Steam Engine Valves and Reversing Gears

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 612 Theory of Machines 17 Features Steam Engine 1. Introduction. 2. D-slide Valve. 3. Piston Slide Valve. Valves and 4. Relative Positions of Crank and Eccentric Centre Lines. 5. Crank Positions for Reversing Admission, Cut off, Release and Compression. 6. Approximate Analytical Method for Crank Positions. Gears 7. Valve Diagram. 8. Zeuner Valve Diagram. 17.1. Introduction 9. Reuleaux Valve Diagram. 10. Bilgram Valve Diagram. The valves are 11. Effect of the Early Point of used to control the steam Cut-off. which drives the piston 12. Meyer’s Expansion Valve. of a reciprocating steam 13. Virtual or Equivalent engine. The valves have Eccentric for the Meyer’s to perform the four dis- Expansion Valve. tinct operations on the 14. Minimum Width and Best Setting of the Expansion steam used on one side Plate. (i.e. cover end) of the pis- 15. Reversing Gears. ton, as shown by the in- 16. Principle of Link Motions. dicator diagram (also Fig. 17.1. Indicator diagram of a 17. Stephenson Link Motion. known as pressure-vol- reciprocating steam engine. 18. Virtual or Equivalent ume diagram) in Fig. Eccentric for Stephenson 17.1. These operations Link Motion. are as follows: 19. Radial Valve Gears. 1. Admission or opening of inlet valve for admission 20. Hackworth Valve Gear. of steam to the cylinder. The point A represents the point for 21. Walschaert Valve Gear. admission of steam just before the end of return stroke and it is continued up to the point B. 612 Chapter 17 : Steam Engine Valves and Reversing Gears 613 2. Cut-off or closing of inlet valve in order to stop the admission of steam prior to expansion. The point B represents the cut-off point of steam. The curve BC represents the expansion of steam in the engine cylinder. 3. Release or opening of exhaust valve to allow the expanded steam to escape from the cylinder to the atmosphere or to the condenser or to a larger cylinder. The point C represents the opening of the valve for releasing the steam. The exhaust continues during the return stroke upto point D. 4. Compression or closing of exhaust valve for stopping the release of steam from the cylinder prior to compression. The point D represents the closing of exhaust valve. The steam which remains in the cylinder is compressed from D to A and acts as a cushion for the reciprocating parts. The same operations, as discussed above, are performed on steam in the same order on the other side (or crank end) of the piston for each cycle or each revolution of the crank shaft. In other words, for a double acting piston, there are eight valve operations per cycle. All these eight opera- tions may be performed (i) by a single slide valve such as D-slide valve, (ii) by two piston valves, one for either end of cylinder, and (iii) by two pairs of valves (one pair for each end of the cylinder), such as corliss valves or drop valves. One valve at each end of the cylinder performs the operations of admission and cut-off while the other valve performs the operations of release and compression. The engine performance depends upon the setting of the valves. In order to set a valve at a correct position, a valve diagram is necessary. Regulator valve Driver’s Firebox cab Fire Boiler Smokebox tubes Cylinder valves Cylinder Piston Sectional view of a steam engine. 17.2. D-slide Valve The simplest type of the slide valve, called the D-slide valve, is most commonly used to control the admission, cut-off, release and compression of steam in the cylinder of reciprocating steam engine. The usual arrangement of the D-slide valve, valve chest and cylinder for a double acting steam engine is shown in Fig. 17.2 (a). 614 Theory of Machines The steam from the boiler is admitted to the steam chest through a steam pipe. The recess R in the valve is always open to the exhaust port which, in turn, is open either to atmosphere or to the condenser. The ports P and P serve to admit steam into the cylinder or to pass out the steam from the 1 2 cylinder. The valve is driven from an eccentric keyed to the crankshaft. It reciprocates across the ports and opens them alternately to admit high pressure steam from the steam chest and to exhaust the used steam, through recess R to exhaust port. The D-slide valve in its mid position relative to the ports is shown in Fig. 17.2 (a). In this position, the outer edge of the valve overlaps the steam port by an amount s. This distance s (i.e. lapping on the outside of steam port) is called the steam lap or outside lap. The inner edge of the valve, also, overlaps the steam port by an amount e. This distance e (i.e. overlapping on the inside) is called the exhaust lap or inside lap. Fig. 17.2. D-slide valve. The displacement of the valve may be assumed to take place with simple harmonic motion, since the obliquity of the eccentric rod is very small. Thus the eccentric centre line OE will be at right angles to the line of stroke when the valve is in its mid-position. This is shown in Fig. 17.2 (b) for clockwise rotation of the crank. Note: Since the steam is admitted from outside the steam chest, therefore the D-slide valve is also known as Outside admission valve. 17.3. Piston Slide Valve The piston slide valve, as shown in Fig. 17.3 (a), consists of two rigidly connected pistons. These pistons reciprocate in cylindrical liners and control the admission to, and exhaust from the two ends of the cylinder. In this case, high pressure superheated steam is usually admitted to the space between the two pistons through O and exhaust takes place from the ends of the valve chest through E. This type of valve is mostly used for locomotives and high pressure cylinders of marine engines. The piston slide valve has the following advantages over the D-slide valve : Since the length of the eccentric rod varies from 15 to 20 times the eccentricity (also known as throw of the eccentric), therefore the effect of its obliquity is very small. The eccentricity or the throw of eccentric is defined as the distance between the centre of crank shaft O and the centre of eccentric E. Thus the distance OE is the eccentricity. Chapter 17 : Steam Engine Valves and Reversing Gears 615 1. Since there is no unbalanced steam thrust between the valve and its seat as the pressure on the two sides is same, therefore the power absorbed in operating the piston valve is less than the D-slide valve. 2. The wear of the piston valve is less than the wear of the D-slide valve. 3. Since the valve spindle packing is subjected to the relatively low pressure and tempera- ture of the exhaust steam, therefore the danger of leakage is less. Fig. 17.3. Piston slide valve. The position of the steam lap (s) and exhaust lap (e) for the piston valve in its mid position is shown in Fig. 17.3 (a). The eccentric position for the clockwise rotation of the crank is shown in Fig. 17.3(b). Note: Since the steam enters from the inside of the two pistons, therefore the piston valve is also known as inside admission valve. 17.4. Relative Positions of Crank and Eccentric Centre Lines Fig. 17.4. Relative positions of crank and eccentric centre lines for D-slide valve. We have discussed the D-slide valve (also known as outside admission valve) and piston slide valve (also known as inside admission valve) in Art. 17.2 and Art. 17.3 respectively. Now we shall discuss the relative positions of the crank and the eccentric centre lines for these slide valves. 616 Theory of Machines 1. D-slide or outside admission valve. The D-slide valve in its mid position is shown in Fig. 17.2 (a). At the beginning of the stroke of the piston from left to right as shown in Fig. 17.4 (a), the crank OC is at its inner dead centre position as shown in Fig. 17.4 (b). A little consideration will show that the steam will only be admitted to the cylinder if the D-slide valve moves from its mid position towards the right atleast by a distance equal to the steam lap (s). It may be noted that if only this minimum required distance is moved by the valve, then the steam admitted to the cylinder will be subjected to severe throttling or wire drawing. Therefore, in actual practice, the displace- ment of the D-slide valve is greater than the steam lap (s) by a distance l which is known as the lead of the valve. In order to displace the valve from its mid position by a distance equal to steam lap plus lead (i.e. s + l ), the eccentric centre line must be in advance of the 90° position by an angle α , such that sl + sin α= OE The angle α is known as the angle of advance of the eccentric. The relative positions of the crank OC and the eccentric centre line OE remain unchanged during rotation of the crank OC, as shown in Fig. 17.4 (b). Note : The eccentricity (or throw of the eccentric) OE is equal to half of the valve travel. The valve travel is the distance moved by the valve from one end to the other end. 2. Piston slide valve or inside admission valve. The piston slide valve in its mid position is shown in Fig. 17.3 (a). At the beginning of the outward stroke of the piston, from left to right as shown in Fig. 17.5 (a), the crank OC is at its inner dead centre as shown in Fig. 17.5 (b). In the similar way as discussed for D-slide valve, the valve should be displaced from its mean position by a distance equal to the steam lap plus lead (i.e. s + l) of the valve. The relative positions of the crank OC and the eccentric centre line OE are as shown in Fig. 17.5 (b). In this case, the angle of advance is (180° + α ), and sl + sin α= OE Fig. 17.5. Relative positions of crank and eccentric centre lines for piston slide valve. 17.5. Crank Positions for Admission, Cut-off, Release and Compression In the previous article, we have discussed the relative positions of the crank and eccentric centre lines for both the D-slide valve and piston slide valve. Here we will discuss only the D-slide valve to mark the positions of crank for admission, cut-off, release and compression. The same principle may be applied to obtain the positions of crank for piston slide valve. Chapter 17 : Steam Engine Valves and Reversing Gears 617 1. Crank position for admission. At admission for the cover end of the cylinder, the outer edge of the D-slide valve coincides with the outer edge of the port P . The valve moves from its mid 1 position towards right, as shown by arrow A in Fig. 17.6 (a), by an amount equal to steam lap s. At the same time, the piston moves towards left as shown by thick lines in Fig. 17.6 (a). The corresponding position of the crank is OC and the eccentric centre line is shown by OE in Fig. 17.6 (b), such that 1 1 ∠ C OE = 90° + α 1 1 Fig. 17.6. Crank positions for admission and cut-off. 2. Crank position for cut-off. A little consideration will show that the cut-off will occur on the cover end of the cylinder when the outer edge of the D-slide valve coincides with the outer edge of the port P while the valve moves towards left as shown by arrow B. The piston now occupies the 1 position as shown by dotted lines in Fig. 17.6 (a). The corresponding position of the crank is OC and 2 the eccentric centre line is shown by OE in Fig. 17.6 (c), such that 2 ∠ C OE = ∠ C OE = 90° + α 2 2 1 1 3. Crank position for release. At release for the cover end of the cylinder, the inner edge of the D-slide valve coincides with the inner edge of the port P . The valve moves from its mid position 1 towards left, as shown by arrow C in Fig. 17.7 (a), by a distance equal to the exhaust lap e. Thus the Fig. 17.7. Crank positions for release and compression. 618 Theory of Machines valve opens the port to exhaust. At the same time, the piston moves towards right as shown by thick lines in Fig. 17.7 (a). The corresponding positions of crank and eccentric centre line are shown by OC and OE in Fig. 17.7 (b), such that 3 3 ∠ C OE = 90° + α 3 3 4. Crank position for compression. At compression, for the cover end of the cylinder, the inner edge of the valve coincides with the inner edge of the port P . The valve moves 1 from its mid position towards right, as shown by arrow D in Fig. 17.7 (a), by a distance equal to the exhaust lap e. The valve now closes the port to exhaust. The piston moves towards left as (a) shown by dotted lines in Fig. 17.7 (a). The corresponding posi- tions of crank and eccentric centre line are shown by OC and 4 OE in Fig. 17.7 (c), such that 4 ∠ C OE = ∠ C OE = 90° + α 4 4 3 3 The positions of crank and eccentric centre line for all the four operations may be combined into a single diagram, as (b) shown in Fig. 17.8 (a). Since the ideal indicator diagram, as shown in Fig. 17.8 (b), is drawn by taking projections from the Fig. 17.8. Combined diagram of crank positions. crank positions, therefore the effect of the obliquity of the con- necting rod is neglected. 17.6. Approximate Analytical Method for Crank Positions at Admission, Cut-off, Release and Compression The crank positions at which admission, cut-off, release and compression occur may be obtained directly by analytical method as discussed below : Chapter 17 : Steam Engine Valves and Reversing Gears 619 Let x = Displacement of the valve from its mid-position, θ = Crank angle, 1 =× Travel of valve, r = Eccentricity or throw of eccentric 2 α = Angle of advance of eccentric. Since the displacement of the valve may be assumed to take place with simple harmonic motion, therefore x = r sin (θ + α) . . . (i) But at admission and cut-off, x = Steam lap, s ∴ s = r sin (θ + α) ...From equation (i) ss   –1 –1 or θ+α = sin , and θ= sin – α . . . (ii)   rr The two values of θ which satisfy the equation (ii) give the crank positions for admission and cut-off. Similarly, at release and compression, x = exhaust lap (e) and is negative as measured from the origin O. ∴ – e = r sin (θ + α) . . . From equation (i) ––ee    –1 –1 or . . . (iii) θ+α = sin , and θ = sin – α    rr  The two values of θ which satisfy the equation (iii) give the crank positions for release and compression. Example 17.1. The D-slide valve taking steam on its outside edges has a total travel of 150 mm. The steam and exhaust laps for the cover end of the cylinder are 45 mm and 20 mm respectively. If the lead for the cover end is 6 mm, calculate the angle of advance and determine the main crank angles at admission, cut-off, release and compression respectively for the cover end. Assume the motion of the valve as simple harmonic. Solution. Given : 2 r = 2 OE = 150 mm or r = OE = 75 mm ; s = 45 mm ; e = 20 mm ; l = 6 mm Angle of advance Let α = Angle of advance. We know that sl++ 45 6 sin α= = = 0.68 OE 75 or α= 42.8° Ans. Crank angles at admission, cut-off, release and compression Let θ , θ , θ and θ = Crank angles at admission, 1 2 3 4 cut-off, release and compression respectively. Prototype of an industrial steam engine. We know that for admission and cut-off, s 45    –1 –1 –1 θ+α = sin = sin = sin (0.6) = 36.87° or 143.13°    r  75 620 Theory of Machines ∴θ = 36.87° – α = 36.87° – 42.8° = – 5.93° Ans. 1 and θ = 143.13° – α = 143.13° – 42.8° = 100.33° Ans. 2 We know that for release and compression, –– e 20 –1 –1 –1 θ+α = sin = sin = sin (– 0.2667)    r  75 = 195.47° or 344.53° ∴θ = 195.47° – α = 195.47° – 42.8° = 152.67° Ans. 3 and θ = 344.53° – α = 344.53° – 42.8° = 301.73° Ans. 4 17.7. Valve Diagram The crank positions for admission, cut-off, release and compression may be easily deter- mined by graphical constructions known as valve diagrams. There are various methods of drawing the valve diagrams but the following three are important from the subject point of view : 1. Zeuner valve diagram. 2. Reuleaux valve diagram, and 3. Bilgram valve diagram. We shall discuss these valve diagrams, in detail as follows. 17.8. Zeuner Valve Diagram The Zeuner’s valve diagram, as shown in Fig. 17.9, is drawn as discussed in the following steps : 1. First of all, draw AB equal to the travel of the valve to some suitable scale. This diameter AB also represents the stroke of the piston to a different scale. Fig. 17.9. Zeuner valve diagram. 2. Draw a circle on the diameter AB such that OA = OB = eccentricity or throw of the eccen- tric. The circle ACBD is known as the valve travel circle, where diameter CD is perpendicular to AB. 3. Draw EOF making an angle α, the angle of advance of the eccentric, with CD. It may be noted that the angle α is measured from CD in the direction opposite to the rotation of the crank and eccentric as marked by an arrow in Fig. 17.9. 4. In case the angle of advance ( α ) is not given, then mark OJ = steam lap (s), and JK = lead (l) of the valve. Draw KE perpendicular to AB which intersects the valve travel circle at E. The angle EOC is now the angle of advance. Chapter 17 : Steam Engine Valves and Reversing Gears 621 5. Draw circles on OE and OF as diameters. These circles are called valve circles. 6. With O as centre, draw an arc of radius OG equal to steam lap (s) cutting the valve circle at M and N. Join OM and ON and produce them to cut the valve travel circle at C and C respectively. 1 2 Now OC and OC represent the positions of crank at admission and cut-off respectively. 1 2 Note : The circle with centre A and radius equal to lead (l) will touch the line C C . 1 2 7. Again with O as centre, draw an arc of radius OH equal to exhaust lap (e) cutting the valve circle at P and Q. Join OP and OQ and produce them to cut the valve travel circle at C and C 3 4 respectively. Now OC and OC represent the position of crank at release and compression respec- 3 4 tively. 8. For any position of the crank such as OC', as shown in Fig. 17.9, the distance OX 1 represents the displacement of the valve from its mid position and the distance X X (the point X 1 2 1 is on the valve circle and the point X is on the arc JGN) gives the opening of the port to steam. The 2 distance X X ( point X is on the arc QHP and point X is on the valve circle) obtained by produc- 3 4 3 4 ing the crank OC', gives the opening of the port to exhaust for the crank position OC'. The proof of the diagram is as follows : Join EX . Now angle EX O = 90°. 1 1 ∴∠ OEX + ∠ X OE = 90° = ∠ AOC = θ + ∠ X OE + α 1 1 1 or ∠ OEX = θ + α 1 Now from triangle OEX , 1 OX = OE sin (θ + α) 1 or x = r sin (θ + α) where x = Displacement of the valve from its mid position, and r = Eccentricity or throw of eccentric. Now OX = OX + X X 1 2 1 2 ∴ Opening of port to steam when the valve has moved a distance x from its mid-position, X X = OX – OX = r sin (θ + α) – s ...(∵ OX = Steam lap, s) 1 2 1 2 2 9. Mark HR = width of the steam port. Now with O as centre, draw an arc through R intersect- ing the valve circle at X and Y . The lines OS and OW through X and Y respectively determines the angle WOS through which the crank turns while the steam port is full open to exhaust. The maximum opening of port to exhaust is HF. A similar construction on the other valve circle will determine the angle through which the crank turns while the steam port is not full open to steam. Fig. 17.9 shows that the steam port is not full open to steam and the maximum opening of the port to steam is GE. Note : The valve diagram, as shown in Fig. 17.9, is for the steam on the cover end side of the piston or for one- half of the D-slide valve. In order to draw the valve diagram for the crank end side of the piston (or the other half of the valve), the same valve circles are used but the two circles and the lines associated with them change places. For the sake of clearness, the valve diagrams for the two ends of the piston is drawn separately. 17.9. Reuleaux’s Valve Diagram The Reuleaux’s valve diagram is very simple to draw as compared to the Zeuner’s valve diagram. Therefore it is widely used for most problems on slide valves. The Reuleaux’s valve dia- gram, as shown in Fig. 17.10, is drawn as discussed in the following steps : 1. First of all, draw AB equal to the travel of the valve to some suitable scale. This diameter AB also represents the stroke of the piston to a different scale. 2. Draw a circle on the diameter AB such that OA = OB = eccentricity or throw of the eccen- 622 Theory of Machines tric. This circle ACBD is known as valve travel circle where diameter CD is perpendicular to AB. 3. Draw EOF making an angle α, the angle of advance of eccentric, with CD. It may be noted that the angle α is measured from CD in the direction opposite to the rotation of crank and eccentric as marked by an arrow in Fig. 17.10. 4. Draw GOH perpendicular to EOF. Now draw chords C C and C C parallel to GH and at distances 1 2 3 4 equal to steam lap (s) and exhaust lap (e) from GH respectively. 5. Now OC , OC , OC and OC represent the 1 2 3 4 positions of crank at admission, cutt-off, release and com- pression respectively. The proof of the diagram is as follows : Fig. 17.10. Reuleaux’s valve diagram. Let OC' be any crank position making an angle θ with the inner dead centre, as shown in Fig.17.10. Draw C' J perpendicular to GH. From right angled triangle OC' J, C' J = C' O sin C' OJ = r sin (θ + α) ...(i) where r = C' O = Eccentricity or throw of eccentric. But the displacement of the valve from its mid-position corresponding to crank angle θ is given by x = r sin (θ + α) ...(ii) From equations (i) and (ii), C' J = x It, therefore, follows that the length of the perpendicular from C' to the diameter GH is equal to the displacement of the valve from mid-position when the crank is in the position OC'. We see from Fig. 17.10, that when the crank is in position OC or OC , the length of the 1 2 perpendicular from C or C on GH is equal to the steam lap (s). Therefore OC and OC must 1 2 1 2 represent the crank positions at admission and cut-off respectively. Similarly, when the crank is in position OC and OC , the length of perpendicular from C or C on GH is equal to the exhaust lap 3 4 3 4 (e). Therefore OC and OC must represent the crank positions at release and compression respec- 3 4 tively. Opening of the port to steam We see from Fig. 17.10, that when the crank is in position OC', the displacement of the valve C'J, from its mid-position, exceeds the steam lap (s) by a distance C' K. The distance C' K represents the amount of port opening to steam. Therefore when the crank is in position OA (i.e. at the inner dead centre), the perpendicular distance from A to GH, i.e. AP represents the displacement of the valve from its mid-position. The distance AP exceeds the steam lap (s) by a distance AQ which is equal to the lead of valve and represents the amount of port opening to steam. The maximum possible opening of the port to steam is equal to NE i.e. (r–s) where r is the throw of the eccentric or half travel of the valve and s is the steam lap. Similarly, the maximum possible opening of the port to exhaust is equal to MF i.e. (r–e) where e is the exhaust lap. The difference (r–e) may exceed the width of the actual port through which the steam is admitted to and exhausted from the cylinder. In that case, the port will remain fully open for a certain period of crank Chapter 17 : Steam Engine Valves and Reversing Gears 623 rotation. In order to find the duration of this period, draw a chord SW parallel to C C at a distance 3 4 equal to the width of the steam port (w). The port will remain fully open to exhaust when the crank rotates from the positon OW to OS. 17.10. Bilgram Valve Diagram The Bilgram valve diagram, as shown in Fig. 17.11, is drawn as discussed in the following steps : 1. First of all, draw AB equal to the travel of the valve to some suitable scale. This diameter AB also represents the stroke of the piston to a different scale. A 1930’s Steam locomotive. 2. Draw a circle on the diameter AB such that OA = OB = eccentricity or throw of the eccen- tric. This circle is known as valve travel circle. 3. Draw diameter GOH making an angle α, the angle of advance, with AB. The angle α is measured from AB in the direction opposite to the rotation of crank and eccentric as marked by an arrow in Fig. 17.11. 4. Draw two circles with centres G and H and radii equal to steam lap (s) and exhaust lap (e) respectively as shown in Fig. 17.11. 5. The lines OC and OC are tangential to the steam lap circles and they represent the crank 1 2 positions for admission and cut-off respectively. Similarly OC and OC are tangential to the exhaust 3 4 lap circles and represent the crank positions for release and compression. The proof of the diagram is as follows : Let OC' be any crank position making an angle θ with the inner dead centre, as shown in Fig. 17.11. Draw perpendiculars GE on OC' and HF on OC' produced. Since the triangles OGE and OHF are similar, therefore GE = HF = OG sin (θ + α) = r sin (θ + α) ...(i) where r = OG = Eccentricity or throw of eccentric. But the displacement of the valve from its mid-position corresponding to crank angle θ, is given by x = r sin (θ + α) ...(ii) 624 Theory of Machines From equations (i) and (ii), GE = x It, therefore, follows that the length of the perpendicular from G (or H) on OC' (or OC' pro- duced) is equal to the displacement of the valve from mid-position when the crank is in the position OC'. Fig. 17.11. Bilgram valve diagram. We see from Fig. 17.11, that the length of the perpendiculars from G and H on OC and OC 1 2 respectively are equal to steam lap (s). Therefore OC and OC must represent the crank positions at 1 2 admission and cut-off respectively, Similarly, the length of perpendiculars from H and G on OC and 3 OC respectively are equal to exhaust lap (e). Therefore OC and OC must represent the crank 4 3 4 positions at release and compression respectively. Opening of the port to steam We see from Fig. 17.11, that when the crank is in position OC', the displacement of the valve GE, from its mid-position, exceeds the steam lap (s) by a distance DE. The distance DE represents the amount of port opening to steam. Therefore, when the crank is in position OA (i.e. at the inner dead centre), the perpendicular distance from G to OA (i.e. GL) represents the displacement of the valve from its mid-position. The distance GL exceeds the steam lap (s) by a distance ML which is equal to lead of the valve and represents the amount of port opening to steam. The maximum opening of the port to steam is equal to OP or (r – s) where r is the throw of eccentric or half travel of the valve and s is the steam lap. Similarly the maximum opening of the port to exhaust is OQ or (r – e) where e is the exhaust lap. Notes : 1. The point G lies on the intersection of the bisectors of angles C OT and RST. 1 2. The Bilgram valve diagram is usually used to determine throw of the eccentric, valve travel, angle of advance of the eccentric, steam and exhaust laps when the crank positions at cut-off and release, lead of valve and width of steam port are known. Example 17.2. The following particulars refer to a D-slide valve : Total valve travel = 150 mm ; Steam lap = 45 mm ; Exhaust lap = 20 mm ; Lead = 6 mm. Draw the Zeuner’s valve diagram for the cover end and determine the angle of advance of the eccentric, main crank angles at admission, cut-off, release and compression, opening of port to steam for 30° of crank rotation and maximum opening of port to steam. If the width of the port is 40 mm, determine the angle through which the crank turns so that the exhaust valve is full open. Solution. Given : AB = 150 mm ; s = 45 mm ; e = 20 mm ; l = 6 mm Chapter 17 : Steam Engine Valves and Reversing Gears 625 Angle of advance of eccentric and main crank angles at admission, cut-off, release and compression The Zeuner’s valve diagram for the cover end is drawn as discussed in the following steps : 1. First of all draw AB = 150 mm, to some suitable scale, to represent the total valve travel. Draw a circle on this diameter AB such that OA = OB = throw of the eccentric. This circle is known as valve travel circle. Draw COD perpendicular to AB. 2. Mark OJ = steam lap = 45 mm, and JK = lead = 6 mm. Through K, draw a perpendicular on AB which intersects the valve travel circle at E. Join OE. Now angle COE represents the angle of advance of the eccentric (α) in a direction opposite to the direction of rotation of crank and eccentric (shown clockwise in Fig. 17.12). By measurement, we find that α = ∠ COE = 42.5° Ans. Fig. 17.12 3. Draw a circle on OE as diameter. This circle is known as valve circle. Now with O as centre, draw an arc of radius equal to steam lap (i.e. 45 mm) which intersects the valve circle at M and N. Join OM and ON and produce them to intersect the valve travel circle at C and C respectively. 1 2 The lines OC and OC represent the crank positions at admission and cut-off respectively. By mea- 1 2 surement, we find that Crank angle at admission from inner dead centre A = ∠ AOC = – 6° Ans. 1 and crank angle at cut-off from inner dead centre A = ∠ AOC = 101° Ans. 2 4. Now draw the diameter EOF. On OF draw a valve circle as shown in Fig. 17.12. With O as centre, draw an arc of radius equal to exhaust lap (i.e. 20 mm) which intersects the valve circle at P and Q. Join OP and OQ and produce them to intersect the valve travel circle at C and C respectively. 3 4 Now OC and OC represent the crank positions at release and compression respectively. By mea- 3 4 surement, we find that Crank angle at release from inner dead centre A = ∠ AOC = 153° Ans. 3 and crank angle at compression from inner dead centre A = ∠ AOC = 302° Ans. 4 Opening of port to steam for 30° of crank rotation and maximum opening of port to steam Let OC' be the crank at θ = 30° from the inner dead centre, as shown in Fig. 17.12. The crank 626 Theory of Machines OC' intersects the valve circle at X and arc MGN at X . Now X X represents the opening of port to 1 2 1 2 steam for 30° of crank rotation. By measurement, we find that X X = 27 mm Ans. 1 2 and maximum opening of port to steam, GE = 30 mm Ans. Angle through which the crank turns so that the exhaust valve is full open Mark HR = width of port = 40 mm as shown in Fig. 17.12. Now with O as centre, draw an arc passing through R which intersects the valve circle at X and Y . The angle XOY represents the crank angle at which the exhaust valve is full open. By measurement, we find that ∠ XOY = 72° Ans. Example 17.3. The following data refer to a D-slide valve : Total valve travel = 120 mm ; Angle of advance = 35° ; Steam lap = 25 mm ; Exhuast lap = 8 mm. If the length of the connecting rod is four times the crank radius, determine the positions of the piston as percentage of the stroke for admission, cut-off, release and compression for both ends of the piston. Solution. Given : AB = 120 mm ; α = 35°, s = 25 mm ; e = 8 mm Positions of the piston as a percentage of the stroke for admission, cut-off, release and compres- sion for cover end of the piston. First of all, determine the crank positions for the cover end either by Zeuner’s or Reuleaux valve diagram. The Reuleaux valve diagram for the cover end, as shown in Fig. 17.13, is drawn as follows : 1. Draw AB = 120 mm to some suitable scale to represent the total valve travel. This diameter AB also represents the stroke of the piston. Draw a circle on diameter AB such that OA = OB = Throw of the eccentric or radius of crank. Fig. 17.13 2. Draw a line GOH making an angle of 35°, the angle of advance, in a direction opposite to the rotation of crank which is clockwise as shown in Fig. 17.13. 3. Draw EOF perpendicular to GOH and mark ON = steam lap = 25 mm and OM = exhaust lap = 8 mm. Through N and M draw lines parallel to GOH which intersect the valve travel circle at C , 1 C , C and C . Now OC , OC , OC and OC represent the crank positions at admission, cut-off 2 3 4 1 2 3 4 release and compression respectively. At inner dead centre A and outer dead centre B, the connecting rod is in line with the crank. Since the connecting rod is 4 times the crank radius OA, therefore mark AA = BB = 4 × OA = 4 × 60 1 1 = 240 mm. Now A B = AB = 120 mm and represents the stroke of the piston. With C , C , C , C as 1 1 1 2 3 4 Chapter 17 : Steam Engine Valves and Reversing Gears 627 centres and radius equal to length of connecting rod i.e. 240 mm, mark the corresponding positions of piston as shown by points P , P , P and P in Fig. 17.13. By measurement, the piston position as 1 2 3 4 percentage of stroke is given by : BP 119 11 At admission of return stroke Ans. =× 100 =× 100= 99.17% 120 BA 11 AP 96 12 At cut-off =× 100 of forward stroke Ans. =× 100= 80% AB 120 11 AP 116 13 At release =× 100 of forward stroke Ans. =× 100= 96.67% AB 120 11 BP 100 14 At compression=× 100 of return stroke Ans. =× 100= 83.33% BA 11 120 Note : The points p , p , p and p on AB are the corresponding points of P , P , P and P respectively. These 1 2 3 4 1 2 3 4 points may be obtained by drawing the arcs through C , C , C and C with their centres at P , P , P and P and 1 2 3 4 1 2 3 4 radius equal to the length of connecting rod. Now the piston positions as percentage of stroke is given by : Bp Ap 1 2 =× 100 =× 100 At admission of return stroke ; At cut-off of forward stroke BA AB Ap Bp 3 4 =× 100 =× 100 At release of forward stroke ; At compression of return stroke AB BA Positions of the piston as a percentage of the stroke for admission, cut-off, release and compres- sion for crank end of the piston. Fig. 17.14 The valve diagram for the crank end is drawn by rotating the valve diagram for the cover end through 180° in the direction of rotation of the crank, as shown in Fig. 17.14. By measurement, the piston positions as percentrage of stroke is given by : Bp BP 1 11 At admission of forward stroke =× 100 of forward stroke =× 100 BA BA 11 119 Ans. =× 100= 99.17% 120 628 Theory of Machines Ap AP 2 12 =× 100 At cut-off of return stroke of return stroke =× 100 AB AB 11 85 Ans. =× 100= 70.83% 120 AP Ap 13 3 At release =× 100 of return stroke=× 100 of return stroke AB AB 11 112 Ans. =× 100= 93.33% 120 BP Bp 14 4 At compression=× 100 of forward stroke=× 100 of forward stroke BA BA 11 106 Ans. =× 100= 88.33% 120 Example 17.4. A slide valve has a travel of 125 mm. The angle of advance of the eccentric is 35°. The cut-off and release takes place at 75 per cent and 95 per cent of the stroke at each end of the cylinder. If the connecting rod is 4 times the crank length, find steam lap, exhaust lap and lead for each end of the valve. Solution. Given : AB = 125 mm ; α = 35° Piston position at cut-off for both ends (i.e. cover and crank end) = 75% of stroke Piston position at release for both ends = 95% of stroke Steam lap, exhaust lap and lead for the cover end The Reuleaux’s diagram for the cover end, as shown in Fig. 17.15, is drawn as discussed below : 1. First of all, draw AB = 125 mm to some suitable scale, to represent the valve travel. This diameter AB also represents the piston stroke. On this diameter AB draw a valve travel circle such that OA = OB = Throw of eccentric. The radius OA or OB also represents the crank radius. 2. Draw a line GOH making an angle of 35°, the angle of advance, in a di- rection opposite to the rotation of the crank which is clockwise as shown in Fig. 17.15. 3. At inner dead centre A and outer dead centre B, the connecting rod is in line Broaching machine. Broaching is a process of machin- ing through holes of any cross sectional shape, straight with the crank. Since the connecting rod is and helical slots, external surfaces of various shapes, 4 times the crank radius, therefore mark AA 1 external and internal toothed gears, splines, keyways = 4 × OA = 4 × 125 /2 = 250 mm. Now and rifling. A B = AB = 125 mm and represents the 1 1 Note : This picture is given as additional information and is stroke of the piston. not a direct example of the current chapter. Chapter 17 : Steam Engine Valves and Reversing Gears 629 4. Since the cut-off takes place at 75 percent of the stroke, therefore AP Ap 12 2 0.75 == AB AB 11 ∴ A P = A p = 0.75 × A B = 0.75 × 125 = 94 mm 1 2 2 1 1 ...(∵ A B = AB = 125 mm) 1 1 With P as centre and radius equal to P p (i.e. length of connecting rod), draw an arc 2 2 2 through p which intersects the valve travel circle at C . This point C represents the crank-pin 2 2 2 position at cut-off. Fig. 17.15 5. From C draw C C parallel to GH which intersects a line EOF (perpendicular to GOH) 2 2 1 at N. The point C represents the crank-pin position at admission and ON is the steam lap. By 1 measurement, Steam lap = ON = 32 mm Ans. 6. Since the release takes place at 95 % of the stroke, therefore AP Ap 13 3 == 0.95 AB AB 11 ∴ ∴ ∴ ∴ ∴ A P = Ap = 0.95 × A B = 0.95 × 125 = 118.8 mm 1 3 3 1 1 With P as centre and radius equal to P p (i.e. length of connecting rod), draw an arc 3 3 3 through p which intersects the valve travel circle at C . This point C represents the crank-pin posi- 3 3 3 tion at release. 7. From C draw C C parallel to GH which intersects a line EOF at M. The point C repre- 3 3 4 4 sents the crank-pin position at compression and OM is the exhaust lap. By measurement, Exhaust lap = OM = 8 mm Ans. 8. In order to find the lead, draw a circle with centre A such that C C is tangential to this 1 2 circle (or draw AL perpendicular to C C ). The perpendicular AL represents the lead of the valve. 1 2 By measurement, Lead = AL = 6 mm Ans. Steam lap, exhaust lap and lead for the crank end Fig. 17.16 630 Theory of Machines The Reuleaux’s valve diagram for the crank end, as shown in Fig. 17.16, is drawn by rotating the valve diagram for the cover end, through 180°. By measurement, Steam lap = ON = 20 mm Ans. Exhaust lap = OM = 12 mm Ans. and Lead = AL = 16 mm Ans. Example 17.5. The following data refer to a D-slide valve for the cover end : Position of the crank at cut off = 0.7 of stroke ; Lead = 6 mm ; Maximum opening of port to steam = 45 mm ; connecting rod length = 4 times crank length. Find the travel of valve, angle of advance and steam lap. Solution. Given : Position of Crank at cut-off = 0.7 of stroke ; Lead = 6 mm ; Maximum opening of port to steam = 45 mm ; Connecting rod length = 4 times the crank length. The travel of valve, angle of advance and steam lap may be obtained by using Bilgram valve diagram as discussed below : 1. Draw A'B' of any convenient length, as shown in Fig. 17.17, to represent the assumed valve travel. Draw the assumed valve travel circle on this diameter A' B' which also represents the piston stroke (assumed). Fig. 17.17 2. Since the length of connecting rod is 4 times the crank OA', therefore mark A'A' , = B' B' 1 1 = 4 × OA'. Now A' B' represents the piston stroke. 1 1 3. The cut-off for the cover end takes place at 0.7 of the stroke, therefore mark ′′ ′ AP A′p 12 2 == 0.7 AB′′ ′′ AB 11 4. Now P' as centre and radius P' p' (i.e. length of connecting rod), draw an arc p' C' . 2 2 2 2 2 Now OC' represents the crank position at cut-off. 2 5. Draw a line RS parallel to A' B' and at a distance equal to the lead i.e. 6 mm, to some suitable scale. The point S lies on the line C' OT. 2 6. With O as centre, draw an arc of radius equal to the maximum opening of port to steam (i.e. 45 mm) which intersects RS at X and OT at Y . Chapter 17 : Steam Engine Valves and Reversing Gears 631 7. Draw the bisector of angle RST. The point G on this bisector is obtained by hit and trial such that the circle with centre G touches the maximum opening arc at P, the lines RS and ST. The point G is a point on the actual valve travel circle and represents the centre for steam lap circle. By measurement, we find that Travel of valve = 2 AO = 2 GO = 216 mm Ans. Angle of advance = ∠ AOG = 40° Ans. Steam lap = GP = 63 mm Ans. Example 17.6. In a steam engine, the D-slide valve has a cut-off at 70 per cent of the stroke at each end of the cylinder. The steam lap and the lead for the cover end are 20 mm and 6 mm respectively. If the length of the connecting rod is 4 times the crank length, find : valve travel, and angle of advance of the eccentric. Determine also the steam lap and lead of the crank end. Solution. Given : Position of piston at cut-off on both sides of the cylinder = 70% of stroke ; Steam lap = 20 mm ; Lead = 6 mm ; Connecting rod length = 4 × crank length. Valve travel and angle of advance of the eccentric Since we have to find the valve travel, therefore the Bilgram valve diagram is used. The position of the crank OC' for cut-off at 70 per cent of stroke is obtained in the similar manner as 2 discussed in the previous example.The Bilgram valve diagram is now completed as follows : 1. Draw RS parallel to A' B' and at a distance equal to the lead i.e. 6 mm, to some suitable scale as shown in Fig. 17.18. The point S lies on the line C' OT. 2 Fig. 17.18 2. Draw the bisector of the angle RST. Obtain the point G on this bisector, by hit and trial, such that a circle with centre G and radius equal to the steam lap i.e. 20 mm touches the lines RS and ST. 3. Now with O as centre and radius equal to OG draw the actual valve travel circle. By measurement, we find that Valve travel = AB = 76 mm Ans. and angle of advance of the eccentric = ∠AOG = 42° Ans. The point G may also be obtained by drawing a perpendicular from A'O such that LG = steam lap + lead = 20 + 6 = 26 mm.

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