page_title: Engine balance
section_title: Steam locomotives
hierarchical_section_title: Engine balance / Steam locomotives
caption_attribution_description: English: A driving wheel on a steam locomotive at the Mid-Continent Railway Museum in North Freedom, Wisconsin.
context_page_description: Engine balance refers to how the forces are balanced within an internal combustion engine or steam engine. The most commonly used terms are primary balance and secondary balance. Unbalanced forces within the engine can lead to vibrations.
context_section_description: This section is an introduction to the balancing of two steam engines connected by driving wheels and axles as assembled in a railway locomotive.
  The effects of unbalanced inertias in a locomotive are briefly shown by describing measurements of locomotive motions as well as deflections in steel bridges. These measurements show the need for various balancing methods as well as other design features to reduce vibration amplitudes and damage to the locomotive itself as well as to the rails and bridges. The example locomotive is a simple, non-compound, type with 2 outside cylinders and valve gear, coupled driving wheels and a separate tender. Only basic balancing is covered with no mention of the effects of different cylinder arrangements, crank angles, etc. since balancing methods for 3 and 4 cylinder locomotives can be complicated and diverse. Mathematical treatments can be found in 'further reading'. For example, Dalby's "The Balancing of Engines" covers the treatment of unbalanced forces and couples using polygons. Johnson and Fry both use algebraic calculations.
  At speed the locomotive will tend to surge fore-and-aft and nose, or sway, from side to side. It will also tend to pitch and rock. This article looks at these motions that originate from unbalanced inertia forces and couples in the 2 steam engines and their coupled wheels (some similar motions may be caused by irregularities in the track running surface and stiffness). The first two motions are caused by the reciprocating masses and the last two by the oblique action of the con-rods, or piston thrust, on the guide bars.
  There are 3 degrees to which balancing may be pursued. The most basic is static balancing of the off-center features on a driving wheel, i.e. the crankpin and its attached parts. In addition, balancing a proportion of the reciprocating parts can be done with additional revolving weight. This weight is combined with that required for the off-center parts on the wheel and this extra weight causes the wheel to be overbalanced resulting in hammer blow. Lastly, because the above balance weights are in the plane of the wheel and not in the plane of the originating unbalance, the wheel/axle assembly is not dynamically balanced. Dynamic balancing on steam locomotives is known as cross-balancing and is 2-plane balancing with the second plane being in the opposite wheel.
  A tendency to instability will vary with the design of a particular locomotive class. Relevant factors include its weight and length, the way it is supported on springs and equalizers and how the value of an unbalanced moving mass compares to the unsprung mass and total mass of the locomotive. The way the tender is attached to the locomotive can also modify its behaviour. The resilience of the track in terms of the weight of the rail as well as the stiffness of the roadbed can affect the vibration behaviour of the locomotive.
  As well as giving poor human ride quality the rough riding incurs maintenance costs for wear and fractures in both locomotive and track components.
caption: A driving wheel on a steam locomotive showing the crescent-shaped balance weight.
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