Frequency Dependence of Damping and Compliance in Loudspeaker Suspensions

A loudspeakers suspension is commonly not, even by small signals, to be regarded as a simple spring following Hooke’s law – as otherwise presumed by traditional theory. Different types of polymers (rubber or plastic, either vulcanized, foamed or TPE) used for surrounds - besides impregnated textiles used for spiders - have more or less visco-elastic properties; best known is the “creep” effect. This phenomenon in itself is normally of little interest in the audio frequency range. It is mainly a DC phenomenon. As such it manifests itself when a static (DC) force probes the speaker voice coil. At first, it moves fast very close to the expected position, but then it “creeps” slowly a little further (see [1, Fig.1]) A widely accepted model giving account for the visco-elastic effects in loudspeaker surrounds is the so called LOG-model evaluated by M.H. Knudsen and J. G. Jensen [1]. It is an empirical model mathematically describing the effects of visco-elasticity in loudspeaker suspensions. The evaluation is to a high degree based on test loudspeakers with rubber surrounds with a high content of plasticizer combining high compliance and high damping. This is very effective to reduce rim resonances, but less used in high quality loudspeakers today – where “Low Loss Rubber Surround” is currently seen as a marketing feature, as it is expected to have positive impact on sound quality. The plasticized type of surround shows significant creep, followed by compliance and damping increasing towards lower frequencies. The LOG-model is found to give good agreement with measurements, also for loudspeakers with low loss surrounds. However, it is not supported by a theory explaining visco-elastic properties in a physical way. Surrounds today are mostly made from SBR rubber for which - with the additives normally used to adjust stiffness and damping - neither frequency dependency of compliance nor creep are significant problems. Despite this, experience shows that frequency dependent mechanical damping nevertheless might be present. In this paper some modifications to the LOG-model are proposed, and a suggestion is given to explain the phenomenon physically. Frequency dependency of damping - despite lack of other visco-elastic characteristics - is explained as a possible effect of mechanical hysteresis. To derive reliable parameters a new method named “Advanced Added Mass” is evaluated and a new “Hysteresis-model” proposed. Different 2 equivalent circuit models for frequency dependency of compliance and damping are tested in order to find the best usable tool for the loudspeaker engineer.