Arc Tappet Valve Motion is a cam-driven valve actuation scheme used in mining percussion machinery — stamp mills, rock drills, and pneumatic hammers — where a curved (arc-profile) tappet rides a rotating cam and converts that rotation into a timed, near-rectangular valve lift. The arc face spreads contact stress across a larger footprint than a flat or roller follower, so the valve opens fast, dwells open through the full power stroke, then snaps shut. That timing is what gives a Rand-style rock drill its sharp blow and clean exhaust at 1,800–2,200 BPM.
Arc Tappet Valve Motion Interactive Calculator
Vary cam angle, lift, timing, and blow rate to see the arc tappet valve lift, open duration, and animated cam-follower motion.
Equation Used
This calculator idealizes the arc tappet valve event as the near-rectangular lift profile shown in the article: the valve is closed before the opening angle, held at full lift through dwell, and closed again at the closing angle. Open time is the angular open fraction multiplied by the cam period from the blow rate.
- One cam revolution produces one valve event and one percussion blow.
- Valve lift is idealized as a sharp-rise, dwell, sharp-close profile.
- Cam angle is normalized over 0 to 360 deg.
- Elastic deflection, lash, and ramp rounding are neglected.
Operating Principle of the Arc Tappet Valve Motion
The arc tappet is a follower with a convex curved face — typically a circular arc of radius 1.5 to 3 times the cam base-circle radius — that sits between the rotating cam and the valve stem. As the cam lobe sweeps under the arc, the contact point migrates across the curve rather than staying at a single fixed pad. That migration is the whole point. A flat tappet sees a single line of wear and a roller tappet adds a pin joint that hates grit, but a hard-faced arc tappet in a dusty stamp mill or rock drill housing keeps wearing evenly and stays within timing tolerance for thousands of hours.
The motion you actually get at the valve is shaped by three things: the cam profile, the arc radius of the tappet, and the stem clearance. Get the arc radius wrong and the valve lift curve flattens or peaks too early — open the valve 5° of cam rotation late on a Sullivan WD-50 drill and you lose pressure rise on the working stroke, and the drill chuffs instead of strikes. Get the clearance wrong — say more than 0.15 mm cold lash on a typical 25 mm valve — and the tappet slams the cam, you hear it, and within 200 hours you'll see brinelling on the cam lobe.
Failure modes cluster around three things: arc-face galling from poor lubrication (you see a polished band turning matte and grey), cam-lobe spalling from over-clearance impact, and stem bind from grit packed into the guide. The fix in every case is the same — set lash to spec, keep the oil mist alive, and inspect the arc face every shift change.
Key Components
- Arc Tappet (Follower): Hardened steel block with a convex arc face, typically 50–60 HRC, riding directly on the cam. The arc radius must match the cam profile within ±0.05 mm or the valve lift curve distorts and timing drifts off-spec.
- Cam (Lobe & Base Circle): Rotating profile that drives the tappet. Base-circle concentricity must hold under 0.02 mm TIR — any more and the closed valve gets bumped open during dwell, leaking working fluid.
- Valve Stem & Guide: Transfers tappet motion to the valve head. Guide clearance lives between 0.04 mm and 0.08 mm on a typical 12 mm stem; tighter binds when hot, looser lets the stem cock and chip the seat.
- Return Spring: Keeps the tappet seated on the cam through the closing ramp. Sized so spring force at full lift exceeds inertial lift-off force at maximum operating RPM by at least 1.5×, otherwise the tappet floats and timing collapses.
- Lash Adjuster (Shim or Screw): Sets cold clearance between the tappet face and the cam base circle. Typical spec on a stamp mill valve is 0.10–0.15 mm — go below 0.05 mm and the valve hangs open as the head warms, go above 0.20 mm and you get audible tappet noise plus accelerated cam wear.
Who Uses the Arc Tappet Valve Motion
Arc tappet valve motion shows up wherever a mining machine needs hard, repeatable percussion timing in a dirty environment. It survives where roller tappets would seize and gives sharper edges on the lift curve than a flat follower can manage. You see it across pneumatic, steam-era, and modern hydraulic percussion equipment.
- Hard Rock Drilling: Ingersoll-Rand Jackleg drills and Atlas Copco BBC-16 stopers use arc-tappet valve gear to time the air admission and exhaust on each blow at roughly 2,000 BPM.
- Stamp Milling (Historic & Restored): California stamp batteries — including the restored 10-stamp mill at the Empire Mine State Historic Park — used arc tappets on the steam admission valves to keep stamp drop timing within 5 ms across all stamps.
- Pneumatic Pick Hammers: Chicago Pneumatic CP-9 demolition hammers run an arc tappet valve set in the back-head to control the reciprocating piston's air switching at 1,500–1,800 BPM.
- Hydraulic Rock Breakers: Sandvik Rammer and Atlas Copco HB-series breakers on excavators use a hardened arc tappet to time the high-pressure oil control valve, surviving silica-laden grit that would destroy a roller follower.
- Underground Loading & Haulage: Older Eimco 21 and 12B mucking machines used arc-tappet air valve gear on the hoist cylinders for the bucket lift cycle, cycling roughly 600 times per shift.
- Diamond Core Drill Feed Mechanisms: Boart Longyear LF-70 surface core rigs use an arc-tappet pilot valve on the chuck-clamp hydraulic circuit for repeatable clamp-and-release timing during rod handling.
The Formula Behind the Arc Tappet Valve Motion
The single most useful calculation for arc tappet valve motion is the valve lift as a function of cam angle, because it tells you whether your valve actually opens far enough, fast enough, and stays open long enough at your operating RPM. At the low end of a typical mining percussion range — say 1,200 BPM — the valve has plenty of time to lift fully and you're limited by cam profile, not dynamics. At the nominal 1,800 BPM the lift curve hits its design sweet spot. Push past 2,400 BPM and tappet inertia starts winning against the spring, the follower lifts off the cam, and the valve floats. The formula below gives you peak lift; the geometry of the arc radius determines how sharp the rise and fall are.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Lv | Valve lift at a given cam angle | mm | in |
| Rc | Cam base circle radius | mm | in |
| hlobe | Cam lobe height above base circle at the angle of interest | mm | in |
| Ra | Arc radius of the tappet face | mm | in |
| e | Eccentricity — offset between cam centreline and tappet centreline at the contact angle | mm | in |
Worked Example: Arc Tappet Valve Motion in a Sandvik DD321 underground jumbo drill
You're rebuilding the air valve gear on the rock drill heads of a Sandvik DD321 underground jumbo running 38 mm bits in a Quebec zinc mine. The cam has a 14 mm base circle radius and a peak lobe height of 6 mm. You're spec'ing a new arc tappet with a 30 mm arc radius, and you need to verify peak valve lift across the operating range from 1,500 to 2,400 BPM, with nominal at 1,800 BPM. Eccentricity at peak lift is 2 mm.
Given
- Rc = 14 mm
- hlobe = 6 mm
- Ra = 30 mm
- e = 2 mm
- Operating BPM = 1500–2400 BPM
Solution
Step 1 — at nominal 1,800 BPM, compute the geometric peak valve lift using the arc tappet formula. First the arc-correction term:
Step 2 — substitute into the lift equation for nominal lift:
That 6.07 mm of peak lift is what the valve actually sees at design RPM — about 1% above the bare cam-lobe height because the arc face tracks slightly outboard of dead-centre. At 1,800 BPM the spring keeps the tappet glued to the cam through the entire ramp, and you get a clean square-edged lift profile.
Step 3 — at the low end, 1,500 BPM, the geometry is identical (geometry doesn't care about RPM) so peak lift is still 6.07 mm, but the dwell-at-peak feels longer in absolute time. The valve breathes easier, exhaust is cleaner, but blow energy per stroke is roughly 17% lower than nominal because you're firing fewer strokes per second.
Step 4 — at the high end, 2,400 BPM, geometric lift is again 6.07 mm in theory. In practice, a typical 8 N/mm tappet return spring on this size valve loses control of the tappet around 2,300 BPM. Above that, the follower lifts off the cam closing ramp, the valve floats 0.3–0.5 mm above its seat at the wrong moment, and you lose 10–15% of blow energy.
Result
Peak valve lift at the nominal 1,800 BPM is 6. 07 mm. That's the sweet spot — fast enough to maintain blow rate for 38 mm bit penetration in zinc ore, slow enough that the spring keeps the tappet planted on the cam through the closing ramp. At 1,500 BPM you get the same 6.07 mm but with longer time-at-peak, which is fine for cleanout passes; at 2,400 BPM the geometry promises 6.07 mm but the dynamics deliver less because the tappet floats. If you measure peak lift below 5.5 mm with a dial indicator on the valve stem, suspect three things in order: (1) lash adjuster set above 0.20 mm, eating the first half-millimetre of lift before the tappet even contacts the cam; (2) arc face galled or worn flat over its central 5 mm contact band, dropping effective Ra; (3) cam lobe spalled at the nose from prior over-clearance impact, taking 0.5–1.0 mm off hlobe.
When to Use a Arc Tappet Valve Motion and When Not To
Arc tappets aren't the only way to drive a valve off a cam. Flat-faced tappets and roller tappets each solve the same problem with different compromises. The choice comes down to how dirty the environment is, how fast you need to cycle, and how much you care about maintenance interval.
| Property | Arc Tappet | Flat-Faced Tappet | Roller Tappet |
|---|---|---|---|
| Max sustained operating speed | ~2,300 BPM before float | ~1,800 BPM (high cam stress) | ~3,500 BPM |
| Tolerance to abrasive grit | High — no pin joint | High — no pin joint | Low — grit destroys roller bearing |
| Contact stress on cam | Moderate — distributed across arc | High — concentrated line | Low — rolling contact |
| Typical service life in mining duty | 6,000–10,000 hours | 3,000–5,000 hours | 1,500–3,000 hours (grit-fouled) |
| Lash setting tolerance | ±0.05 mm | ±0.05 mm | ±0.03 mm |
| Replacement cost (per follower) | $40–$120 | $15–$40 | $80–$250 |
| Best application fit | Pneumatic/hydraulic mining percussion | Slow steam/air valve gear | High-RPM IC engines, clean environments |
Frequently Asked Questions About Arc Tappet Valve Motion
One-sided wear means the tappet centreline is offset from the cam centreline beyond design eccentricity — the contact point isn't migrating across the arc the way the geometry intends. The usual cause is a worn or shimmed-incorrectly tappet guide bore, letting the follower cock under spring load and ride one edge of the cam lobe.
Pull the tappet, measure the guide bore — if it's gone above the spec clearance (typically 0.08 mm on a 20 mm tappet body), you ream and sleeve or replace the guide. Running it as-is will spall the cam lobe within a few hundred hours because contact stress on the narrow band is 3–4× design.
Float onset RPM is sensitive to three things the spec sheet doesn't always show: actual spring rate (springs lose 5–8% rate after 2,000 hours), tappet mass (an aftermarket follower might be 15% heavier than OEM), and lash. Add 0.05 mm of extra lash and the spring sees less preload at lift-off, dropping float threshold by roughly 200 BPM.
Check spring free length first — if it's more than 2% below new-spec free length, the spring is tired. Then weigh the tappet against the OEM drawing. Most field cases of premature float trace to a tired return spring, not the cam or tappet itself.
If the oil is genuinely clean — filtered to ISO 4406 18/16/13 or better — and you're targeting cycle rates above 2,500 BPM, the roller wins on cam life and parasitic loss. Arc tappets only beat rollers when grit gets into the valve cavity, which is the normal case in pneumatic mining tools but not in a sealed hydraulic circuit.
The catch is filter integrity over the machine's life. One torn filter element, one cracked breather, and a roller's needle bearing eats itself in under 100 hours. Field reliability data on Sandvik and Rammer breakers shows arc tappets edge out rollers in real fleet duty even on hydraulic units, simply because filtration discipline slips.
Start with Ra = 2 × Rc as a baseline — that gives the contact point enough sweep to wear evenly without making the arc so flat it behaves like a flat follower. Then check the cam-tappet contact stress at peak lift using a Hertzian line-contact calculation; if peak stress exceeds 1,000 MPa for a 60 HRC steel pair, increase Ra.
The hard limit is when Ra grows large enough that contact eccentricity at peak lift exceeds half the tappet face width. Past that you get edge loading and the whole point of the arc collapses. For most mining valve cams that limit lands around Ra = 3 × Rc.
That's thermal growth in the valve stem outpacing growth in the housing. On a steel stem in an aluminium housing, the housing grows faster, opening up clearances and effectively absorbing some lift. But on an all-steel stack with a long stem, the stem grows enough to eat into your hot lash and reduce effective lift if the cold lash was set too tight.
Rule of thumb: every 100°C of stem temperature rise on a 150 mm steel stem adds about 0.18 mm of growth. Set cold lash so hot lash lands at 0.08–0.10 mm — typically 0.15 mm cold for a percussion drill that runs the valve stack at 80–100°C above ambient.
Only if the regrind preserves the original arc radius within ±0.05 mm and removes no more than 0.5 mm of total material. Beyond that you've changed the geometry enough that lift timing shifts, and you've cut into the case-hardened layer — most arc tappets are case-hardened to a depth of 1.0–1.5 mm, and grinding through that exposes softer core steel that galls within a shift.
Practical check: measure case depth on a sectioned scrap tappet from the same batch. If you can keep the regrind inside the upper third of the case layer, regrind is fine. Otherwise replace.
References & Further Reading
- Wikipedia contributors. Tappet. Wikipedia
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