That is a nice summation. Thanks. I recall from Malcolm Smith's Cambridge paper that the tested configuration was an inerter in series with a damper/spring, though that was a single DOF system. So parallel arrangement must be better for a motorsport application, it seems.DaveW wrote:In a good damper (with a correctly sized & loaded reservoir) the gas spring force of a non-through rod damper should constant, and equal to the charge pressure multiplied by the rod area. It acts exactly like preloading a spring, and has (or should have) no impact on the dynamic behaviour on the suspension.GSpeedR wrote:Dave, do you have idea of how the in-damper inerter is configured? I wonder if the resultant inerter forces are in series with the 'normal' damper forces or with the gas spring force(?).
An inerter acts (normally) directly across the damper. It generates a force proportional to its "equivalent mass" times the acceleration on one end of the damper relative to the other. In a similar way, a (coil over) spring generates a change in force proportional to the displacement of one end of the damper relative to the other, and an ideal damper generates a change in force proportional to the velocity of one end of the damper relative to the other.
Hence a suspension transfer function, comprising spring stiffness K, inerter equivalent mass M, and a damper strength C, can be written
,
whereis the frequency, and
is the square root of -1.
This demonstrates that an inerter acts to reduce the dynamic spring rate at low frequencies. It has a number of other characteristics, useful or otherwise, & interesting things start to happen when the dynamic spring stiffness becomes less than zero...
I hope this helps.
So in the undamped case, dynamic stiffness has a zero at