Variable Speed or Cone Gearing is a power-transmission arrangement that changes output speed by shifting a belt or roller across a stepped or tapered cone, giving the operator multiple ratios from a single input shaft. Henry Maudslay's early-1800s screw-cutting lathes used cone pulleys for exactly this reason. The mechanism trades a fixed gear pair for a continuum (or stepped set) of effective diameters, so one motor can drive many cutting speeds. Modern Reeves drives and lathe headstocks still use the principle to deliver 4:1 to 10:1 speed ranges without a gearbox.
Variable Speed Cone Gearing Interactive Calculator
Vary the driver and driven pulley diameters to see speed ratio, ideal torque change, and belt-tension diameter-sum error.
Equation Used
The cone pulley speed ratio is the driver effective diameter divided by the driven effective diameter. For a stepped cone pair, the matching step diameters should add to the same target sum so belt tension stays nearly constant.
- No belt slip
- Diameters are effective pitch diameters
- Ideal torque multiplier is inverse of speed ratio
- Matched steps keep the diameter sum equal to the target sum
Operating Principle of the Variable Speed or Cone Gearing
Variable Speed or Cone Gearing, also called a Variable Speed Bevel Gear in some older drafting texts, works by changing the effective pitch diameter of the driving or driven element while keeping the shaft centres fixed. In its simplest form — the cone pulley on a bench lathe — you stop the machine, shift a flat or V-belt from one step to the next, and the ratio between motor and spindle changes in discrete jumps. In its continuous form — a Reeves drive or PIV — two opposing cones (or split-sheave pulleys) move axially so the belt rides on a smoothly varying diameter, giving you any ratio in the range without stopping.
The geometry has to be right or the belt will not behave. On a stepped cone pulley the sum of the two matching step diameters must stay constant — if step 1 on the headstock is 60 mm and the matching countershaft step is 120 mm, the next pair might be 80 mm and 100 mm, but 60 + 120 must equal 80 + 100. Get this wrong by even 2 mm and the belt either goes slack on one pair or stretches on the next, and you would be amazed how fast a slack flat belt walks off a cone. On a Reeves-type continuous drive the spring-loaded sheave halves must close in synchrony — if one sheave lags by more than about 0.5 mm of axial travel the belt rides cocked, the V-flanks wear unevenly, and you get a buzzing vibration that telegraphs straight up the column.
Failure modes are predictable. Belt slip under load is the number one complaint, almost always traced to glazed belts, undersized contact arc on the smallest step, or a worn shifter fork that lets the belt drift to the edge. On Reeves drives, the killers are spring fatigue in the moving sheave and grit ingress into the splined hub — once the hub binds, you lose the variable part of variable speed.
Key Components
- Stepped Cone Pulley (driver): A series of fixed-diameter steps machined or cast on a single hub, typically 3 to 5 steps. Each step diameter is chosen so that pairing it with the matching countershaft step gives a useful spindle RPM. Concentricity must be within 0.05 mm TIR or the belt will slap audibly at the seam.
- Mating Cone Pulley (driven): Inverted geometry on the countershaft or spindle so that step diameters sum to a constant — this keeps belt centre distance fixed and tension constant across all ratios. Step face must be parallel within 0.1 mm to keep the belt tracking centred.
- Belt (flat, V, or wedge): Transmits torque between cones via friction. Flat belts on classical lathes ride on crowned steps; V-belts on Reeves drives ride between the sheave flanks. Belt section dictates power capacity — an A-section V-belt handles roughly 1.5 kW per belt at 1000 RPM.
- Movable Sheave Halves (Reeves type): On continuously variable drives, one or both sheaves split into two halves that move axially under spring or hydraulic actuation. As one sheave closes, its mating sheave opens, keeping belt length constant while changing the effective diameter.
- Shifter Fork or Control Lever: On stepped designs, a manual fork lifts the belt step-to-step. On Reeves drives, a screw-jack handwheel moves the control sheave, typically giving a 4:1 to 10:1 speed range with sub-1% repeatability between settings.
- Spring or Tensioner Assembly: Maintains belt preload as ratio changes. On Reeves drives, a coil spring of around 200–400 N/mm rate sits behind the floating sheave. Spring fatigue beyond 15% relaxation is the leading cause of slip in old Reeves units.
Where the Variable Speed or Cone Gearing Is Used
Variable Speed or Cone Gearing shows up wherever a single prime mover has to drive a process at multiple speeds without the cost or complexity of a true gearbox. The Variable Speed Bevel Gear variant — where one of the cones carries bevel teeth instead of a friction surface — survives in a few specialty mills and older agricultural equipment. The cone pulley itself remains everywhere a hobbyist or production lathe earns its keep.
- Machine tools: South Bend Heavy 10L bench lathe — 4-step cone pulley headstock giving spindle speeds from 35 to 1200 RPM with back-gear engaged.
- Industrial conveyors: Reeves Vari-Speed Motodrive on a Hytrol EZLogic accumulation conveyor at a regional UPS hub, trimming line speed from 30 to 90 m/min to balance with downstream sortation.
- Bottling and packaging: PIV continuous variable drive on a Krones filler-to-labeller link belt at a Coca-Cola bottling plant in Wakefield, England, where line speed has to track upstream filler output within ±2 bottles/min.
- Drill presses: Walker Turner 20-inch radial drill — 5-step cone pulley with countershaft cone giving 60 to 1800 RPM for spindle speed selection across drill diameters from 3 mm to 32 mm.
- Textile machinery: Variable Speed Bevel Gear ratio change on a Saurer ring spinning frame to taper draw ratio during bobbin build at a worsted mill in Bradford.
- Agricultural equipment: Reeves drive on a John Deere 9000-series combine harvester header drive — letting the operator match cutter-bar speed to crop condition without stopping.
- Woodworking: Delta DP-350 12-inch drill press — 5-step poly-V cone pulley giving 250 to 3000 RPM for boring brass through hardwood.
The Formula Behind the Variable Speed or Cone Gearing
The core calculation is the ratio between input and output speed as a function of the engaged step diameters. At the low end of the typical speed range — small driver step against large driven step — you trade speed for torque, useful for threading or large-diameter facing. At the high end you flip the pair, getting fast spindle RPM for small drills or finish cuts but losing torque proportionally. The sweet spot for most general-purpose lathe work sits around the middle pair, where belt wrap angle is balanced and spindle speed lands in the cutting-speed band for mild steel at typical work diameters.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Nout | Output (driven) shaft speed | RPM | RPM |
| Nin | Input (driver) shaft speed from motor | RPM | RPM |
| Ddriver | Engaged step pitch diameter on the driving cone | mm | in |
| Ddriven | Engaged step pitch diameter on the driven cone | mm | in |
Worked Example: Variable Speed or Cone Gearing in a Colchester Student lathe headstock cone
You are setting the spindle speed on a Colchester Student Mk1 lathe in a vocational training shop in Coventry. The motor runs a 1440 RPM 1.5 kW Brook Crompton 4-pole at the countershaft. The headstock cone has 4 steps with pitch diameters 50, 75, 100, and 125 mm. The countershaft cone is the inverse — 125, 100, 75, 50 mm — so the diameters sum to 175 mm on every pair. You need to pick the step pair for finish-turning a 40 mm mild-steel shaft at a target cutting speed of about 30 m/min.
Given
- Nin = 1440 RPM
- Ddriver options = 125, 100, 75, 50 mm
- Ddriven options = 50, 75, 100, 125 mm
- Workpiece diameter = 40 mm
- Target cutting speed = 30 m/min
Solution
Step 1 — work out the required spindle RPM for the cut. Cutting speed v = π × D × N, so N = v / (π × D):
Step 2 — at the nominal middle pair (driver 100 mm, driven 75 mm), compute output speed:
That overshoots by a factor of 8 — the back-gear (typically 6:1 reduction on a Colchester) brings 1920 down to 320 RPM, close to target. Acceptable for finish work but a touch fast.
Step 3 — at the low end of the speed range (driver 50 mm, driven 125 mm), through back-gear:
96 RPM gives a cutting speed of about 12 m/min on the 40 mm bar — too slow, the tool will rub instead of cut, and you will see a glazed surface and rapid edge wear on HSS. This pair is for threading or large-diameter work, not 40 mm bar.
Step 4 — at the high end (driver 125 mm, driven 50 mm), direct drive (no back-gear):
3600 RPM on a 40 mm bar gives 452 m/min — way past HSS territory and into carbide-only speeds. The Colchester spindle is rated to 2500 RPM max, so this pair is forbidden on this workpiece. It exists for small-diameter drilling and reaming.
Result
The correct selection is the middle pair (100 mm driver / 75 mm driven) engaged through back-gear, giving a spindle speed of about 320 RPM and a cutting speed near 40 m/min — slightly fast but in-band for HSS on mild steel. Across the range, the low pair creeps at 96 RPM (good for threading 1" Whitworth but useless for a 40 mm finish cut), the middle pair sits in the sweet spot, and the high pair at 3600 RPM is over the spindle limit and would only be selected for small drills. If you measure 280 RPM instead of the predicted 320, check three things in order: (1) belt slip under load — glazed flat belts on a Colchester drop output by 10–15%, (2) a worn back-gear bull-wheel bushing letting the gear walk axially and disengage partially, or (3) a stretched flat belt sitting on a smaller effective diameter than the step face suggests.
When to Use a Variable Speed or Cone Gearing and When Not To
Variable Speed or Cone Gearing competes against fixed-ratio gearboxes, electronic VFDs (variable frequency drives), and modern CVTs. Each wins on different axes — cost, ratio range, control resolution, and maintenance burden. The Variable Speed Bevel Gear variant, while clever, is largely obsolete now that VFDs are cheap.
| Property | Variable Speed or Cone Gearing | Fixed-Ratio Gearbox | VFD + AC Motor |
|---|---|---|---|
| Speed range (typical) | 4:1 to 10:1 | Fixed single ratio per gear | 20:1 to 100:1 with constant torque to base speed |
| Ratio resolution | Stepped: 3-5 ratios. Reeves: continuous | Discrete only | Continuous, 0.1 RPM resolution |
| Capital cost (per kW) | Low — $50-200 for a stepped cone, $400-800 for a Reeves drive | Medium — $200-500 | Medium — $150-400 for VFD plus motor |
| Reliability / lifespan | 10-20 years on stepped, 5-10 on Reeves before sheave-spring fatigue | 20-40 years with proper oil changes | 10-15 years; capacitors and IGBTs age |
| Maintenance interval | Belt inspection every 500 hours; Reeves spring check yearly | Oil change every 5000-10000 hours | Cooling fan and capacitor check every 2 years |
| Load capacity | Limited by belt — typical 0.5 to 30 kW | Up to MW range | Limited by motor frame, typically up to 500 kW commercially |
| Application fit | Manual machine tools, retrofit jobs, infrequent ratio changes | High-torque continuous duty, fixed-speed processes | Modern automation, frequent speed changes, closed-loop control |
| Complexity | Mechanically simple, no electronics | Mechanically complex but mature | Electronically complex, mechanically simple |
Frequently Asked Questions About Variable Speed or Cone Gearing
At minimum output speed the driven sheave is fully closed and the driver sheave is fully open, so the belt is riding on the smallest effective diameter on the input side. Wrap angle there can drop below 120°, which is the friction limit for a V-belt under load. The belt slips, the spring momentarily pushes the sheave closed harder, grip recovers, the belt grabs, and the cycle repeats — that's your oscillation.
Fix: don't run a Reeves drive in the bottom 10% of its rated range under load. If you genuinely need the low speed, add a fixed reduction gearbox downstream so the Reeves runs in its mid-band.
Ask how often the operator changes speed. If it's a few times per shift — typical lathe or drill press work — a stepped cone is cheaper, more reliable, and the operator will not miss continuous variability. If speed has to track an upstream process in real time (line balancing, tension control, harvester ground speed matching crop), you need the Reeves.
The other deciding factor is dirt. Reeves splined hubs hate grit. In a foundry, brewery, or anywhere with airborne particulate, a stepped cone with a guarded belt outlasts a Reeves drive 3 to 1.
Three usual suspects. First, belt thickness — the formula assumes the belt rides on the step pitch diameter, but a thick flat belt rides 2-4 mm above the step face, raising effective diameter and skewing your ratio by 5-8% on small steps. Second, belt creep under torque — V-belts elastically slip 1-2% even when not visibly slipping. Third, motor slip — a 4-pole induction motor labelled 1440 RPM is actually doing 1420-1435 RPM under load, not synchronous 1500.
Add all three together and a 'predicted 320 RPM' calculation lands somewhere between 295 and 315 in the real world. That's normal. If you're 20% off, something else is wrong.
Yes, and a lot of restoration shops do exactly this — leave the belt on the middle step and use a VFD on the motor to fine-tune speed within that band. But don't throw the cone pulley away. A VFD running an induction motor below about 30% of base speed loses torque badly because cooling drops with shaft RPM. The cone pulley gives you a coarse mechanical ratio change so the motor stays in its happy zone (40-100% base speed) while the VFD handles fine adjustment.
Combined, you get a 30:1 usable speed range with full torque, which neither system delivers alone.
Both are continuously variable, both use moving sheaves. The Reeves uses a friction V-belt — quiet, cheap, slips under shock load (which is sometimes desirable as a torque limiter). The PIV (Positive Infinitely Variable) uses a chain with radial slats that mesh with grooves on the sheave faces, giving positive engagement and no slip.
PIV handles 5x the torque of an equivalent Reeves but costs 3-4x as much and is noisier. Choose Reeves for general industrial drives up to 30 kW, PIV for high-torque applications like rolling mill auxiliary drives or stone-crusher feeders.
Yes — Variable Speed Bevel Gear is an older drafting-room name for the same family of mechanisms, used when one of the cones carried bevel teeth meshing with a movable pinion rather than a friction belt. The kinematic principle is identical: shift the engagement point along a tapered element to change the effective ratio.
The toothed variant survives in a few legacy machines but fell out of favour because tooth engagement on a continuously varying diameter is hard to keep clean — modern designs use friction belts or chains exclusively.
Two causes, both geometric. Either the cone steps aren't crowned (flat belts need a slight crown — typically 0.3-0.5 mm rise across a 50 mm step face — to self-centre), or the countershaft and headstock shafts aren't parallel. Even 1° of misalignment over a 600 mm centre distance drives the belt sideways at about 10 mm/sec.
Diagnostic: with the belt removed, lay a straightedge across both step faces of a matched pair. Gap should be even top and bottom. If it's wedge-shaped, shim the countershaft pillow blocks until parallel. Then re-crown the steps if needed — a cylindrical grinder makes quick work of it.
References & Further Reading
- Wikipedia contributors. Continuously variable transmission. Wikipedia
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