Crankshaft Balancing

Why a crankshaft has to be balanced

A reciprocating engine is, by its geometry, a vibration machine. Every revolution of the crank, four pistons in an inline-4 — or six, or eight, depending on the layout — accelerate, decelerate, reverse direction, and accelerate again. A piston accelerating means a force is acting on it; an equal and opposite force is acting on the engine block. Multiply by the mass of one piston (typically 300–500 g for a passenger car, 2–4 kg for a truck) and the square of the crank's angular velocity, and the forces in the cylinder head at 6000 rpm reach several kilonewtons. If those forces do not cancel one another out across the cylinders, what is left is transmitted through the engine mounts into the chassis, the steering wheel, the seat, the driver's molars.

An unbalanced engine does more than annoy. The same oscillating force that buzzes the mirrors fatigues the crankshaft main bearings, work-hardens the engine mounts until they crack, loosens fasteners, eats the head gasket, and — at sustained high rpm — can break the crankshaft itself. NVH (noise, vibration and harshness) engineers do not chase tenths-of-a-decibel improvements for fun. They are buying durability with smoothness.

Primary and secondary forces — the algebra

Consider a single piston of mass m attached by a connecting rod of length L to a crank of radius r. The vertical position of the piston, measured from the crank centre, is

y(θ) = r·cos(θ) + √(L² − r²·sin²(θ))

For realistic rod ratios (L/r ≈ 3–4) the square root can be Taylor-expanded, giving the workhorse approximation

y(θ) ≈ r·cos(θ) + (r²/4L)·cos(2θ) + const

Differentiate twice with respect to time, recognise that θ̇ = ω is the crank's angular velocity, and the piston acceleration is

a(θ) = −ω²·[ r·cos(θ) + (r²/L)·cos(2θ) ]

The reciprocating inertia force is F = m·a, and it splits into two distinct components:

F_primary   = m ω² r · cos(θ)       (oscillates at 1× crank speed)
F_secondary = m ω² r² / L · cos(2θ) (oscillates at 2× crank speed)

The primary force is the textbook one — it is what you would have if the connecting rod were infinitely long and the piston motion were perfectly sinusoidal. The secondary force is the finite-rod correction. Its amplitude is smaller than the primary's by the rod ratio r/L (typically a factor of 3 to 4), but it oscillates at twice the frequency and, because no part of the crankshaft itself rotates at 2ω, you cannot cancel it with a counterweight on the crank.

Both forces also produce moments (couples) along the crankshaft, because they act at different points along the shaft's length. A force balance asks whether the linear forces cancel; a moment balance asks whether the torques about a transverse axis cancel. Both must be satisfied for an engine to feel smooth.

The inline-4 — perfect primary, brutal secondary

The canonical inline-4 has a 180° crankshaft with throws at 0°, 180°, 180°, 0°. Cylinder 1 and 4 are 180° apart from cylinders 2 and 3. When 1 and 4 are at top dead centre, 2 and 3 are at bottom dead centre. The primary forces are equal and opposite — they cancel as a pair, and they cancel pair by pair, so the primary moment also cancels. Inline-4s are sometimes praised for "perfect primary balance", and that is technically true.

Now look at the secondary. The secondary force is proportional to cos(2θ). At θ = 0° (cylinders 1 and 4 at TDC) it is at its positive peak. At θ = 180° (cylinders 1 and 4 at BDC, cylinders 2 and 3 at TDC) it is at cos(360°) = +1 — also a positive peak. Both pairs of cylinders contribute secondary force in the same direction at the same time. Instead of cancelling, the secondary forces add. The combined vertical secondary force on an inline-4 is

F_2 = 4 · m ω² · r²/L · cos(2θ)

For a 2.0 L inline-4 with m ≈ 0.4 kg, r = 0.045 m, L = 0.16 m, at 6000 rpm (ω ≈ 628 rad/s) this comes to roughly 1.8 kN — a force the size of a small adult, oscillating up and down 200 times a second. You feel it as a fine, high-frequency buzz that gets worse as the rpm climbs. It is the inline-4's defining vibration, and it is why a 1.5 L Honda Fit can be lively at 7000 rpm while a 2.5 L Camry needs balance shafts to remain civilised at half that speed.

Lanchester balance shafts — cancelling 2ω with 2ω

Frederick Lanchester patented the solution in 1904: add two extra shafts, geared to spin at exactly twice crank speed, in opposite directions, each carrying an eccentric mass. Each shaft produces a rotating force at 2ω. The horizontal components of those two forces cancel because the shafts spin opposite ways. The vertical components add. By choosing the eccentric mass and the phase, the engineer can make the combined vertical force from the balance shafts equal and opposite to the engine's own secondary force. The result: zero net vertical 2ω force, at every crank angle.

The two shafts are usually placed above and below the crankshaft centreline — not for the linear cancellation (which would work with both shafts at any height) but to also cancel the small secondary pitching couple that arises because the inline-4's four cylinders are not all in exactly the same vertical plane. Mitsubishi was the first manufacturer to ship a Lanchester-equipped engine in volume — the 4G54 of the 1970s — and Porsche then licensed the design for the Porsche 944. Today every inline-4 above about 2.0 L of displacement carries balance shafts, either chain-driven from the crank or geared via the oil pump. Below 2.0 L the secondary force is small enough that many manufacturers omit them to save mass, cost, and a few percent of parasitic loss.

The inline-6 — the layout that needs no help

An inline-6 has six cylinders in a row, with crank throws at 0°, 120°, 240°, 240°, 120°, 0°. The arrangement is symmetric about the centre of the crankshaft: cylinders 1 and 6 mirror each other, 2 and 5 mirror each other, 3 and 4 mirror each other. The mirror symmetry means that for every piston accelerating upward there is a mirror-image piston accelerating downward at the same instant — and the two are equidistant from the crank centre, so their moments about the centre also cancel.

Crucially, the symmetry survives at 2ω as well. The cos(2θ) terms come in matched pairs that destructively interfere both in force and in moment. The inline-6 is the only common straight-cylinder layout in which primary forces, primary moments, secondary forces, and secondary moments all cancel without help from counterweights, balance shafts, or special crankshaft planes.

This is why every manufacturer that wanted to advertise smoothness for a century built inline-6 engines. The BMW M30 ran from 1968 to 1995, replaced by the M50 and its descendants — BMW's straight-six is the longest continuous engine family in the industry. Toyota's 2JZ-GTE and the Nissan RB26DETT powered the Supra and Skyline. Cummins, Caterpillar and Detroit Diesel all favour inline-6 heavy-truck engines because the inherent balance is worth the extra crankshaft length when an engine has to run for a million miles. The recent resurgence of inline-6 in passenger cars (Mercedes M256, BMW B58, Ineos Grenadier) is largely a return to physics that was always favourable.

V8 — flat-plane versus cross-plane

A V8 has two banks of four cylinders, usually at a 90° bank angle. The interesting variable is the crankshaft plane.

A cross-plane V8 has crank throws at 0°, 90°, 180°, 270° — four throws spaced 90° apart, forming a cross when viewed end-on. Each bank operates as an inline-4 with a 90° offset, and the geometry is such that the secondary forces of one bank are cancelled by those of the other bank. The result: smooth, low vibration, modest balance shaft requirements (sometimes a single small one in the V), and the characteristic uneven exhaust pulse pattern of an American V8. The firing order alternates banks asymmetrically — for example L-R-L-L-R-L-R-R on a small-block Chevrolet — because the 90° crank pin offsets don't yield a clean cross-bank pattern. That asymmetric exhaust pulse is what makes a Mustang sound like a Mustang and a 911 sound like a 911 doesn't.

A flat-plane V8 has crank throws at 0°, 180°, 180°, 0° — the same as an inline-4, just laid out on a wider crank. Each bank carries a full inline-4's worth of secondary imbalance, and unlike the cross-plane geometry, the two banks add rather than cancel. The engine vibrates noticeably at 2ω. So why use it? Two reasons. First, the firing order becomes a clean L-R-L-R-L-R-L-R, so the exhaust pulses leaving each bank are evenly spaced — perfect for symmetric exhaust scavenging through equal-length headers and into a single collector per bank, which is worth significant peak horsepower. Second, the crankshaft has no big counterweights at 90° and is much lighter, so the engine accelerates faster and revs higher. Ferrari has used flat-plane V8s since the 308 (1975); the Porsche 918 Spyder, McLaren MP4-12C, and Ford Mustang GT350's "Voodoo" 5.2 L all chose flat-plane crankshafts for the same trade.

The other common layouts at a glance

Layout	Primary force	Primary moment	Secondary force	Secondary moment	Typical fix
Inline-3 (120°)	Balanced	Unbalanced (rocking couple)	Balanced	Unbalanced	One balance shaft
Inline-4 (180°)	Balanced	Balanced	Unbalanced (2× vertical)	~Balanced	Lanchester balance shafts
Inline-5 (72°)	Balanced	Unbalanced	Balanced	Unbalanced	Counterweights tuned per throw
Inline-6 (120°)	Balanced	Balanced	Balanced	Balanced	None needed
V6, 60° bank (120° crank)	Balanced	Unbalanced	Balanced	Unbalanced	Heavy counterweights, sometimes a balance shaft
V6, 90° bank (uneven)	Unbalanced	Unbalanced	Unbalanced	Unbalanced	Split-pin crank + balance shaft
V8 cross-plane	Balanced	Balanced	Balanced	~Balanced	Counterweights only
V8 flat-plane	Balanced	Balanced	Unbalanced	Unbalanced	Accepted as the cost of revs
Flat-4 boxer	Balanced	Small rocking couple	Balanced	Small rocking couple	Live with the couple
Flat-6 boxer	Balanced	Balanced	Balanced	Balanced	None needed
V12 (60° bank)	Balanced	Balanced	Balanced	Balanced	None — two inline-6s share a crank

The pattern is consistent: layouts whose firing order has 360°/N symmetry around the crank — inline-6, boxer-6, V12, V8 cross-plane — get force and moment cancellation for free. Everything else trades smoothness for compactness, exhaust character, or weight.

Counterweights — what they do and what they don't

Every crankshaft except a flat-plane V8 with a "no-counterweight" lightweight build has heavy lobes opposite each throw. Their job is twofold:

• Cancel the rotating mass of the connecting-rod big end. The big end of the rod, plus a fraction (typically a few grams) of the rod's overall mass that follows the crankpin's circular path, is a rotating mass. Like any rotating mass, it produces a centrifugal force at 1× crank speed. A counterweight of equal moment on the opposite side of the crank centre cancels it.
• Partially cancel the reciprocating primary force in V-engines and unbalanced inline layouts. In an inline-4, where the primary forces already cancel across cylinders, the counterweights only need to deal with the rotating big-end mass. In a 90° V8, however, the primary force of one cylinder is not exactly cancelled by another; counterweights are sized to partially absorb the difference (typically 50% of the reciprocating mass is rolled into the bob weight for V8 balancing).

What counterweights cannot do is cancel a reciprocating force at any frequency other than 1ω. Their angular position rotates at crank speed; their centrifugal force is therefore a vector at 1ω. To produce a 2ω force, the angular position would have to rotate at 2ω — which is what a Lanchester balance shaft does, and what no part of the crankshaft itself can.

Static vs dynamic balancing — what the spin balance machine measures

A finished crankshaft, before it is assembled into an engine, passes through two distinct balancing operations.

Static balancing. The crank is supported on knife edges or low-friction rollers. If any throw is heavier than the rest, gravity rotates the crank until that throw points downward. Material is drilled out of the heavy side (or, less often, lead or tungsten plugs are added) until the crank rests at any angle. This catches gross errors in the casting or forging — chunks of extra material left in counterweight lobes, oil holes drilled off-centre. A statically balanced crank has zero net mass offset from the rotation axis.

Dynamic balancing. A crank can be statically balanced and yet still produce a rotating couple if its residual unbalanced masses are located at different axial positions. Picture a perfectly symmetric crank with two small equal weights added — one at the front, on the "top", and one at the back, on the "bottom". Statically the two weights cancel: the crank rests anywhere. But when you spin it, the top weight makes the front of the crank want to swing outward while the bottom weight makes the back swing outward — a couple at 1ω that wobbles both ends of the shaft. This is dynamic imbalance, and it is felt as a "wallow" rather than a buzz.

Dynamic balancing is performed on a horizontal spin-balance machine: the crank is supported on bearings at both ends, spun up to 500–1000 rpm, and force sensors at each support read the magnitudes and phases of the residual imbalance forces. Software then locates exactly where on the crank to remove material (usually by drilling into a counterweight) to bring both bearings' imbalance below the spec — typically 5 g·mm or better per main journal for a passenger-car crank, and even tighter (1–2 g·mm) for a high-performance racing crank.

Bob weights are essential for getting the V- and inline-engine balance correct in this stage. A bob weight is a steel clamp the technician bolts onto each crankpin to simulate the rotating mass that will eventually live there — the big end of the connecting rod, plus a defined fraction (usually 50 percent) of the reciprocating mass (piston, rings, pin, small end). The crank is then balanced as a system. Skip the bob weights and the counterweights end up undersized once the rods are fitted; the engine will buzz at idle and shake at high rpm.

Worked example — how much secondary force on a 2.0 L inline-4?

Take a generic 2.0 L inline-4 four-cylinder. Specifications:

bore          = 86 mm
stroke        = 86 mm   → r = 43 mm = 0.043 m
rod length    = 144 mm  → L = 0.144 m
piston + rings + pin + small-end of rod = m ≈ 0.40 kg
engine speed  = 5000 rpm  → ω = 5000·2π/60 ≈ 524 rad/s

One piston's secondary force amplitude is

F_2,one = m ω² r² / L
        = 0.40 · 524² · 0.043² / 0.144
        ≈ 0.40 · 274576 · 0.001849 / 0.144
        ≈ 1410 N per piston

All four pistons contribute in phase, giving a combined vertical secondary force amplitude of

F_2,total = 4 × 1410 N ≈ 5.6 kN

oscillating at 2 × 5000 / 60 ≈ 167 Hz. That is a force comparable to the engine's own weight, applied vertically twice per revolution. Without balance shafts, that force is transmitted to the chassis through three or four engine mounts, each of which would have to be tuned to attenuate a specific frequency. With Lanchester shafts, the residual transmitted force drops to a few percent of the unbalanced value, and standard hydraulic mounts handle the rest with ease.

Common pitfalls and misconceptions

• "Inline-4 is perfectly balanced". Only the primary force and primary moment are balanced. The secondary force adds across all four cylinders and is what every Lanchester shaft is fighting.
• "Counterweights cancel secondary forces". They cannot. Counterweights rotate at 1ω and produce a force at 1ω. Secondary forces are at 2ω. Only something that rotates at 2ω — a balance shaft — or a layout whose secondaries inherently cancel can deal with them.
• "A statically balanced crank is good enough". It is not. The dynamic couple at the operating rpm can be many times the static imbalance load. Modern OEM specs require dynamic balancing on a spin-balance machine.
• "Flat-plane V8s are smooth because they're V8s". Cross-plane V8s are smooth. Flat-plane V8s vibrate roughly as much as an unbalanced 4-cylinder, on both banks. The trade is for revs and a sharper exhaust note.
• "Boxer means horizontally opposed, so the pistons cancel". Two opposing pistons whose wrist pins sit on the same crank throw move in the same direction and add their forces. Boxer engines specifically use opposing throws so the opposing pistons move in opposite directions and cancel. A "180° V-engine" (Ferrari Boxer 512 BB, despite the name) uses shared throws and is not a true boxer.
• "More cylinders = smoother". Not automatically. An inline-5 is smoother than an inline-4 in terms of frequency content but still leaves an unbalanced primary moment. The geometry matters more than the count.
• "Adding balance shafts costs nothing". A few percent of crankshaft power, weight, packaging volume, and one more chain or gear to fail. Performance engines sometimes delete them at the cost of a noisier engine bay.

Why your Subaru and the BMW M3 don't feel the same

Pick any engine and you can predict, from the layout alone, roughly how it will feel:

• Subaru Outback (flat-4 boxer, 2.5 L). Primary and secondary forces cancel; a tiny rocking couple remains. Feels smoother than an inline-4 of the same displacement, but the small couple gives the engine a distinctive growl. No balance shafts needed.
• Porsche 911 (flat-6 boxer, 3.0–4.0 L). Primary and secondary, forces and moments all cancel. The smoothest layout for its physical length; this is why Porsche has stayed with it since 1963 even though it is structurally more complex than an inline-6.
• BMW M3 G80 (inline-6, 3.0 L S58). Pure inherent balance, no balance shafts, very stiff crankshaft. The benchmark for a daily-drivable performance engine.
• Ferrari 458 (flat-plane V8, 4.5 L). Carries an inline-4's worth of secondary buzz on both banks but spins to 9000 rpm with a clean exhaust pulse pattern. The vibration is the price of admission for the noise.
• Ford Mustang GT (cross-plane V8, 5.0 L). Smooth, characteristic burble, revs to 7250 rpm but no higher. Heavy crankshaft, lazy by Ferrari standards, lasts forever.
• Toyota Camry (inline-4, 2.5 L). Twin Lanchester balance shafts cancel the inevitable secondary force; the result is an engine that feels inline-6-smooth from idle to redline despite being a four. The shafts are roughly 7% of the engine's friction budget — a tax happily paid for refinement.