ERRATA BELT CONVEYORS FOR BULK MATERIALS, 7th edition. As of February 1, 2015

Transcription

1 Conveyor Equipment Manufacturers Association 567 Strand Ct., Suite, Naples, Florida Tel: (39) Fax: (39) Web Site: ERRATA BELT CONVEYORS FOR BULK MATERIALS, 7th edition As of February 1, 015 New Errata Items are listed below in 'Red'. The pages following the listed Errata will reflect the 'error' in red on the left hand side and then the corrected page will be on the right hand side. CHAPTER 4 Page 69 Move close parentheses in equation 4.15 Change of equation reference in A meaning (Equation 4.1 should read Equation 4.5 ) Page 7 Change of figure reference in figure 4.1 (Figure 4.4 should read Figure 4.11 or 4.13 ) Page 74 Change of equation reference in equation 4.5 (Equation 4.6 should read Equation 4.15 ) Change in elements of equation 4.6 (b c should read w s in denominator) Change in elements of equation 4.8 as follow: Page 75 Change of figure reference in figure 4.9 (Figure 4.5 should read Figure 4.3 or Figure 4.1 with A=A s ) After value of A s, add w s = Change in elements of d s formula as follow: Page 76 CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED Lacks a Square function (It should read ) in equation 4.3 Page 78 Change of equation reference in figure 4.37 (Figure 4.8 should read Equation 4.11 and 4.13 ) Remove one of sub w s (should read ) in the formula of A f. THE VOICE OF THE CONVEYOR INDUSTRY OF THE AMERICAS

2 Page 80 - Change table reference in figure 4.38 (Table 4.44 should read Table 4.43 ) CHAPTER 5 Page Change in figure (It should read K3A 500 (rpm)/n (rpm)) CHAPTER 6 Page Change in elements of formula in figure 6.15 as follow: Page Change Css = x m ss to x μ ss in nomenclature table. Page Change Ris to Rris in equation 6.5 Page Add ft(m) at the end of Sin meaning (It should read n ft (m)) Page Change in elements of formulas in figure 6.40 as follow: Page Change in the KbiR-L meaning (Equation 6.60 should read Equation 6.57 ) Page With: Dm Equation 6.70 should read dm from Equation 4.17 for Dm using A from Equation Pages for As, = bulk density, Si = idler spacing CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED - Corrections in table 6.47 to Type Rubber values from constant a1 to the end. Page Type 1 table should be labeled Type 3 and Type 3 table should be labeled Type 1 in table THE VOICE OF THE CONVEYOR INDUSTRY OF THE AMERICAS

3 Page In figure 6.50, Typos (9.4 o C) should read (-9.4 o C) in operating temperature. Page Pj should to be added in KbiR-S formula - T0 = 9.4 C should read T = C - Move the 3 lines starting at From table 6.47 up to ahead of s = - Replace (15 F - 3 F)/1.8 with -9.4 C; 9.4 C in the numerator should read -9.4 C - The value of s should read in xf formula Page Pj should to be added in KbiR-S formula - Move From F calculation:... down to directly above "Since the value wiw - Move the finish xp calculation below of From Table C should read C in xp formula ( Places) - Eliminate from xp calculations Page Remove Pj in Tbi formula - Add formula for KbiR-S including Pj below Calculate KbiR-S - Delete entire line "BW = 48 in..." - Move the line "Xld =..." to below "Use Rbi = 1.0 line - Add x Pj; x and change the result to = in KbiR-S formula and move it up to under For fabric belts: csd =... - Remove x Pj in the Note and 0.5 should read Page Change in wrrir and wrl meanings (lbf/im should read lbf/in ). CHAPTER 8 Page 38 - In Equation 8.33, in superscript should be added in D formula as follow: CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED CHAPTER 1 Page In Figure 1.73, ɸ in the drawing should be ɸi THE VOICE OF THE CONVEYOR INDUSTRY OF THE AMERICAS

4 Page 55 - In Figure 1.95, Replace: 'Vs=Tangential Velocity, fps, of the cross sectional area center of gravity of the load shape' with: Vs=Velocity of the load cross section used for plotting the trajectory Page In Figure 1.109, Greek letters are incorrect, there is a font error for phi describing the angle of incline of the conveyor. It is showing the 'capital phi' not in lower case as it should be. (ϕ should be φ ( places) and γ should be ϒ (1 place)). Page In the paragraph between Equation and Equation 1.11; the reference to Table 4.4, should read Table In the Figure 1.110, this should read: Vs = Velocity of the load cross section used for plotting the trajectory: 1. Belt velocity, V, is used as the velocity of the material at its center of mass if the discharge point is at the tangency of the belt to discharge pulley (Vs = V). Velocity of the material at its center of mass, Vcg, is used as the velocity of the material for all other conditions of discharge after the point of belt to discharge pulley tangency. (Vs= Vcg) APPENDIX B Page Change definition of Vs to be consistent with changes in Chapter 1 Trajectories. Vcg also added CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED THE VOICE OF THE CONVEYOR INDUSTRY OF THE AMERICAS

5 CAPACITIES, BELT WIDTHS AND SPEEDS 4 CEMA Standard Cross Sectional Area, A s s, for standard CEMA three equal roll troughing idlers based on the average CEMA center roll length circular surcharge surface and the CEMA standard belt edge. wmc calculated from b w and with b we set to the standard dimensions: A s = BW r s sch sin ( s) cos( s ) + b c b wmc sin ( ) sin( ) cos + b wmc ( ) Equation 4.15 A s, CEMA standard cross sectional area w = b c + b wmc cos( ) Equation 4.16 with standard cross sectional area A s A A s = Standard material cross sectional area based on design criteria [ft (m )] (Equation 4.1) = CEMA Standard Cross Sectional Area, bulk material cross sectional area based on three equal roll CEMA troughing idler, the surcharge angle with circular top surface, and standard edge distance [ft (m )] BW = Belt width, [in (mm)] b c b d = Dimensionless ratio of the effective upper surface of the belt above the center roll to the belt width, BW = Dimensionless ratio of maximum depth of material above the belt at the center roll to the belt width, BW b we = Dimensionless ratio of the standard edge distance to the belt width, BW b wmc = Dimensionless ratio of the length of material on the wing roll to the belt width, BW d m w = Dimensionless ratio of depth of the material above the belt at the center roll to the belt width, BW = Dimensionless ratio of the widest part of the load to the belt width, BW = Idler trough angle, (degrees when used with a trig function, otherwise radians) s = Material surcharge angle, (degrees when used with a trig function, otherwise radians) r sch = Dimensionless ratio of the radius tangent to the surcharge angle at the belt edge to the belt width, BW CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED d m = b wmc sin( ) + b c sin s ( ) move close parenthesis to the end cos + ( ) b wmc sin( s ) ( 1cos( s ) Equation 4.17 d m standard cross sectional area, A s 69

6 CAPACITIES, BELT WIDTHS AND SPEEDS 4 CEMA Standard Cross Sectional Area, A s s, for standard CEMA three equal roll troughing idlers based on the average CEMA center roll length circular surcharge surface and the CEMA standard belt edge. wmc calculated from b w and with b we set to the standard dimensions: A s = BW r s sin ( s) cos( s ) + b c b wmc sin ( ) sin( ) cos + b wmc ( ) Equation 4.15 A s, CEMA standard cross sectional area w = b c + b wmc cos( ) Equation 4.16 with standard cross sectional area A s A = Standard material cross sectional area based on design criteria [ft (m )] (Equation 4.5) A s = CEMA Standard Cross Sectional Area, bulk material cross sectional area based on three equal roll CEMA troughing idler, the surcharge angle with circular top surface, and standard edge distance [ft (m )] BW = Belt width, [in (mm)] b c b d = Dimensionless ratio of the effective upper surface of the belt above the center roll to the belt width, BW = Dimensionless ratio of maximum depth of material above the belt at the center roll to the belt width, BW b we = Dimensionless ratio of the standard edge distance to the belt width, BW b wmc = Dimensionless ratio of the length of material on the wing roll to the belt width, BW d m w = Dimensionless ratio of depth of the material above the belt at the center roll to the belt width, BW = Dimensionless ratio of the widest part of the load to the belt width, BW = Idler trough angle, (degrees when used with a trig function, otherwise radians) s = Material surcharge angle, (degrees when used with a trig function, otherwise radians) r sch = Dimensionless ratio of the radius tangent to the surcharge angle at the belt edge to the belt width, BW CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED d m = b wmc sin( ) + b c sin s ( ) cos + ( ) b wmc sin( s ) ( 1cos( s ) Equation 4.17 d m standard cross sectional area, A s 69

7 4 CAPACITIES, BELT WIDTHS AND SPEEDS Example: Non-standard Edge Distance Assume: CEMA standard three equal roll troughing idler, Q = 1800 tph, V = 500 fpm, m = 60 lbf/ft 3 Given: BW = 48.0 inches, = 35 degrees, s = 0 degrees From Figure 4.4: b c = and b w = A = a' b' c' Q = V m 1800 t lbf 000 h t 500 ft = min lbf min h ft 3 = cos() sin( s ) s sin( s ) cos( s ) ( ) 3,600,000 lbf h =.0 ft lbf 1,800,000 h ft ( ) + cos( ) sin( ) = ( ) ) (0.340) = = cos = b c sin( ) + b c ( ) sin( s ) ( sin s ( s) cos( s ) = ( 0.340) ( ) = = = b c A BW sin( s ) sin s ( s) cos( s ) ( ) in = - ft ( 48.0) = = b wmc = -b' + Figure 4.11 or 4.13 ( b' ) - 4 a' c' = ( ) (0.1166) a' = = b we = b w - b wmc = = B we = b we BW = in =.6 in (65 mm) CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED Figure 4.1 Example of calculating non standard belt edge distance from known idler, belt width and cross sectional area, A 7

8 4 CAPACITIES, BELT WIDTHS AND SPEEDS Example: Non-standard Edge Distance Assume: CEMA standard three equal roll troughing idler, Q = 1800 tph, V = 500 fpm, m = 60 lbf/ft 3 Given: BW = 48.0 inches, = 35 degrees, s = 0 degrees From Figure 4.11 or 4.13: b c = and b w = A = a' b' c' Q = V m 1800 t lbf 000 3,600,000 lbf h t 500 ft = h =.0 ft min lbf lbf ,800,000 min h ft 3 h ft ( ) + cos( ) sin( ) = cos() sin( s ) sin s ( s) cos( s ) ( ) = ( ) ) (0.340) = = cos = b c sin( ) + b c ( ) sin( s ) ( s sin( s ) cos( s ) = ( 0.340) ( ) = = b c A = BW sin( s ) s sin( s ) cos( s ) ( ) in = - ft ( 48.0) = = b wmc = -b' + ( b' ) - 4 a' c' = ( ) (0.1166) a' = = CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED b we = b w - b wmc = = B we = b we BW = in =.6 in (65 mm) Figure 4.1 Example of calculating non standard belt edge distance from known idler, belt width and cross sectional area, A 7

9 4 CAPACITIES, BELT WIDTHS AND SPEEDS s, is greater than the standard center roll effective width, b c 4.15 If w s > b c recalculate A s (Equation 4.6) using: b wmc = b s b c cos ( ) Equation 4.5 d ms = A BW b s s sin s ( ) - cot ( s) ( ) sin - ( ) 4 b c - b s cos( ) Equation 4.6 d ms Ws d s = b b s c b s Ws D ms = d ms BW Equation 4.7 D ms wws d w tan( )+b ms + b s 1 sin( s ) 1 tan( s ) Equation 4.8 d s CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 74

10 4 CAPACITIES, BELT WIDTHS AND SPEEDS s, is greater than the standard center roll effective width, b c If w s > b c recalculate A s (Equation 4.15) using: b wmc = w s b c cos ( ) Equation 4.5 d ms = A BW w s s sin s ( ) - cot ( s) ( ) sin - ( ) 4 b c - w s cos( ) Equation 4.6 d ms d s = w b s c w s D ms = d ms BW Equation 4.7 D ms tan( )+ d ms + w s 1 sin( s ) 1 tan( s ) Equation 4.8 d s CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 74

11 CAPACITIES, BELT WIDTHS AND SPEEDS Figure 4.3 or Figure 4.1 with A =A s 4 Example: Height of Bulk Material between Skirtboards, D s and D ms Given: BW = 48.0 inches, =35 degrees, s = 0 degrees From Figure 4.5 b c = b s = A s = 1.8 ft W s = Calculate the heigth of material rubbing on the skirtboards: A s BW b s s sin( s ) - cot ( sin s) - ( ) b ( c- b s ) 4 cos( ) d ms = b s in ft - 1 (48.0) (0.340) - (.7475) = ( 0.376) -( ) ) [ (.7)( ] = = ( ) = D ms = d ms BW = =.5 in (6.5 mm) W s d W s Calculate the maximum depth of material between the skirboards: d s = b s b c tan( )+b ms + b s 1 sin( s ) 1 tan( s ) = x = = D s = d s BW = x 48.0 = 10. in (3 mm) Figure 4.9 make experience based choices to modify the recommended measurements. The width of the skirtboards as, samplers or dust collection, or anticipated mistracking. Multiple loading points on a belt require either skirting the multiple load points as one continuous skirtboard, or making successive skirtboards wider in the direction of belt travel. The lump size discussion in this chapter governs the belt width and therefore skirtboard should be generous enough to handle the lump sizes, and to allow for the material volume in the turbulent loading area having a loose bulk density. The height and length of the skirtboard is often aid in controlling dust exiting the skirtboarded area. CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 75

12 CAPACITIES, BELT WIDTHS AND SPEEDS 4 Example: Height of Bulk Material between Skirtboards, D s and D ms Given: BW = 48.0 inches, =35 degrees, s = 0 degrees From Figure 4.3 (or Figure 4.1 with A = A s ) b c = w s = A s = 1.8 ft Calculate the height of material rubbing on the skirtboards: A s BW b s s sin( s ) - cot ( sin s) - ( ) b ( c- b s ) 4 cos( ) d ms = b s in ft - 1 (48.0) (0.340) - (.7475) = ( 0.376) -( ) ) = 0.115[ (.7)( ] = ( ) = D ms = d ms BW = =.5 in (6.5 mm) Calculate the maximum depth of material between the skirtboards: d s = w s b c tan( )+b + w s 1 sin( s ) 1 d ms tan( s ) = x = = D s = d s BW = x 48.0 = 10. in (3 mm) Figure 4.9 make experience based choices to modify the recommended measurements. The width of the skirtboards as, samplers or dust collection, or anticipated mistracking. Multiple loading points on a belt require either skirting the multiple load points as one continuous skirtboard, or making successive skirtboards wider in the direction of belt travel. The lump size discussion in this chapter governs the belt width and therefore skirtboard should be generous enough to handle the lump sizes, and to allow for the material volume in the turbulent loading area having a loose bulk density. The height and length of the skirtboard is often aid in controlling dust exiting the skirtboarded area. CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 75

13 4 CAPACITIES, BELT WIDTHS AND SPEEDS 100% Full, Edge To Edge, Cross Sectional Area, A f porting the conveyor system should be designed for the dead loads plus the live material load as if the belt f, d f and r schf are introduced for calculations for a we wmc w and b w is used to calculate A f and d f. The s with b we set to zero. d f Figure 4.30 A f, Cross sectional area dimensionless nomenclature for 100% full, edge to edge, Equation 4.31 r schf A f = BW Equation 4.3 A f b c w f A f s r schf CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED b w 1-cos r schf = ( ( ) b c + cos ( ) sin( s ) r schf s - sin ( s) cos( s ) + b c b w xsin( ) +b sin( )cos w ( ) ß d f = b w sin( )+ b c +b w cos ( ) 1 sin( s ) - 1 tan( s ) Equation 4.33 d f 76

14 4 CAPACITIES, BELT WIDTHS AND SPEEDS 100% Full, Edge To Edge, Cross Sectional Area, A f porting the conveyor system should be designed for the dead loads plus the live material load as if the belt f, d f and r schf are introduced for calculations for a we wmc w and b w is used to calculate A f and d f. The s with b we set to zero. d f Figure 4.30 A f, Cross sectional area dimensionless nomenclature for 100% full, edge to edge, Equation 4.31 r schf A f = BW Equation 4.3 A f b c w f A f s r schf CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED b w 1-cos r schf = ( ( ) b c + cos ( ) sin( s ) r schf s - sin ( s) cos( s ) + b c b w xsin( ) +b w ß sin( )cos ( ) d f = b w sin( )+ b c +b w cos ( ) 1 sin( s ) - 1 tan( s ) Equation 4.33 d f 76

15 4 CAPACITIES, BELT WIDTHS AND SPEEDS Example: 100% Full, Edge to Edge, Belt Cross Sectional Area, A f Given: BW = 48.0 inches, =35 degrees, s = 0 degrees From Figure 4.8 b c = b w = cos r schf = ( ( )) b c + cos( ) sin( s ) ( = ) = = A f = BW r schf s - sin ( s) cos( s ) + b c b w sin( ) +b sin( ) cos ww x ( ) 4608 = in + [ ] ft = 3.0 [ ]= =.6 ft (0.4 m ) d f = b w sin( )+ b c +b w cos( ) 1 sin( s ) - 1 tan( s ) = = = D f = d f BW = = 1.4 in (314 mm) Equation 4-11 and 4-13 Figure 4.37 CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 78

16 4 CAPACITIES, BELT WIDTHS AND SPEEDS Example: 100% Full, Edge to Edge, Belt Cross Sectional Area, A f Given: BW = 48.0 inches, =35 degrees, s = 0 degrees From Equations 4.11 and 4.13 b c = b w = cos r schf = ( ( )) b c + cos( ) sin( s ) ( = ) = = A f = BW r schf s - sin ( s) cos( s ) + b c b w sin( ) +b sin( ) cos w x ( ) 4608 = in + [ ] ft = 3.0 [ ]= =.6 ft (0.4 m ) d f = b w sin( )+ b c +b w cos( ) 1 sin( s ) - 1 tan( s ) = = = D f = d f BW = = 1.4 in (314 mm) Figure 4.37 CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 78

17 4 CAPACITIES, BELT WIDTHS AND SPEEDS General Applications: Capacity Derating one conveyor to a common cause of transfer point spillage and plugging is the time it takes for the discharged load to settle down and reach the receiving belt speed and direction. It is common practice, in and bulk material degradation. Coal Fired Power Generating Plant: Capacity Derating plants and handling other bulk materials subject to degradation and the hazards associated with spillage, leakage and dust generation. It is common practice not to load conveyors handling these bulk materials to their capacity in order to reduce degradation, accommodate surge loads and to reduce spillage and Example: Capacity Derating Required capacity: Q = 400 tph Bulk Material Properties: m = 90 lbf ft s= 0deg 3 ft Initial design choices: BW = 48 in = 35 deg V = 600 Angle of incline, = 0 deg min Calculate conveyed cross sectional area, A (Ref. Equation 4.5) 400 t Q A = = h 1 h lbf ,000 lbf 60 min t V m 600 ft = min = 1.48 ft lbf lbf 90 54,000 min ft 3 min ft 4.43 Derate loading of cross section to 85%, DF = 1.18 Minimum A s = A DF = 1.48 ft 1.18 = 1.75 ft (0.16 m ) From Table 4.44 at = 35 and s = 0 deg: 48-inch belt, A s = ft (0.168 m ) The initial design choice (BW = 48 in and V = 600 fpm) appears appropriate from a capacity standpoint Figure 4.38 Capacity derating example CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 80

18 4 CAPACITIES, BELT WIDTHS AND SPEEDS General Applications: Capacity Derating one conveyor to a common cause of transfer point spillage and plugging is the time it takes for the discharged load to settle down and reach the receiving belt speed and direction. It is common practice, in and bulk material degradation. Coal Fired Power Generating Plant: Capacity Derating plants and handling other bulk materials subject to degradation and the hazards associated with spillage, leakage and dust generation. It is common practice not to load conveyors handling these bulk materials to their capacity in order to reduce degradation, accommodate surge loads and to reduce spillage and Example: Capacity Derating Required capacity: Q = 400 tph Bulk Material Properties: m = 90 lbf ft s= 0deg 3 ft Initial design choices: BW = 48 in = 35 deg V = 600 Angle of incline, = 0 deg min Calculate conveyed cross sectional area, A (Ref. Equation 4.5) 400 t Q A = = h 1 h lbf ,000 lbf 60 min t V m 600 ft = min = 1.48 ft lbf lbf 90 54,000 min ft 3 min ft Derate loading of cross section to 85%, DF = 1.18 Minimum A s = A DF = 1.48 ft 1.18 = 1.75 ft (0.16 m ) From Table 4.4 at = 35 and s = 0 deg: 48-inch belt, A s = ft (0.168 m ) The initial design choice (BW = 48 in and V = 600 fpm) appears appropriate from a capacity standpoint Figure 4.38 Capacity derating example CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 80

19 BELT CONVEYOR IDLERS 5 Step No. 3: K Effect Of Load On Predicted Bearing L 10 Life R ) is less than the CEMA load rating of the class of idler selected the earing L life will increase. K Factor Figure 5.30 K L Step No. 4: K 3A Effect Of Belt Speed On Predicted Bearing L 10 Life CEMA L life ratings are ased on r. lower seeds increase life and faster seeds decrease life. igre. shows this relationshi. K 3A Factor CIL (Calulated Idler Load) ILR (Idler Load Rating) K = CIL ILR 1 K = CIL ILR 500 (rpm) L 10 n (rpm) Belt Speed Roll Speed = Roll Circumference (rpm) Figure 5.31 K 3A ct o t o rct ar L 10 o CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 3.3 K 3A (Roller Bearings) 3.0 (Ball Bearings) 109

20 BELT CONVEYOR IDLERS 5 Step No. 3: K Effect Of Load On Predicted Bearing L 10 Life R ) is less than the CEMA load rating of the class of idler selected the earing L life will increase. K Factor Figure 5.30 K L Step No. 4: K 3A Effect Of Belt Speed On Predicted Bearing L 10 Life CEMA L life ratings are ased on r. lower seeds increase life and faster seeds decrease life. igre. shows this relationshi. K 3A Factor CIL (Calulated Idler Load) ILR (Idler Load Rating) K = CIL ILR 1 K = CIL ILR K 3A 500 (rpm) n (rpm) Belt Speed Roll Speed = Roll Circumference (rpm) Figure 5.31 K 3A ct o t o rct ar L 10 o CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 3.3 (Roller Bearings) 3.0 (Ball Bearings) 109

21 6 BELT TENSION AND POWER ENGINEERING T nenergy Gravity paths due to the potential energy change in the bulk material and belt for a height change H n. The tension is sensitive to the direction of travel so that with uphill movement the tension increases and a downhill or negative slope angle causes reduction in this component of tension along the conveyance direction as gravity pulls the conveyor down the slope. Gravity or potential energy is considered to have a continuous effect on tension along the length of any side belt cancel each other out from the perspective of total conveyor T e but need to be included in circuit calculations to identify the local tension at any point. T Hn = H n ( W b + W m ) Equation 6.14, Flight tension change due to elevate n ), the belt and the load Where: T Hn = Tension change in fligh "n" due to lift H n = Elevation change in flight "n" W b = Weight of the belt per unit length from manufacturer W m = Weight of the bulk material on the belt per unit length 5.9 8, ,958 T H5 = H 5 ( W b + W m ) = 44.0 ft (6.3 lbf lbf Add ) = 7,68.8 lbf (3,304 kgf) ft ft Figure 6.15 Example calculation of tension needed to elevate material in flight 5 n as the net change in elevation Bulk Material Acceleration Work or kinetic energy must be provided to the bulk material to accelerate it to match the speed of the belt. The accelerating force is provided by the belt through an increase in tension at the loading point(s) in the direction of belt movement. Using the amount of Kinetic Energy added to the bulk material allows the calculation of belt tension effects without concern for the acceleration rate or the dynamics involved with impact, although these can be important issues for belt and chute wear and material degradation. CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 148

22 6 BELT TENSION AND POWER ENGINEERING T nenergy Gravity paths due to the potential energy change in the bulk material and belt for a height change H n. The tension is sensitive to the direction of travel so that with uphill movement the tension increases and a downhill or negative slope angle causes reduction in this component of tension along the conveyance direction as gravity pulls the conveyor down the slope. Gravity or potential energy is considered to have a continuous effect on tension along the length of any side belt cancel each other out from the perspective of total conveyor T e but need to be included in circuit calculations to identify the local tension at any point. T Hn = H n ( W b + W m ) Equation 6.14, Flight tension change due to elevate n ), the belt and the load Where: T Hn = Tension change in flight "n" due to lift H n = Elevation change in flight "n" W b = Weight of the belt per unit length from manufacturer W m = Weight of the bulk material on the belt per unit length T H5 = H 5 ( W b + W m ) = 5.9 ft (6.3 lbf lbf ) = 8,738.4 lbf (3,958 kgf) ft ft Figure 6.15 Example calculation of tension needed to elevate material in flight 5 n as the net change in elevation Bulk Material Acceleration Work or kinetic energy must be provided to the bulk material to accelerate it to match the speed of the belt. The accelerating force is provided by the belt through an increase in tension at the loading point(s) in the direction of belt movement. Using the amount of Kinetic Energy added to the bulk material allows the calculation of belt tension effects without concern for the acceleration rate or the dynamics involved with impact, although these can be important issues for belt and chute wear and material degradation. CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 148

23 BELT TENSION AND POWER ENGINEERING 6 Skirtboard Seal Friction A skirt seal which rides on the belt is commonly used to contain dust and small particles. The calculation predicts the resistance as the product of a friction factor and the unit normal force between the moving belt and the seal without inuence from the material loading. The values are provided below apply to a generic rubber edge seal as shown in igure. for ight n that is sealed along its full length on both sides. Where: F ss F ss L n Figure 6.0 Skirtboard seal drag on conveyor belt Equation 6.1 T ssn, Calculation of skirtboard seal drag T ssn = Tension change due to belt sliding on skirtboard sealed flight, "n" C ss = m ss F ss R rss Frictional resistance to the belt movement μ ss = Sliding friction coefficient between belt and seal rubber (dimensionless) F ss = Effective normal force between belt and seal = Modifying Factor (dimensionless) R rss μ T ssn = C ss L n R rss L 1 = 15.0 ft μ ss = 1.0 F ss = 3.0 lbf / ft R rss = 1.0 C ss = lbf x 1.0 = 6.0 lbf/ft ft T ss1 = C ss L 1 R rss = 6.0 lbf 15.0 ft 1.0 = 90.0 lbf (40.9 kgf) ft CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED Figure 6. T ss1, Skirtboard seal example calculation arious specialty sealing products are available to perform this function with varying performance life and drag. Typical values for design are μ ss. and ss = 3.0 lbfft. kgf/m) of skirt seal for conventional slab rubber skirt board seals shown in igure.0. ss is calculated by multiplying by a factor of because it is assumed that both sides of the belt have a skirt seal. Therefore an estimate of.0 lbf/ft.0 151

24 BELT TENSION AND POWER ENGINEERING 6 Skirtboard Seal Friction A skirt seal which rides on the belt is commonly used to contain dust and small particles. The calculation predicts the resistance as the product of a friction factor and the unit normal force between the moving belt and the seal without inuence from the material loading. The values are provided below apply to a generic rubber edge seal as shown in igure. for ight n that is sealed along its full length on both sides. Where: F ss F ss L n Figure 6.0 Skirtboard seal drag on conveyor belt Equation 6.1 T ssn, Calculation of skirtboard seal drag T ssn = Tension change due to belt sliding on skirtboard sealed flight, "n" C ss = µ ss F ss R rss Frictional resistance to the belt movement μ ss = Sliding friction coefficient between belt and seal rubber (dimensionless) F ss = Effective normal force between belt and seal = Modifying Factor (dimensionless) R rss T ssn = C ss L n R rss L 1 = 15.0 ft μ ss = 1.0 F ss = 3.0 lbf / ft R rss = 1.0 C ss = lbf x 1.0 = 6.0 lbf/ft ft T ss1 = C ss L 1 R rss = 6.0 lbf 15.0 ft 1.0 = 90.0 lbf (40.9 kgf) ft CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED Figure 6. T ss1, Skirtboard seal example calculation arious specialty sealing products are available to perform this function with varying performance life and drag. Typical values for design are μ ss. and ss = 3.0 lbfft. kgf/m) of skirt seal for conventional slab rubber skirt board seals shown in igure.0. ss is calculated by multiplying by a factor of because it is assumed that both sides of the belt have a skirt seal. Therefore an estimate of.0 lbf/ft.0 151

25 BELT TENSION AND POWER ENGINEERING (0.68) Drag for One Roll lbf-in (N-m) 5.0 (0.57) 4.0 (0.45) 3.0 (0.34).0 (0.3) 1.0 (0.11) 0 0 K iv = Slope Figure 6.4 Drag from a single idler roll rpm T ir = K iv R riv ( N i rpm)+ K is R is Equation 6.5 ir, Drag from a single idler roll T isn = K it T ir n r Equation 6.6 T isn, Idler seal friction CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED S in L n ris D r 153

26 BELT TENSION AND POWER ENGINEERING (0.68) Drag for One Roll lbf-in (N-m) 5.0 (0.57) 4.0 (0.45) 3.0 (0.34).0 (0.3) 1.0 (0.11) 0 0 K iv = Slope Figure 6.4 Drag from a single idler roll rpm T ir = K iv R riv ( N i rpm)+ K is R r is Equation 6.5 ir, Drag from a single idler roll T isn = K it T ir n r Equation 6.6 T isn, Idler seal friction CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED S in L n D r 153

27 6 BELT TENSION AND POWER ENGINEERING Where: T ir = Change in tension for single roll from idler seal resistance lbf (N) T isn = Change in tension in flight "n" from idler seal resistance lbf (N) D r = Idler roll diameter in (mm) K iv = Slope of torsional speed curve per roll lbf-in N-m rpm Table 6.9 rpm K is = Seal torsional resistance per roll at 500 rpm lbf-in (N-m) Table 6.9 K it = Temperature correction factor (dimensionless) Figure 6.7 K itb = Curve fit constants for temperature correction [R 1 (K 1 )] L n n r N i R ris R riv S in K IT Note: R = Rankine, K = Kelvin [T R = F (T K = C K)] = Length of flight "n" ft (m) = Number of rolls per idler set = Actual rpm of idler based on diameter and belt speed rpm = Modifying Factor for seal torsional resistance (dimensionless) = Modifying Factor for torsional speed effect (dimensionless) = Carrying or return idler spacing in flight "n" ft(m) CEMA C&D CEMA E CEMA Historical (-40) (-8) (-18) (-4) (4) (16) (7) (38) (49) Temperature F ( C) Figure 6.7 K it Teerre rrei r re r ier r idler seal drag and it is accounted for by the multiplying factor, K it ember products hae been independently tested and the euations published reect seal drag change with temperature. This comparison of results with the CEMA Historical correction is graphically shown in igure.. CEMA published K it values should only be used with published K is and K iv values. Testing shows designs can vary widely and using design specic K is or K iv values with the K it calculated by euations in igure. can misrepresent true performance. CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 154

28 6 BELT TENSION AND POWER ENGINEERING Where: T ir = Change in tension for single roll from idler seal resistance lbf (N) T isn = Change in tension in flight "n" from idler seal resistance lbf (N) D r = Idler roll diameter in (mm) K iv = Slope of torsional speed curve per roll lbf-in N-m rpm Table 6.9 rpm K is = Seal torsional resistance per roll at 500 rpm lbf-in (N-m) Table 6.9 K it = Temperature correction factor (dimensionless) Figure 6.7 K itb = Curve fit constants for temperature correction [R 1 (K 1 )] L n n r N i R ris R riv S in K IT Note: R = Rankine, K = Kelvin [T R = F (T K = C K)] = Length of flight "n" ft (m) = Number of rolls per idler set = Actual rpm of idler based on diameter and belt speed rpm = Modifying Factor for seal torsional resistance (dimensionless) = Modifying Factor for torsional speed effect (dimensionless) = Carrying or return idler spacing in flight "n" ft(m) CEMA C&D CEMA E CEMA Historical (-40) (-8) (-18) (-4) (4) (16) (7) (38) (49) Temperature F ( C) Figure 6.7 K it Teerre rrei r re r ier r idler seal drag and it is accounted for by the multiplying factor, K it ember products hae been independently tested and the euations published reect seal drag change with temperature. This comparison of results with the CEMA Historical correction is graphically shown in igure.. CEMA published K it values should only be used with published K is and K iv values. Testing shows designs can vary widely and using design specic K is or K iv values with the K it calculated by euations in igure. can misrepresent true performance. CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED 154

29 6 BELT TENSION AND POWER ENGINEERING There are no generally available tabulated indentation values for various belt constructions for either the small or large sample methods. CEMA does not endorse any particular method so long as it accurately predicts the indentation resistance on a single idler for different temperatures and loads and can be used to determine T bin for specic belt constructions being considered in the conveyor design. ndentation loss is usually a maor factor on long overland conveyors. The magnitude of the indentation loss for short horiontal or inclined conveyors is usually not a signicant loss component in the total tension requirement. While the indentation qualities of the belt covers are an important consideration for energy consumption, it is important to balance other requirements for the cover design such as abrasion resistance or ame retardancy hen considering rubber compounds including a lo rolling resistance (LRR) conveyor belt cover. Equation 6.37 T bin, Tension increase from viscoelastic indentation reaction between roller and belt Figure 6.38 ivalent load distribtion from tree roll idler cross sectional area Two methods for K bir are provided for the small sample (K bir-s ) and large sample (K bir-l ) methods. To arrive at T bin it is necessary to adjust for the uneven loading (igure.) on the rollers to arrive at an average pressure between the belt and roller. The equation for c wd is derived from the geometry of the cross sectional area based on the load area, A and represents a correction to the average line load, w iw. Equation 6.39 c wd, Load distribution factor T bin = K bir c wd (W b + W m ) L n R rbi D m s A Area Distribution BW Equivalent Load Distribution c wd = X ld BW s CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED ß w iw Division sign X ld = m S i X ldref X ldref = 5. lbf in 36,000 N mm Equation 6.40 X ld, Loading pressure adjustment factor 160

30 6 BELT TENSION AND POWER ENGINEERING There are no generally available tabulated indentation values for various belt constructions for either the small or large sample methods. CEMA does not endorse any particular method so long as it accurately predicts the indentation resistance on a single idler for different temperatures and loads and can be used to determine T bin for specic belt constructions being considered in the conveyor design. ndentation loss is usually a maor factor on long overland conveyors. The magnitude of the indentation loss for short horiontal or inclined conveyors is usually not a signicant loss component in the total tension requirement. While the indentation qualities of the belt covers are an important consideration for energy consumption, it is important to balance other requirements for the cover design such as abrasion resistance or ame retardancy hen considering rubber compounds including a lo rolling resistance (LRR) conveyor belt cover. Equation 6.37 T bin, Tension increase from viscoelastic indentation reaction between roller and belt Figure 6.38 ivalent load distribtion from tree roll idler cross sectional area Two methods for K bir are provided for the small sample (K bir-s ) and large sample (K bir-l ) methods. To arrive at T bin it is necessary to adjust for the uneven loading (igure.) on the rollers to arrive at an average pressure between the belt and roller. The equation for c wd is derived from the geometry of the cross sectional area based on the load area, A and represents a correction to the average line load, w iw. Equation 6.39 c wd, Load distribution factor T bin = K bir c wd (W b + W m ) L n R rbi D m s A Area Distribution BW Equivalent Load Distribution c wd = X ld BW s CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED ß w iw Equation 6.40 X ld, Loading pressure adjustment factor 160

31 BELT TENSION AND POWER ENGINEERING 6 Where: T bin = Tension increase from viscoelastic deformation of belt cover rubber K birs = Viscoelastic characteristic of belt cover rubber from the small sample method Equation 6.4 K bir-l = Viscoelastic characteristic of belt cover rubber from the large sample method Equation 6.60 c wd = Load distribution factor (dimensionless) R rbi = Modifying factor (dimensionless) S i = Idler spacing [ft (m)] X ld = Loading pressure adjustment factor (dimensionless) = Troughing angle (deg) s = Surcharge angle (deg) = Bulk density of conveyed material m Small Sample Indentation Loss Method Rubber indentation energy loss aries ith the idler rolls indentation into the belt oer thiness and with the nominal deformation work as affected by the idler roll radius and the normal load. Just as important is the degree to which the rubber reacts elastically to return the energy of deformation to the system. This is affected by the rubber composition, the amount of deformation or strain, the rubber temperature and, to a lesser degree, the belt speed. The rubber composition is a design variable through the viscoelastic concepts of Storage Modulus and Loss Modulus with their ratio, known as tan delta, as an index of the rubbers loss characteristic. These properties are best obtained from harmonic testing and vary with frequency, temperature and strain, paralleling the idler indentation of interest. The loss may be then considered to be the area within the steady cycles of stress and strain along the transient path of the indentation. The contribution of the rubber material is incorporated into the indentation prediction with K bir-s. n effect, it sets the width of the ellipse in igure.. or a particular rubber, the applicable value varies with the temperature, belt speed and loading. This requires a series of calculations with application details and a set of numerical values for the particular rubber. Constants for several example rubber cover compounds are provided for evaluation and consideration. Belt manufacturer should be contacted for selection, application and specication of compounds for specic applications. Stress Compression Steady Cycle Transient Cycle Indentation Loss CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED Tension 6.57 Negative 0 Strain Positive Figure

32 BELT TENSION AND POWER ENGINEERING 6 Where: T bin = Tension increase from viscoelastic deformation of belt cover rubber K birs = Viscoelastic characteristic of belt cover rubber from the small sample method Equation 6.4 K bir-l = Viscoelastic characteristic of belt cover rubber from the large sample method Equation 6.57 c wd = Load distribution factor (dimensionless) R rbi = Modifying factor (dimensionless) S i = Idler spacing [ft (m)] X ld = Loading pressure adjustment factor (dimensionless) = Troughing angle (deg) s = Surcharge angle (deg) = Bulk density of conveyed material m Small Sample Indentation Loss Method Rubber indentation energy loss aries ith the idler rolls indentation into the belt oer thiness and with the nominal deformation work as affected by the idler roll radius and the normal load. Just as important is the degree to which the rubber reacts elastically to return the energy of deformation to the system. This is affected by the rubber composition, the amount of deformation or strain, the rubber temperature and, to a lesser degree, the belt speed. The rubber composition is a design variable through the viscoelastic concepts of Storage Modulus and Loss Modulus with their ratio, known as tan delta, as an index of the rubbers loss characteristic. These properties are best obtained from harmonic testing and vary with frequency, temperature and strain, paralleling the idler indentation of interest. The loss may be then considered to be the area within the steady cycles of stress and strain along the transient path of the indentation. The contribution of the rubber material is incorporated into the indentation prediction with K bir-s. n effect, it sets the width of the ellipse in igure.. or a particular rubber, the applicable value varies with the temperature, belt speed and loading. This requires a series of calculations with application details and a set of numerical values for the particular rubber. Constants for several example rubber cover compounds are provided for evaluation and consideration. Belt manufacturer should be contacted for selection, application and specication of compounds for specic applications. Stress Compression Steady Cycle Transient Cycle Indentation Loss CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED Tension Negative 0 Strain Positive Figure

33 BELT TENSION AND POWER ENGINEERING 6 The contribution of the rubber material is incorporated into the indentation prediction with K bir-s - the temperature, belt speed and loading. This requires a series of calculations with application details and a set of constant values for the particular rubber. Constants for several example rubber cover compounds are provided for evaluation and consideration. Belt manufacturer should be contacted for selection, ap- Where: Where: F = b 1 + [b (x F )] + [b 3 (x F )] + [b 4 (x 3 F )] (dimensionless) b 5 + [b 6 (x F )] + x F Equation 6.44 F, Normalized indentation factor x F = - C 1 ( T T 0 ) C + ( T T 0 ) + log ( v u)- s (dimensionless) s = a 1 + [a (x s )] + [a 3 (x s )] + [a 4 (x 3 s )] (dimensionless) T = Operating temperature ( o C) v u = Belt speed m s Note: v umust be in m s units in x F equation 1/3 w x S = iw (dimensionless) w max d m from Equation 4.17 for D m using A from Equation 4.5 for A s With: D m Equation 6.70, m = bulk density, S i = idler spacing w max = 85.5 lbf in Note : 50,000 N m For constants a i, b i, C 1, C and T 0 see Table 6.47 w iw = D m m + W b S BW i Equation 6.45 w iw CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED BW = Belt width in (mm) D m = Maximum depth of material on three roll idler in (mm) m = Bulk density lbf kgf ft 3 S i = Idler spacing ft (m) m 3 W b = Belt weight per unit length lbf ft N m 163

34 BELT TENSION AND POWER ENGINEERING 6 The contribution of the rubber material is incorporated into the indentation prediction with K bir-s - the temperature, belt speed and loading. This requires a series of calculations with application details and a set of constant values for the particular rubber. Constants for several example rubber cover compounds are provided for evaluation and consideration. Belt manufacturer should be contacted for selection, ap- Where: Where: F = b 1 + [b (x F )] + [b 3 (x F )] + [b 4 (x 3 F )] (dimensionless) b 5 + [b 6 (x F )] + x F Equation 6.44 F, Normalized indentation factor x F = - C 1 ( T T 0 ) C + ( T T 0 ) + log ( v u)- s (dimensionless) s = a 1 + [a (x s )] + [a 3 (x s )] + [a 4 (x 3 s )] (dimensionless) T = Operating temperature ( o C) v u = Belt speed m s Note: v umust be in m s units in x F equation x S = w iw w max 1/3 (dimensionless) With: d m from Equation 4.17 for D m using A from Equation 4.5 for A s, m = bulk density, S i = idler spacing w max = 85.5 lbf in Note : 50,000 N m For constants a i, b i, C 1, C and T 0 see Table 6.47 w iw = D m m + W b S BW i Equation 6.45 w iw CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED BW = Belt width in (mm) D m = Maximum depth of material on three roll idler in (mm) m = Bulk density lbf kgf ft 3 m 3 S i = Idler spacing ft (m) W b = Belt weight per unit length lbf ft N m 163

35 6 BELT TENSION AND POWER ENGINEERING Where: P = c + [c (x )] + [c (x 1 P 3 P)] + [c 4 (x 3 P )] (dimensionless) c 5 + [c 6 (x P )] + x P x P = - C 1 ( T T 0 ) + log( v C + ( T T 0 ) u ) (dimensionless) Notes : For constants c i see Table 6.48 For constants C 1, C and T 0 see Table 6.47 Equation 6.46 P, Rubber strain level adjustment T = Operating temperature ( o C) v u = Belt speed m s Note: v u must be in m s units in x F equation tual loading strain which is commonly in the range of nonlinear stress strain behavior. classes of conveyor belt rubber covers. These values are incorrect Constant Default Rubber Type 1 Rubber Type Rubber Type 3 Rubber T 0 ( C) E 0 (N/m ) C C a a a a b b b b b b CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED Table 6.47 bir-s F factor 164

36 6 BELT TENSION AND POWER ENGINEERING Where: P = c + [c (x )] + [c (x 1 P 3 P)] + [c 4 (x 3 P )] (dimensionless) c 5 + [c 6 (x P )] + x P x P = - C 1 ( T T 0 ) + log( v C + ( T T 0 ) u ) (dimensionless) Notes : For constants c i see Table 6.48 For constants C 1, C and T 0 see Table 6.47 Equation 6.46 P, Rubber strain level adjustment T = Operating temperature ( o C) v u = Belt speed m s Note: v u must be in m s units in x F equation tual loading strain which is commonly in the range of nonlinear stress strain behavior. classes of conveyor belt rubber covers. Constant Default Rubber Type 1 Rubber Type Rubber Type 3 Rubber T 0 ( C) E 0 (N/m ) C C a a a a b b b b b b CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED Table 6.47 bir-s F factor 164

37 BELT TENSION AND POWER ENGINEERING 6 c i Intervals: Data for Type 1 and Type 3 was transposed Each c i constant is linearly interpolated for w iw, relative to the seven levels of w ref and extrapolated past the last row. Cover Compound w ref (N/m) c 1 c c 3 c 4 c 5 c 6 (dimensionless) Default Type 1 Type Type CEMA 7th ed. Belt Book ERRATA-FEBRUARY 1, 015-COPYRIGHTED Table 6.48 bir-s P factor at several w ref values compounds for common covers for more conservative designs that operate at lower temperatures. Type 1 constants are for a low rolling resistance rubber cover compound considered for applications where 165