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.