Seven-cylinder radial engine with its valve train

A seven-cylinder four-stroke air-cooled radial of the 220 hp class, with the bore, stroke and compression ratio of the Continental R-670 (References read) but not a copy of it, and with its valve train, drawn at full size: a two-piece cast-grey crankcase cut away at the front, a built-up single-throw crankshaft, a one-piece master rod with six articulated rods on knuckle pins, seven pistons with rings, seven finned cylinders (two of them opened), and the valve gear: a double-track cam ring that turns at one sixth of the crank speed against it, through reduction gears, in a nose case cut open to show it, with fourteen roller tappets, pushrods, rockers and poppet valves. One engine cycle of t, two crank turns, drives everything through mates and couplings. The seven piston-and-rod loops are solved as one mechanism, and the model measures the difference between the cylinders that the master-and-articulated rod system really has. The tappets and valves follow formulas of the same lift law the cam lobes are drawn from, and the contact between roller and lobe and between rocker and valve tip is measured over the motion, not assumed.

What it shows

• Seven closed loops on one master rod (mate.add cylindrical and revolute, a variable Crank_drive_angle driving the crank). Six articulated rods hinge on knuckle pins in the master rod's flange (Knuckle_2 … Knuckle_7 fixed, Link_2 … Link_7 revolute); each piston slides in its bore on a cylindrical mate and its roll is stopped by the wrist pin revolute, as in the real thing. assembly.solve leaves 0 degrees of freedom. The motion is one driver: the variable Crank_drive_angle, a formula of t.

• A rigid subassembly placed seven times (parts/cylinder.json, an assembly.new script): the barrel, the head, the two rocker brackets with their pins and the two valve springs are one unit, placed by instance.add with its bore, deck height and chamber height in params, and mated by name through the subassembly (Cylinder[3]/Barrel/Mount, Cylinder[3]/Head/Rocker I).

• Parts of several bodies, fitted: the valve with its two split locks and its retainer, the tappet with its roller and the axle pressed into its fork, the rocker bracket with its pin, the cam ring with its locating spigot: each is one part whose bodies stay apart by their fits (asserted in the part from below and above), so each can be put together, and none adds a mate.

• A fit as a proven minimum and a measured maximum: each fit of the valve gear is a clearance (or distance) assertion with its min, whose lower bound is proven, and a variable.measure of the same gap with a value assertion carrying the max, so a loose fit fails instead of reading not proven (A-041). The pressed fits (the tappet's axle, the rocker pin) and the cam ring's spigot are measured face to face with distance, which is proven at those gaps where clearance is not.

• A large fit measured face to face: the cam ring's 300 mm spigot in the nose case is asserted with distance between the two cylinder faces, found by query (surface, radius, in), because clearance between bodies does not prove a gap of 0.08 mm at that size (A-034).

• A chained sketch.pattern: the barrel's sixteen fins are one fin and its gap repeated as a chained run, closed by a sketch.line from the run's last point (e34[last]; sketch.path cannot start or end there, A-022). Drawn out segment by segment, the barrel alone was 48 KB larger and the packed file over 1 MB.

• One source placed twice: the crankcase is drawn as a half with its parting plane at the cylinder centre line; placed twice (the front half turned about the cylinder 1 axis), a section_cut parameter cuts the front half open and carries the through-bolts.

• Configurations by params: two opened cylinders (open_section) are configurations of the same source (a when on the section cut); the piston, barrel and head follow bore, the rods follow rod_ratio, the crank follows stroke.

• A measured difference between cylinders. jointDistance of each piston's cylindrical mate is asserted against an independently derived closed form at every sample (assert.add, motion.check); each cylinder's top and bottom dead centre and compression ratio come out different from the master cylinder's. This is the real thing's behaviour, not a model artefact: see The motion.

• Firing order as a check of the model. The cylinders' placement is measured (rotation) against the table of the firing sequence 1-3-5-7-2-4-6 at intervals of 720°/7.

• A cam is not a mate (A-003): each tappet and valve is a slider driven by a formula of t, the lift law; the cam lobes are drawn by sketch.curve from the same law (a cos² lift over the lobe), offset by the roller radius.

• A gear reduction by couplings: gear couplings tie the crank to the idler and the idler to the cam ring, 24:36 and 20:80 teeth drawn as plain pitch cylinders, so the ring turns at 1/6 against the crank.

• Closure through a pushrod: the rocker is only a revolute; a tappet slider, two revolute pins and the rocker close a loop per valve, and the rocker's angle is solved, while the valve follows a formula of the loop's closed form: the solved rocker angle (jointAngle) and the gap at the rocker pad (clearance) are the checks that the two agree.

The real thing

References read (and what each gave):

Everything else (crank pin 70 mm, knuckle pin 26 mm, wrist pin 34 mm, flange and web sizes, the fit values, the fin pitch and the counterweights) is a judgement of the class made for this model, stated here and not proven to any manufacturer's drawing. The enginehistory.org details are of the A-70, the R-670's predecessor, whose layout the R-670 kept. The model's overall diameter across the rockers is about 1040 mm (boxMax of Rocker[1I], 519.8 mm from the crank axis), against the 1079.5 mm quoted for the R-670. This model is a demonstration: it is not a design and carries no load calculations.

Valve train. A double-track cam ring (cam-ring, three lobes per track; FAA figure 1-27: three lobes at 1/6 of the crank, against it) runs in a nose case on the front of the crankcase (its bolts to the crankcase are not drawn). The ring is held concentric with the crankshaft by a locating spigot on its front face, 300 mm across and engaging 11.9 mm, running in a groove in the 20 mm nose plate with 0.08 mm radial clearance; the groove's floor locates it forward with 0.1 mm. Rearward nothing locates it in this model: moved 2 mm aft, it would land on the front face of the idler's large gear, which turns at another speed. A real ring runs on a bearing of its own (the W670's gear table names a "Cam Ring Bearing Gear" turning with the crank); that bearing and a rearward thrust face are not drawn. It is driven from the crank through a compound idler on a stud in the nose plate: crank gear 24 teeth, idler 36 and 20, an internal gear of 80 teeth on the ring, ratio 1/6 reversed, as the W670's "Intermediate Cam Drive Gear CCW 0.1667:1". The gears are drawn as plain pitch cylinders, without teeth.

Each cylinder has an intake and an exhaust side, each with a roller tappet in a guide boss of the nose case (30 mm of guide; the roller on an axle pressed into the tappet's fork), a pushrod with ball ends, a rocker on a pin pressed through a two-cheek bracket on the head, and a poppet valve with a 45° seat face. The valve's head sits on a seat in a pocket of the chamber roof, 0.05 mm off it, with a throat of 48.2 mm above it, smaller than the 56 mm head; the head is drawn as one casting with the seat machined into it, where the A-70 shrank in aluminium-bronze seat rings. The stem carries two split locks in a groove (two half-cones with a 10° split between them), and the locks a retainer.

Simplifications, said plainly. The valves stand side by side across a flat-roofed chamber, so that each rocker stays in one plane; real radials set them fore and aft, the intake facing away from the propeller and the exhaust toward it (enginehistory.org), in a chamber that is "generally semispherical" (FAA). The rocker boxes, the pushrod housings and the ports and pipes are left off to show the gear; the real engine's valve gear is fully enclosed. The spring is drawn at its installed height (33 mm) seated between the head and the retainer (0.05 mm at each end while the valve is shut), and it does not compress: while the valve is open the retainer passes into it, a contact listed in meta.json; at full lift the top coil shows above the retainer. A spring that compresses was probed and costs too much bake (see Platform notes). The rocker pad stands 0.05 mm off the valve tip, and that gap is kept constant over the motion: it stands for the valve lash but is not taken up, so the valve moves as soon as the tappet does. The lobe follows a cos² lift over the lobe's duration (tappet lift 10 mm, intake 260°, exhaust 265°), the rocker ratio is 46 to 40: a judgement for this class; the opening and closing angles are within the ranges FAA-H-8083-32B gives. The spark plug enters the chamber through a 14 mm hole in its boss; its thread is not drawn.

Fits as drawn (each measured as a radial gap): knuckle pin in the master flange 0.01 mm (drawn as the pressed fit, FAA's first case: a nominal gap in place of interference, so it reports no overlap, and the pin is fixed to the rod); knuckle pin in its rod 0.02 mm; wrist pin in the piston bosses 0.015 mm and in the rods 0.02 mm; big end on the crank pin 0.05 mm; main journals in their bearings 0.05 mm; piston in the bore 0.16 mm; rings in the bore 0.05 mm; cam ring spigot 0.08 mm; tappet plunger in its guide 0.08 mm; tappet roller on its axle 0.03 mm and the axle in the fork 0.01 mm (pressed); rocker on its pin 0.02 mm and the pin in the bracket 0.01 mm (pressed); valve stem in its guide 0.03 mm; split locks on the stem 0.02 mm and in its groove 0.05 mm; retainer on the locks 0.05 mm. Bearings are drawn as plain bores of the stated gap, where the R-670 has roller main bearings (enginehistory.org, of the A-70).

Materials and processes. The crankcase is a two-piece casting split on the centre line of the cylinders, cast grey: a rounded heptagon whose seven flats are the machined seats of the cylinders, the corners cast with a 16 mm radius, the rear wall drafted into its ring and bearing boss (asserted with draft) and rounded into the boss, seven ribs on the rear wall. There is no fillet at a pad junction, because there are no pads: round pads on a round ring with a 3.5 mm rolling-ball fillet at the junction cost 12 to 27 s of CPU for that one part (findings/A-033-fillet-cost-pad-junction/; the budget for the whole engine is 12 s), so the crankcase became a heptagon whose flats need none. The heptagon's sides and corners and the ribs are drafted 1.2° and 1.5° from the parting plane (feature.draft), and one patterned cut machines the seven seats flat again so the flanges sit square; the cut covers the flange, the rest of each side stays drafted. Draft is asserted on a cast corner of the heptagon, a face that runs along the pull (1 to 1.4°). Core prints, machining allowances and wall sections are not modelled, and it is not a foundry pattern. The cast heads have no draft or fillets beyond their fin profile. The crank webs are rounded into the journals (2 mm) and the front web into the crank pin (1.5 mm), by arcs in the turned profiles; the webs' own edges are sharp. Crank halves, rods, knuckle pins and wrist pins are alloy steel forgings, ground and polished (one-piece master rod, as on the R-670's predecessor A-70, so the crankshaft is built up). Pistons are forged aluminium with cast-iron rings, four to a piston, drawn alike; the wrist pin is full-floating with an aluminium plug in each end against the bore. Barrels are alloy steel forgings machined with integral fins, nitrided in the bore; heads are cast aluminium with a flat-roofed chamber 23.7 mm above the deck, two valve pockets in its roof that are ports when the valve is shut, screwed and shrunk on (this model shows the barrel and head meeting at a single seat). Fins taper from 2.3 to 1.5 mm, FAA-H-8083-32B's 0.090–0.060 in. The propeller hub is a copper-plated forged steel hub on the taper of the crank nose, held by a retaining nut on the threaded end (the thread is not drawn, nor is the hub's key).

The counterweights are integral with the crank webs and are not sized to balance: the two webs' sectors put about 350 kg·mm about the crank axis (computed from the drawn outline at 7.85 g/cm³), against a rough 900 kg·mm that a reviewer estimated for this class (an estimate, not a sourced figure; the reciprocating and rotating masses are not modelled, and no balance is claimed). Larger sectors would reach the piston skirts at bottom dead centre.

Parts and assembly order

Assembly order, part by part, each step reachable from the side the next part leaves open:

1. On the bench, the six articulated rods go between the plates of the master rod's flange with their knuckle pins pressed in, and the lock plates close the pins' ends on both sides.

2. The rod group's Ø200 flange and Ø70.1 eye go over the crank pin of the front crank half, where it stands free, since the rear web is not on it yet. Then the rear crank half is put on the spigot and clamped by its bolt.

3. The crank's rear journal is put into the rear crankcase half, then the front half is closed on the front journal, and the two halves are bolted through the ring by the seven through-bolts, each with a head on one side and a nut on the other.

4. The studs are screwed into the seats, seven times eight; each cylinder's skirt enters its seat and its flange goes over the studs. Before a cylinder goes on, its piston is put on its rod with the wrist pin and plugs (the pistons are reached through the open seat), and the rings are compressed into the barrel as it comes down.

5. The valves go into their guides from the chamber side before the cylinder is mounted (step 4); on top of the head the spring goes over the stem, the retainer is pressed down on it and the two split locks go into the stem's groove, and the retainer comes up over them. The brackets go on the head, and each rocker between its cheeks on the pin pressed through them.

6. The crank gear goes on the nose. The nose case is built up off the engine, from its open rear, in this order (the sizes are the drawn ones):

   1. the idler stud is fixed in its seat in the nose plate;
   2. the tappets, each with its roller on the axle pressed through its fork, go into their guide bosses from inside: the fork (24 × 26 mm) cannot pass the 24.16 mm guide, so they cannot go in from outside;
   3. each tappet is held out 10 to 12 mm while the cam ring slides past: the lobe tips need more than 10 mm (the tappet lift), and at 12 mm the fork reaches the boss. That is a 2 mm window;
   4. the cam ring goes in from the rear, over the stud (inside its 120.2 mm gear bore), until its spigot enters the groove in the nose plate, and the tappets are let down onto it;
   5. the idler goes onto its stud through the ring: its small gear (r 119.9 mm from the crank axis) passes the ring's 124 mm rear bore and meshes in the 120.2 mm internal gear. Its large gear (r 143.9 mm) could not pass the ring, which is why the idler goes on after it;
   6. the nose case goes onto the crankcase front (its bolts are not drawn), the idler's large gear sliding axially into mesh with the crank gear.

   The pushrods go in between tappet and rocker last, and the hub goes on the taper of the nose, held by its nut.

The motion

t is one engine cycle, two full turns of the crankshaft: Crank_drive_angle = start_angle + 720 deg * t, so every cylinder runs its four strokes once and the cam ring turns a third of a turn, and the motion closes on itself (one turn would end with other valves open than it started with). The crank pin carries the master rod; the master rod's piston (cylinder 1) moves as a plain slider-crank. The six articulated rods swing on their knuckle pins, whose paths are not circles, and drive pistons 2 to 7. There is no free degree of freedom; the crank turns clockwise seen from the rear, and the cylinders are numbered the same way, No. 1 at the top.

Because all six knuckle pins sit at one radius, the cylinders do not all behave alike. The table below gives the piston's distance from the crank axis at top and bottom dead centre, from a separate numerical solution of the linkage with no 3DCraft in it (a Newton iteration on the loop equations, 72,000 steps per turn; an unpublished check: its script is not in this repository). The model agrees: at 721 samples over the two turns (one per degree of crank) motion.check of the pistons' jointDistance reads strokes of 117.50, 117.56, 118.61 and 118.26 mm for cylinders 1, 2 and 7, 3 and 6, 4 and 5 (the small differences from the table are the sampling: an extreme falls between samples).

An articulated cylinder's top dead centre is off the master's by up to 2.7 mm and off its nominal crank angle by up to 6°; its stroke is up to 1.1 mm longer. With one combustion chamber per cylinder that gives compression ratios from 5.03 to 5.40. This is uncorrected on purpose: the difference is the point of this model, and it is what a real radial designs out, by giving each knuckle pin its own radius from the crank pin (Angle, 1932; FAA-H-8083-32B). The firing order and the 102.86° firing interval are part of the model, at the nominal placement of the cylinders only. The pistons' own top-dead-centre intervals are uneven (108.6, 94.0, 104.5, 105.9, 104.5, 94.0, 108.6°, from the table above); this engine compensates nothing, neither in the rod geometry nor with a compensated magneto as FAA-H-8083-32B describes, and fires at nominal placement.

The valve train in crank degrees. The ring turns at 1/6 of the crank, against it, through two gear couplings; with three lobes per track that gives every cylinder one event per two crank turns, in firing order. The valve events, in crank degrees after the firing top dead centre of each cylinder, are: exhaust opens at 115° (65° before bottom dead centre) and closes at 380° (20° after top dead centre), intake opens at 340° (20° before top dead centre) and closes at 600° (60° after bottom dead centre), so the valves overlap for 40° around top dead centre on the exhaust stroke. The tappet of a valve follows 10 mm · cos²(π x / D) with x in crank degrees from the lobe centre and D the duration; the same law is what sketch.curve draws on the ring, offset by the roller radius (and a 0.04 mm gap, so that contact can be measured). The rocker is a real closed loop (tappet, pushrod, rocker, solved), the rocker ratio is 46:40 and the peak valve lift 11.5 mm.

Parameters

Public parameters (variable.publish): bore (126–134 mm), stroke (116–122 mm), rod ratio (3.95–4.20, the master rod length over the crank radius), and start angle (0–355°, where the crank stands at t = 0, on the firing turn of cylinder 1). The ranges are limited by the pistons of neighbouring cylinders: their skirts come close near the bottom of the stroke (the clearance is asserted over the motion at the defaults and at 8 of the 16 corners of these ranges). A short stroke with a short rod would collide. The piston, barrel and head follow bore; the crank, the rods and the deck height follow stroke and rod ratio.

Checks

At rest (document.check): every mate solved, 0 degrees of freedom; pin and bearing fits measured from above and below; every piston's and ring pack's diameter against the bore, and the barrels and heads by volume (barrel 1 against an independent integration of its drawn profile, an unpublished check, at the default sizes; the others against cylinder 1; the opened 2 and 3 against the share the section cut leaves); the firing order against the measured placement of every cylinder; the master cylinder's compression ratio. That ratio is not an independent measurement of the chamber: the head's measured volume is subtracted from a constant calibrated from this same head, so it detects a head that has changed, and away from the nominal sizes it falls back to the formula and its bound (2 to 12) cannot fail. The rear crankcase half carries the casting's draft check.

Over the motion (motion.check at 145 samples, one every 5° of crank; all of it at the samples):

• every piston's solved jointDistance against an independent closed form of the linkage, to 0.02 mm, and the independent table of top and bottom dead centres at the default sizes (within 0.15 mm at the sample nearest each extreme);
• the cam ring at one sixth of the crank, against it (jointAngle of Cam_drive against -crank_angle / 6, 0.02°): the gears are couplings, so this is the ratio the solve keeps; a wrong gear value fails it;
• roller on the cam by measure: clearance of the roller of tappets 1 and 4, intake and exhaust, to its lobe track, 0.005 to 0.13 mm at every sample (0.04 mm drawn; it reads 0.040 mm at every sample). The lobe is a separate body drawn from the law, the tappet a slider driven by it: a ring turned out of phase, or a lobe drawn on another law, overlaps or stands off, and fails;
• lift against the published timing: the intake tappets of all seven cylinders and the exhaust tappets of cylinders 1 and 4 against the lift computed from a table of opening and closing angles in crank degrees (timing: intake 340° to 600°, exhaust 115° to 380° after the firing top dead centre) and the firing order, to 0.02 mm. The table is not the lobe variables, so a phase moved in the law and the cam together fails here;
• the valve gear agrees with itself: each of the 14 rockers, solved through its pushrod, stands at the angle the valve formula assumes (0.01°), and the rocker pads of valves 1I, 1E, 4I and 4E keep 0.01 to 0.12 mm to their valve tips;
• piston-to-valve clearance of all 14 valves, at least 25 mm at every sample. The crown of piston 1 comes to 26.7 mm from the chamber roof at top dead centre (the articulated pistons stop up to 2.7 mm lower), so this holds only while the valves are within 1.7 mm of their seats when the piston is up: in the overlap the closest is 25.91 mm, valve 1I just after the master piston's top dead centre on the exhaust stroke (t = 0.505, from a finer sampling around the closest of the 145 check samples, which reads 25.93 mm at t = 0.507). This is a timing check more than a safety margin: the flat chamber is deeper than the 11.5 mm valve lift, so in this head even a fully open valve at top dead centre would clear the crown by about 15 mm;
• the cam ring held by its spigot: distance between the spigot's face and the groove's face at least 0.04 mm, and the same distance as an output at most 0.12 mm (0.08 mm drawn, it reads 0.08 at every sample), while the ring turns; a loose bore fails it;
• the spring seated: springs 1I and 4E stand 0.02 to 0.08 mm under their retainers whenever the valve is shut;
• the rocker of valve 1I on its pin, 0.01 to 0.03 mm; the clearances of rods, pistons and crankcase, and the pin and bearing fits of the engine.

In the parts: the split locks in the stem's groove and the retainer on the locks, the roller on its axle and the axle in the fork, the rocker pin in its bracket, each from above and below.

No collision at 121 moments at the defaults and 31 at each of 8 of the 16 corners of the ranges, except the listed contact of the valve retainers with the springs while the valves are open (the springs are drawn at their installed height and do not compress).

What the samples do not cover: between samples. Contact at the cam and the rocker pad is measured on four of the fourteen valves (the rocker angle on all fourteen), the spring seat on two, the rocker pin on one. Springs do not compress and the gear teeth are not drawn, so the gear contact is the coupling's ratio only.

The README in the model's repository has the rest (Files, Rebuild, Difficulty, Platform notes, Licence): the whole README on GitHub.