REVISION PROPOSALJuly 12, 2010 – Brett DeVries P.E., Flexco



REVISION PROPOSALJuly 12, 2010 – Brett DeVries P.E., FlexcoCEMA STANDARD NO. 575-2000Bulk Material Belt Conveyor Impact Bed/CradleDiscussionDuring the 2010 CEMA Engineering conference, solicitation was made for help simplifying the rating method used in CEMA standard 575-2000. The request was to eliminate the force capacity rating of the bed classes and only use the impact (potential) energy of the falling material to rate the classes. One challenge is that the current method calculates the flowing force of a homogeneous stream of material in pounds while the impact energy of the large lumps is measured in ft-lbs. These units are not equivalent. Equations for converting the flowing force into an equivalent hypothetical lump mass were needed.In addition, experience has suggested to some CEMA accessory members that the flowing force was not a large contributor to the impact energy delivered to the bed. Once converted to equivalent units, perhaps the calculations would show the flowing force contribution could be neglected. PurposeThis document presents a mathematical method for converting flowing force into an equivalent hypothetical lump mass. It also opens a discussion whether this factor is of continued need in the CEMA 575-2000 standard.MethodIn the idealized case of a conveyor transfer point, potential energy of the material is converted into kinetic energy by the force of gravity, which is then transformed into spring energy at maximum deflection upon impact with the impact bed. In real life, energy is also absorbed by impact with chute walls, impact with the belt, impact within the flowing stream of material, and hysteresis losses within the flexible bed elements. For this discussion, the idealized case will be considered in which no energy is assumed lost to those other events. Not only is it computationally simpler, but it also results in worst case numbers for the rating of the bed.By conservation of energy, potential energy of the falling material equals spring energy of the bed and the energy equation can be written as:mg(h+δ) = 12kδ2Where: m= mass of the lump (lbs)g=gravitational acceleration ( 32.2 ft/sec2)h=drop height (ft)δ=bed deflection (ft)k=bed spring rate (lbf/ft)However, since bed deflection is small compared to the drop height (h) in conveyor applications, for simplicity it will be ignored in the potential energy equations for the remainder of the document.Using the existing formula from CEMA 575-2000 figure 4 for the impact force of a stream of material,F= .1385*Q*handk=F/δandδ=F/k(The existing force equation uses a constant value of .1389 based on gravitational acceleration equal to 32 ft/sec. The value .1385 is calculated using 32.2 ft/sec.)Substituting for k in the energy equation we getmgh=12FδSubstituting for δ we can rewrite the energy equation as :mgh=F22kSubstituting the flowing force equation into the energy equation yields:mgh=12k*.13852*Q2*hSimplifying, the conversion equation becomes:m=7.99*10-4*Q2kWhere Q is in tons per hour, k is in lbs/in and m is in lbm.This equation calculates the hypothetically equivalent mass representing the impact energy of the homogeneous flowing stream. It could be added to the largest lump mass and together with the height used to score the duty class needed using the Impact Energy ratings in Table 1 of the CEMA 575-2000 publication.However, an examination of the equation reveals that unless k is quite small, this value may be negligible. An examination of reasonable k values for impact beds and their effects on this equivalent value follows below.ApplicationIf we use the existing impact bed rating chart (Table 1 from 575-2000) and the conservation of energy equation:12kδ2 and k=Fδ yields 12Fδ=mghIt is interesting to plug the maximum impact energy and the maximum force values from table 1 of the 575-2000 standard into these equations. Maximum impact energy from the table is substituted for mgh and maximum impact force from the table is substituted for F. The following values result from the standard’s Table 1:Light duty: max deflection = .565 inches; k = 15050 lbf/inchMedium duty: max deflection = 2.00 inches; k = 6000 lbf/inchHeavy duty: max deflection = 2.82 inches; k = 6020 lbf/inchIronically, the Table 1 forces the light duty bed to have the stiffest spring constant. This is probably the opposite of standard practice. It is also surprising that including both maximum impact energy and maximum impact force in the standard leads to these design constraints. CEMA should consider dropping the maximum impact force from the rating chart since it is potentially dictating design.However, the calculated k values could be used as a reasonable baseline for estimating a typical k value for impact beds which can now be plugged into the conversion equation. For the sake of argument, assume k values fall somewhere between 3000 lbf/inch and 9000lbf/inch. The following graph illustrates the contribution various tons per hour at different k values contribute to the equivalent hypothetical lump weight. The X axis is Q in tons per hour, the Y-axis is k in pounds-force/inch, and the Z-axis is the calculated lump mass equivalent to the flow rate. From the graph and chart, the maximum equivalent lump size is 9.65 pounds for 6000 tph flow rate and a k value equal to 3000lbf/inch. It can also be seen that this calculated lump mass is very small for flow rates up to 3000 tph. It is also observed that the lump mass decreases as the k of the bed increases for the same flow rate.ConclusionIt seems viable that impact bed classes could be rated solely based on impact energy capacity. If adopted, there are three methods this investigation suggests.Eliminate the flow rate component in the capacity calculation for Impact beds. The contribution to the overall impact energy is small and well within the error encountered when estimating the maximum lump size. The impact energy calculation is also an idealized freefall and conservative. Real systems will absorb energy and probably exceed what the flow rate calculated contribution would make.Include the conversion equation and state it is only necessary for tonnages above 3000 tph. Consult a CEMA member for the k value for your application if needed. This method demonstrates that CEMA is aware of the flowing force and provides a guideline and calculation method which demonstrates technical authority. Downside to this method is that the k value still needs to be obtained for higher tonnage applications. Also, it may be seen as an obstacle to competition since measuring the actual k value for a particular bed is difficult and costly.Establish a minimum k value for each duty class of impact bed. This allows the rating calculation to be performed entirely from data contained within the standard. This is probably not dictating design since the physics of the application seem to be requiring at least a minimum level. However, this option could be objectionable to CEMA members because verifying k values are above the minimum level on existing product may be seen as unnecessary.Respectfully submitted: May 25, 2011Brett DeVries P.E.Flexco ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download