A Caltech Library Service

An Investigation of Some of the Laws Governing the Grinding of Materials in Ball and Tube Mills with Special Reference to the Size Distributions of the Particles in the Product


Knapp, Robert Talbot (1929) An Investigation of Some of the Laws Governing the Grinding of Materials in Ball and Tube Mills with Special Reference to the Size Distributions of the Particles in the Product. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/REHD-1C28.


1. General Statement of the Problem. The purpose of this investigation was to determine the effects of some of the factors involved in the grinding of dry materials in laboratory size ball mills. The major part of the work has been directed towards ascertaining the effects of variations in,

(1) Size of the material fed to the mill,

(2) Size of the balls used in the mill,

(3) Ratio of the amount of charge to the amount of balls in the mill,

(4) Time of grinding,

upon the size distribution of the resulting product and upon the amount of new surface produced for equal amounts (i.e. times) of grinding.

2. Defects of Old Experimentation. This problem has been attacked several times before. Practically all of the old investigations, however, have been handicapped by lack of information concerning the size distribution of the fine part of the product, i.e., that which passed through the finest reliable screens. This handicap has been very serious, as can be appreciated when it is realized that from 10 to 95 percent of the material involved lies in this class.

3. Defects of Recent Experimentation. The recent experimenters have tried to overcome this difficulty in many ways. All of the accounts of their work that could be obtained show that their methods for the determination of this size distribution of fine particles has been such a laborious process that the experimenters have been limited to the study of comparatively few samples from a correspondingly few runs in their experimental mills.

This has made it impossible to cover very wide variations of the different factors involved in the grinding operation; or to allow of many check runs, either of mill operation, or of size distribution of the product.

4. Scope of the Present Investigation. The present investigation has endeavored to cover a wider field in a more intensive manner, in an attempt to reach conclusions that would be more universal in character than have hitherto been possible.

5. Method of Attack on the Previous Defects. When the problem was first considered it was felt that the possibility of success depended upon the development of a method for determining the size distribution of the fine material quickly and accurately. Therefore the work was divided into two parts; first, the development of a method and apparatus for size distribution analysis; second, a study of some of the phenomena of grinding in a laboratory mill, carried on with the aid of this apparatus.

6. Summary of Results.

a. Size Distribution Apparatus. An instrument, called the Microneter, has been developed by means of which it is possible to make routine analyses of the size distribution of particles ranging from 8 to 74 microns in diameter. The lower limit of this range can be shifted downward to 2 to 3 microns if desirable, at the sacrifice of speed. For routine analysis work with a lower limit of 8 microns two men and a helper have completed 30 analyses a day, continuously.

b. Laboratory Mill Studies. A large number of runs have been made in the laboratory jar mill. The major results obtained to date are illustrated most clearly by two series, Series E and No. 2 Time Runs. These two groups represent about three hundred separate runs, exclusive of any checks. The principal results are summarized below,

(1) Rittenger's Law, that equal expenditures of energy produce equal increments of surface, holds over wide limits for given conditions of ball size and initial charge particle size.

(2) The grinding efficiency is not affected by variations in the amount of charge present in the mill Of the ball load is kept constant. However, the capacity is slightly decreased if the charge is larger than that required to fill the voids between the balls.

(3) The size distribution of particles in that part of the product passing the 200 mesh sieve depends upon the ratio of the initial particle diameter to the ball size. The larger this ratio the larger is the amount of very fine (-10 micron) material produced. The smaller this ratio the more uniform is the size gradation.

(4) The grinding efficiency depends upon the ratio of particle diameter/ball diameter3. There is an optimum value for this ratio and deviations in either direction cause losses in efficiency.

(5) A tentative theory is offered that the amount of energy required for grinding depends upon the modulus of resilience of the material and the size reduction desired.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Unknown, Unknown
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1929
Record Number:CaltechTHESIS:01302019-172828535
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11367
Deposited By: Mel Ray
Deposited On:31 Jan 2019 22:34
Last Modified:16 Aug 2023 22:06

Thesis Files

[img] PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page