Finding the Working Results Given by a D Slide Valve

Although not strictly within the line of duty of an engineer or engine driver, he is nevertheless sometimes called upon to find out how a valve of given proportions will dispose of the steam, or what proportions to give to a valve to accomplish certain results.

This is easy enough when either the travel of the valve or the amount of the lap and the width of the port are given, but if the width of the port alone is given, and all the other elements are to be found, it becomes a more difficult problem.

An engineer, however, is rarely called upon to solve the question from this stand-point, which properly belongs to the draughtsman or engine designer.

If the amount of valve travel is given, however, all the other elements may readily be found by the following construction:

Suppose that in Fig. 3311 a D valve is to be designed to cut off the steam when the piston has travelled from position b′ to r′, or at three-quarters of its stroke. Then to find the position the crank pin will be in when the cut off occurs, we draw a circle, b d, representing the path of the crank on the same scale that the length of the piston stroke is represented. The straight line from b to d will, therefore, represent the piston stroke without drawing the piston or cylinder at all (this being done in the figure to make the explanation clear). When the crank is on its dead centre, b, the piston, will be at b′, and the valve in the position shown (supposing it to have no lead). As soon as the crank and valves begin to move, the steam will enter steam port a, and to find where the crank will be when the piston is at three-quarters stroke, and is, therefore, in position r′, we mark a point at r three-quarters of the distance from b to d. Then, taking no account of the length of the connecting rod, we draw a vertical line y from r to the circle, and this line gives at h the position the crank will be in when the piston is at r. We have so far, therefore, that while the piston travels from b′ to r′, the crank will travel from b to h. Now, it will be found that if we set a pair of compasses from b to f, which is half-way from b to h, and then rest the compasses at d, and mark an arc v, then a line from v to the centre of the crank will give us the proper position of the eccentric. As the centre of the crank pin and also the centre of the eccentric both travel in a circle, we may, therefore, take a circle having a diameter equal to twice the throw of the eccentric, (or, what is the same thing, equal to the full travel of the valve), and let it represent the paths of both the eccentric centre and the crank pin centre, the latter being drawn to a scale that is found by dividing the length of the piston stroke by the travel of the valve; thus, if the travel is 3 inches and the stroke 30 inches, the diameter of a 3 inch circle will represent the valve travel full size, and the piston stroke one-tenth full size, because 30 ÷ 3 = 10. It has been shown on page 376 that the length of the connecting rod affects the motion of the piston by distorting it, and it is necessary to take this into account in constructing the actual diagram, which may be done as follows:

The valve travel and point of cut off being given, to find the required amount of lap, there being no lead, draw a circle equal in diameter to the travel of the valve, and draw the line of centres b d, Fig. 3312; mark on the line of centres a point r, representing the position the piston is to be in at the time the cut off is to take place.

Set a pair of compasses to represent the length of the connecting rod on the same scale as the circle b d represents the path of the crank; thus, if the connecting rod is three times the length of the stroke, the compasses would be set to three times the diameter of the circle b d.

A straight line from b to d and passing through the centre c of the crank will represent the line of centres of the engine, which must be prolonged to the right sufficiently to rest the compasses on it and draw the arc y, which will give at h the position of the crank when the piston is at r, and the cut off is to occur.

We have thus found that the amount of circular path the crank will move through from the dead centre to the point of cut off is from b to h, and as the eccentric is fast upon the same shaft, it will, in the same time, of course, move through the same part of a circle.

One half of its motion will be to open and one half to close the port, so that we may by means of the arcs at f get the point f, which is midway between b and h, and with the compasses set from b to f, mark from d the two arcs v and v′ whose distance apart will obviously be the same as from b to h.

Then from v to v′ draw the line p, and from this line to the centre c of the crank shaft is the amount of steam lap necessary for the valve, while from this line (p) to d is the width of the steam port.

The proof of the diagram is as follows:

When the crank is on the dead centre, the centre of the eccentric is at v, its throw line being represented by the line from v to c, and the valve is about to open the port as shown in the figure.

While the eccentric is moving from v to d, the valve will move in the direction of the arrow and will fully open the port, while the crank pin will move from b to f.

Then, while the crank moves from f to h, the eccentric will have moved the valve to the position it occupies in the figure, having closed the port and effected the cut off.

We have here found the amount of lap and the position of the eccentric necessary for a given point of cut off when the latter is given in terms of the piston stroke. If, however, the point of cut off had been given in terms of the crank pin position, we might find the required amount of lap at once, by simply drawing a line from the centre b, the point to h where the crank pin is to be when the cut off occurs.

From this line we could then draw the dotted circle g, and just meeting the line p, which would give the eccentric position.

To find the piston position, the arc y would require to be drawn by the same means as before.

If the valve is to have lead, the diagram may be constructed as in Fig. 3313, in which the circle has a diameter equal to the travel of the valve and the cut off is to occur when the piston is at r and the crank at h.

When the valve is at the end of its travel and has fully opened the port, the eccentric will be at d, hence from d we mark an arc g distant from d to an amount equal to the width of the steam port, drop the vertical m from g, and at its lower end v′ is the position of the eccentric centre at the point of cut off. Then draw a line p, distant from m equal to the lead, which will give at v the position of the eccentric when the crank is on the dead centre, and the valve is open to the amount of the lead. The lap is obviously the distance from the centre c of the crank shaft to the arc g.

We have here found all the points necessary except the point at which the valve will open the port for the lead, and this we may find by setting a pair of compasses to the radius b h (or to radius v v′, as both these radii are equal), and from v as a centre, mark at a an arc, which will give the crank pin position at the time the port first opens for the lead, or in other words it will give the position. The proof of the construction is, that if we set the compasses to the distance between the crank pin position on the dead centre and the point of cut off (or from b to h), we may apply the compasses to the points v, v′, which represent the eccentric position when the port is opened to the amount of the lead, and when the cut off occurs.

If the point of cut off only is to be found, we mark from c, Fig. 3314, an arc g representing the amount of valve lap and arc s representing the lead. A vertical p gives the eccentric position v when the crank is on the dead centre at b, and a vertical m from g gives at v′ the eccentric position at the point of cut off. Then with the compasses set to the points v v′, we may mark from b an arc, locating at h the position of the crank at the point of cut off, and from this with compasses set to represent the length of the connecting rod on the same scale as the circle represents the path of the crank, we may, from a point on the line of centres, mark an arc y giving at r the piston position at the point of cut off.

When, therefore, the lap is given, we mark it from the center c of the crank shaft, and find the other elements from it, whereas, when the lap is to be found, we mark the width of the port from the end d of the valve travel, and find the other elements from that.

A proof of all the constructions is given in Fig. 3314, in which the letters of reference correspond to those in the previous figures, and the positions of the parts are marked in degrees of angle.

To find the piston position at the point of cut off, measured in inches, of the piston stroke it must be borne in mind that as the circle b d represents the full travel of the valve, the diagram gives all the positions of the eccentric and valve full size, but that as it represents the crank path on a reduced scale, therefore we must multiply the measurement on the diagram by that scale.

Suppose, for example, that the piston stroke is 10 inches, and the valve travel 2⁄2 inches, and the circle being 2⁄2 inches in diameter, is, when considered with relation to the eccentric motion, full size, but when considered with relation to the piston or crank motion, it is only ⁄4 the size, hence to find the piston position at the time of cut off, we must multiply the distance from b to r by 4.