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Monster Media 1996 #14
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Monster Media No. 14 (April 1996) (Monster Media, Inc.).ISO
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mixing10.zip
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SHAFT.TXT
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1991-08-02
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SHAFT RATING PROGRAM
INSTRUCTIONS
Insert the disk into the A drive or install all the included
programs onto your hard disk. The shaft rating program is
called SHAFT.EXE , but it will not work without the other
files also named SHAFT on this disk.
The program is started in the usual manner by giving the
command SHAFT. The program will first ask if you want to
run the program or load an existing data file. Type in an R
to run the program.
The shaft rating screen will be shown and you must input the
information required for the shaft. First give the number of
impellers. You may input up to 6 impellers.
Next input the data for the Bearing span in inches, the total
shaft length (inches), the diameter of the shaft (inches) and
the rotation speed of the mixer in rpm.
The agitator data must also be provided for the number of
impellers specified. Input the weight of the impeller in
lbs, the length to the top bearing in inches , the impeller
diameter in inches and the hydraulic BHP of each individual
impeller. The Original mixer program can be run to provide
some of this data.
All data must be inputted with no zeros. Press the F10 key
when all the data is in.
The Right and Left arrow keys can be used to correct data
input if errors are noted. The number of impellers however
can only be changed after the F10 key has been pressed and
the other data input requirements are satisfied.
The program calculates the torque and moment of the impellers
in inch-lbs from the BHP and impeller data. The program will
calculate the minimum acceptable shaft diameters for the
stress and tensile requirement. The design yield and tensile
stress for the material are added on the shaft material
screen discussed later.
The Equivalent weights, Natural Frequency and the ratio of
the agitator RPM to the natural frequency are calculated for
top supported and Shafts with bottom steady bearings.
The command line permits you to print the screen results,
Revise the input and do case studies, Perform disk
operations such as saving and recalling data files and to
modify the material information.
The shaft Materials window is addressed by pressing the
letter M. on the command line.
The Shaft Material properties are specified for Steel in the
as a default. You may override this data and input new
Density, Elastic Modulus and Design Tensile an Shear Stress
as you require. To accept the numbers provided by the
program just press the return key. Press F10 when all data
is satisfactory.
METHODOLOGY
TORQUE The torque is calculated by the following equation.
TORQUE = SUM(63025 * BHP OF IMPELLERS / RPM)
MOMENT The Bending Moment is calculated as the sum of the
product of the hydraulic forces and the distance from the
individual impellers to the first bearing.
MOMENT = SUM( 19000 * BHP OF IMPELLER * LENGTH / (RPM*DIAM))
DIAMETER STRESS and DIAMETER TENSILE are calculated by the
formulas given below. They are based upon the torque and
Moment values and the design allowable shear and tensile
stress imputted in the materials section. These design
stresses for steel are 6000 psi shear and 10,000 tensile.
TOP SUPPORTED SHAFT
EQUIVALENT WEIGHT
The equivalent weight for the Overhung shaft calculates the
weights of a multi-impeller system as thought all the
impellers were at the end of the shaft. With corrections to
the impeller weight for the impellers higher up in the shaft.
The weight of 1/4 the shaft is also added into the equivalent
weight.
The formula use is as follows for agitators 1 to n. where w
is the mass per inch of the shaft.
Weq = W1 + W2(L2/L1)^3 + .. + Wn(Ln/L1)^3 + w*L1/4
L1 is total length to the end impeller .. Number 1.
NATURAL FREQUENCY
The natural frequency is calculated by the standard method as
given in MECHANICAL VIBRATIONS BY DEN HARTOG. and in the
Marks Standard Handbood for mechanical Engineers.
frequency in rpm = 60* omega / ( 2 * 3.1416 )
omega = ( K / M )^0.5
M = Weq / 389 ; equiv. wt in lb/in sec2
g = 389
K = 3*EI / L1^3 ; for single support
E = ELASTIC MODULUS = 30 * 10^6 FOR STEEL
I = MOMENT OF INERTIA = 0.05 * DIAM ^4 for round
cylinders
L1 = distance in inches from top bearing to lowest
impeller. Here called number one.
BOTTOM STEADY BEARING
The Equivalent weight of the bottom supported shaft
calculates an equivalent weight of a mass located at the
midpoint of the shaft. 50% of the shaft weight is included
in this calculation.
EQUIVALENT WEIGHT for multiple impellers is calculated by
the formula given in OldShues Fluid Mixing Technology on page
412. as follows
Weq = B1*W1 + B2*W2 + .. Bn*Wn
Bn = 8.895*((L1-Ln)/L1)^2*(1 - (L1-Ln)/L1)^3*(3+(L1-Ln)/L1)
Note that 1/2 the shaft weight must also be added to Weq
calculated from this equation.
NATURAL FREQUENCY
The same equations and method are used as described above for
the overhung shaft except that the value for K has changed.
K = element stiffness for double clamped shaft as given in
Marks Mech.Engr HandBood 8th Ed. 5-70 Table 2.
K = 192 * E*I / L1^3
Where E,I, and L1 are as defined previously.
EFFECT OF DAMPING
The effects of viscous damping are not included in this
program, but can be estimated from the graph given on page 5-
71 of Marks Handbook. 50% damping will increase the natural
frequency by roughly 70 percent.
SHAFT DEFLECTION can be calculated by the relationship
deflection ( inch ) = (187.7/Nc)^0.5 Where Nc is Natural
Frequency in RPM.
Note: If the distance to the first agitator ( the bottom
one) equals the shaft length , then the bottom steady bearing
case will not be calculated.
The program uses L1 the length to agitator 1 as the total
shaft length for the top supported vibration calculations.