ANSI/CEMA STANDARD B105.1-2015 of ANSI/CEMA STANDARD …€¦ · 12 (305) thru 26 (660) 0.250...

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CEMA Standard B105.1‐2015 ‐ Specifications for Welded Steel Conveyor Pulleys with Compression Type Hubs

DISCLAIMER

The information provided herein in advisory only. These recommendations provided by CEMA are general in nature and are not intended as a substitute for professional advice. Users should seek the advice, supervision and/or consultation of qualified engineers, safety consultants, and other qualified professionals. Any use of this publication, or any information contained herein, or any other CEMA publication is made with agreement and understanding that the user and the user’s company assume full responsibility for the designs, safety, specifications, suitability and adequacy of any conveyor system, system component, mechanical or electrical device designed or manufactured using this information. The user and user’s company understand and agree that CEMA, its member companies, its officers, agents and employees are not and shall not be liable in any manner under any theory of liability to anyone for reliance on or use of these recommendations. The user and the user’s companies agree to release, hold harmless and indemnify and defend CEMA, its member companies, successors, assigns, officers, agents and employees from any and all claims of liability, costs, fees (including attorney’s fees), or damages arising in any way out of the use of this information. CEMA and its member companies, successors, assigns, officers, agents and employees make no representations or warranties whatsoever, either expressed or implied, about the information contained heed to, representations or warranties that the information and recommendations contained herein conform to any federal, state or local laws, regulations, guidelines or ordinances.

Conveyor Equipment Manufacturers Association 5672 Strand Ct, Suite 2

Naples, Florida 34110-3314 www.cemanet.org Copyright © 2015

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FOREWORD

Welded steel conveyor pulleys have been in common use since the 1930’s. MPTA formed a Steel Pulley Engineering Committee in 1958 to develop recommended pulley load ratings. This Committee consisted of pulley and conveyor engineers who studied available information on pulley design, theoretical stress analysis, and data from actual tests. All parts of the pulley and shaft assembly were included in the study. In May, 1960, recommended load ratings for standard conveyor pulleys were published. In June, 1966 - The combined revised standard was approved as B105.1 U. S. STANDARD SPECIFICATION FOR WELDED STEEL CONVEYOR PULLEYS. In November, 1987 - The standard was transferred to the Conveyor Equipment Manufacturers Association (CEMA). The CEMA Engineering Committee reviewed the standard and decided to revise the method used for determining Drive Shaft diameters so that the method would conform to the ANSI B106.1M-1985 “Design of Transmission Shafting” standard. Also, a run-out tolerance on pulley diameters was added. This industry standard is not intended in any way to limit the design of any manufacturer. ANSI B106.1M was withdrawn in 1994. 1995, the CEMA Eng. Conference determined that the methods used by this former standard were technically sound and consistent with modern fatigue analysis methods. Therefore, the relevant data from ANSI B106.1M remains incorporated in this standard, and in Chapter 8 of CEMA’s Publication “Belt Conveyors for Bulk Materials.” In the 2003 edition, the Conveyor Pulley Subsection:

1) Revised the Scope to clarify that the standard is not applicable to cone clamping keyless locking devices

2) Added Section 2.6 Shaft Run-out 3) Added information to Section 3.2 and a footnote to Table 2 describing the origin of the Load

Ratings In the 2009 edition, the Conveyor Pulley Subsection reviewed the standard and:

1) Added capability to use keyless locking devices in Scope and 3.6 Hub and bushing types 2) Added data and trapezoidal crown to 2.5 Crown 3) Clarified applications where better than standard tolerance is recommended in 2.6 Shaft Run-out 4) Added Section 2.7 limiting belt speed to 800 fpm. 5) Added overload information for 6th belt book into 3.4 Overloads 6) Standard has had selection method and examples intermingled. Created a generic selection

method (4.1 – 4.7) and put examples into Appendix IV. 7) Inserted figures and tables in area of use rather than grouped at the end. 8) Reduced maximum PIW to 800 in Table 1 of Section 4.1 Pulley Diameter selection. 9) Added resultant load updates from 6th Belt Book into Section 4.2 and added discussion of use

without weight. 10) Created section 4.3 overhung loads, added Appendix III for more background and historical

reference. 11) Added overhung load multiplier to section 4.4 Shaft Fatigue. 12) Added Section 4.5 Pulley Fatigue Life. 13) Added overhung load and fatigue factors into Section 4.6 Pulley Selection. Clarified deflection

versus stress control in Table 2. Added shaded area to clarify loads potentially exceeding 800 PIW.

In the 2015 edition, the Conveyor Pulley Subsection reviewed the standard and:

1) Metric equivalents and examples added. 2) Added figure 4 and figure 5 in appendix III. 3) Added appendix V describing Mine Duty and Engineered Pulleys. 4) Edited text, references, and tables numbers, for internal consistency and ease of reading 5) Added an index of tables and figures

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TABLE OF CONTENTS

1. Scope

2. Dimensions and Tolerances

3 Pulley Selection General Information

4. Pulley Size Selection Method

4.1 Pulley diameter selection

4.2 Belt resultant loads

4.3 Overhung loads

4.4 Shaft fatigue

4.5 Pulley fatigue

4.6 Pulley shaft size selection

4.7 Pulley availability

APPENDICES:

I. Conversion factors to SI Units

II. Shaft deflection formula

III. Overhung load derivation and discussion

IV. Example Pulley selections

1. Non-drive pulley (no torque or overhung load)

2. Drive pulley (no overhung load)

3. Drive pulley (with overhung loads)

4. Non-symmetric multiple overhung loads (Drive Pulley with backstop)

V. Other than CEMA Class Pulleys

INDEX OF TABLES AND FIGURES

III

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1. SCOPE

1.1 This standard applies to a series of straight face and crowned face welded steel conveyor pulleys that have a continuous rim and two end discs each with a compression type hub to provide a clamp fit on the shaft. It is not applicable to single disc pulleys, wing or slat type pulleys, or cast pulleys. This standard applies to pulleys using compression type hubs and high pressure keyless locking assemblies. It does not cover pulleys welded to the shaft. The standard establishes load ratings, allowable variation from nominal dimensions, permissible crown dimensions and such overall dimensions as are normally necessary to establish clearances for location of adjacent parts. It is not intended to specify construction details, other than as outlined above, nor to establish the actual dimensions of any component parts. The series of pulley sizes and shaft combinations shown in Tables 5-A and 5-B, and the load ratings shown in Tables 4-A and 4-B, cover the majority of combinations of welded steel pulleys with compression type hubs normally used in belt conveyor and elevator practice. Only the series shown are covered by this standard. This standard is not intended to provide thorough guidance on shaft design at all potential failure points. The standard is intended to provide a shaft diameter at the pulley connection consistent with other external components such as bearings and drive components. It is assumed that the shaft is a consistent diameter throughout and layout clearances between components are minimized. 1.2 Welded steel conveyor pulleys covered by this standard should not be used with steel cable and other high modulus belts because such belts create stress concentrations and demand manufacturing tolerances beyond the capacities of these pulleys. High modulus belts are defined as those having operating tension ratings greater than 800 PIW (140 kN/m) or a modulus greater than 80,000 PIW (14000 kN/m). Consult your CEMA pulley manufacturer for assistance.

2. DIMENSIONS AND TOLERANCES

2.1 Diameters

Standard welded steel pulley diameters are as shown in Tables 5-A and 5-B. All other sizes are considered special. These nominal diameters apply to straight and crown face pulleys and are for bare pulleys only; they do not include any increase brought about by lagging.

2.2 Diameter Variations

Permissible diameter variations from nominal diameter are based on face width as follows:

FACE WIDTH in (mm)

OVER NOMINAL DIAMETER in (mm)

UNDER NOMINAL DIAMETER in (mm)

12 (305) thru 26 (660) 0.250 (6.35) 0.125 (3.18)

over 26 (660) thru 66 (1676) 0.625 (15.88) 0.125 (3.18)

These limitations apply equally to straight face and crown face pulleys with nominal diameter measured at the midpoint of the face width. The diameter is defined as the bare diameter exclusive of lagging. Permissible diameter variations listed are not to be considered as diameter run-out tolerances. Listed nominal diameter variation may occur from one pulley to another. Diameter run-out tolerance at midpoint of the bare pulley face is as follows:

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DIAMETERS in (mm)

MAXIMUM TOTAL INDICATOR READING (TIR) in (mm)

8 (203) thru 24 (610) 0.125 (3.18)

over 24 (610) thru 48 (1219) 0.188 (4.75)

over 48 (1219) thru 60 (1524) 0.250 (6.35)

2.3 Face Width Variations

Permissible face width variation from nominal face width is plus or minus 0.125 in (3.18 mm) for all sizes. Face width is defined as the length of the rim along the shaft axis. The permissible face width variation is not to be construed as an edge run-out tolerance. The listed variation in face width may occur from one pulley to another. Edge run-out tolerance is specified by the individual CEMA pulley manufacturers. 2.4 Clearance along the Shaft

The distance between the outer faces of the hubs shall never exceed the overall pulley face width. 2.5 Crown

Crown is defined as the amount (expressed in inches) per foot of total face width by which the diameter at the center of the face exceeds the diameter at the edge. Crowns running the full face are often made at a set diameter to face travel change rate, which results in the diameter difference increasing with face width. Amount of crown may be from 1/16 to 1/8 in per foot (5.2 to 10.4 mm per meter) of total face width. Trapezoidal crowns have a center section of uniform diameter with tapered sections on either end. The difference in diameter from center to end ranges from 1/8 to 1/4 in (3.2 mm to 6.4 mm) regardless of face width. Crowned end sections typically have a diameter versus face travel rate of change similar to full crowns. 2.6 Shaft Run-out

The shaft extension run-out is measured from the bearing journals after the shaft is installed in the pulley. Radial shaft extension Total Indicator Reading (TIR) shall not exceed 0.002 in per in (0.002 mm per mm) of shaft extension beyond the bearing center. Typically bearings will introduce an additional run-out, which is not included in this limit. Flexible couplings, backstops and parallel shaft mount reducers are used with this limit as long as components remain close to bearing, torque restraint has ample flexibility and visual motion is permitted. Examples of situations where a more conservative limit may be desired are given. Consult your CEMA pulley manufacturer for details.

As shaft extension increases, run-out may become visually noticeable. A perception issue may occur even when component attachments are designed to tolerate the run-out.

Right angle reducer/motor assemblies supported by pulley shaft commonly require lower limits. These assemblies tend to be quite long, which accentuates the run-out.

Drives attached with rigid couplings commonly require lower limits. The coupling essentially increases the shaft extension which accentuates the run-out.

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2.7 Belt Speed

It is not recommended to operate standard drum pulleys above a belt speed of 800 fpm (4 m/s). For higher speeds consult your CEMA pulley manufacturer.

3. PULLEY SELECTION - GENERAL INFORMATION

3.1 Pulley Diameter and Face Width

The following selection procedures assume the pulley diameter and face width have been established consistent with belting and conveyor design requirements. 3.2 Ratings

The tabulated ratings for pulley and shaft combinations are based on the use of non-journalled shafting with pulleys centrally located between two bearings. Ratings are based on SAE 1018 shaft material using either a maximum shaft bending stress of 8000 psi (55.16 MPa) or a maximum free shaft deflection slope at the hub of 0.0023 in per in (0.0023 mm per mm) or [tangent of 8 min], whichever governs. (See Appendix II for shaft deflection formula.) Pulleys used on shafting selected with a bending stress greater than 8000 psi (55.16 MPa), or a slope exceeding 0.0023 in per in (0.0023 mm per mm), are special and are not covered by this standard. High strength shafting may be used in drive pulleys to withstand the added torsional shaft stresses. See Section 4.4 and Appendix III and IV for shaft calculations, or consult your CEMA pulley manufacturer for assistance. 3.3 Rating Interpolation

Four values are listed in Tables 4-A and 4-B, Load Ratings (Pounds & Kilonewtons) for Pulleys and Shaft Combinations. In this table, interpolation may be used for determining a load rating for an unlisted value of bearing centers minus face width. 3.4 Overloads

Excessive belt tensions may result in premature failure of pulleys, shafting or bearings. Differentiating between transient tension increases and steady state running tensions is important for proper pulley design. Transient, or dynamic tension increases happen for a short period and then subside. These periods generally last for a few minutes or less and represent less than 1 percent of operating time. Some examples are starting, stopping and jam-ups. Transient loads should not exceed design loads by more than 50 percent. If greater than 50 percent or more than 1 percent of running time, mine duty or engineered pulleys are recommended, and this information should be provided to your CEMA pulley manufacturer. Steady state running tensions happen for a significant period of time and represent the fundamental operating conditions. Conditions that can increase running tensions are excessive belt misalignment, excessive material loaded, excessive take-up weight, gravity take-up frictional increases and over tightening of screw take-ups. Normal running tensions for engineered pulleys should not exceed ratings within this standard. 3.5 Hub Size

The rating tables are based upon using the smallest hub size that will accommodate the required shaft diameter. Specifying a larger hub size, in some cases, results in a decreased rather than an increased

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Page 4

allowable load rating of the pulley. Selecting a larger hub size than required by the shaft should be done only after consultation with the CEMA pulley manufacturer. 3.6 Hub and Bushing Types

It is possible to design pulleys capable of performing with loads defined within using many different bushing and locking assembly types. Historically this standard has applied to single taper compression hubs requiring shaft keys in torsion applications. Using good design practices many other types may be used including keyless locking assemblies. At a minimum the pulley engineer should review for:

‐ Sufficient torsion capacity. ‐ Sufficient bending moment capacity. ‐ Sufficient hub stiffness clamping pressures. ‐ Shaft deflections less than 0.0023 in/in (0.0023 mm/mm) may be required for some shaft

attachment types. ‐ Stress concentration factors.

4. PULLEY SIZE SELECTION METHOD

4.1 Pulley Diameter Selection

Calculate PIW or kN/m by dividing highest running belt tension on pulley by belt width. On Tables 1-A and 1-B, use appropriate belt arc of contact row and calculated PIW (kN/m) to determine minimum pulley diameter. Select an actual diameter greater than or equal to the minimum.

Table 1-A. Maximum belt tension (Pounds per Inch of Belt Width)

A R C OF C ON T A C T

(deg) 8 10 12 14 16 18 20 24 30 36 42 48 54 60

10 65 80 95 120 145 175 205 260 345 430 520 605 690 775

20 50 60 75 95 115 135 160 200 265 335 400 465 535 600

30 45 55 65 80 100 115 140 175 230 290 345 405 460 520

40 35 45 55 70 85 100 120 150 200 245 295 345 395 445

50 30 40 45 60 70 85 100 130 170 215 255 300 340 385

60 30 40 45 60 70 85 100 125 165 205 250 290 330 375

70 30 40 50 60 75 85 105 130 175 220 260 305 350 395

80 35 45 50 65 80 95 115 140 190 235 285 330 375 425

90 35 45 55 70 85 100 120 150 200 255 305 355 405 455

100 40 50 60 75 90 110 130 160 215 270 325 380 430 485

110 45 55 65 80 100 115 140 175 230 290 345 405 460 520

120 45 55 65 85 105 120 145 185 245 305 365 425 490 550

130 50 60 75 95 115 135 160 200 265 335 400 465 535 600

140 55 70 80 105 125 150 180 225 300 375 450 525 600 675

150 60 75 90 115 140 170 200 250 335 420 505 590 670 755

160 70 85 100 130 160 185 225 280 375 465 560 650 745 800

170 75 95 115 145 175 205 250 310 415 520 620 725 800 800

180 85 105 125 160 195 230 275 345 460 575 690 800 800 800

190 75 95 115 145 175 205 250 310 415 520 620 725 800 800

200 70 85 100 130 160 185 225 280 375 465 560 650 745 800

210 60 75 90 115 140 170 200 250 335 420 505 590 670 755

220 55 70 80 105 125 150 180 225 300 375 450 525 600 675

230 50 60 75 95 115 130 160 200 265 335 400 465 535 600

240 45 55 65 85 105 120 145 185 245 305 365 425 490 550

PULLEY DIAMETER (in)

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Table 1-B. Maximum belt tension (kN per Meter of Belt Width)

4.2 Determination of Actual Resultant Radial Belt Load

The resultant pulley radial load is the vector sum of the belt tensions, pulley weight, and weight of the shaft. The force from the weights always acts downward and the forces from the belt act in the path of the belt and away from the pulley. Resultant radial load calculations for typical pulley arrangements and a general case are illustrated using trigonometric methods in Figure 1.

A R C OF C ON T A C T

(deg) 203 254 305 356 406 457 508 610 762 914 1067 1219 1372 1524

10 11 14 17 21 25 31 36 46 60 75 91 106 121 136

20 9 11 13 17 20 24 28 35 46 59 70 81 94 105

30 8 10 11 14 18 20 25 31 40 51 60 71 81 91

40 6 8 10 12 15 18 21 26 35 43 52 60 69 78

50 5 7 8 11 12 15 18 23 30 38 45 53 60 67

60 5 7 8 11 12 15 18 22 29 36 44 51 58 66

70 5 7 9 11 13 15 18 23 31 39 46 53 61 69

80 6 8 9 11 14 17 20 25 33 41 50 58 66 74

90 6 8 10 12 15 18 21 26 35 45 53 62 71 80

100 7 9 11 13 16 19 23 28 38 47 57 67 75 85

110 8 10 11 14 18 20 25 31 40 51 60 71 81 91

120 8 10 11 15 18 21 25 32 43 53 64 74 86 96

130 9 11 13 17 20 24 28 35 46 59 70 81 94 105

140 10 12 14 18 22 26 32 39 53 66 79 92 105 118

150 11 13 16 20 25 30 35 44 59 74 88 103 117 132

160 12 15 18 23 28 32 39 49 66 81 98 114 130 140

170 13 17 20 25 31 36 44 54 73 91 109 127 140 140

180 15 18 22 28 34 40 48 60 81 101 121 140 140 140

190 13 17 20 25 31 36 44 54 73 91 109 127 140 140

200 12 15 18 23 28 32 39 49 66 81 98 114 130 140

210 11 13 16 20 25 30 35 44 59 74 88 103 117 132

220 10 12 14 18 22 26 32 39 53 66 79 92 105 118

230 9 11 13 17 20 23 28 35 46 59 70 81 94 105

240 8 10 11 15 18 21 25 32 43 53 64 74 86 96

PULLEY DIAMETER (mm)

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Typical Drive Pulley Arrangements

Figure 1 – Resultant Radial Load Diagrams

Resultant Load for Drive Pulley with 180 Wrap and Horizontal

21 2R = T + T +W

Resultant Load for Drive Pulley with 180 Wrap and Inclined

2 2

1 2 1 2cos sinR T T T T W

Resultant Load for Drive Pulley with >180 Wrap and Horizontal

2 2

1 2 2cos sinR T T T W

Resultant Load for Drive Pulley with >180 Wrap and Inclined

2 2

1 1 2 2 1 1 2 2cos cos sin sinR T T T T W

Resultant Load for Tail Pulley

2 2

32R T W

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Resultant Load for Vertical Gravity Take-up Pulley

32R T W

Resultant Load for Vertical Gravity Take-up Bend Pulley

22

3 3cos 1 sinR T T W

Resultant Load for Snub Pulley

2 2

3 31 cos sinR T T W

Resultant Load for General Case

2 2

1 2 1 2cos cos sin sinccw cw ccw cwR T T T T W

Where:

T1 = Tight side tension [lbf (kN)] T2 = Slack side tension [lbf (kN)] T3 = Tension (non driving pulleys) [lbf (kN)] W = Weight [lbm (kN)] R = Resultant pulley load [lbf (kN)] Ø, Ø1, Ø2 = Belt tension angles (deg), positive as shown Y1, Y2 = Belt tension angles (deg), positive as shown

For simplicity, at times it is acceptable to omit weight (W) in the resultant load calculations. The examples in Figure 2 show common pulley examples and compare the resultant load calculation with and without weight. Examples in the upper group are candidates for weight omission. Examples in the lower group show significant impact from weight and are NOT good candidates for omission. In general, good weight omission candidates are those with belt tension vectors and weight vector 90°-180° apart, as shown in Figure 1. Poor weight omission candidates have belt tensions and weight vector 0° to 90° apart with worst case being 0°.

Table 2-A. Impact of Pulley Weight on Resultant Load (lbf)

Tccw Ψ1 Tcw Ψ2 W R R (less W)

lbf deg lbf deg lbm lbf lbf

Horizontal Head Drive 180° wrap 11,100 180 4,500 180 1,256 15,650 15,600 0.3%

15° Head Drive 210° wrap 11,100 195 4,500 165 1,256 15,357 15,165 1.3%

Horizontal Tail 180° wrap 4,500 180 4,500 180 850 9,040 9,000 0.4%

Gravity Take-up or Elevator Boot 4,500 90 4,500 90 850 8,150 9,000 -9.9%

Elevator Drive 180° wrap 11,100 270 4,500 270 1,256 16,856 15,600 7.7%

Drive Snub 30° wrap 4,500 345 4,500 195 440 2,769 2,329 17.3%

Upper Take-up bend 75° wrap 4,500 270 4,500 15 660 5,904 5,479 7.5%

Lower Take-up bend 105° wrap 4,500 195 4,500 270 660 7,674 7,140 7.2%

Upper Take-up bend 90° wrap 4,500 270 4,500 0 660 6,847 6,364 7.3%

Lower Take-up bend 190° wrap 4,500 180 4,500 270 660 6,847 6,364 7.3%

PULLEY POSITION % diff

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Table 2-B. Impact of Pulley Weight on Resultant Load (kN)

4.3 Overhung Loads

THIS CALCULATION IS ONLY NECESSARY WHEN A POWER TRANSMISSION ATTACHMENT CREATES LOADS IN ADDITION TO BELT PROPULSION TORQUE. IF NOT APPLICABLE, USE K=1 FOR CALCULATIONS IN LATER STEPS. OVERHUNG LOADS CREATE SHAFT DESIGN CONSIDERATIONS BEYOND DIAMETER AT PULLEY ATTACHMENT. THESE ARE BEYOND THE SCOPE AND CONSULTATION WITH YOUR CEMA PULLEY MANUFACTURER IS RECOMMENDED. Power Transmission (PT) components often create loads impacting pulley selection. Examples of these include, but are not limited to:

‐ Shaft mounted drive assemblies. ‐ Rigidly coupled drive assemblies. ‐ Direct connected sprocket or belt drives. ‐ Brake discs. ‐ Backstops.

Overhung loads often: ‐ Include multiple force components, such as weight and reaction forces, which should be vector

summed similar to the methods in section 4.2. ‐ are worst case at conditions other than peak running. An example is a right angle shaft mounted

reducer having force “P” greatest at idle and less with power applied. Safe design requires review of all foreseeable scenarios.

For pulley selection the overhung load analysis creates a modifying factor (K) equivalent to the increase in bending moment at the pulley moment arm “A” location, reference Figure 2. The calculations for K are as follows: Overhung Load Moment (Mo at pulley attachment location A): If one PT component is attached:

o

B AM P C

B

Tccw Ψ1 Tcw Ψ2 W R R (less W)

kN deg kN deg kN kN kN

Horizontal Head Drive 180° wrap 49.373 180 20.016 180 5.587 69.611 69.389 0.3%

15° Head Drive 210° wrap 49.373 195 20.016 165 5.587 68.308 67.454 1.3%

Horzontal Tail 180° wrap 20.016 180 20.016 180 3.781 40.210 40.032 0.4%

Gravity Take-up or Elevator Boot 20.016 90 20.016 90 3.781 36.251 40.032 -9.9%

Elevator Drive 180° wrap 49.373 270 20.016 270 5.587 74.975 69.389 7.7%

Drive Snub 30° wrap 20.016 345 20.016 195 1.957 12.317 10.359 17.3%

Upper Take-up bend 75° wrap 20.016 270 20.016 15 2.936 26.261 24.371 7.5%

Lower Take-up bend 105° wrap 20.016 195 20.016 270 2.936 34.134 31.759 7.2%

Upper Take-up bend 90° wrap 20.016 270 20.016 0 2.936 30.455 28.307 7.3%

Lower Take-up bend 190° wrap 20.016 180 20.016 270 2.936 30.455 28.307 7.3%

PULLEY POSITION % diff

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If two PT components attached and layout is symmetric about belt centerline:

oM P C

Reference Appendix III and IV for guidance on analysis of more involved overhung situations. Belt Resultant Load Moment (M at pulley attachment location A):

2

AM R

Maintaining limitations detailed in the scope, a comparison of M to Mo should be made. As the value of Mo approaches that of M, shaft design criteria away from the pulley attachment becomes more of a concern. This standard limits Mo to not exceed M, which typically results in a shaft diameter adequate for components external to pulley. It is recommended that a thorough analysis of the shaft design at all potential failure sites be made, which is beyond the scope of this standard. Overhung Load Ratio (K at pulley attachment location A):

2 2 2 coso oM M M M EK

M

If K < 1 then K = 1

Figure 2. Pulley Dimensions and Nomenclature

A = Moment arm for pulley [in (mm)]. See Table 3.

B = Bearing centers [in (mm)].

C = Moment arm for overhung load [in (mm)].

D = Shaft diameter [in (mm)].

E = Angle between P and R (deg)

L = B minus face width [in (mm)]

N = L / 2 [in (mm)]

P = Resultant overhung load [lbf (kN)].

R = Resultant pulley load [lbf (kN)]

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Shaft Diameter (in) A (in) Shaft Diameter (mm) A (mm)1-3/16 to 2-7/16 N + 1-5/8 30.163 to 61.913 N + 41

2-11/16 to 2-15/16 N + 1-3/4 68.263 to 47.613 N + 443-7/16 N + 2-1/2 87.313 N + 64

3-15/16 N + 2-3/4 100.013 N + 704-7/16 N + 3 112.713 N + 76

4-15/16 N + 3-1/4 125.413 N + 835-7/16 to 6 N + 4-1/2 138.113 to 152.400 N + 1146-1/2 to 7 N + 5 165.100 to 177.800 N + 1277-1/2 to 8 N + 5-1/4 190.500 to 203.200 N + 133

8-1/2 to 10 N + 6-1/4 215.900 to 254.000 N + 159

Table 3. Typical Pulley Moment Arms 4.4 Minimum Shaft diameter (Fatigue):

THIS CALCULATION IS ONLY NECESSARY WHEN TRANSMITTING A TORQUE.

22

332 F.S. 3

4f y

KM TD

S S

For pulley and shaft applications within the scope of Standard B105.1, the recommended values are: D = Minimum Shaft Diameter, [in (mm)]. F.S. = Factor of Safety = 1.5 Sf = Corrected shaft fatigue limit = ka kb kc kd ke kf kg · Sf* Where: ka = surface factor = 0.8 for machined shaft kb = size factor = (D)-0.19 in (1.85 (D)-0.19 mm) kc = reliability factor = 0.897 kd = temperature factor = 1.0 for - 70o F to + 400o F (-57°C to 204 °C) ke = duty cycle factor = 1.0 provided cyclic stresses do not exceed Sf* kf = fatigue stress concentration factor:

Steel Profiled Keyway Sled Runner Keyway

Annealed (less than 200 BHN) 0.63 0.77 Quenched and Drawn (Over 200 BHN) 0.50 0.63

kg = miscellaneous factor = 1.0 for normal conveyor service

Sf* = 29,000 psi (200 MPa) for SAE 1018

= 41,000 psi (283 MPa) for SAE 1045

= 47,500 psi (328 MPa) for SAE 4140 (annealed) (Sf* = 0.5 tabulated ultimate tensile strength)

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Sy = Yield Strength = 32,000 psi (220 MPa) for SAE 1018

45,000 psi (310 MPa) for SAE 1045

60,500 psi (417 MPa) for SAE 4140 (annealed)

M = Resultant Load Bending moment (lbf-in or N-mm)2

AR

Reference Table 3 for typical moment arm (A) values. T = Torsional moment (lbf-in or N-mm)

eT r ; where r = pulley radius [in (mm)].

K = Overhung Load Modifying factor from 4.3 4.5 Pulley Fatigue Life: Pulley and shaft components deflect under applied loads and material stresses result. When rotated these stresses fluctuate subjecting components to fatigue loading. Primary variables impacting life are loads, speed, running time and running conditions. A fatigue multiplication factor (Z) is used to modify the resultant load calculated in section 4.2. Recommended values of Z range from 1 to 1.5. Belt speed, running time percentage and conveyor criticality are important considerations for pulley selection. Applications with belt speeds less than 400 fpm (122 m/min) and less than 50% running time are common applications using a fatigue factor (Z) = 1. As belt speed increases up to 800 fpm (244 m/min), running time percentage increases toward 100% or pulley is in a non-redundant critical conveyor the fatigue factor should increase. Fatigue factor selection in the range of Z = 1.0 to 1.5 is recommended. Note: non-drive pulleys on low tension side of belt often see similar belt tensions regardless if material is being conveyed. Estimating actual running time for these pulleys should include time when conveyor is moving without material. It is recommended that loads used represent worst case running conditions. 4.6 Pulley Selection: Select a shaft diameter from Tables 4-A and 4-B under Ratings for Pulley and Shaft Combinations using resultant load properly modified by overhung load and life factors. Resultant Load for Tables 4A and 4-B is product of resultant load from section 4.2, overhung load factor (K) from section 4.3 and life factor (Z) from section 4.5. If applicable, selection should be greater than or equal to minimum shaft diameter from section 4.4.

Modified (Tables 2)R Z K R (Section 4.2)

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12 14 16 18 20 22 26 32 38 44 51 57 63 66

2 1,000 920 780 670 590 530 440 350 290 240 210 180 170 1606 570 520 440 380 340 300 250 200 160 140 120 100 94 9010 400 370 310 270 230 210 170 140 110 96 82 73 66 6314 300 280 240 200 180 160 130 110 87 74 63 56 51 483 1,500 1,500 1,400 1,200 1,100 950 790 620 510 440 370 330 300 2906 1,000 1,000 950 820 720 640 530 420 350 300 250 220 200 19010 700 700 660 570 500 450 370 290 240 210 180 160 140 13014 540 540 510 440 390 350 290 230 190 160 140 120 110 1003 2,400 2,400 2,400 2,300 2,000 1,800 1,500 1,200 980 830 710 630 570 5406 1,600 1,600 1,600 1,600 1,400 1,200 1,000 800 660 560 480 430 380 37010 1,100 1,100 1,100 1,100 960 850 700 560 460 390 340 300 270 26016 780 780 780 750 660 590 490 380 320 270 230 210 180 1803 3,700 3,700 3,700 3,700 3,500 3,100 2,600 2,100 1,700 1,400 1,200 1,100 990 9406 2,500 2,500 2,500 2,500 2,400 2,100 1,800 1,400 1,100 980 840 740 670 64010 1,700 1,700 1,700 1,700 1,700 1,500 1,200 970 800 680 580 520 470 44016 1,200 1,200 1,200 1,200 1,100 1,000 840 670 550 470 400 360 320 3103 5,300 5,300 5,300 5,300 5,300 5,100 4,200 3,300 2,800 2,400 2,000 1,800 1,600 1,5008 2,900 2,900 2,900 2,900 2,900 2,800 2,300 1,900 1,500 1,300 1,100 990 890 85012 2,200 2,200 2,200 2,200 2,200 2,100 1,700 1,400 1,100 970 820 730 660 63018 1,500 1,500 1,500 1,500 1,500 1,500 1,200 980 810 690 590 530 470 4504 6,300 6,300 6,300 6,300 6,300 6,300 5,600 4,400 3,700 3,100 2,700 2,400 2,100 2,0008 4,000 4,000 4,000 4,000 4,000 4,000 3,600 2,900 2,400 2,000 1,700 1,500 1,400 1,30012 3,000 3,000 3,000 3,000 3,000 3,000 2,700 2,100 1,700 1,500 1,300 1,100 1,000 97018 2,100 2,100 2,100 2,100 2,100 2,100 1,900 1,500 1,300 1,100 910 810 730 6904 8,100 8,100 8,100 8,100 8,100 8,100 8,100 6,400 5,300 4,500 3,800 3,400 3,100 2,9008 5,300 5,300 5,300 5,300 5,300 5,300 5,300 4,200 3,400 2,900 2,500 2,200 2,000 1,90012 3,900 3,900 3,900 3,900 3,900 3,900 3,900 3,100 2,600 2,200 1,900 1,600 1,500 1,40018 2,800 2,800 2,800 2,800 2,800 2,800 2,800 2,200 1,800 1,600 1,300 1,200 1,100 1,0004 10,600 10,600 10,600 10,600 10,600 10,600 10,600 9,100 7,500 6,400 5,500 4,900 4,400 4,2008 6,900 6,900 6,900 6,900 6,900 6,900 6,900 6,000 4,900 4,200 3,600 3,200 2,900 2,70014 4,600 4,600 4,600 4,600 4,600 4,600 4,600 3,900 3,200 2,800 2,300 2,100 1,900 1,80020 3,400 3,400 3,400 3,400 3,400 3,400 3,400 2,900 2,400 2,000 1,700 1,600 1,400 1,3006 11,600 11,600 11,600 11,600 11,600 11,600 11,600 11,600 10,100 8,500 7,200 6,400 5,700 5,50010 8,500 8,500 8,500 8,500 8,500 8,500 8,500 8,500 7,400 6,300 5,300 4,700 4,200 4,00014 6,700 6,700 6,700 6,700 6,700 6,700 6,700 6,700 5,800 4,900 4,200 3,700 3,300 3,20020 5,100 5,100 5,100 5,100 5,100 5,100 5,100 5,100 4,400 3,800 3,200 2,800 2,500 2,4006 16,700 16,700 16,700 16,700 16,700 16,700 16,700 16,700 16,700 14,200 12,000 10,600 9,500 9,00010 12,400 12,400 12,400 12,400 12,400 12,400 12,400 12,400 12,400 10,600 8,900 7,900 7,100 6,70014 9,800 9,800 9,800 9,800 9,800 9,800 9,800 9,800 9,800 8,400 7,100 6,300 5,600 5,30020 7,500 7,500 7,500 7,500 7,500 7,500 7,500 7,500 7,500 6,400 5,400 4,800 4,300 4,1008 19,600 19,600 19,600 19,600 19,600 19,600 19,600 19,600 19,600 19,100 16,100 14,200 12,700 12,10012 15,300 15,300 15,300 15,300 15,300 15,300 15,300 5,300 15,300 14,800 12,500 11,100 9,900 9,40016 12,500 12,500 12,500 12,500 12,500 12,500 12,500 12,500 12,500 12,100 10,300 9,100 8,100 7,70022 9,800 9,800 9,800 9,800 9,800 9,800 9,800 9,800 9,800 9,500 8,100 7,100 6,400 6,0008 25,200 25,200 25,200 25,200 25,200 25,200 25,200 25,200 25,200 23,600 20,800 18,500 17,60012 19,900 19,900 19,900 19,900 19,900 19,900 19,900 19,900 19,900 18,600 16,400 14,600 13,90016 16,400 16,400 16,400 16,400 16,400 16,400 16,400 16,400 16,400 15,400 13,500 12,100 11,50022 13,000 13,000 13,000 13,000 13,000 13,000 13,000 13,000 13,000 12,200 10,700 9,600 9,10010 26,600 26,600 26,600 26,600 26,600 26,600 26,600 26,600 26,600 25,100 22,300 21,10014 22,000 22,000 22,000 22,000 22,000 22,000 22,000 22,000 22,000 20,700 18,400 17,50018 18,700 18,700 18,700 18,700 18,700 18,700 18,700 18,700 18,700 17,700 15,700 14,90024 15,300 15,300 15,300 15,300 15,300 15,300 15,300 15,300 15,300 14,500 12,800 12,20010 35,700 35,700 35,700 35,700 35,700 35,700 35,700 35,700 35,700 35,700 33,100 31,30014 29,500 29,500 29,500 29,500 29,500 29,500 29,500 29,500 29,500 29,500 27,300 25,90018 25,100 25,100 25,100 25,100 25,100 25,100 25,100 25,100 25,100 25,100 23,300 22,10024 20,600 20,600 20,600 20,600 20,600 20,600 20,600 20,600 20,600 20,600 19,000 19,00012 39,200 39,200 39,200 39,200 39,200 39,200 39,200 39,200 39,200 39,200 38,00016 33,200 33,200 33,200 33,200 33,200 33,200 33,200 33,200 33,200 33,200 32,10020 28,800 28,800 28,800 28,800 28,800 28,800 28,800 28,800 28,800 28,800 27,80026 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000 24,000 23,20012 49,000 49,000 49,000 49,000 49,000 49,000 49,000 49,000 49,000 49,000 49,00016 44,400 41,400 41,400 41,400 41,400 41,400 41,400 41,400 41,400 41,400 41,40020 35,900 35,900 35,900 35,900 35,900 35,900 35,900 35,900 35,900 35,900 35,90026 29,900 29,900 29,900 29,900 29,900 29,900 29,900 29,900 29,900 29,900 29,90014 54,100 54,100 54,100 54,100 54,100 54,100 54,100 54,100 54,100 54,100 54,10018 46,500 46,500 46,500 46,500 46,500 46,500 46,500 46,500 46,500 46,500 46,50022 40,800 40,800 40,800 40,800 40,800 40,800 40,800 40,800 40,800 40,800 40,80028 34,400 34,400 34,400 34,400 34,400 34,400 34,400 34,400 34,400 34,400 34,40014 65,700 65,700 65,700 65,700 65,700 65,700 65,700 65,700 65,700 65,700 65,70018 56,400 56,400 56,400 56,400 56,400 56,400 56,400 56,400 56,400 56,400 56,40022 49,500 49,500 49,500 49,500 49,500 49,500 49,500 49,500 49,500 49,500 49,50028 41,800 41,800 41,800 41,800 41,800 41,800 41,800 41,800 41,800 41,800 41,80016 67,700 67,700 67,700 67,700 67,700 67,700 67,700 67,700 67,70020 59,400 59,400 59,400 59,400 59,400 59,400 59,400 59,400 59,40024 52,900 52,900 52,900 52,900 52,900 52,900 52,900 52,900 52,90030 45,400 45,400 45,400 45,400 45,400 45,400 45,400 45,400 45,40016 80,400 80,400 80,400 80,400 80,400 80,400 80,400 80,400 80,40020 70,500 70,500 70,500 70,500 70,500 70,500 70,500 70,500 70,50026 59,500 59,500 59,500 59,500 59,500 59,500 59,500 59,500 59,50032 51,500 51,500 51,500 51,500 51,500 51,500 51,500 51,500 51,50016 94,500 94,500 94,500 94,500 94,500 94,500 94,500 94,500 94,50022 78,100 78,100 78,100 78,100 78,100 78,100 78,100 78,100 78,10028 66,500 66,500 66,500 66,500 66,500 66,500 66,500 66,500 66,50034 57,900 57,900 57,900 57,900 57,900 57,900 57,900 57,900 57,90016 110,000 110,000 110,000 110,000 110,000 110,000 110,000 110,000 110,00022 91,100 91,100 91,100 91,100 91,100 91,100 91,100 91,100 91,10028 77,600 77,600 77,600 77,600 77,600 77,600 77,600 77,600 77,60036 64,800 64,800 64,800 64,800 64,800 64,800 64,800 64,800 64,800

Left of dark line represents stress constrained and right of dark line represents deflection constrained.

10

* Based on SAE 1018 material, using either a bending stress of 8000 psi from resultant load (no torque), or a free shaft deflection at the hub of 0.0023 inches per inch (tan of 8 minutes), Highlight reflects loads potentially exceeding scope of B105.1. Review belt PIW and modulus.

8 1/2

9

9 1/2

7

7 1/2

8

5 7/16

6

6 1/2

3 15/16

4 7/16

4 15/16

2 11/16

2 15/16

3 7/16

1 15/16

2 3/16

2 7/16

1 3/16

1 7/16

1 11/16

( D ) SHAFT DIAMETER

(in)

( L ) BEARING CENTERS

MINUS FACE (in)

PULLEY FACE WIDTH (in)

Table 4-A. Load Ratings (lbf) for Pulley and Shaft Combinations*

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305 356 406 457 508 559 660 813 965 1118 1295 1448 1600 1676

51 4.45 4.09 3.47 2.98 2.62 2.36 1.96 1.56 1.29 1.07 0.93 0.80 0.76 0.71152 2.54 2.31 1.96 1.69 1.51 1.33 1.11 0.89 0.71 0.62 0.53 0.44 0.42 0.40254 1.78 1.65 1.38 1.20 1.02 0.93 0.76 0.62 0.49 0.43 0.36 0.32 0.29 0.28356 1.33 1.25 1.07 0.89 0.80 0.71 0.58 0.49 0.39 0.33 0.28 0.25 0.23 0.2176 6.67 6.67 6.23 5.34 4.89 4.23 3.51 2.76 2.27 1.96 1.65 1.47 1.33 1.29

152 4.45 4.45 4.23 3.65 3.20 2.85 2.36 1.87 1.56 1.33 1.11 0.98 0.89 0.85254 3.11 3.11 2.94 2.54 2.22 2.00 1.65 1.29 1.07 0.93 0.80 0.71 0.62 0.58356 2.40 2.40 2.27 1.96 1.73 1.56 1.29 1.02 0.85 0.71 0.62 0.53 0.49 0.4476 10.68 10.68 10.68 10.23 8.90 8.01 6.67 5.34 4.36 3.69 3.16 2.80 2.54 2.40

152 7.12 7.12 7.12 7.12 6.23 5.34 4.45 3.56 2.94 2.49 2.14 1.91 1.69 1.65254 4.89 4.89 4.89 4.89 4.27 3.78 3.11 2.49 2.05 1.73 1.51 1.33 1.20 1.16406 3.47 3.47 3.47 3.34 2.94 2.62 2.18 1.69 1.42 1.20 1.02 0.93 0.80 0.8076 16.46 16.46 16.46 16.46 15.57 13.79 11.56 9.34 7.56 6.23 5.34 4.89 4.40 4.18

152 11.12 11.12 11.12 11.12 10.68 9.34 8.01 6.23 4.89 4.36 3.74 3.29 2.98 2.85254 7.56 7.56 7.56 7.56 7.56 6.67 5.34 4.31 3.56 3.02 2.58 2.31 2.09 1.96406 5.34 5.34 5.34 5.34 4.89 4.45 3.74 2.98 2.45 2.09 1.78 1.60 1.42 1.3876 23.57 23.57 23.57 23.57 23.57 22.68 18.68 14.68 12.45 10.68 8.90 8.01 7.12 6.67

203 12.90 12.90 12.90 12.90 12.90 12.45 10.23 8.45 6.67 5.78 4.89 4.40 3.96 3.78305 9.79 9.79 9.79 9.79 9.79 9.34 7.56 6.23 4.89 4.31 3.65 3.25 2.94 2.80457 6.67 6.67 6.67 6.67 6.67 6.67 5.34 4.36 3.60 3.07 2.62 2.36 2.09 2.00102 28.02 28.02 28.02 28.02 28.02 28.02 24.91 19.57 16.46 13.79 12.01 10.68 9.34 8.90203 17.79 17.79 17.79 17.79 17.79 17.79 16.01 12.90 10.68 8.90 7.56 6.67 6.23 5.78305 13.34 13.34 13.34 13.34 13.34 13.34 12.01 9.34 7.56 6.67 5.78 4.89 4.45 4.31457 9.34 9.34 9.34 9.34 9.34 9.34 8.45 6.67 5.78 4.89 4.05 3.60 3.25 3.07102 36.03 36.03 36.03 36.03 36.03 36.03 36.03 28.47 23.57 20.02 16.90 15.12 13.79 12.90203 23.57 23.57 23.57 23.57 23.57 23.57 23.57 18.68 15.12 12.90 11.12 9.79 8.90 8.45305 17.35 17.35 17.35 17.35 17.35 17.35 17.35 13.79 11.56 9.79 8.45 7.12 6.67 6.23457 12.45 12.45 12.45 12.45 12.45 12.45 12.45 9.79 8.01 7.12 5.78 5.34 4.89 4.45102 47.15 47.15 47.15 47.15 47.15 47.15 47.15 40.48 33.36 28.47 24.46 21.80 19.57 18.68203 30.69 30.69 30.69 30.69 30.69 30.69 30.69 26.69 21.80 18.68 16.01 14.23 12.90 12.01356 20.46 20.46 20.46 20.46 20.46 20.46 20.46 17.35 14.23 12.45 10.23 9.34 8.45 8.01508 15.12 15.12 15.12 15.12 15.12 15.12 15.12 12.90 10.68 8.90 7.56 7.12 6.23 5.78152 51.60 51.60 51.60 51.60 51.60 51.60 51.60 51.60 44.92 37.81 32.03 28.47 25.35 24.46254 37.81 37.81 37.81 37.81 37.81 37.81 37.81 37.81 32.92 28.02 23.57 20.91 18.68 17.79356 29.80 29.80 29.80 29.80 29.80 29.80 29.80 29.80 25.80 21.80 18.68 16.46 14.68 14.23508 22.68 22.68 22.68 22.68 22.68 22.68 22.68 22.68 19.57 16.90 14.23 12.45 11.12 10.68152 74.28 74.28 74.28 74.28 74.28 74.28 74.28 74.28 74.28 63.16 53.38 47.15 42.26 40.03254 55.16 55.16 55.16 55.16 55.16 55.16 55.16 55.16 55.16 47.15 39.59 35.14 31.58 29.80356 43.59 43.59 43.59 43.59 43.59 43.59 43.59 43.59 43.59 37.36 31.58 28.02 24.91 23.57508 33.36 33.36 33.36 33.36 33.36 33.36 33.36 33.36 33.36 28.47 24.02 21.35 19.13 18.24203 87.18 87.18 87.18 87.18 87.18 87.18 87.18 87.18 87.18 84.96 71.61 63.16 56.49 53.82305 68.05 68.05 68.05 68.05 68.05 68.05 68.05 23.57 68.05 65.83 55.60 49.37 44.04 41.81406 55.60 55.60 55.60 55.60 55.60 55.60 55.60 55.60 55.60 53.82 45.81 40.48 36.03 34.25559 43.59 43.59 43.59 43.59 43.59 43.59 43.59 43.59 43.59 42.26 36.03 31.58 28.47 26.69203 112.09 112.09 112.09 112.09 112.09 112.09 112.09 112.09 112.09 104.97 92.52 82.29 78.28305 88.52 88.52 88.52 88.52 88.52 88.52 88.52 88.52 88.52 82.73 72.95 64.94 61.83406 72.95 72.95 72.95 72.95 72.95 72.95 72.95 72.95 72.95 68.50 60.05 53.82 51.15559 57.82 57.82 57.82 57.82 57.82 57.82 57.82 57.82 57.82 54.27 47.59 42.70 40.48254 118.32 118.32 118.32 118.32 118.32 118.32 118.32 118.32 118.32 111.64 99.19 93.85356 97.86 97.86 97.86 97.86 97.86 97.86 97.86 97.86 97.86 92.07 81.84 77.84457 83.18 83.18 83.18 83.18 83.18 83.18 83.18 83.18 83.18 78.73 69.83 66.28610 68.05 68.05 68.05 68.05 68.05 68.05 68.05 68.05 68.05 64.50 56.93 54.27254 158.79 158.79 158.79 158.79 158.79 158.79 158.79 158.79 158.79 158.79 147.23 139.22356 131.22 131.22 131.22 131.22 131.22 131.22 131.22 131.22 131.22 131.22 121.43 115.20457 111.64 111.64 111.64 111.64 111.64 111.64 111.64 111.64 111.64 111.64 103.64 98.30610 91.63 91.63 91.63 91.63 91.63 91.63 91.63 91.63 91.63 91.63 84.51 84.51305 174.36 174.36 174.36 174.36 174.36 174.36 174.36 174.36 174.36 174.36 169.02406 147.67 147.67 147.67 147.67 147.67 147.67 147.67 147.67 147.67 147.67 142.78508 128.10 128.10 128.10 128.10 128.10 128.10 128.10 128.10 128.10 128.10 123.65660 106.75 106.75 106.75 106.75 106.75 106.75 106.75 106.75 106.75 106.75 103.19305 217.95 217.95 217.95 217.95 217.95 217.95 217.95 217.95 217.95 217.95 217.95406 197.49 184.15 184.15 184.15 184.15 184.15 184.15 184.15 184.15 184.15 184.15508 159.68 159.68 159.68 159.68 159.68 159.68 159.68 159.68 159.68 159.68 159.68660 133.00 133.00 133.00 133.00 133.00 133.00 133.00 133.00 133.00 133.00 133.00356 240.64 240.64 240.64 240.64 240.64 240.64 240.64 240.64 240.64 240.64 240.64457 206.83 206.83 206.83 206.83 206.83 206.83 206.83 206.83 206.83 206.83 206.83559 181.48 181.48 181.48 181.48 181.48 181.48 181.48 181.48 181.48 181.48 181.48711 153.01 153.01 153.01 153.01 153.01 153.01 153.01 153.01 153.01 153.01 153.01356 292.23 292.23 292.23 292.23 292.23 292.23 292.23 292.23 292.23 292.23 292.23457 250.87 250.87 250.87 250.87 250.87 250.87 250.87 250.87 250.87 250.87 250.87559 220.18 220.18 220.18 220.18 220.18 220.18 220.18 220.18 220.18 220.18 220.18711 185.93 185.93 185.93 185.93 185.93 185.93 185.93 185.93 185.93 185.93 185.93406 301.13 301.13 301.13 301.13 301.13 301.13 301.13 301.13 301.13508 264.21 264.21 264.21 264.21 264.21 264.21 264.21 264.21 264.21610 235.30 235.30 235.30 235.30 235.30 235.30 235.30 235.30 235.30762 201.94 201.94 201.94 201.94 201.94 201.94 201.94 201.94 201.94406 357.62 357.62 357.62 357.62 357.62 357.62 357.62 357.62 357.62508 313.58 313.58 313.58 313.58 313.58 313.58 313.58 313.58 313.58660 264.66 264.66 264.66 264.66 264.66 264.66 264.66 264.66 264.66813 229.07 229.07 229.07 229.07 229.07 229.07 229.07 229.07 229.07406 420.34 420.34 420.34 420.34 420.34 420.34 420.34 420.34 420.34559 347.39 347.39 347.39 347.39 347.39 347.39 347.39 347.39 347.39711 295.79 295.79 295.79 295.79 295.79 295.79 295.79 295.79 295.79864 257.54 257.54 257.54 257.54 257.54 257.54 257.54 257.54 257.54406 489.28 489.28 489.28 489.28 489.28 489.28 489.28 489.28 489.28559 405.21 405.21 405.21 405.21 405.21 405.21 405.21 405.21 405.21711 345.16 345.16 345.16 345.16 345.16 345.16 345.16 345.16 345.16914 288.23 288.23 288.23 288.23 288.23 288.23 288.23 288.23 288.23

Left of dark line represents stress constrained and right of dark line represents deflection constrained.

254.000

* Based on SAE 1018 material, using either a bending stress of 55.2 Mpa from resultant load (no torque), or a free shaft deflection at the hub of 0.0023 mm per Highlight reflects loads potentially exceeding scope of B105.1. Review belt kN and modulus.

215.900

228.600

241.300

177.800

190.500

203.200

138.113

152.400

165.100

100.013

112.713

125.413

68.263

74.613

87.313

49.213

55.563

61.913

30.163

36.513

42.863

( D ) SHAFT DIAMETER

(mm)

( L ) BEARING CENTERS

MINUS FACE (mm)

PULLEY FACE WIDTH (mm)

Table 4-B. Load Ratings (kN) for Pulley and Shaft Combinations*

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4.7 Availability: Refer to Tables 5-A and 5-B to make sure pulley diameter, face width, and shaft diameter selected are available. If the combination is not available it will be necessary to go to a larger pulley or shaft.

Table 5-A. Available Shaft Diameters (in)

PULLEY DIAMETER (in)

FACE WIDTH (in)

12 14 16 18 20 22 26 32 38 44 51 57 63 66

8

1 3/16 1 3/16 1 3/16 1 3/16 1 3/16 1 3/16 1 3/16 1 7/16 1 7/16 1 11/16 1 15/16 2 3/16 2 7/16 -

thru thru thru thru thru thru thru thru thru thru thru thru

2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 -

10

1 3/16 1 3/16 1 3/16 1 3/16 1 3/16 1 3/16 1 3/16 1 7/16 1 7/16 1 11/16 1 15/16 2 3/16 2 7/16 -

thru thru thru thru thru thru thru thru thru thru thru thru thru

2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 -

12

1 3/16 1 3/16 1 3/16 1 3/16 1 3/16 1 3/16 1 3/16 1 7/16 1 11/16 1 15/16 1 15/16 2 3/16 2 7/16 2 11/16

thru thru thru thru thru thru thru thru thru thru thru thru thru thru

3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16

14

1 7/16 1 7/16 1 7/16 1 7/16 1 7/16 1 7/16 1 7/16 1 7/16 1 11/16 1 15/16 1 15/16 2 3/16 2 7/16 2 11/16


3 7/16 3 7/16 3 7/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16

16

1 7/16 1 7/16 1 7/16 1 7/16 1 7/16 1 7/16 1 7/16 1 11/16 1 15/16 1 15/16 2 3/16 2 7/16 2 7/16 2 11/16


3 7/16 3 7/16 3 15/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16

18

1 11/16 1 11/16 1 11/16 1 11/16 1 11/16 1 11/16 1 11/16 1 15/16 2 3/16 2 3/16 2 7/16 2 7/16 2 7/16 2 11/16


3 7/16 3 7/16 3 15/16 4 7/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16

20

1 15/16 1 15/16 1 15/16 1 15/16 1 15/16 1 15/16 1 15/16 1 15/16 2 3/16 2 3/16 2 7/16 2 7/16 2 7/16 2 11/16


3 7/16 3 7/16 3 15/16 4 7/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16 4 15/16

24

1 15/16 1 15/16 1 15/16 1 15/16 1 15/16 1 15/16 1 15/16 2 3/16 2 7/16 2 7/16 2 7/16 2 11/16 2 11/16 2 15/16


4 7/16 4 15/16 6 6 6 6 6 6 6 6 6 6 6 6

30

2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 7/16 2 11/16 2 11/16 2 15/16 3 15/16 3 15/16


4 7/16 4 15/16 6 8 8 8 8 8 8 8 8 8 8 8

36

2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 2 15/16 3 7/16 3 7/16 3 7/16


4 7/16 4 15/16 6 8 8 9 9 9 10 10 10 10 10 10

42

- 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 7/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16


- 4 15/16 6 8 8 9 9 9 10 10 10 10 10 10

48

- 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16 3 15/16


- 4 15/16 6 8 8 9 9 9 10 10 10 10 10 10

54

- 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16


- 4 15/16 6 8 8 9 9 9 10 10 10 10 10 10

60

- 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16 4 7/16


- 4 15/16 6 8 8 9 9 9 10 10 10 10 10 10

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Table 5-B. Available Shaft Diameters (mm)

END OF STANDARD APPENDICES FOLLOW

PULLEY DIAMETER

(mm)

FACE WIDTH (mm) 305 356 406 457 508 559 660 813 965 1118 1295 1448 1600 1676

203

30.163 30.163 30.163 30.163 30.163 30.163 30.163 36.513 36.513 42.863 49.213 55.563 61.913 -

thru thru thru thru thru thru thru thru thru thru thru thru

61.913 61.913 61.913 61.913 61.913 61.913 61.913 61.913 61.913 61.913 61.913 61.913 -

254

30.163 30.163 30.163 30.163 30.163 30.163 30.163 36.513 36.513 42.863 49.213 55.563 61.913 -


74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 -

305

30.163 30.163 30.163 30.163 30.163 30.163 30.163 36.513 42.863 49.213 49.213 55.563 61.913 68.263


87.313 87.313 87.313 87.313 87.313 87.313 87.313 87.313 87.313 87.313 87.313 87.313 87.313 87.313

356

36.513 36.513 36.513 36.513 36.513 36.513 36.513 36.513 42.863 49.213 49.213 55.563 61.913 68.263


87.313 87.313 87.313 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013

406

36.513 36.513 36.513 36.513 36.513 36.513 36.513 42.863 49.213 49.213 55.563 61.913 61.913 68.263


87.313 87.313 100.013 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713

457

42.863 42.863 42.863 42.863 42.863 42.863 42.863 49.213 55.563 55.563 61.913 61.913 61.913 68.263


87.313 87.313 100.013 112.713 125.413 125.413 125.413 125.413 125.413 125.413 125.413 125.413 125.413 125.413

508

49.213 49.213 49.213 49.213 49.213 49.213 49.213 49.213 55.563 55.563 61.913 61.913 61.913 68.263


87.313 87.313 100.013 112.713 125.413 125.413 125.413 125.413 125.413 125.413 125.413 125.413 125.413 125.413

610

49.213 49.213 49.213 49.213 49.213 49.213 49.213 55.563 61.913 61.913 61.913 68.263 68.263 74.613


112.713 125.413 152.400 152.400 152.400 152.400 152.400 152.400 152.400 152.400 152.400 152.400 152.400 152.400

762

61.913 61.913 61.913 61.913 61.913 61.913 61.913 61.913 61.913 68.263 68.263 74.613 100.013 100.013


112.713 125.413 152.400 203.200 203.200 203.200 203.200 203.200 203.200 203.200 203.200 203.200 203.200 203.200

914

74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 74.613 87.313 87.313 87.313


112.713 125.413 152.400 203.200 203.200 228.600 228.600 228.600 254.000 254.000 254.000 254.000 254.000 254.000

1067

- 87.313 87.313 87.313 87.313 87.313 87.313 87.313 87.313 100.013 100.013 100.013 100.013 100.013


- 125.413 152.400 203.200 203.200 228.600 228.600 228.600 254.000 254.000 254.000 254.000 254.000 254.000

1219

- 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013 100.013


- 125.413 152.400 203.200 203.200 228.600 228.600 228.600 254.000 254.000 254.000 254.000 254.000 254.000

1372

- 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713


- 125.413 152.400 203.200 203.200 228.600 228.600 228.600 254.000 254.000 254.000 254.000 254.000 254.000

1524

- 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713 112.713


- 125.413 152.400 203.200 203.200 228.600 228.600 228.600 254.000 254.000 254.000 254.000 254.000 254.000

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APPENDIX I: CONVERSION FACTORS TO SI UNITS

This appendix is not part of the standard, but is included for the information of those who wish to become acquainted with the international system of units called SI. The following SI conversion factors are used for the units shown in this standard:

To Convert From To Multiply

By inches (in) millimeters (mm) 25.40 pounds-mass (lbm) kilograms (kg) 0.45359 pounds-force (lbf) Newton (N) 4.44822 pound-inches (lb-in) Newton-meters (N-m) 0.11298 pounds per square inch (psi) megaPascal (MPa) 0.006895 foot per minute (fpm) meters/second (m/s) 0.00508 pounds per inch width (PIW) kilonewton per meter (kN-m) 0.1751

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APPENDIX II: SHAFT DEFLECTION FORMULA

Determine the shaft deflection slope at the pulley end disc using the following equation:

2Tan

4 y

RA B A

E I

Where: A = Moment arm for pulley [in (mm)] B = Bearing centers [in (mm)] R = Resultant pulley load [(lbf (N)] Ey = Young’s modulus for steel [psi (MPa)] 29 X 106 psi (200,000 MPa) I = Area moment of inertia of shaft 0.049087 D4 [in4 (mm4)] D = Diameter of shaft [in (mm)] Tan α = Tangent of the angle made by the deflected shaft and its neutral axis before bending, at the pulley hub. Allowable Slope:

Tan α = 0.0023 in per in (0.0023 mm per mm) or tangent of 8 minutes. If the slope is greater than 0.0023 in per in (0.0023 mm per mm), it will be necessary to go to a larger shaft diameter or consult your pulley manufacturer.

Note: the resultant deflection calculated using these formulas will exceed the actual deflection which will depend on the end disc constraint.

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APPENDIX III: OVERHUNG LOAD DERIVATION AND DISCUSSION

In the 2009 edition, the overhung load calculations were changed to create a direct relationship of the design equations to the physical situation. With this the method can be applied to situations beyond a single radial overhung load vector.

Using the pulley assembly shown in Figure 2 a shaft free body diagram with overhung load (P) is shown. For pulley selection the greater bending moment at the pulley attachment is used in section 4.3. If identical overhung loads exist on both shaft ends the moment at the pulley attachment is the sum of both moments shown and Mo = P*C. Figure 3: Free Body Diagram

Figure 4: Shaft Mounted Drive Figure 5: Swing Base Drive Considering the drive depicted in Figure 4 the dead load (W) will be made up of the weight of all drive components supported by the shaft. The load (W) will counteract the weight component of the pulley that is located between the bearings. We will also have a live load (F) due to the torque being applied to the shaft to drive the belt. For a drive pulley we have T1 and T2 for belt tension, with the difference being Te. The belt is driven by supplying Torque to the pulley. The torque is equal to the distance from the center of the shaft to the centerline of the belt times Te. The force (F) in the torque arm is determined by dividing the Torque by the Torque Arm Distance (D). Then the resultant of the drive can be determined by vector

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summation of the weight component and the torque component. The force in the torque arm will have an equal and opposite force that will act at the shaft. See example 3 for a sample solution for this case. Likewise with Figure 5 we have a dead load (W) and a live load (F) in the torque arm, however the dead load here cannot be determined by summation of the component weights of the drive. It will be required here to determine the component weights with regard to the location of the torque arm to determine the component of the drive weight supported by the shaft. This case will also have a torque component, but here it is also important to note that the direction of the torque component is dependent on the orientation of the drive. For the case shown in Figure 5, if the pulley is located on the other side of the drive and the rotation is clockwise we would calculate a negative force. This force transferred to the shaft would be pointing up in direction. This would give us a worst case since it would be working in conjunction with the pulley weight component of the resultant load. See example 4 for a sample solution for this case. The drive orientation shown in example 4 would provide a result that is not as severe as noted above. As a historical reference, earlier B105.1 versions calculated an overhung load factor (J) which was a ratio of belt resultant load moment and overhung load moment at the pulley connection divided by two.

2oM

JM

or

P C B AJ

R A B

for single PT component.

The moment modifying factor (K) was then read from table 6 using J and angle E from Figure 2 in section 4.3. Table 6 is included here for historical preservation.

Table 6. Overhung Load K Factor

J (E) Angle (deg)

0 30 60 90 120 150 180

0.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.05 1.00 1.00 1.00 1.01 1.05 1.09 1.10

0.10 1.00 1.00 1.00 1.02 1.11 1.18 1.20

0.15 1.00 1.00 1.00 1.04 1.18 1.27 1.30

0.20 1.00 1.00 1.00 1.08 1.25 1.36 1.40

0.25 1.00 1.00 1.00 1.12 1.32 1.45 1.50

0.30 1.00 1.00 1.00 1.17 1.40 1.55 1.60

0.35 1.00 1.00 1.00 1.22 1.48 1.64 1.70

0.40 1.00 1.00 1.00 1.28 1.56 1.74 1.80

0.45 1.00 1.00 1.00 1.35 1.65 1.84 1.90

0.50 1.00 1.00 1.00 1.41 1.73 1.93 2.00

0.55 1.00 1.00 1.05 1.49 1.82 2.03 2.10

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APPENDIX IV: EXAMPLE SELECTION

Imperial Example 1a: Non-Drive Pulley (no torque or overhung load) An 18° surge pile feed conveyor has an existing gravity take-up lower bend pulley which has experienced multiple fatigue failures around the pulley hub. The maintenance manager has tried various brands of standard pulleys with similar results. His most recent pulley manufacturer suggests reviewing the pulley selection. Often the plant runs rock directly to the crushing and screening area and at these times the surge pile conveyors are turned off. This conveyor runs approximately 50% of the time at a speed of 350 feet per minute. The existing pulley is a 24 in x 44 in drum with a 2 15/16 in shaft diameter at the pulley and bearing. Bearing centers are measured at 58 in and belt width is measured at 42 in. Gravity take-up system, including take-up pulley, frame, and weight box is lifted with a crane and its scale indicates 8,000 lbm total, or 4,000 lbf belt tension. Review of selection is as follows: Step 1. Pulley Diameter Selection, section 4.1. A tension of 4,000 lbf divided by a 42 in belt width = 95 PIW. In Tables 1-A and 1-B for 24 in diameter and 110° arc of contact, an allowable PIW of 175 is shown. Therefore, a 24 in pulley diameter is acceptable. Step 2. Resultant Radial Load, section 4.2. Pulley and shaft weight W is estimated from a manufacturer’s catalog to be 800 lbm. Being a lower bend for a vertical gravity take-up, the belt wrap is 90° plus the incline of 18° as shown in Figure 1. Resultant load R = 7,130 lbf. Step 3. Overhung Load, section 4.3. This is a bend pulley without any power transmission components. Overhung loads do not apply, K=1. Step 4. Minimum Shaft Diameter (fatigue), section 4.4. This is a bend pulley without any power transmission components. This step can be omitted. Step 5. Pulley Fatigue Life, section 4.5. Based on 50% run time expectations and 350 fpm belt speed a fatigue multiplication factor (Z) of 1.0 is appropriate. Step 6. Pulley Selection, section 4.6. In this case K = Z = 1, so no resultant load modification is necessary. Distance L = 14 in is calculated using bearing center = 58 in and face width = 44 in. In Table 2-A, using 44 in face width, 2 15/16 in shaft diameter, and L = 14 in a maximum resultant load of 2,800 lbf is obtained. This is significantly less than the actual value of 7,130 lbf calculated in step 2. To determine the correct selection the designer goes to Table 2-A, 44 in face width, L = 14 in and R = 7,130 lbf, a 3-15/16 in diameter shaft with a rating of 8,400 lbf is required in this case.

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Step 7. Availability, section 4.7. In Table 5-A, for a 24 in diameter by 44 in face pulley, a 3-15/16 in shaft diameter is available. The maintenance manager desires to upgrade to the pulley with a 3 15/16 in shaft diameter, but doesn’t have room for a larger bearing. Going beyond the scope of CEMA B105.1, the pulley designer performs additional calculations indicating that with special control of shaft material, surface finishes, and journal radii a shaft design is possible allowing the use of the existing 2-15/16 in bearing size.

Metric Example 1b: Non-Drive Pulley (no torque or overhung load) An 18° surge pile feed conveyor has an existing gravity take-up lower bend pulley which has experienced multiple fatigue failures around the pulley hub. The maintenance manager has tried various brands of standard pulleys with similar results. His most recent pulley manufacturer suggests reviewing the pulley selection. Often the plant runs rock directly to the crushing and screening area and at these times the surge pile conveyors are turned off. This conveyor runs approximately 50% of the time at a speed of 1.8 m/s. The existing pulley is a 610 mm x 1,118 mm drum with a 74.613 mm shaft diameter at the pulley and bearing. Bearing centers are measured at 1,473 mm and belt width is measured at 1,067 mm. Gravity take-up system, including take-up pulley, frame, and weight box is lifted with a crane and its scale indicates 3,629 kg total, or 17.8 kN belt tension. Review of selection is as follows: Step 1. Pulley Diameter Selection, section 4.1. A tension of 17.8 kN divided by a 1,067 mm belt width = 16.7 kN/m. In Table 1-B for 610 mm diameter and 110° arc of contact, a maximum belt tension of 31 kN/m is shown. Therefore, a 610 mm pulley diameter is acceptable. Step 2. Resultant Radial Load, section 4.2. Pulley and shaft weight W is estimated from a manufacturer’s catalog to be 363 kg. Being a lower bend for a vertical gravity takeup, the belt wrap is 90° plus the incline of 18° as shown in Figure 1. Resultant load R = 31.7 kN Step 3. Overhung Load, section 4.3. This is a bend pulley without any power transmission components. Overhung loads do not apply, K=1. Step 4. Minimum Shaft Diameter (fatigue), section 4.4. This is a bend pulley without any power transmission components. This step can be omitted. Step 5. Pulley Fatigue Life, section 4.5. Based on 50% run time expectations and 1.8 m/s belt speed a fatigue multiplication factor (Z) of 1.0 is appropriate.

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Step 6. Pulley Selection, section 4.6. In this case K = Z = 1, so no resultant load modification is necessary. Distance L = 355 mm is calculated using bearing center = 1,473 mm and face width = 1,118 mm. In Table 2-B, using 1,118 mm face width, 74.613 mm shaft diameter and L = 356 mm a maximum resultant load of 12.45 kN is obtained. This is significantly less than the actual value of 31.7 kN calculated in step 2. To determine the correct selection the designer goes to Table 2-B using 1,118 mm face width, L = 356 mm and R = 31.7 kN, a 100.013 mm diameter shaft with a rating of 37.36 kN is required in this case. Step 7. Availability, section 4.7. In Table 5-B for a 610 mm diameter by 1,118 mm face pulley, a 100.013 mm shaft diameter is available. The maintenance manager desires to upgrade to the pulley with a 100.013 mm shaft diameter, but doesn’t have room for a larger bearing. Going beyond the scope of CEMA B105.1, the pulley designer performs additional calculations indicating that with special control of shaft material, surface finishes, and journal radii a shaft design is possible allowing the use of the existing 74.613 mm bearing size. Imperial Example 2a: Drive Pulley (no overhung load) An in plant transfer conveyor is being designed with a 36 in wide fabric belt. There is an existing 30 in x 38 in CEMA drum pulley with a 4 7/16 in shaft. Pillow block bearing are mounted at 54 in centers. The pulley assembly was driven over the plants scale and its weight measured 900 lbf. Belt is inclined at 4.5° and is snubbed to 215° arc of contact. The drive assembly will be mounted to a concrete footing and attached to the shaft with a flexible coupling. Belt speed is 600 fpm and the conveyor is planned to run two 10 hours shifts 6 days per week. Review of selection is as follows: Step 1. Pulley Diameter Selection, section 4.1. A tension of 7,100 lbf divided by a 36 in belt width = 197 PIW. In Table 1-A, for 30 in diameter, interpolating between 210° and 220° arc of contact, a value of 318 PIW is determined. Therefore, a 30 in pulley diameter is acceptable. Step 2. Resultant Radial Load, section 4.2. Using equation for an inclined drive with >180° wrap from Figure 1, the resultant load R = 9,440 lbf.

1

2

4.5

30.5

Step 3. Overhung Load, section 4.3. Assuming proper alignment and runouts specified within limits of flexible coupling, radial overhung loads should be negligible and purely torsional loads are assumed. Overhung loads do not apply, K=1.

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Step 4. Minimum Shaft Diameter (fatigue), section 4.4.

1 2 65,400 lbf-in ,where r = pull

. 1.5

3 9440 8 351,920 lbf-in

2 2 2T T 7100 274 ey radius0 15 ine

F S

R NR AM

r T T r

32,000

* 29,000

0.8 0.7534 0.897 1 1 0.63 1 29,000 9,877

y

f

f a b c d e f g f

S psi

S psi

S k k k k k k k S psi

2 2

332 1.5 51,920 3 65,400

4.39 3.14159 9,877 4 32,000

D in

The 4-7/16 in diameter shaft is found to be adequate. Step 5. Pulley Fatigue Life, section 4.5. Two 10 hour shifts 6 days per week is a 71% run time expectation at 600 fpm belt speed. Using the guidelines in section 4.5 the designer chose a fatigue multiplication factor (Z) of 1.25. Step 6. Pulley Selection, section 4.6. Using multipliers K = 1 and Z = 1.25, with the resultant load from Step 2 a value of 11,800 lbf is used to compare with Table 1-A. Distance L = 16 in is calculated using bearing center = 54 in and face width = 38 in. In Table 4-A, a maximum resultant load of 12,500 lbf is obtained. Which is greater than 11,800 lbf calculated and this pulley is expected to perform well in the application. Step 7. Availability, section 4.7. Not applicable since this pulley is already on site.

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Metric Example 2b: Drive Pulley (no overhung load) An in-plant transfer conveyor is being designed with a 914 mm (0.914 m) wide fabric belt. There is an existing 762 mm x 965 mm CEMA drum pulley with a 112.713 mm shaft. Pillow block bearing are mounted at 1372 mm centers. The pulley assembly was driven over the plants scale and its weight measured 408 kg. Belt is inclined at 4.5° and is snubbed to 215° arc of contact. The drive assembly will be mounted to a concrete footing and attached to the shaft with a flexible coupling. Belt speed is 3.05 m/s and the conveyor is planned to run two 10 hours shifts 6 days per week. Review of selection is as follows: Step 1. Pulley Diameter Selection, section 4.1. A tension of 31.58 kN divided by a 0.914 m belt width = 34.6 kN/m. In Table 1-B, for 762 mm diameter, interpolating between 210° and 220° arc of contact, a value of 55.7 kN/m is determined. Therefore, a 762 mm pulley diameter is acceptable. Step 2. Resultant Radial Load, section 4.2. Using equation for an inclined drive with >180° wrap from Figure 1 the resultant load is R = 42.0 kN.

1

2

4.5

30.5

Step 3. Overhung Load, section 4.3. Assuming proper alignment and runout specified within limits of flexible coupling, radial overhung loads should be negligible and purely torsional loads are assumed. Overhung loads do not apply, K=1. Step 4. Minimum Shaft Diameter (fatigue), section 4.4.

1 2 N-mm ,where r = pull

. 1.5

0.076 42,000 203 765,859,000 N-mm

2 2 2T T 31,580 12,190 381 7,387,590

220

ey radius m

* 200

0.8 0.7534 0.897 1 1 0.6 8

m

3 1 200 6

e

y

f

f a b c d e f g f

F S

R NR AM

r T T r

S MPa

S MPa

S k k k k k k k S

.1 MPa

2 2

332 1.5 5,859,000 3 7,387,590

111.5 mm3.14159 68.1 4 220.0

D

The 112.713 mm diameter shaft, is found to be adequate. Step 5. Pulley Fatigue Life, section 4.5. Two 10 hour shifts 6 days per week is a 71% run time expectation at 3.05 m/s belt speed. Using the guidelines in section 4.5 the designer chose a fatigue multiplication factor (Z) of 1.25.

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Step 6. Pulley Selection, section 4.6. Using multipliers K = 1 and Z = 1.25, with the resultant load from Step 2, a value of 52.5 kN is used to compare with Table 1-B. Distance L = 406 mm is calculated using bearing center = 1,371.6 mm and face width = 965.2 mm. In Table 4-B, a maximum resultant load of 55.6 kN is obtained. Which is greater than 52.5 kN calculated and this pulley is expected to perform well in the application. Step 7. Availability, section 4.7. Not applicable since this pulley is already on site. Imperial Example 3a: Drive Pulley (with overhung load) A conveyor is being designed to move rock up a 10° hill. A 36 in belt was previously chosen to run at 475 fpm. The power requirement calculated is 12 hp without material load and 63 hp with normal running load. A 75 hp motor is selected. A hollow parallel shaft mount reducer is desired. The drive will be snubbed to 210° and a gravity take-up is used.

T1 = Belt Tension Carrying Side (lbf)

T2 = Belt Tension Return Side (lbf) Review of selection is as follows: Step 1. Pulley Diameter Selection, section 4.1. Belt tensions are determined at various running conditions using CEMA methods. Applicable equations from other standards given below.

2

1 2

33,000 /

0.38e

e e

e

T hp fpm

T Cw T T

T T T

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It is anticipated belt will slip on pulley at 150 % of full horsepower so this is taken as maximum possible condition. Other operating conditions anticipated are stationary with no power, running without load, running at normal load and full motor power.

Condition HP Te

(lbf) T2

(lbf) T1

(lbf) PIW

No Power 0 0 1,980 1,980 55 No Load 12 834 1,980 2,814 78 Normal Load 63 4,377 1,980 6,357 177 Full Power 75 5,211 1,980 7,191 200 Max. Possible 112.5 7,816 1,980 9,796 272

Comparing full power PIW of 200 and a 210° belt wrap with Table 1-A, results in a match with the upper limit for a 20 in diameter pulley. The designer chose the 24 in diameter to maintain a conservative selection. Step 2. Resultant Radial Load, section 4.2. Based on the analysis of belt tension vectors versus pulley weight vectors this is a case where weight has a negligible impact on the pulleys resultant load. For simplicity pulley weight has been omitted.

0.52 2

1 2 1 22 cos pR T T T T W

1 1 2 2

1 1 2 2

sin sinrctan

cos cos

T TA

T T

Belt Resultant Load Moment

2

AM R

Step 3. Overhung Load, section 4.3. Moment from Weights: Drive component weights, and dimensions shown on the example drawing are obtained from component manufacturer literature. Total overhung weight (Pw) = ∑ component weights (lbm) = 990 + 30 + 1,065 + 25 = 2,110 lbm

Condition Resultant

(lbf)

Resultant Angle (deg)

M (lbf-in)

No Power 3,825 355 20,082 No Load 4,635 358 24,336 Normal Load 8,132 3 42,693 Full Power 8,960 4 47,041 Max. Possible 11,553 5 60,653

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Individual drive component centers of gravity used to calculate the drive assembly center of gravity (Cd) are: Motor: 17 in from bearing center Reducer: 20 in from bearing center Motor Mount: 20 in from bearing center Belt & Sheaves: 30 in from bearing center

Component weight component CG

Total weight (Pw)

990 17 1065 20 30 20 25 30 18.71

2110

Cd

lbf in lbf in lbf in lbf inin

lbf

Rounded to 19 in for further calculations.

50 10.5 2110 19 31,671 lbf-in

50 o

in inM lbf in

in

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Moment from Torque Arm Reaction: This is a general method to calculate the torque arm reaction force. Exact solution method will vary based on drive details. The entire assembly is selected as the free body diagram and moments are summed about the pulley shaft centerline. Belt resultant load and bearing reactions pass through the shaft centerline and fall out of the analysis. This leaves torque arm reaction as a function of Te.

∑ Moments = 0

0.52 2

/ 2 20.3 6 0

Substituting tan 30

And solving for ;

/ (2 20.3 6 tan 30

e x y

y x

x

x e

t x y

T D P P

P P

P

P T D

P P P

Referring to Mo calculation in 4.3 the torque arm reaction Mo component is:

50 10.5

13 50

o t

in inM P in

in

Condition Pt

(lbf) Mo from Pt

(lbf-in) No Power 0 0 No Load 486 4,989 Normal Load 2,552 26,190 Full Power 3,038 31,179 Max. Possible 4,557 46,768

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Vector Sum of Moments: When more than one overhung load exists, the total moment is calculated by vector addition of the components.

Condition M

(lbf-in)


Mo from weight (lbf-in)

Angle (deg)

Mo from torque arm (lbf-in)

Angle (deg)

Total Mo (lbf-in)

No Power 20,082 355 31,671 90 0 30 38,951

No Load 24,336 358 31,671 90 4,989 30 40,444

Normal Load 42,693 3 31,671 90 26,190 30 46,974

Full Power 47,041 4 31,671 90 31,179 30 48,546

Max Possible 60,653 5 31,671 90 46,768 30 53,522 Example calculations are for the normal load scenario. ∑ Moments in horizontal direction

42,693cos 3.0 31,671cos 90 26,190cos 30

19,953 lbf-in

∑ Moments in vertical direction

42,693sin 3.0 31,671sin 90 26,190sin 30

42,526 lbf-in

0.52 2 19,953 42,526 46,974 lbf-inTotal Moment

Moments from each load component are highest in phase with the load vector and transition to zero 90° to the vector and are as follows. B105.1 Applicability Review: Since typical running Mo values, calculated in Vector Sum of Moments above, are less than design M value of 47,041 lb-in, the overhung loads are within the scope of this standard.

48,546 lbf-inTotal Moment

K 1.03247,041 lbf-inM

Step 4. Minimum Shaft Diameter (fatigue), section 4.4. Design shaft for 1045 steel. Ka = 0.8 Kb = 0.7249 assuming ø 5.4375 in shaft using Kb = D-0.19

Kc = 0.897 Kd = 1.0 Ke = 1.0 Kf = 0.63 for profiled keyway Kg = 1.0 Sf* = 41,000 psi 0.8 0.7249 0.897 0.63 41,000 13,436 fS psi

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2 2

332 1.5 1.032 47,041 lbf-in 3 62,532 lbf-in

3.9 in13,436 psi 4 41,000 psi

D

Step 5. Pulley Fatigue Life, section 4.5. This conveyor will run continuously 6 days a week and is the only method for moving material to downstream plant processes. A fatigue multiplication factor (Z) of 1.5 is chosen. Step 6. Pulley Selection, section 4.6. In this case;

K 1.032

Z 1.5

R 8,960 lbf at full power

Modified 1.032 1.5 8,960 13,870 lbfR Distance L B Fw

50 38

12 in

Interpolating from Table 4-A, a 4.4375 in shaft is selected. Step 7. Availability, section 4.7. A 24 x 38 pulley with 4.4375 in shaft is available per Table 5-A.

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Metric Example 3b: Drive Pulley (with overhung load) A conveyor is being designed to move rock up a 10° hill. A 914 mm belt was previously chosen to run at 2.4 m/s. The power requirement calculated is 8.9 kW without material load and 47 kW with normal running load. A 56 kW motor is selected. A hollow parallel shaft mount reducer is desired. The drive will be snubbed to 210° and a gravity take-up is used.

T1 = Belt Tension Carrying Side (kN) T2 = Belt Tension Return Side (kN)

Review of selection is as follows: Step 1. Pulley Diameter Selection, section 4.1. Belt tensions are determined at various running conditions using CEMA methods. Applicable equations from other standards given below.

2

1 2

/ belt speed in m/s

0.38e

e e

e

T kW

T Cw T T

T T T

It is anticipated belt will slip on pulley at 150 % of full horsepower so this is taken as maximum possible condition. Other operating conditions anticipated are stationary with no power, running without load, running at normal load and full motor power.

Condition kW Te

(kN) T2

(kN) T1

(kN) kN-m

No Power 0.0 0.00 8.81 8.81 10

No Load 8.9 3.71 8.81 12.52 14

Normal Load 47.0 19.47 8.81 28.28 31

Full Power 55.9 23.18 8.81 31.98 35

Max Possible 83.9 34.77 8.81 43.57 48

Comparing full power of 35 kN/m and a 210° belt wrap with Table 1-B, results in a match with the upper limit for a 508 mm diameter pulley. The designer chose the 610 mm diameter to maintain a conservative selection.

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Step 2. Resultant Radial Load, section 4.2. Based on the analysis of belt tension vectors versus pulley weight vectors this is a case where weight has a negligible impact on the pulleys resultant load. For simplicity pulley weight has been omitted.

0.52 2

1 2 1 22 cos pR T T TT W

1 1 2 2

1 1 2 2

sin sinrctan

cos cos

T TA

T T

Belt Resultant Load Moment

2

AM R

Step 3. Overhung Load, section 4.3. Moment from Weights: Drive component weights, and dimensions shown on the example drawing are obtained from component manufacturer literature. Total overhung weight (Pw) = ∑ component weights = 449 + 14 + 483 + 11 = 957 kg or 9.39 kN Individual drive component centers of gravity used to calculate the drive assembly center of gravity (Cd) are: Motor: 432 mm from bearing center Reducer: 508 mm from bearing center Motor Mount: 508 mm from bearing center Belt & Sheaves: 762 mm from bearing center

Component weight component CG

Total weight (Pw)

449 kg 432 mm 483 kg 508 mm 14 kg 508 mm 11 kg 762 mm 475 mm

957 kg

1270 mm 267 mm9.39 kN 475 mm

1270 mm3.52 kN-m

1000o

Cd

M

Condition Resultant

(kN)


M (kN-m)

No Power 17.01 355 2.27

No Load 20.62 358 2.75

Normal Load 36.17 3 4.82

Full Power 39.86 4 5.31

Max Possible 51.39 5 6.85

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Moment from Torque Arm Reaction: This is a general method to calculate the torque arm reaction force. Exact solution method will vary based on drive details. The entire assembly is selected as the free body diagram and moments are summed about the pulley shaft centerline. Belt resultant load and bearing reactions pass through the shaft centerline and fall out of the analysis. This leaves torque arm reaction as a function of Te.

∑ Moments = 0

0.52 2

/ 2 516 152 0

Substituting tan 30

And solving for ;

/ (2 516 152tan 30

e x y

y x

x

x e

t x y

T D P P

P P

P

P T D

P P P

Referring to Mo calculation in 4.3 the torque arm reaction Mo component is:

330 mm 1,270 mm 267 mm

1,000 1,270 mmo tM P

Condition Pt

(kN) Mo from Pt

(kN-m) No Power 0 0 No Load 2.16 0.56 Normal Load 11.35 2.96 Full Power 13.51 3.52 Max. Possible 20.27 5.28

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Vector Sum of Moments: When more than one overhung load exists, the total moment is calculated by vector addition of the components.

Condition M

(kN-m)


Mo from weight (kN-m)

Angle (deg)

Mo from torque arm

(kN-m)

Angle (deg)

Total Mo

(kN-m)

No Power 2.27 355 3.58 90 0.00 30 4.40

No Load 2.75 358 3.58 90 0.56 30 4.57

Normal Load 4.82 3 3.58 90 2.96 30 5.31

Full Power 5.31 4 3.58 90 3.52 30 5.48

Max Possible 6.85 5 3.58 90 5.28 30 6.05

Example calculations are for the normal load scenario. ∑ Moments in horizontal direction

4.82cos 3.0 3.58cos 90 2.96cos 30

2.25 kN-m


4.82sin 3.0 3.58 sin 90 2.96 sin 30

4.80 kN-m

0.52 2Total Moment 2.25 4.80 5.31 kN-m

Moments from each load component are highest in phase with the load vector and transition to zero 90° to the vector and are as follows. B105.1 Applicability Review: Since typical running Mo values, calculated in Vector Sum of Moments above, are less than design M value of 5.31 kN/m, the overhung loads are within the scope of this standard.

5.48 kN-mTotal Moment

K 1.0325.31 kN-mM

Step 4. Minimum Shaft Diameter (fatigue), section 4.4. Design shaft for 1045 steel. Ka = 0.8 Kb = 0.725 assuming ø 138 mm shaft using Kb = 1.85 * D-0.19

Kc = 0.897 Kd = 1.0 Ke = 1.0 Kf = 0.63 for profiled keyway Kg = 1.0 Sf* = 283 MPa

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0.8 0.725 0.897 0.63 283 93

M 5.31 kN/m 1,000,000 5,317,020 N-mm

T 9.81 / 2 23.18 kN 1,000 610 mm / 2 7,070,214 N-mm

f

e

S MPa

T D

2 2

3min

32 1.5 1.032 5,317,020 N-mm 3 7,070,214 N-mm99 mm

93 MPa 4 283 MPaD

Step 5. Pulley Fatigue Life, section 4.5. This conveyor will run continuously 6 days a week and is the only method for moving material to downstream plant processes. A fatigue multiplication factor (Z) of 1.5 is chosen. Step 6. Pulley Selection, section 4.6. In this case;

K 1.032

Z 1.5

R 39.86 kN at full power

Modified 1.032 1.5 39.86 61.70 kNR Distance L B Fw

1270 965

305 mm

Interpolating from Table 4-B, a 112.713 mm shaft is selected. Step 7. Availability, section 4.7. A 610 mm x 965 mm pulley with 112.713 mm shaft is available per Table 5-A. General discussion on parallel shaft mount drive assemblies of this orientation Drive assemblies of the type and orientation shown in example 3 often have an overhung load factor (K) near one. This is due to the weight load vector being approximately 90° to belt tensions and torque arm reaction being approximately in the same direction as belt tensions. At the pulley attachment, overhung loads tend to cancel belt loads. In these situations it is common for a design firm to perform this calculation with brand data internally used and develop a general factor specific to their use. This factor often ranges from K = 1.05 to 1.10. Note that even in this case weight and torque reaction loads can be significant and may impact shaft design at other locations such as bearing attachment, reducer attachment, changes in shaft diameter and others. It is recommended a thorough analysis of the shaft design at all potential failure sites be made, which is beyond the scope of this standard. Subtle differences in orientation of parallel shaft mount drive assemblies can have a significant impact on the overhung load factor. For example, if this drive assembly is used as a 180° wrap tail drive with torque arm angle of 0° on a horizontal conveyor the result is K = 1.9. At the pulley attachment, overhung loads tend to compound belt loads.

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Imperial Example 4a: Non-symmetric multiple overhung loads (Drive Pulley with backstop) A conveyor is being designed to move material up a 20° hill. A 48 in belt was previously chosen to run at 600 fpm. The power requirement calculated is 75 hp without material load and 175 hp with normal running load. A 200 hp motor is selected. A right angle shaft mount reducer is desired and a backstop is used. The drive will be snubbed to 210° and a gravity take-up is used.

Review of selection is as follows: Step 1. Pulley Diameter Selection, section 4.1. Determine belt tensions at various running conditions using CEMA methods. Applicable equations from other standards given below.

2

1 2

33,000 /

0.38e

e e

e

T hp fpm

T Cw T T

T T T

High speed coupling will be set to maximum of 125% of full horsepower so this is taken as maximum possible condition. Other operating conditions anticipated are stationary with no power, running without load, running at normal load and full motor power.

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Drive

Condition Backstop Condition

hp Te

(lbf) T1

(lbf) PIW

No Power Not Engaged 0 0 4,180 87 No Power Normal Load 100 5,500 9,680 202 No Power Full Power 125 6,875 11,055 230 No Power Max Probable 175 9,625 13,805 288 No Load Not Engaged 75 4,125 8,305 173 Normal Load Not Engaged 175 9,625 13,805 288 Full Power Not Engaged 200 11,000 15,180 316 Max Power Not Engaged 250 13,750 17,930 374

Comparing full power PIW of 316 and 210° belt wrap with Table 1-A, results in a match with a 30 in diameter pulley. Step 2. Resultant Radial Load, section 4.2. Overhung load direction is likely to be oriented with pulley weight. This is a case where pulley weight should be included in resultant load calculations. Based on catalog information, an estimate of 1,834 lbm is made.

Drive Condition

Backstop Condition

Resultant (lbf)


M (lbf-in)

No Power Not Engaged 8,435 162 44,285 No Power Normal Load 13,932 162 73,143 No Power Full Power 15,307 161 80,360 No Power Max Probable 18,056 161 94,794 No Load Not Engaged 12,558 162 65,927 Normal Load Not Engaged 18,056 161 94,794 Full Power Not Engaged 19,431 161 102,011 Max Power Not Engaged 22,180 161 116,446

Resultant load calculated using general equation from section 4.2.

1 1 2 2

1 1 2 2

sin sinrctan

cos cos

Belt Resultant Load Moment2

T TA

T T

AM R

Step 3. Overhung Load, section 4.3. Drive Assembly Moment from Weights: Component weights, and dimensions shown on the example drawing are obtained from component manufacturer literature. Total overhung weight (Pw) = ∑ component weights (lbm) = 2,400 + 400 + 1,250 + 400 + 800 = 5,250 lbm

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Individual drive component centers of gravity used to calculate the drive assembly center of gravity (Cd) are:

Reducer: 35 in from bearing center High Speed Coupling: 35 in from bearing center Motor: 35 in from bearing center Base: 35 in from bearing center Rigid Coupling: 15 in from bearing center

component weight component CG

Total weight (Pw)

2,400 35 400 35 1250 35 400 35 800 15 32

5,250

63 in 10.5 in5,250 lbf 32 in 140,000 lbf-in (At p

63 ino

Cd

lbm in lbm in lbm in lbm in lbm inin

lbm

M

ulley hub nearest drive assembly)

10.5 in 5,250 lbf 32 in 28,000 lbf-in At pulley hub furthest from drive assembly

63 inoM

Backstop Moment from Weights: Component weights, and dimensions shown on the example drawing are obtained from component manufacturer literature.

63 in 10.5 in350 lbf 15 in 4,375 lbf-in (At pulley hub furthest from drive assembly)

63 in10.5 in

350 lbf 15 in 875 lbf-in At pulley hub nearest drive assembly63 in

o

o

M

M

Moment from Torque Arm Reactions: This is a general method to calculate the torque arm reaction force. Exact solution method will vary based on drive details. The entire assembly is selected as the free body diagram and moments are summed about the pulley shaft centerline. Belt resultant load and bearing reactions pass through the shaft centerline and fall out of the analysis. This leaves torque arm reaction as a function of Te.

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∑ Moments = 0

/ 2 moments Distance Distance 0e yT D Wt P

For Drive assembly:

Distance2

28

63 in 10.5 in25 in At pulley hub nearest drive

63 in

10.5 in25 in At pulley hub furthest from drive

63 in

e

y

o y

o y

DT Wt

P

M P

M P

For Backstop;

Distance2

48

63 in 10.5 in15 in At pulley hub furthest from drive

63 in

10.5 in15 in At pulley hub nearest drive

63 in

e

y

o y

o y

DT Wt

P

M P

M P

Drive Condition

Backstop Condition

Drive Assy Py

(lbf)

Back Stop Py

(lbf)

Mo from Drive Py

(lbf-in) Mo from Back Stop Py

(lbf-in)

Hub near drive

Hub near back stop

Hub near drive

Hub near back stop

No Power Not Engaged -5,180 -73 -107,924 -21,585 -182 -911

No Power Normal Load -5,180 -1,792 -107,924 -21,585 -4,479 -22,396

No Power Full Power -5,180 -2,221 -107,924 -21,585 -5,553 -27,767

No Power Max Probable -5,180 -3,081 -107,924 -21,585 -7,702 -38,509

No Load Not Engaged -7,390 -73 -153,962 -30,792 -182 -911

Normal Load Not Engaged -10,337 -73 -215,346 -43,069 -182 -911

Full Power Not Engaged -11,073 -73 -230,692 -46,138 -182 -911

Max Power Not Engaged -12,546 -73 -261,384 -52,277 -182 -911

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Vector Sum of Moments: When more than one overhung load exists the total moment is calculated by vector addition of the components. Example calculations are for the normal load drive condition with backstop not engaged at the pulley hub nearest the drive assembly.

∑ Moments in horizontal direction

94,794 cos 161

89,737 lbf-in


94,794 sin 161 140,000 875 215,346 182

44,104 lbf-in

Total Moment

0.52 289,737 44,104

100,038 lbf-in

Round off in sample calculation values will create slight variance with tables.

Drive Condition

Backstop Condition

Resultant Load

Moment M

(lbf-in)

Hub Near Drive Hub Near Back Stop

Total overhung

load moment

Mo (lbf-in)

Total Moment (lbf-in)

Overhung Load Ratio (K)

Total overhung

load moment

Mo (lbf-in)

Total Moment (lbf-in)


No Power Not Engaged 44,285 32,560 46,408 0.45 9,837 42,377 0.42

No Power Normal Load 73,143 28,263 69,551 0.68 ‐11,647 70,322 0.69

No Power Full Power 80,360 27,189 76,165 0.75 ‐17,018 76,640 0.75

No Power Max Probable 94,794 25,041 89,889 0.88 ‐27,761 89,762 0.88

No Load Not Engaged 65,927 ‐13,478 63,002 0.62 629 65,732 0.64

Normal Load Not Engaged 94,794 ‐74,862 100,038 0.98 ‐11,647 91,698 0.90

Full Power Not Engaged 102,011 ‐90,208 112,145 1.10 ‐14,717 98,231 0.96

Max Power Not Engaged 116,446 ‐120,900 137,786 1.35 ‐20,855 111,397 1.09

Resultant load moment at full power running condition with backstop not engaged is used as denominator in all overhung load ratio calculations. B105.1 Applicability Review: Mo values (32,500 to -120,900) are slightly higher than design M value of 102,011 lbf-in. It is recommended a complete shaft design review be made with analysis at all potential failure locations.

112,145 lbf-in moment

K 1.10 (at full power)102,011 lbf-in

Total

M

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Step 4. Minimum Shaft Diameter (fatigue), section 4.4. Design shaft for 1,045 steel. Ka = 0.8 Kb = 0.7249 assuming ø 5.4375 in shaft using Kb = D -0.19 Kc = 0.897 Kd = 1.0 Ke = 1.0 Kf = 0.63 for profiled keyway Kg = 1.0 Sf* = 41,000 psi

0.8 0.7249 0.897 0.63 41,000 13,436 psi

M 102,011 lbf-in

T / 2 11,000 30 / 2 165,000 lbf-in

f

e

S

T D

2 2

332 1.5 1.10 102,011 lbf-in 3 165,000 lbf-in

5.17 in13,436 psi 4 41,000 psi

D

Step 5. Pulley Fatigue Life, section 4.5. This conveyor will operate 2 eight hour shifts 5 days a week. There are two identical conveyors giving the ability to run at partial capacity if a conveyor goes down. A fatigue multiplication factor (Z) of 1.3 is chosen. Step 6. Pulley Selection, section 4.6. In this case;

K 1.1

Z 1.3

R 19,431 lbf at full power

Modified 1.1 1.3 19,431 27,786 lbfR Distance L B Fw

63 51

12 in

Interpolating from table 4-A, a 6 in shaft is selected. Step 7. Availability, section 4.7. A 30 x 51 pulley with 6 in shaft is available per table 5-A.

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Metric Example 4b: Non-symmetric multiple overhung loads (Drive Pulley with backstop) A conveyor is being designed to move material up a 20° hill. A 1,219 mm belt was previously chosen to run at 3 m/s. The power requirement calculated is 56 kW without material load and 130.5 kW with normal running load. A 149 kW motor is selected. A right angle shaft mount reducer is desired and a backstop is used. The drive will be snubbed to 210° and a gravity take-up is used.

Review of selection is as follows: Step 1. Pulley Diameter Selection, section 4.1. Determine belt tensions at various running conditions using CEMA methods. Applicable equations from other standards given below.

2

1 2

kW / (Belt Speed in m/s)

0.38e

e e

e

T

T Cw T T

T T T

High speed coupling will be set to maximum of 125% of full horsepower so this is taken as maximum possible condition. Other operating conditions anticipated are stationary with no power, running without load, running at normal load and full motor power.

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Drive Condition

Backstop Condition

kW Te

(kN) T1

(kN) kN-m

No Power Not Engaged 0.0 0.00 18.59 15

No Power Normal Load 74.6 24.47 43.06 35

No Power Full Power 93.2 30.58 49.17 40

No Power Max Probable 130.5 42.81 61.41 50

No Load Not Engaged 55.9 18.35 36.94 30

Normal Load Not Engaged 130.5 42.81 61.41 50

Full Power Not Engaged 149.1 48.93 67.52 55

Max Power Not Engaged 186.4 61.16 79.76 65

Comparing full power of 55 kN/m and 210° belt wrap with Table 1, results in a match with a 762 mm diameter pulley. Step 2. Resultant Radial Load, section 4.2. Overhung load direction is likely to be oriented with pulley weight. This is a case where pulley weight should be included in resultant load calculations. Based on catalog information, an estimate of 832 kg is made.

Resultant load calculated using general equation from section 4.2.

1 1 2 2

1 1 2 2

sin sinrctan

cos cos

Belt Resultant Load Moment2

T TA

T T

AM R

Step 3. Overhung Load, section 4.3. Drive Assembly Moment from Weights: Component weights, and dimensions shown on the example drawing are obtained from component manufacturer literature. Total overhung weight (Pw) = ∑ component weights = 1,089 + 181 + 567 + 181 + 363 = 2,381 kg or as a force 23.35 kN

Drive Condition

Backstop Condition

Resultant (kN)


M (kN-m)

No Power Not Engaged 37.52 162 5.00

No Power Normal Load 61.97 162 8.26

No Power Full Power 68.09 161 9.08

No Power Max Probable 80.32 161 10.71

No Load Not Engaged 55.86 162 7.45

Normal Load Not Engaged 80.32 161 10.71

Full Power Not Engaged 86.43 161 11.53

Max Power Not Engaged 98.66 161 13.16

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Individual drive component centers of gravity used to calculate the drive assembly center of gravity (Cd) are:

Reducer: 889 mm from bearing center High Speed Coupling: 889 mm from bearing center Motor: 889 mm from bearing center Base: 889 mm from bearing center Rigid Coupling: 381 mm from bearing center

component weight component CG

Total weight (Pw)

1,089 889 mm 181 kg 889 mm 567 kg 889 mm 181 kg 889 mm 363 kg 381 mm 812 mm

2,381 kg

1,600 26723.35 kN 812 mm

1,600M 15.82 kN-m At pulley 1,000o

Cd

kg

hub nearest drive assembly

26723.35 kN 812 mm

1,600 3.16 kN-m At pulley hub furthest from drive assembly1,000oM

Backstop Moment from Weights: Component weights, and dimensions shown on the example drawing are obtained from component manufacturer literature.

1,600 2671.56 kN 381 mm

1,600 0.49 kN-m (At pulley hub furthest from drive assembly)1,000

2671.56 kN 381 mm

1,600 0.10 kN-m At pulley hub nearest drive assembly1,000

o

o

M

M

Moment from Torque Arm Reactions: This is a general method to calculate the torque arm reaction force. Exact solution method will vary based on drive details. The entire assembly is selected as the free body diagram and moments are summed about the pulley shaft centerline. Belt resultant load and bearing reactions pass through the shaft centerline and fall out of the analysis. This leaves torque arm reaction as a function of Te.

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∑Moments = 0

/ 2 moments Distance Distance 0e yT D Wt P

For Drive assembly:

Distance2

7111,600 267

635 mm1,600 At pulley hub nearest drive

1,000

267635 mm

1,600 At pulley hub furthest from drive1,000

e

y

y

o

y

o

DT Wt

P

PM

PM

For Backstop:

Distance2

12191,600 267

635 mm1,600 At pulley hub furthest from drive

1,000

267635 mm

1,600 At pulley hub nearest drive1,000

e

y

y

o

y

o

DT Wt

P

PM

PM

Drive Condition

Backstop Condition

Drive Assy Py

(kN)

Back Stop Py

(kN)

Mo from Drive Py

(kN-m) Mo from Back Stop Py

(kN-m) Hub near

drive Hub near back stop

Hub near drive

Hub near back stop

No Power Not Engaged -23.04 -0.32 -12.19 -2.44 -0.02 -0.10 No Power Normal Load -23.04 -7.97 -12.19 -2.44 -0.51 -2.53 No Power Full Power -23.04 -9.88 -12.19 -2.44 -0.63 -3.14 No Power Max Probable -23.04 -13.70 -12.19 -2.44 -0.87 -4.35 No Load Not Engaged -32.87 -0.32 -17.39 -3.48 -0.02 -0.10 Normal Load Not Engaged -45.98 -0.32 -24.33 -4.87 -0.02 -0.10 Full Power Not Engaged -49.26 -0.32 -26.06 -5.21 -0.02 -0.10 Max Power Not Engaged -55.81 -0.32 -29.53 -5.91 -0.02 -0.10

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Vector Sum of Moments: When more than one overhung load exists the total moment is calculated by vector addition of the components. Example calculations are for the normal load drive condition with backstop not engaged at the pulley hub nearest the drive assembly.

∑ Moments in horizontal direction

10.71 cos 161

10.13 kN-m


10.71 sin 161 15.82 0.10 24.33 0.10

4.98 kN-m

Total Moment

0.52 210.13 4.98

11.30 kN-m

Round off in sample calculation values will create slight variance with tables.

Drive Condition

Backstop Condition

Resultant Load

Moment M (kN-m)

Hub Near Drive Hub Near Back Stop

Total overhung

load moment

Mo (kN-m)

Total Moment (kN-m)


Total overhung

load moment Mo (kN-m)

Total Moment (kN-m)

Overhung Load Ratio

(K)

No Power Not Engaged 5.00 3.68 5.24 0.45 1.11 4.79 0.42 No Power Normal Load 8.26 3.19 7.86 0.68 -1.32 7.94 0.69 No Power Full Power 9.08 3.07 8.61 0.75 -1.92 8.66 0.75

No Power Max Probable 10.71 2.83 10.16 0.88 -3.14 10.14 0.88

No Load Not Engaged 7.45 -1.52 7.12 0.62 0.07 7.43 0.64 Normal Load Not Engaged 10.71 -8.46 11.30 0.98 -1.32 10.36 0.90

Full Power Not Engaged 11.53 -10.19 12.67 1.10 -1.66 11.10 0.96 Max Power Not Engaged 13.16 -13.66 15.57 1.35 -2.36 12.59 1.09

Resultant load moment at full power running condition with backstop not engaged is used as denominator in all overhung load ratio calculations. B105.1 Applicability Review: Mo values (3.68 to -13.66) are slightly higher than design M value of 11.53 kN-m. It is recommended a complete shaft design review be made with analysis at all potential failure locations.

12.67 kN-mTotal Moment

K 1.10 (at full power)M 11.53 kN-m

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Page 47

Step 4. Minimum Shaft Diameter (fatigue), section 4.4. Design shaft for 1045 steel. Ka = 0.8 Kb = 0.725 assuming ø 138.113 mm shaft using Kb = 1.85 * D-0.19 Kc = 0.897 Kd = 1.0 Ke = 1.0 Kf = 0.63 for profiled keyway Kg = 1.0 Sf* = 283 MPa

0.8 0.725 0.897 0.63 283 93

M 11.53 kN/m 1,000,000 11,526,750 N-mm

T 1,000 / 2 48.93 kN 1,000 762 mm / 2 18,646,936 N-mm

f

e

S MPa

T D

* Results slightly vary due to rounding of values.

2 2

332 1.5 1.10 11,526,750 N-mm 3 18,646,936 N-mm

131 mm93 MPa 4 283 MPa

D

Step 5. Pulley Fatigue Life, section 4.5. This conveyor will operate 2 eight hour shifts 5 days a week. There are two identical conveyors giving the ability to run at partial capacity if a conveyor goes down. A fatigue multiplication factor (Z) of 1.3 is chosen. Step 6. Pulley Selection, section 4.6. In this case;

K 1.1

Z 1.3

R 86.43 kN at full power

Modified 1.1 1.3 86.43 123.59 kNR Distance L B Fw

1,600 1,295

305 mm

Interpolating from Table 4-B, a 152.400 mm shaft is selected. Step 7. Availability, section 4.7. A 762 mm x 1295 mm pulley with 152.400 mm shaft is available per Table 5-B.

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Page 48

APPENDIX V: OTHER THAN CEMA CLASS PULLEYS

This appendix is not part of the standard but is included for the information of those who wish to become acquainted with other classes of pulleys other than CEMA Class Pulleys. Below is a description of two common classes of pulleys that fall outside the scope of the standard. For additional information please consult with the manufacturer.

Mine Duty Pulleys Mine Duty Pulleys can be considered in a conveyor application requiring heavier construction and more conservative design to give greater service life where abrasion is a factor; or there are longer conveyor running hours to consider. Mine duty pulleys are pre-engineered, not to a specific application or for a particular purpose but will have lower stress and deflection on the various components and offer greater service factors over standard CEMA rated pulleys. These increased ratings can be achieved by design and manufacturing considerations including increased rim thickness, increased end disk thickness and increased rigidity of shafts through the use of manufacturing processes that increase the endurance strength of the pulley. No CEMA standard governs the load ratings or material thicknesses of mine duty pulleys. Each CEMA pulley manufacturer should be contacted for specific details on their mine duty pulley design and manufacturing process.

Engineered Pulleys Engineered Pulleys are specifically designed to meet the load conditions of a particular conveyor. Specific information is required for proper and economical design, since the designer must allow for sufficient strength in design of the pulley, shaft, and mounting system to carry the belt loads and to assure proper pulley to shaft connection. Each CEMA pulley manufacturer should be contacted for specific details on their engineered class pulleys.

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Page 49

INDEX

Caption Page

Table 1-A Maximum Belt Tension (Pounds Per Inch of Belt Width) 4 Table 1-B Maximum Belt Tension (kN per Meter of Belt Width) 5 Table 2-A Impact of Pulley Weight on Resultant Load (lbf) 7 Table 2-B Impact of Pulley Weight on Resultant Load (kN) 8 Table 3 Typical Pulley Moment Arms 10 Table 4-A Load Ratings (lbf) for Pulley and Shaft Combinations 12 Table 4-B Load Ratings (kN) for Pulley and Shaft Combinations 13 Table 5-A Available Shaft Diameters (in) 14 Table 5-B Available Shaft Diameters (mm) 15 Table 6 Overhung Load K Factor 19

Caption Page

Figure 1 Resultant Radial Load Diagrams 6 Figure 2 Pulley Dimensions and Nomenclature 9 Figure 3 Free Body Diagram 18 Figure 4 Shaft Mounted Drive 18 Figure 5 Swing Base Drive 18

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CONVEYOR EQUIPMENT5672 StNaple

23www

Page 50

T MANUFACTUtrand Ct., Suites, Florida 3411

39 514 3441w.cemanet.org

URERS ASSOCIAe 210

g

ATION

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