Development of an Experimental Setup for the Measurement of the Coefficient of Restitution under Vacuum Conditions

Summary

The coefficient of restitution is a parameter that describes the loss of kinetic energy during collision. Here, a free-fall setup under vacuum conditions is developed to be able to determine the coefficient of restitution parameter for particles in micrometer range with high impact velocities.

Abstract

The Discrete Element Method is used for the simulation of particulate systems to describe and analyze them, to predict and afterwards optimize their behavior for single stages of a process or even an entire process. For the simulation with occurring particle-particle and particle-wall contacts, the value of the coefficient of restitution is required. It can be determined experimentally. The coefficient of restitution depends on several parameters like the impact velocity. Especially for fine particles the impact velocity depends on the air pressure and under atmospheric pressure high impact velocities cannot be reached. For this, a new experimental setup for free-fall tests under vacuum conditions is developed. The coefficient of restitution is determined with the impact and rebound velocity which are detected by a high-speed camera. To not hinder the view, the vacuum chamber is made of glass. Also a new release mechanism to drop one single particle under vacuum conditions is constructed. Due to that, all properties of the particle can be characterized beforehand.

Introduction

Powders and granules are everywhere around us. A life without them is impossible in modern societies. They appear in food and drinks as grains or even flour, sugar, coffee and cocoa. They are needed for daily used objects like the toner for laser printer. Also the plastic industry is not imaginable without them, because plastic is transported in granular form before it is melted and given a new shape. After Ennis et al.¹ at least 40% of the value added to the consumer price index of the United States of America by the chemical industry (agriculture, food, pharmaceuticals, minerals, munitions) is connected to particle technology. Nedderman²

Protocol

1. Experiments with Particles Coarser or Equal to 700 µm

1. Preparation of the experimental setup
   1. Remove the sleeve and lift the top cover of the vacuum chamber. Place the baseplate consisting of the desired wall material in the vacuum chamber. Turn the lower part of the vacuum chamber sideways to slide in the plate carefully by hands.
   2. Place exactly one of the particles to be examined with tweezers in the center of the baseplate. Afterwards adjust the height of the camera with a tripod in such a way that the baseplate is in the lowest quarter of the visual field and focus on the particle.
   3. Remove the particle using tweeze....

Results

For the analysis glass particles with a diameter of 100 µm to 4.0 mm were dropped from an initial height of 200 mm on a stainless steel baseplate with a thickness of 20 mm.

Figure 6 shows the mean values as well as the maximum and minimum values for the COR depending on the particle size for atmospheric pressure and vacuum. The mean value of the COR is found to be approximately e = 0.9 for particles gre.......

Discussion

To validate the functionality of the experimental setup in general, tests with similar material combinations as in other established setups (Antonyuk et al.⁵ and Wong et al.¹³) were performed. Since very similar results were obtained, the general procedure seems to work. Nevertheless, caution has to be taken towards the procedure and the analysis and further improvements are necessary.

The main limitation of the experimental setup is the quality of the v.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
High-speed camera Olympus i-SPEED 3	Olympus		High-speed camera to capture the particle impact
Screen Olympus i-SPEED CDU	Olympus		Screen to work with the high-speed camera
Light source Olympus ILP-2	Olympus		Light source necessary for taking videos at high frame rates
Vacuum pump Alcatel Pascale 2005 D	Alcatel		Vacuum pump to generate the vacuum during the experiments
Vacuum gauge Alcatel CFA 212	Alcatel		Vacuum gauge to measure the vacuum level
i-SPEED Software Suite (Control version)	Olympus		Software to evaluate the videos
Glass beads	Sigmund Lindner GmbH		SiLibeads Type P (0.700, 1.588, 2.381, 2.780, 3.680, 4.000 mm) SiLibeads Type S (0.1-0.2, 0.2-0.3, 0.3-0.4 mm) http://www.sigmund-lindner.com (see supplier's website for more information about the glass properties)
Safety goggles