An Analytical Model for Force Estimation on Arms of Concrete Mixers

Claudio Braccesi Perugia University Dep. of Industrial Engineering Via G. Duranti 1, 06125 Perugia Italy Luca Landi* Perugia University Dep. of Industrial Engineering Via G. Duranti 1, 06125 Perugia Italy ABSTRACT The main task of our research is to achieve a proper analytical model to describe the forces exchanged between the mixing arms of a mechanical mixing machine and concrete during the whole mixing process. The model has been validated through experimental tests on a real type of mixer. The behavior of the sand- cement mix is very different in the three principal phases of a possible mixing operation: Phase 1: first mixing phase, sand and concrete are inserted in the mixer without water, “dry - phase”, Phase 2: a proper quantity of water is added to the dry mix for final mixing, “wet phase”, Phase 3: final mixing for complete homogenization of the mix. The electrical power necessary in the three phases is very different and in close relation to very different theoretical model that we will discuss later in the article. The main correlations between the geometrical shape of a so called omega mixer and the force exchanged is presented in the article. At the end of the article the coupling between the theoretical and the experimental data is presented. 1 INTRODUCTION The mechanical design of a mechanical mixer is based on forces exchanged between the mixing arms - blades and the concrete. These forces change abruptly during the mixing process but the precise entities of these forces is ignored [1]. Also in some latter published article tests on concrete mixing machine have been carried out and a precise correlation between the paste composition and the power necessary for the mixer is investigated [2]. Nowadays when a new machine is to be designed some very rough calculations for power consumption is usually made. So the design process is based on rough calculation of blade forces using an experimental investigation on a particular mixer already designed with a particular concrete mix [3]. These forces cannot be used for the design process of innovative machines nor for force estimation on machine of the “same family” but of different size. For fatigue strength investigation of a new family of mixer is still necessary to build some prototypes of the main components of the machine and some “early design stage problems” for fatigue problems are expected. On the other hand there is a lot of research focused on the behavior of granular material and concrete material as the ones in [4-9]. If high performance concrete is to be obtained, all the studies agree on the necessity of a controlled phase of mixing with an automated process. Moreover the controlled addiction of small quantities of different additives can abruptly change the final behavior of these materials, see for examples the articles [10-12]. In this paper we will show how the well known Brinch-Hansen formula [4] and the Bingham theory of fluids [8] can be used to describe the behaviour of concrete respectively in the so called dry and final mixing phases. The application of these two general different analytical models for concrete in the different phases, to a specific case of mixer will be presented in the paper. The full mixing process will be investigated in the article focusing the force exchanged between the mixer and the concrete. This model covers all the main phases of the granular mixing in the worst case of a wrong loading procedure (higher forces): 1. loading of the dry material in the tank , taking into account the loading law (constant flow– step law), 2. water addition phase , also if the transient behavior of the material is quite impossible to predict, it is