Thermal-error modeling for complex physical systems: the-state-of-arts review

Thermal errors are very important to modern systems including both physical and biological systems. It is well known that temperature rise causes thermal expansion of an object and may induce internal stresses in the object when it is subject to constraints. It is further known that friction is a passive source of heat causing temperature rise in many systems. In this paper we present a critical review of the work, published in the last decade, towards modeling of thermal errors due to the friction-induced heat in complex physical systems. We first develop a framework of the issues so that we can place each significant work in a proper location in the framework. To model a phenomena, we consider that there are two general schools, namely principle-based (or white-box) and empirical-based (or black-box). We further classify the principle-based model into the analytical model and numerical model and the empirical-based model into the static model and dynamic model. We discuss the key studies reported in the literature by examining the issues that the studies have addressed and the modeling techniques or methods that the studies employed. As a result, we conclude several new research divisions such as (1) modeling of the whole physical process of thermal errors (i.e., from the heat source, especially due to friction, to the thermal deformation, and from the deformation to friction, and to the heat further-a closed-loop process), (2) studies of reliability and resiliency of the thermal-error management along with accuracy in prediction of thermal errors, and (3) studies of an integrated principle-based and empirical-based modeling and management approach to thermal errors.