacement over the period of port reversal.
FIGS. 5 and 6 illustrate the conditions which obtain if a dwell period is provided at the crest of a cam lobe. The point I represents the normal point of intersection of the zero line by a flank of a velocity/stroke trapezium, but when the ball
is required to remain stationary in its cylinder for a brief period, its velocity falls to zero along the curve 22 before it reaches the point I and begins to increase from zero along the curve 20 from a point beyond it. The intervening dwell period is
represented by the distance I'. During this period the ball travels over the flattened crest 23a (FIG. 6) of the cam lobe 23. In these circumstances, each period of constant velocity must be extended at each end by an amount at least equal to one half
the dwell period I' on a complementary curve so as to ensure that it will be possible for the dwell period of any one ball to be "covered" by a conjugate ball in contact with a constant velocity segment of the cam track.
This is illustrated in FIG. 7, which is a diagram similar to FIG. 1 but relating to a six ball, single lobe cam machine. In this FIG., the velocity/stroke curves for balls Nos. 1--5 are shown in full lines for obtaining a constant torque
characteristic without a dwell period, as explained with reference to FIGS. 1--4. The curve for ball No. 6 is shown partly dotted to indicate the profile modification necessary to introduce a chosen short dwell at each dead center position, the duration
of this dwell being determined by the minimum requirements for smooth port connection reversal for each cylinder. The same form of notation if used in FIG. 7 to indicate complementary ball conditions determining the limits of the constant velocity
periods as is used in FIGS. 1 and 2, except that the extended limits of such periods to complement part of a dwell period of another ball are marked by a numeral with a supplementary dash (e.g. 6' on curve 2) and the limits of a dwell period are marked
by numerals with two supplementary dashes (e.g. 2" on curve 4). In all cases, the numeral itself identifies the complementary curve. For illustration purposes, dwell periods are indicated on even numbered curves only, and only their positions, and the
positions of the limits of extension of the constant velocity periods are shown on curves 2 and 4 for simplicity of drawing, it being understood that the profile modifications illustrated on curve 6 will be repeated on all the other curves when dwell
periods are incorporated.
Referring to specific instances of dwells and constant velocity period extensions as shown in FIG. 7, it will first be noted that the zero intersections of the basic curve of ball No. 6 determine the finish points of the constant velocity periods
of balls Nos. 2 and 4 (assuming that the displacements of the cylinders relative to the cam track are in the direction of the arrow R). Hence the limit point (6) of each constant velocity period of ball No. 2 is extended to (6') to complement the
second half of the dwell period of ball No. 6 which terminates at (2"). The first half of this dwell period which begins at (4") is complemented by the advance of the start of the constant velocity period of the negative-going trapezium of ball No. 4
from the point (6) to the point (6"). Similarly each dwell period of each other ball is complemented by extensions of the constant velocity periods of two other balls. Since each dwell period of a ball represents a power loss in the machine, the
periods of dwell are kept to the minimum consistent with smooth reversal of cylinder port connections.
Due to high mutual convexity of the ball and the cam track in the regions of the crests of the lobes, high Herzian stresses are apt to occur, accelerating surface fatigue failure at these points. These stresses may be mitigated by local
modifications of the grooving of the cam track adjacent the inner dead center position. These modifications are illustrated diagrammatically in FIGS. 8A--8D. The lines A-A, B-B, C-C and D-D on the curve of ball No. 9 in FIG. 1 mark successive points
along the cam track at which the groove is as shown in the corresponding FIGS. 8A, 8B, 8C, and 8D. At the section A-A of FIG. 1, the groove is shallow as shown at 15a in FIG. 7A. At the section B-B, the groove is deeper, as indicated at 15b in FIG. 8B,
whilst at the section C-C it is deeper still, as illustrated at 15c in FIG. 8C. Maximum depth is reached at D-D, as indicated at 15d in FIG. 8D, which represents the transverse cross section of the crest of the cam track 14 at the inner dead center
position. The radius of the groove is slightly greater than that of the ball--say, 1.025 x r-- where r is the ball radius.
Practical embodiments of the invention are illustrated, by way of example, in the remaining FIGS. of the accompanying drawings in which:
FIG. 9 is a simplified velocity/stroke diagram of a pump or motor having nine balls and eight lobes, the ordinates being calibrated in terms of oil displacement per unit of time (or angle) and the abscissae in time (or angle) of rotation;
FIG. 10 is a transverse cross section of a machine operating on the principle of FIG. 9;
FIG. 11 is a longitudinal cross section through the machine of FIG. 10;
FIG. 12 is a section similar to FIG. 10 of a nine ball, six lobe machine as analyzed in FIG. 1;
FIG. 13 is a diagrammatic section similar to FIG. 10 of a 16 ball, four lobe machine; and
FIG. 14 is a velocity/stroke diagram for the machine of FIG. 13.
Referring first to FIG. 9, the machine represented has nine ball pistons and eight cam lobes. Assuming that the machine is a pump driven at constant speed; that the zero position of the shaft coincides with the commencement of a period of
constant acceleration of ball No. 1 on a working stroke, and that the pump delivers against a constant high pressure, the curve of volumetric output per second (or per degree of rotation) provided by ball No. 1 is the trapezium marked 1 at the origin of
the coordinate axes. Output first rises linearly with time or angle, during the period (21/2.degree.) of constant piston acceleration. When this changes to constant velocity, the output remains constant, and when this in turn changes to constant
deceleration the output falls linearly.
Since the cam track has eight lobes, each lobe subtends 45.degree. at the axis, and each stroke of a ball, whether working or idle, subtends an angle of 221/2 . Hence the base of the trapezium is 221/2.degree., and successive trapezia for the
same ball are spaced by 221/2.degree..
While the first ball is executing its period of constant velocity on its working stroke, ball No. 2 begins its period of acceleration on its working stroke. This is shown in the trapezium numbered 2 commencing at a shaft angle of 5.degree.. It
spans the range of shaft angles 5.degree. to 271/2.degree. -- i.e. 221/2.degree. as before--and it will be noted that the curve of rising output for the period of uniform acceleration of ball No. 2 is exactly coextensive with, and of equal but
opposite slope to, that of uniform deceleration of conjugate ball No. 7. This balance of outputs occurs at each 5.degree. interval of shaft rotation, the period of deceleration of ball No. 1 coinciding with the period of acceleration of conjugate ball
No. 5. Hence, the total output is a constant. Since the output pressure is assumed to remain constant, the values of the ordinate also represent torque output in the case of a motor, and this torque thus remains constant.
FIGS. 10 and 11 show a practical construction of machine operating in accordance with FIG. 9 and having the locus of its ball centers derived from the velocity curves of FIG. 9. The cam profile shown in FIG. 10 is diagrammatic since it is not
possible to indicate, in a drawing on this scale, the details of shape as rigorously derived so as to reproduce the ball motions defined by FIG. 9. The rigorous cam profile is the envelope of a series of circles, having the same radius as the balls,
whose centers lie on a ball center locus derived from FIG. 9. The cam track may be machined by a substantially spherical cutter, of radius equal to the ball radius, whose rotational axis is constrained to follow the locus of the ball center.
The machine is basically a conventional ball piston machine having a rotary cylinder block 40 carrying ball pistons 1--9 in radial cylinders 41--49. The balls run on an eight-lobe cam track 50 formed on the internal circumference of a cam ring
51. The cylinder block 10 runs in antifriction bearings 52, 53 in a rigid housing 54, and a pintle 55 is supported at its outer end in a stepped bore 56, 57 in a port block 58 secured to the housing, and at its inner end in needle bearings 59 in the
cylinder block 40. The pintle 55 has the usual system of inlet and exhaust ports 60, 61 which register successively with each cylinder 41--49 in turn, and are connected to the external hydraulic circuit 62 through respective longitudinal ducts 63, 64.
The positions of r.sub.o and r.sub.1 are marked for one lobe in FIG. 10.
FIG. 12 illustrates the arrangement of a ball piston machine which fulfills the condition of operation represented in FIG. 1, and exhibits radial balance of forces on the pintle and cam track. The balls 1, 2 3...work in respective cylinders 41,
42, 43...angularly spaced at 40.degree. around a cylinder block 40. The balls run on a six lobe cam track 50 formed on a cam ring 51, each half-lobe being divided into three segments defined by the limits of angle for equations (1)--(3) above, and its
profile being derived from the locus of the ball center as described with reference to FIGS. 10 and 11. The positions of r.sub.o and r.sub.1 for one half-lobe are shown in FIG. 12. The construction of this machine is otherwise similar to that shown in
FIGS. 10 and 11.
In both the foregoing machines, the cam track 20 must be accurately machined. The balls 1--9 must also be accurately ground and a good sealing fit in their respective cylinders 41--49. There is no fixed relationship between ball diameter and
cam profile, constancy of the torque being maintained.
Since a machine of the general layout of FIGS. 10 and 11 or FIG. 12 can be designed to have a minimum value of trapped oil between the balls 1--9 and the servocontrol valve (not shown), the invention is particularly suitable for servomotor
systems. In a machine as shown in FIG. 12 constructed in accordance with the present invention, the following operating data were recorded:
Displacement --22 in.sup.3 /rev
Hydraulic Stiffness --590 lb. in/rad. 590,000
Natural Frequency --230 c/s.
Maximum Pressure --2000 lb./in.sup.2
Torque per lb./in.sup.2 --3.5. lb. in.
Overall Dimensions --81/4" Dia. 9" long.
Weight --45 lb.
FIG. 13 is a diagram of a four lobe cam in a 16-piston machine. The cam track is represented at 35, and the axes of the ball pistons at 36.
FIG. 14 shows a ball stroke/velocity diagram for this machine. In the expression 1 - 21x/n, x can have only the value 2, since l = 4 and n/2l, which represents the maximum permissible value of x, is equal to 2. The machine has four complete
groups of conjugate balls in each of which the relative position of each ball on a cam lobe exactly corresponds with that of a counterpart ball of each other group on its respective cam lobe. In FIG. 14, the curves for the group of balls Nos. 13--16
are shown with a dwell extending over 4.degree., at each inner dead center, and this is balanced by a constant velocity period of the same duration.
In the preceding description of the invention reference has been made to machines in which the pistons consist of balls. Variants are possible in which each ball is backed by a cylindrical piston element the form of which can vary between a
sealing ring to reduce the leakage of a ball piston and a cylindrical piston in which the role of the ball is that of a mere cam follower; in the case of the latter the diameter of the ball can be less than the diameter of the cylindrical piston element,
or the ball may be replaced by a cam follower wheel journaled in a bifurcated end of the cylindrical piston element.
Machines of this modified construction are subject to the same rules for obtaining constant torque and are within the scope of the invention.
* * * * *
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