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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.
When an unbalanced system is rotating, periodic linear and/or torsional forces are generated which are perpendicular to the axis of rotation. The periodic nature of these forces is commonly experienced as vibration. These off-axis vibration forces may exceed the design limits of individual machine elements, reducing the service life of these parts.
In a straight-six engine and flat-six engine, the rocking forces are naturally balanced out, therefore balance shafts are not required. V6 engines are inherently unbalanced, regardless of the V-angle. Any inline engine with an odd number of cylinders has a primary imbalance, which causes an end-to-end rocking motion.
A static balance (sometimes called a force balance [2] [3]) occurs when the inertial axis of a rotating mass is displaced from and parallel to the axis of rotation.Static unbalances can occur more frequently in disk-shaped rotors because the thin geometric profile of the disk allows for an uneven distribution of mass with an inertial axis that is nearly parallel to the axis of rotation.
When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium. [17]: 566 Hence, equilibrium occurs when the resultant force acting on a point particle is zero (that is, the vector sum of all forces is zero). When dealing with an extended body, it is also necessary that the net torque be zero.
Another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point. The numerator gives the total moment that is then balanced by an equivalent total force at the center of mass. This can be generalized to three points and four points to define projective coordinates in the plane, and in space ...
The forces acting on a body add as vectors, and so the total force on a body depends upon both the magnitudes and the directions of the individual forces. When the net force on a body is equal to zero, then by Newton's second law, the body does not accelerate, and it is said to be in mechanical equilibrium .
A balanced rudder is a rudder in which the axis of rotation of the rudder is behind its front edge. This means that when the rudder is turned, the pressure of water caused by the ship's movement through the water acts upon the forward part to exert a force which increases the angle of deflection, so counteracting the pressure acting on the after part, which acts to reduce the angle of deflection.
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