Mechanical Engineers Data Handbook Episode 8 pps

FLUID MECHANICS 165 Drag coefficients for various bodies (continued) Shape L d Cd - A Re 104 - Arrangement Hollow hemisphere flow on 0.80 0.1 lrd’ convex face 4 Hollow hemisphere flow on 1.42 0.1 lrd2 concave face 4 - - (a) High-drag car > 0.55 50 0.45 50 - (b) d-b - (c) Low-drag car <0.30 50 (b) Medium-drag car 4.7 Fluid machines 4.7. I Centrifugal pump A centrifugal pump consists of an impeller with vanes rotating in a suitably shaped casing which has an inlet at the centre and usually a spiral ‘volute’ terminating in an outlet branch of circular cross-section to suit a vipe. Fluid enters the impeller axially at its centre of rotation through its ‘eye’and is discharged from its rim in a spiralling motion having received energy from the rotating impeller. This results in an increase in both pressure and velocity. The kinetic energy is mostly converted to pressure energy in the volute and a tapered section of the discharge branch. 166 Some pumps have a ring of fixed (diffuser) vanes into which the impeller discharges. These reduce the velocity and convert a proportion of the kinetic energy into pressure energy. Symbols used: D, =mean inlet diameter of impeller D, =outlet diameter of impeller b, =mean inlet width of impeller b, = outlet width of impeller t = vane thickness at outlet b1 =vane inlet angle bz =vane outlet angle N = impeller rotational speed K = whirl coefficient Q = flow H=hMd Z=number of vanes p = fluid density 1 refers to impeller inlet 2 refers to impeller outlet 3 refers to diffuser outlet P =power Vt = tangential velocity Vw = whirl velocity V, =flow velocity V, = velocity relative to vane V= absolute velocity of fluid qh = hydraulic efficiency q, =volumetric efficiency q,, = mechanical efficiency qo = overall efficiency a =diffuser inlet angle d,=diffuser inlet width d, =diffuser outlet width a, =diffuser inlet area = bd, a, =diffuser outlet area = bd, V, =diffuser outlet velocity p = pressure rise in pump b = diffuser breadth (constant) MECHANICAL ENGINEER'S DATA HANDBOOK Head Refemng to velocity triangles Theoretical head Hth = It is usually assumed that V,, is zero, Le. there is no 'whirl' at inlet. The outlet whirl velocity V,,, is reduced by a whirl factor K to KVw,(K < I). Then: ( vw2 Vt 2 - vw I vt I ) 9 vwZ VtZqh Actual head H = 9 where tfh= hydraulic efficiency. Or: Pressure rise p = pK Vw, VtZqh Flow Q= V,,A,= Vf,A, ="D,b,Vf,tl" where qv = volumetric efficiency I Velocity relationships FLUID MECHANICS 167 Power and eficiency Overall efficiency rt. = flmrtvrth Input power P = p - gHQ ‘IO Inlet angles Diffuser (fixed vanes): Vf2 Inlet angle a = tan - - VW2 a2 Outlet velocity V3 = V2 - a3 Vane : Vfl Inlet angle fl, =tan- - (assuming no whirl) VI1 lbCI- II Pump volute Q Velocity in volute V, = - A4 where: A4=maximum area. Then: A4 Pump outlet velocity V, = V, - A0 where: A,=outlet area. v: v,’ Pressure head at outlet Ho= H K” 5 28 where: K,=dHuser and volute discharge coefficient. A Static and total eficiencies % Static head = H, Static pressure=po=pgHo Total pressum=Pp,=pgHt Static efficiency = ‘I, =o PQ Total efficiency = q1 = P~Q - P P Total head HI= no+- v: 4.1.2 Pump characteristics Pump characteristics are plotted to a base of flow rate for a fixed pump speed. Head (or pressure), power and efficiency are plotted for dl&rent speeds to give a family of curves. For a given speed the point at which maximum efficiency is attained is called the ‘best etficiency point’ (B.E.P.). If the curves are plotted nondimensionally a single curve is obtained which is also the same for all geometrically similar pumps. 168 Head (H), power (P) and efficiency (q) are plotted against flow at various speeds (N) and the B.E.P. can be determined from these. MECHANICAL ENGINEER’S DATA HANDBOOK vapour pressure at the operating temperature and also on the ‘specific speed’. Symbols used: p=fluid density pa = atmospheric pressure p, = vapour pressure of liquid at working V, =suction pipe velocity h, = friction head loss in suction pipe plus any other losses Ha =pump head u, =cavitation constant which depends on vane Minimum safe suction head temperature design and specific speed Hmin=Pa/Pg-(ocHa+ C/2g+hr+Pv/Pg) 0 Non-dimensional characteristics To give single curves for any speed the following non-dimensional quantities, (parameters) are plotted (see figure): Head parameter X,=gH/N2DZ Flow parameter X, = Q/ND3 Power parameter X,= PIpN3DS 4.7.3 Cavitation If the suction pressure of a pump falls to a very low value, the fluid may boil at a low pressure region (e.g. at the vane inlet). A formula is given for the minimum suction head, which depends on the fluid density and Range of 6,: Safe region u, >0.0005Nf.37, where N,=specific speed. Dangerous region u, < O.OOO~~N:.~’ A ‘doubtful zone’ exists between the two values. 4.7.4 Centrifugal fans The theory for centrifugal fans is basically the same as that for centrifugal pumps but there are differences in construction since fans are used for gases and pumps for liquids. They are usually constructed from sheet metal and efficiency is sacrificed for simplicity. The three types are: the radial blade fan (paddle wheel fan); the backward-curved vane fan, which is similar in design to the centrifugal pump; and the forward- curved vane fan which has a wide impeller and a large number of vanes. Typical proportions for impellers, maximum efficiencies and static pressures are given together with the outlet-velocity diagram for the impeller. ~~ ~ Max. Static efficiency No. of pressure Velocity Type and application Arrangement blD (%I vanes (cm H,O) triangle Radial vanes: Ve- v, w6 h (paddle wheel), 0.35-0.45 60-70 6-8 mill exhaust ve* v, Backward-curved vanes: 0.25-0.45 75-90 3- air conditioning 8-12 12-15 Forwardcurved vanes: ventilation 0.50-0.60 55-60 16-20 7-10 170 MECHANICAL ENGINEER’S DATA HANDBOOK 4.7.5 Impulse (Pelton) water turbine This is a water turbine in which the pressure energy of the water is converted wholly to kinetic energy in one or more jets which impinge on buckets disposed around the periphery of a wheel. The jet is almost completely reversed in direction by the buckets and a high efficiency is attained. Formulae are given for the optimum pipe size to give maximum power, and for the jet size for maximum power (one jet). Symbols used: 8 =bucket angle H = available head H, = friction head D = mean diameter of bucket wheel D, = pipe diameter d =jet diameter p = water density f= pipe friction factor L=length of pipe N = wheel speed C, =jet velocity coefficient V=jet velocity V, = pipe velocity qo = overall efficiency H,,, = total head T l- H V R Available head H = (HIoI - H,) Shaft power P = pgHq, Jet velocity V=C,m Mean bucket speed U = nDN nd2 V Flow through jet Q=- 4 Hydraulic efficiency qh = 2r( 1 -I)( 1 + k cos 0) where: r = -, 0 =bucket angle (4-7”), U V k =friction coefficient (about 0.9). (1 + k cos 8) 2 Maximum efficiency (at r = 0.5): qh(max) = Overall efficiency qo = qhqm Maximum power when Hr=-=L. Hence: HtOI 4ftv2 3 29Dp Optimum size of supply pipe D,= - F (approximately) Jet size for maximum power d = - (z)’ 4.7.6 Reaction (Francis) water turbine The head of water is partially converted to kinetic energy in stationary guide vanes and the rest is converted into mechanical energy in the ‘runner’. The water first enters a spiral casing or volute and then into the guide vanes and a set of adjustable vanes which are used to control the flow and hence the power. The water then enters the runner and finally leaves via the ‘draft tube’ at low velocity. The draft tube tapers to reduce the final velocity to a minimum. FLUID MECHANICS 171 Velocity triangles Radial velocities: V,, =Q/nb,D, (inlet) V,, = Q/nbzD, (outlet) Tangential velocities: VI, = xD, N (inlet) Whirl velocities: V,, =gHqh/Vl, (inlet, usually) VI, = nD,N (outlet) Vw2 =O (outlet, usually) Guide vane velocity: V, = vanes 0 Vane and blade angles Guide vanes: a=tan-'V,,/V,, Blade inlet: B1 =tan- Vrl/( Vll - V,,) Blade outlet: & =tan- V,,/V,, Overall efficiency q,, = qmqh Shaft power = pgHQq, Available head H = HI,, - H, - Vf/2g where: V,=draft tube outlet velocity. Specific speed of pumps and turbines It is useful to compare design parameters and charac- teristics of fluid machines for different sizes. This is done by introducing the concept of 'specific speed', which is a constant for geometrically similar machines. 4.7.7 Specific speed of pumps and turbines Symbols used: N = speed of rotation H = head P = power Q = flow Specific speed of pump N, = - NA Hi Specific speed of turbine Ns=~ NJ7; H2 ~ Manufacturing technology 5.1 Metal processes Metals can be processed in a variety of ways. These can be classified roughly into casting, forming and machin- ing. ites. The following table gives characteristics of different processes for metals, although some may also apply to non-metallic materials such as plastics and compos- General characteristics of metal processes Minimum Economic Materials Optimum section Holes Inserts Process quantity (typical) size (mm) possible possible Sand casting Die casting, gravity Die casting, pressure Centrifugal casting Investment casting Closed die forging Hot extrusion Hot rolling Cold rolling Drawing Spinning Impact extrusion Sintering Machining Smallbarge Large Large Large Smallbarge Large Large Large Large Smallbarge One-off, large Large Large One-off, No limit AI, Cu, Mg, Zn alloys AI, Cu, Mg, Zn alloys No limit No limit No limit No limit No limit No limit AI, Cu, Zn, mild steel Al, Cu, Zn, mild steel AI, Pb, Zn, Mg, Sn Fe, W, bronze No limit 1400 kg 1-50 kg 50g to 5 kg 30mm to lm diameter 50g to 5Okg 3000 cm3 500mm diameter - - 3 mm/6 m diameter 6mm/4.5m diameter 6-l00mm diameter 80g to 4kg - 3 3 1 3 1 3 1 - - 0.1 0.1 0.1 0.5 - Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes No No No No No No No Yes No Yes - No Yes Yes Yes Yes - large MANUFACTURING TECHNOLOGY 173 ~~ 5.2 Turning 5.2. I In metal cutting, a wedge-shaped tool is used to remove material from the workpiece in the form of a ‘chip’. Two motions are required: the ‘primary motion’, e.g. the rotation of the workpiece in a lathe; and the ‘secondary motion’,e.g. the feed ofa lathe tool. Single-point tools are used for turning, shaping, planing, etc., and multi-point tools are used for milling, etc. It is necessary to understand the forces acting on the tool and their dects on power require- ment, tool life and production cost. In the following tables of tool forces and formulae specific power consumption, metal removal rate, tool life, etc., are given. A graph shows the tool life plotted against cutting speed for high-speed steel, carbide and ceramic tools. Single point metal cutting 5.2.2 Cutting tool forces Tool forces vary with cutting speed, feed rate, depth of cut and rake angle. Force may be measured experi- mentally by using a ‘cutting tool dynamometer’ in which the tool is mounted on a flexible steel diaphragm and its deflections in three planes measured by three electrical transducers. Three meters indicate the force, typically of 25 N up to, say, 2000 N. Graphs show typical characteristics. Symbols used: F, =cutting force (in newtons) F, = radial force (in newtons) F,=feed force (in newtons) Resultant force on tool in horizontal plane = Jm: newtons 5.2.3 Cutting power, P Let: D = work diameter (mm) d-depth of cut (mm) N = number of revolutions per minute V P = F, - (watts) 60 x(D -d)N lo00 (m min - ’ ) where: v= (an3 min-’) n(D-d)d fN lo00 Metal removal rate Q = where: f=feed rate (mm rev-’). Specific power consumption P,=- (wattscrr-3 min- P Q 174 MECHANICAL ENGINEER’S DATA HANDBOOK Typkd values of P. Material Specific power consumption, P. Plain carbon steel 34 Alloy steel 71 Cast iron 24 Aluminium alloy 12 Brass 25 5.2.4 Tool life, T T= - (min) Values of C and n Wear lend Tool material C n Wear land width (mm) Roughing Finishing ~~ High-speed steel &IO0 0.08-0.15 1.5 0.25-0.38 Cemented carbide 200-330 0.16-0.5 0.75 0.25-0.38 Ceramic 330-600 0.404.6 0.25-0.38 0.25-0.38 5.2.5 Tool ch8racteristics Force versus cutting speed F, is constant over normal range of cutting speed. F, increases slowly with cutting speed. Force versus depth of cut F, increases with depth of cut. F, increases at decreasing rate with depth of cut. 1200 lo00 i- 400 200 0 0.5 1.0 1.5 2.0 2.5 Wdcut. d(mm) Force versus rake angle F, and F, fall slowly with rake angle. [...]... steel 0.55 0.50 02 5 01 3 01 3 0.30 0.50 03 5 03 5 0.30 0. 18 0. 18 0.30 0.20 0.20 02 8 0.30 0.40 02 5 0.20 03 3 01 8 0. 18 0.22 01 5 01 3 01 5 0.20 01 3 0.10 01 5 02 5 01 8 01 8 0.07 0.10 0.07 00 5 00 7 0.13 0.10 0.10 HSS, high-speed steels These values should be lowered for finishing and increased for rough milling  188 MECHANICAL ENGINEER’SDATA HANDBOOK Metal removal rate in milling Material being cut... 8. 0 10.0 12.0 14.0 16.0 0.35 0.40 0.45 0.50 0.60 0.70 0 .80 1.o 1.25 1s o 1.75 2.00 2.00 1.20 1.60 2.05 2.50 2.90 3.30 4.20 5.30 6 .80 8. 50 10.20 12.00 14.00 Thread pitch (mm) Tap drill size (mm) 20.0 24.0 30.0 36.0 42.0 48. 0 56.0 64.0 72.0 80 .0 90.0 100.0 2.50 3 O 3.50 4.00 4.50 5.00 5.50 6.00 6.00 6.00 6.00 6.00 17.5 21.0 26.5 32.0 37.5 43.0 50.5 58. 0 66.0 74.0 84 .0 94.0 182 MECHANICAL ENGINEER’S DATA. .. Thermosetting plastic 70-100 70-100 40-70 35-50 35-70 85 -135 15-20 35-50 5-10 10-15 35-50 90-120 90-120 50 -80 45-60 50-90 110-150 18- 25 45-60 7-12 12- 18 45-60 Stellite > 200 170-250 70-150 6 0 70-150 85 -135 25-45 70-120 20-35 30-50 70-120 Tungsten carbide > 350 350-500 150-250 9CL120 100-300 85 -135 50 -80 100-200 176 5.2.7 MECHANICAL ENGINEER’SDATA HANDBOOK Turning of plastics Turning of plastics - depth... moulded or cast Extruded, moulded or cast Moulded 33 0.12 0.25 0.30 0. 38 0.46 0.50 0.64 0.76 33 0.05 0.10 0 0.15 33 0.05 0.12 0.1 0.20 0.25 0.30 0. 38 0. 38 Moulded or extruded Cast, moulded or filled Cast, moulded or filled 66 0.03 0.05 0 0.10 0.13 0.15 0. 18 0.20 50 0. 08 0.13 0.20 0.25 0.30 0. 38 0. 38 33 0.05 0.13 0.15 0.20 0.25 0.30 0. 38 0. 38 Nylon, acetals, polycarbonate Polystyrene Soft grades of thermosetting... Thin 186 2.4.2 MECHANICAL ENGINEER'S DATA HANDBOOK Milling parameters Power for peripheral milling Symbols used: P = power (watts) u = cutting speed (m s- ') z=number of teeth b=chip width (mm) C = constant f=feed per tooth (mm) d = depth of cut (mm) r = radius of cutter (mm) x, y =indices k =constant Values of x, y, k and C are given in the tables Material X Y k Steels Cast iron 0 .85 0.70 0.925 0 .85 ... : D =cutter diameter (mm), N =number of revolutions per minute Cutting speed v=nDN/1000(mmin-') 980 (120 BHN) 1620 (125 BHN) 1460 (125 BHN) 1190 ( 180 BHN) 2240 (225 BHN) 2200 (270 BHN) 1600 (150 BHN) 182 0 (170 BHN) 635 (100 BHN) 1110 (annealed) 1960 ( 280 BHN) 2 380 (190 BHN) 1330 (263 BHN) 1240 (as cast) 187 MANUFACTURING TECHNOLOGY Milling cutting speeds at a f e d rate of 0.2mm per tootb Cutting speed... suggested angles for drills is given  180 MECHANICAL ENGINEER'SDATA HANDBOOK Drilling feeds Higb-speeddrill s p e d Feed (mm rev.- ') Drill diameter (mm) Hard materials* Soft materials? 1.5 3.O 6 O 9.0 12.0 19.0 25.0 0.05 0.05 0.05 0.07 0.07 0.10 0.12 0. 18 0.22 Speed* (ms-') Material 0.10 0.15 0.20 0.30 0.35 Cast iron Mild steel 60140 brass Medium carbon steel O.M.6 0.3-4.5 0 .8- 1.0 0.2-0.3 ' *Speed =nDN/60... staggered periphery Face tooth teeth on alternate sides Deep slots Up to 200mm diameter, 32mm wide Single angle Teeth on conical surface and flat face Angled surfaces and chamfers 60 -85 " in 5" steps 184 MECHANICAL ENGINEER'S DATA HANDBOOK Types of milling cutter (continued) Type Arrangement of teeth Application Size Double angle Teeth on two conical faces Vee slots 45", 60", 90" Rounding Concave quarter... 1=side clearance angle $ =side rake angle Another feature is the 'chip breaker' which breaks long, dangerous and inconvenient streamers of 'swarf' into chips Single-point tool Chip breaker 1 78 MECHANICAL ENGINEER’SDATA HANDBOOK Tool setting The tool must not be set too high or too low, or inclined at an angle The effects are shown in the figure \ Inclineddownwards Inclined upwards TOOL SEl-rING Above centre:... plastic Hard grades of thermosetting plastic Brazed carbide 50 145 160 0.25 53 160 175 4 Material Throwaway carbide tip 0.25 50 160 175 4 0.25 18 50 65 4 0.25 50 160 175 4 0.25 48 145 160 Depth of cut (mm) Feed (mm rev- ’) HSS 4 0.25 4 HSS, high-speed steels 5.2 .8 Typical standard times for capstan and turret lathe operations Time Time Operation (s) Operation (SI Change speed Change feed Index tool post . High-speed steel &IO0 0. 08- 0.15 1.5 0.25-0. 38 Cemented carbide 200-330 0.16-0.5 0.75 0.25-0. 38 Ceramic 330-600 0.404.6 0.25-0. 38 0.25-0. 38 5.2.5 Tool ch8racteristics Force versus. 35-50 35-70 85 -135 15-20 35-50 5-10 10-15 35-50 90-120 90-120 50 -80 45-60 50-90 110-150 18- 25 45-60 7-12 12- 18 45-60 > 200 170-250 70-150 60 70-150 85 -135 25-45 70-120. 20-35 30-50 70-120 > 350 350-500 150-250 9CL120 100-300 50 -80 85 -135 - 100-200 176 MECHANICAL ENGINEER’S DATA HANDBOOK 5.2.7 Turning of plastics Turning of plastics - depth