Machinery''''s Handbook 2th Episode 3 Part 10 ppsx

BALL AND ROLLER BEARINGS 2315 Radial Roller Bearings: The magnitude of the Rating Life, L 10 , in millions of revolu- tions, for a radial roller bearing application is given by the formula: (12) where C=the basic load rating in newtons (pounds), see Formula (13); and, P=equiva- lent radial load in newtons (pounds), see Formula (14). For radial roller bearings, C is found by the formula: (13) where f c =a factor which depends on the geometry of the bearing components, the accu- racy to which the various bearing parts are made, and the material. Maximum values of f c are given in Table 31 i=number of rows of rollers in the bearing l eff =effective length, mm (inches) α =nominal contact angle, degrees Z=number of rollers per row in a radial roller bearing D=roller diameter, mm (inches) (mean diameter for a tapered roller, major diam- eter for a spherical roller) When rollers are longer than 2.5D, a reduction in the f c value must be anticipated. In this case, the bearing manufacturer may be expected to establish load ratings accordingly. In applications where rollers operate directly on a shaft surface or a housing surface, such a surface must be equivalent in all respects to the raceway it replaces to achieve the basic load rating of the bearing. When calculating the basic load rating for a unit consisting of two or more similar single- row bearings mounted “in tandem,” properly manufactured and mounted for equal load distribution, the rating of the combination is the number of bearings to the 7⁄9 power times the rating of a single-row bearing. If, for some technical reason, the unit may be treated as a number of individually interchangeable single-row bearings, this consideration does not apply. The magnitude of the equivalent radial load, P, in newtons (pounds), for radial roller bearings, under combined constant radial and constant thrust loads is given by the formula: (14) where F r =the applied radial load in newtons (pounds) F a =the applied axial load in newtons (pounds) X=radial load factor as given in Table 33 Y=axial load factor as given in Table 33 Table 33. Values of X and Y for Computing Equivalent Radial Load P for Radial Roller Bearing e = 1.5 tan α Bearing Type XYXY Self-Aligning and Tapered Roller Bearings a α ≠ 0° a For α = 0°, F a = 0 and X = 1. Single Row Bearings 1 0 0.4 0.4 cot α Double Row Bearings a 10.45 cot α 0.67 0.67 cot α L 10 C P ⎝⎠ ⎛⎞ 10 3⁄ = Cf c il eff αcos() 79⁄ Z 34⁄ D 29 27⁄ = PXF r YF a += F a F r e≤ F a F r e> Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY 2316 BALL AND ROLLER BEARINGS Typical Bearing Life for Various Design Applications Roller bearings are generally designed to achieve optimized contact; however, they usu- ally support loads other than the loading at which optimized contact is maintained. The 10⁄3 exponent in Rating Life Formulas (12) and (15) was selected to yield satisfactory Rat- ing Life estimates for a broad spectrum from light to heavy loading. When loading exceeds that which develops optimized contact, e.g., loading greater than C/4 to C/2 or C a /4 to C a /2, the user should consult the bearing manufacturer to establish the adequacy of the Rating Life formulas for the particular application. Thrust Roller Bearings: The magnitude of the Rating Life, L 10 , in millions of revolutions for a thrust roller bearing application is given by the formula: (15) where C a =basic load rating, newtons (pounds). See Formulas (16) to (18) P a =equivalent thrust load, newtons (pounds). See Formula (19) For single row, single and double direction, thrust roller bearings, the magnitude of the basic load rating, C a , in newtons (pounds), is found by the formulas: (16) Uses Design life in hours Uses Design life in hours Agricultural equipment 3000 – 6000 Gearing units Aircraft equipment 500 – 2000 Automotive 600 – 5000 Automotive Multipurpose 8000 – 15000 Race car 500 – 800 Machine tools 20000 Light motor cycle 600 – 1200 Rail Vehicles 15000 – 25000 Heavy motor cycle 1000 – 2000 Heavy rolling mill > 50000 Light cars 1000 – 2000 Machines Heavy cars 1500 – 2500 Beater mills 20000 – 30000 Light trucks 1500 – 2500 Briquette presses 20000 – 30000 Heavy trucks 2000 – 2500 Grinding spindles 1000 – 2000 Buses 2000 – 5000 Machine tools 10000 – 30000 Electrical Mining machinery 4000 – 15000 Household appliances 1000 – 2000 Paper machines 50000 – 80000 Motors ≤ 1 ⁄ 2 hp 1000 – 2000 Rolling mills Motors ≤ 3 hp 8000 – 10000 Small cold mills 5000 – 6000 Motors, medium 10000 – 15000 Large multipurpose mills 8000 – 10000 Motors, large 20000 – 30000 Rail vehicle axle Elevator cables sheaves 40000 – 60000 Mining cars 5000 Mine ventillation fans 40000 – 50000 Motor rail cars 16000 – 20000 Propeller thrust bearings 15000 – 25000 Open–pit mining cars 20000 – 25000 Propeller shaft bearings > 80000 Streetcars 20000 – 25000 Gear drives Passenger cars 26000 Boat gearing units 3000 – 5000 Freight cars 35000 Gear drives > 50000 Locomotive outer bearings 20000 – 25000 Ship gear drives 20000 – 30000 Locomotive inner bearings 30000 – 40000 Machinery for 8 hour service which are not always fully utilized 14000 – 20000 Machinery for short or intermittent opearation where service interruption is of minor importance 4000 – 8000 Machinery for 8 hour service which are fully uti- lized 20000 – 30000 Machinery for intermittent service where reliable opearation is of great importance 8000 – 14000 Machinery for continuous 24 hour service 50000 – 60000 Instruments and apparatus in frequent use 0 – 500 L 10 C a P a ⎝⎠ ⎛⎞ 10 3⁄ = for α 90 ° =, C a f c l eff 79⁄ Z 34⁄ D 29 27⁄ = Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY 2318 BALL AND ROLLER BEARINGS Table 34. Values of X and Y for Computing Equivalent Thrust Load P a for Thrust Roller Bearings e = 1.5 tan α Life Adjustment Factors.—In certain applications of ball or roller bearings it is desirable to specify life for a reliability other than 90 per cent. In other cases the bearings may be fab- ricated from special bearing steels such as vacuum-degassed and vacuum-melted steels, and improved processing techniques. Finally, application conditions may indicate other than normal lubrication, load distribution, or temperature. For such conditions a series of life adjustment factors may be applied to the fatigue life formula. This is fully explained in AFBMA and American National Standard “Load Ratings and Fatigue Life for Ball Bear- ings”ANSI/AFBMA Std 9–1990 and AFBMA and American National Standard “Load Ratings and Fatigue Life for Roller Bearings”ANSI/AFBMA Std 11–1990. In addition to consulting these standards it may be advantageous to also obtain information from the bearing manufacturer. Life Adjustment Factor for Reliability: For certain applications, it is desirable to specify life for a reliability greater than 90 per cent which is the basis of the Rating Life. To determine the bearing life of ball or roller bearings for reliability greater than 90 per cent, the Rating Life must be adjusted by a factor a 1 such that L n = a 1 L 10 . For a reliability of 95 per cent, designated as L 5 , the life adjustment factor a 1 is 0.62; for 96 per cent, L 4 , a 1 is 0.53; for 97 per cent, L 3 , a 1 is 0.44; for 98 per cent, L 2 , a 1 is 0.33; and for 99 per cent, L 1 , a 1 is 0.21. Life Adjustment Factor for Material: For certain types of ball or roller bearings which incorporate improved materials and processing, the Rating Life can be adjusted by a factor a 2 such that L 10 ′ = a 2 L 10 . Factor a 2 depends upon steel analysis, metallurgical processes, forming methods, heat treatment, and manufacturing methods in general. Ball and roller bearings fabricated from consumable vacuum remelted steels and certain other special analysis steels, have demonstrated extraordinarily long endurance. These steels are of exceptionally high quality, and bearings fabricated from these are usually considered spe- cial manufacture. Generally, a 2 values for such steels can be obtained from the bearing manufacturer. However, all of the specified limitations and qualifications for the applica- tion of the Rating Life formulas still apply. Life Adjustment Factor for Application Condition: Application conditions which affect ball or roller bearing life include: 1) lubrication; 2) load distribution (including effects of clearance, misalignment, housing and shaft stiffness, type of loading, and thermal gradi- ents); and 3) temperature. Items 2 and 3 require special analytical and experimental techniques, therefore the user should consult the bearing manufacturer for evaluations and recommendations. Operating conditions where the factor a 3 might be less than 1 include: a) exceptionally low values ofNd m (rpm times pitch diameter, in mm); e.g.,Nd m < 10,000; b) lubricant vis- cosity at less than 70 SSU for ball bearings and 100 SSU for roller bearings at operating temperature; and c) excessively high operating temperatures. Bearing Type Single Direction Bearings Double Direction Bearings XY X Y X Y Self-Aligning Tapered Thrust Roller Bearings a α ≠ 0 a For α = 90°, F r = 0 and Y = 1. tan α 1 1.5 tan α 0.67 tan α 1 F a F r e> F a F r e≤ F a F r e> Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY BALL AND ROLLER BEARINGS 2319 When a 3 is less than 1 it may not be assumed that the deficiency in lubrication can be overcome by using an improved steel. When this factor is applied, L 10 ′ = a 3 L 10 . In most ball and roller bearing applications, lubrication is required to separate the rolling surfaces, i.e., rollers and raceways, to reduce the retainer-roller and retainer-land friction and sometimes to act as a coolant to remove heat generated by the bearing. Factor Combinations: A fatigue life formula embodying the foregoing life adjustment factors is L 10 ′ = a 1 a 2 a 3 L 10 . Indiscriminate application of the life adjustment factors in this formula may lead to serious overestimation of bearing endurance, since fatigue life is only one criterion for bearing selection. Care must be exercised to select bearings which are of sufficient size for the application. Ball Bearing Static Load Rating.—For ball bearings suitably manufactured from hard- ened alloy steels, the static radial load rating is that uniformly distributed static radial bear- ing load which produces a maximum contact stress of 4,000 megapascals (580,000 pounds per square inch). In the case of a single row, angular contact ball bearing, the static radial load rating refers to the radial component of that load which causes a purely radial dis- placement of the bearing rings in relation to each other. The static axial load rating is that uniformly distributed static centric axial load which produces a maximum contact stress of 4,000 megapascals (580,000 pounds per square inch). Radial and Angular Contact Groove Ball Bearings: The magnitude of the static load rat- ing C o in newtons (pounds) for radial ball bearings is found by the formula: (20) where f o =a factor for different kinds of ball bearings given in Table 35 i=number of rows of balls in bearing Z=number of balls per row D=ball diameter, mm (inches) α =nominal contact angle, degrees This formula applies to bearings with a cross sectional raceway groove radius not larger than 0.52 D in radial and angular contact groove ball bearing inner rings and 0.53 D in radial and angular contact groove ball bearing outer rings and self-aligning ball bearing inner rings. The load carrying ability of a ball bearing is not necessarily increased by the use of a smaller groove radius but is reduced by the use of a larger radius than those indicated above. Radial or Angular Contact Ball Bearing Combinations: The basic static load rating for two similar single row radial or angular contact ball bearings mounted side by side on the same shaft such that they operate as a unit (duplex mounting) in “back-to-back” or “face- to-face” arrangement is two times the rating of one single row bearing. The basic static radial load rating for two or more single row radial or angular contact ball bearings mounted side by side on the same shaft such that they operate as a unit (duplex or stack mounting) in “tandem” arrangement, properly manufactured and mounted for equal load distribution, is the number of bearings times the rating of one single row bearing. Thrust Ball Bearings: The magnitude of the static load rating C oa for thrust ball bearings is found by the formula: (21) where f o =a factor given in Table 35 Z=number of balls carrying the load in one direction D=ball diameter, mm (inches) α =nominal contact angle, degrees C o f o iZD 2 αcos= C oa f o ZD 2 αcos= Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY BALL AND ROLLER BEARINGS 2321 Note: Based on modulus of elasticity = 2.07 × 10 5 megapascals (30 × 10 6 pounds per square inch) and Poisson's ratio = 0.3. Radial Roller Bearings: The magnitude of the static load rating C o in newtons (pounds) for radial roller bearings is found by the formulas: (22a) (22b) where D=roller diameter, mm (inches); mean diameter for a tapered roller and major diameter for a spherical roller d m =mean pitch diameter of the roller complement, mm (inches) i=number of rows of rollers in bearing Z=number of rollers per row l eff =effective length, mm (inches); overall roller length minus roller chamfers or minus grinding undercuts at the ring where contact is shortest α =nominal contact angle, degrees Radial Roller Bearing Combinations: The static load rating for two similar single row roller bearings mounted side by side on the same shaft such that they operate as a unit is two times the rating of one single row bearing. The static radial load rating for two or more similar single row roller bearings mounted side by side on the same shaft such that they operate as a unit (duplex or stack mounting) in “tandem” arrangement, properly manufactured and mounted for equal load distribution, is the number of bearings times the rating of one single row bearing. Thrust Roller Bearings: The magnitude of the static load rating C oa in newtons (pounds) for thrust roller bearings is found by the formulas: (23a) (23b) where the symbol definitions are the same as for Formulas (22a) and (22b). Thrust Roller Bearing Combination: The static axial load rating for two or more similar single direction thrust roller bearings mounted side by side on the same shaft such that they operate as a unit (duplex or stack mounting) in “tandem” arrangement, properly manufac- tured and mounted for equal load distribution, is the number of bearings times the rating of one single direction bearing. The accuracy of this formula decreases in the case of single direction bearings when F r > 0.44 F a cot α where F r is the applied radial load in newtons (pounds) and F a is the applied axial load in newtons (pounds). 0.46 7.1 1030 2.8 399 23.5 3400 0.47 6.9 1000 2.8 404 22.9 3320 0.48 6.7 977 2.8 410 22.4 3240 0.49 6.6 952 2.9 415 21.8 3160 0.50 6.4 927 2.9 421 21.2 3080 a Use to obtain C o or C oa in newtons when D is given in mm. b Use to obtain C o or C oa in pounds when D is given in inches. Table 35. (Continued) f o for Calculating Static Load Rating for Ball Bearings Radial and Angular Contact Groove Type Radial Self-Aligning Thrust Metric a Inch b Metric a Inch b Metric a Inch b D αcos d m C o 44 1 D αcos d m – ⎝⎠ ⎛⎞ iZl eff D αcos= (metric) C o 6430 1 D αcos d m – ⎝⎠ ⎛⎞ iZl eff D αcos=(inch) C oa 220 1 D αcos d m – ⎝⎠ ⎛⎞ Zl eff D αsin= (metric) C oa 32150 1 D αcos d m – ⎝⎠ ⎛⎞ Zl eff D αsin=(inch) Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY 2322 BALL AND ROLLER BEARINGS Ball Bearing Static Equivalent Load.—For ball bearings the static equivalent radial load is that calculated static radial load which produces a maximum contact stress equal in magnitude to the maximum contact stress in the actual condition of loading. The static equivalent axial load is that calculated static centric axial load which produces a maximum contact stress equal in magnitude to the maximum contact stress in the actual condition of loading. Radial and Angular Contact Ball Bearings: The magnitude of the static equivalent radial load P o in newtons (pounds) for radial and angular contact ball bearings under com- bined thrust and radial loads is the greater of: (24) (25) where X o =radial load factor given in Table 36 Y o =axial load factor given in Table 36 F r =applied radial load, newtons (pounds) F a =applied axial load, newtons (pounds) Table 36. Values of X o and Y o for Computing Static Equivalent Radial Load P o of Ball Bearings Thrust Ball Bearings: The magnitude of the static equivalent axial load P oa in newtons (pounds) for thrust ball bearings with contact angle α ≠ 90° under combined radial and thrust loads is found by the formula: (26) where the symbol definitions are the same as for Formulas (24) and (25). This formula is valid for all load directions in the case of double direction ball bearings. For single direc- tion ball bearings, it is valid where F r /F a ≤ 0.44 cot α and gives a satisfactory but less con- servative value of P oa for F r /F a up to 0.67 cot α. Thrust ball bearings with α = 90° can support axial loads only. The static equivalent load for this type of bearing is P oa = F a . Roller Bearing Static Equivalent Load.—The static equivalent radial load for roller bearings is that calculated, static radial load which produces a maximum contact stress act- ing at the center of contact of a uniformly loaded rolling element equal in magnitude to the maximum contact stress in the actual condition of loading. The static equivalent axial load is that calculated, static centric axial load which produces a maximum contact stress acting Contact Angle Single Row Bearings a a P o is always ≥ F r . Double Row Bearings X o Y o b b Values of Y o for intermediate contact angles are obtained by linear interpolation. X o Y o b RADIAL CONTACT GROOVE BEARINGS c,a c Permissible maximum value of F a /C o (where F a is applied axial load and C o is static radial load rating) depends on the bearing design (groove depth and internal clearance). α = 0° 0.6 0.5 0.6 0.5 ANGULAR CONTACT GROOVE BEARINGS α = 15° 0.5 0.47 1 0.94 α = 20° 0.5 0.42 1 0.84 α = 25° 0.5 0.38 1 0.76 α = 30° 0.5 0.33 1 0.66 α = 35° 0.5 0.29 1 0.58 α = 40° 0.5 0.26 1 0.52 SELF-ALIGNING BEARINGS … 0.5 0.22 cot α 10.44 cot α P o X o F r Y o F a += P o F r = P oa F a 2.3F r αtan+= Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY BALL AND ROLLER BEARINGS 2323 at the center of contact of a uniformly loaded rolling element equal in magnitude to the maximum contact stress in the actual condition of loading. Radial Roller Bearings: The magnitude of the static equivalent radial load P o in newtons (pounds) for radial roller bearings under combined radial and thrust loads is the greater of: (27) (28) where X o =radial factor given in Table 37 Y o =axial factor given in Table 37 F r =applied radial load, newtons (pounds) F a =applied axial load, newtons (pounds) Table 37. Values of X o and Y o for Computing Static Equivalent Radial Load P o for Self-Aligning and Tapered Roller Bearings The static equivalent radial load for radial roller bearings with α = 0° and subjected to radial load only is P or = F r . Note: The ability of radial roller bearings with α = 0° to support axial loads varies considerably with bearing design and execution. The bearing user should therefore consult the bearing manufac- turer for recommendations regarding the evaluation of equivalent load in cases where bearings with α = 0° are subjected to axial load. Radial Roller Bearing Combinations: When calculating the static equivalent radial load for two similar single row angular contact roller bearings mounted side by side on the same shaft such that they operate as a unit (duplex mounting) in “back-to-back” or “face-to- face” arrangement, use the X o and Y o values for a double row bearing and the F r and F a val- ues for the total loads on the arrangement. When calculating the static equivalent radial load for two or more similar single row angular contact roller bearings mounted side by side on the same shaft such that they oper- ate as a unit (duplex or stack mounting) in “tandem” arrangement, use the X o and Y o values for a single row bearing and the F r and F a values for the total loads on the arrangement. Thrust Roller Bearings: The magnitude of the static equivalent axial load P oa in newtons (pounds) for thrust roller bearings with contact angle α ≠ 90°, under combined radial and thrust loads is found by the formula: (29) where F a =applied axial load, newtons (pounds) F r =applied radial load, newtons (pounds) α =nominal contact angle, degrees The accuracy of this formula decreases for single direction thrust roller bearings when F r > 0.44 F a cot α. Thrust Roller Bearing Combinations: When calculating the static equivalent axial load for two or more thrust roller bearings mounted side by side on the same shaft such that they operate as a unit (duplex or stack mounting) in “tandem” arrangement, use the F r and F a values for the total loads acting on the arrangement. Bearing Type Single Row a a P o is always ≥ F r . Double Row X o Y o X o Y o Self-Aligningand Tapered α ≠ 0 0.5 0.22 cot α 10.44 cot α P o X o F r Y o F a += P o F r = P oa F a 2.3F r αtan+= Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY 2324 STANDARD METAL BALLS STANDARD METAL BALLS Standard Metal Balls.—American National Standard ANSI/AFBMA Std 10-1989 pro- vides information for the user of metal balls permitting them to be described readily and accurately. It also covers certain measurable characteristics affecting ball quality. On the following pages, tables taken from this Standard cover standard balls for bearings and other purposes by type of material, grade, and size range; preferred ball sizes; ball hardness corrections for curvature; various tolerances, marking increments, and maximum surface roughnesses by grades; total hardness ranges for various materials; and minimum case depths for carbon steel balls. The numbers of balls per pound and per kilogram for fer- rous and nonferrous metals are also shown. Definitions and Symbols.—The following definitions and symbols apply to American National Standard metal balls. Nominal Ball Diameter, D w : The diameter value that is used for the general identifica- tion of a ball size, e.g., 1 ⁄ 4 inch, 6 mm, etc. Single Diameter of a Ball, D ws : The distance between two parallel planes tangent to the surface of a ball. Mean Diameter of a Ball, D wm : The arithmetical mean of the largest and smallest single diameters of a ball. Ball Diameter Variation, V Dws : The difference between the largest and smallest single diameters of one ball. Deviation from Spherical Form, ∆R w : The greatest radial distance in any radial plane between a sphere circumscribed around the ball surface and any point on the ball surface. Lot: A definite quantity of balls manufactured under conditions that are presumed uni- form, considered and identified as an entirety. Lot Mean Diameter, D wmL : The arithmetical mean of the mean diameter of the largest ball and that of the smallest ball in the lot. Lot Diameter Variation, V DwL : The difference between the mean diameter of the largest ball and that of the smallest ball in the lot. Nominal Ball Diameter Tolerance: The maximum allowable deviation of any ball lot mean diameter from the Nominal Ball Diameter. Container Marking Increment: The Standard unit steps in millionths of an inch or in micrometers used to express the Specific Diameter. Specific Diameter: The amount by which the lot mean diameter (D wmL ) differs from the nominal diameter (D w ), accurate to the container marking increment for that grade; the specific diameter should be marked on the unit container. Ball Gage Deviation, ∆S: The difference between the lot mean diameter and the sum of the nominal mean diameter and the ball gage. Surface Roughness, R a : Surface roughness consists of all those irregularities that form surface relief and are conventionally defined within the area where deviations of form and waviness are eliminated. (See Handbook Surface Texture Section.) Ordering Specifications.—Unless otherwise agreed between producer and user, orders for metal balls should provide the following information: quantity, material, nominal ball diameter, grade, and ball gage. A ball grade embodies a specific combination of dimen- sional form, and surface roughness tolerances. A ball gage(s) is the prescribed small amount, expressed with the proper algebraic sign, by which the lot mean diameter (arith- metic mean of the mean diameters of the largest and smallest balls in the lot) should differ from the nominal diameter, this amount being one of an established series of amounts as shown in the table below. The 0 ball gage is commonly referred to as “OK”. Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY STANDARD METAL BALLS 2325 Preferred Ball Gages for Grades 3 to 200 Table 1. AFBMA Standard Balls — Tolerances for Individual Balls and for Lots of Balls Allowable ball gage (see text) deviation is for Grade 3: + 0.000030, − 0.000030 inch (+0.75, − 0.75 µm); for Grades 5, 10, and 16: + 0.000050, − 0.000040 inch (+ 1.25, − 1 µm); and for Grade 24: + 0.000100, − 0.000100 inch (+ 2.5, − 2.5 µm). Other grades not given. Examples:A typical order, in inch units, might read as follows: 80,000 pieces, chrome alloy steel, 1 ⁄ 4 -inch Nominal Diameter, Grade 16, and Ball Gage to be −0.0002 inch. Grade Ball Gages (in 0.0001-in. units) Ball Gages (in 1µm units) Minus OK Plus Minus OK Plus 3, 5 − 3 − 2 − 10+ 1 + 2 + 3 − 8 − 7 − 6 − 5 − 4 − 3 − 2 − 1 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 10, 16 − 4 − 3 − 2 − 10+ 1 + 2 + 3 + 4 − 10 − 8 − 6 − 4 − 2 0 + 2 + 4 + 6 + 8 + 10 24 − 5 − 4 − 3 − 2 − 1 0 + 1 + 2 + 3 + 4 + 5 − 12 − 10 − 8 − 6 − 4 − 2 0 + 2 + 4 + 6 + 8 + 10 + 12 48 − 6 − 4 − 20+ 2 + 4 + 6 − 16 − 12 − 8 − 40+ 4 + 8 + 12 + 16 100 0 0 200 0 0 Grade Allowable Ball Diameter Variation Allowable Deviation from Spheri- cal Form Maximum Surface Roughness R a Allowable Lot Diameter Variation Nominal Ball Diameter Tolerance (±) Container Marking Increments For Individual Balls For Lots of Balls Millionths of an Inch 3 3 3 0.5 5 a a Not applicable. 10 5 5 5 0.8 10 a 10 10 10 10 1 20 a 10 16 16 16 1 32 a 10 24 24 24 2 48 a 10 48 48 48 3 96 a 50 100 100 100 5 200 500 a 200 200 200 8 400 1000 a 500 500 500 a 1000 2000 a 1000 1000 1000 a 2000 5000 a Micrometers 3 0.08 0.08 0.012 0.13 a 0.25 5 0.13 0.13 0.02 0.25 a 0.25 10 0.25 0.25 0.025 0.5 a 0.25 16 0.4 0.4 0.025 0.8 a 0.25 24 0.6 0.6 0.05 1.2 a 0.25 48 1.2 1.2 0.08 2.4 a 1.25 100 2.5 2.5 0.125 5 12.5 a 200 5 5 0.2 10 25 a 500 13 13 a 25 50 a 1000 25 25 a 50 125 a Machinery's Handbook 27th Edition Copyright 2004, Industrial Press, Inc., New York, NY [...]... 51⁄4 23 4 31 ⁄2 45⁄16 51⁄2 21⁄8 27⁄8 35 ⁄8 43 32 53 8 51⁄2 67⁄8 71⁄4 73 4 81⁄4 15⁄8 21⁄8 5⁄ 8 5⁄ 8 3 4 3 4 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 21⁄8 23 4 31 ⁄2 43 16 51⁄16 51⁄2 63 4 43 4 61⁄4 7 13 16 7 7 7 15 11⁄8 11⁄8 17⁄8 21⁄4 25⁄8 33 ⁄4 33 ⁄4 33 ⁄4 33 ⁄4 33 ⁄4 7 31 ⁄2 4 83 4 101 ⁄2 121⁄4 14 41⁄2 151⁄2 5 17 51⁄2 6 171⁄2 18 3 7 7 8 9 91⁄2 10 3 31⁄2 43 8 43 4 51⁄4 53 4 61⁄4 63 4 1 1 9 111⁄4 12 131 ⁄2 151⁄2 16 K 1 13 8 13 4 2... 10 700 7 500 5 470 4 110 3 160 2 490 1 990 1 620 1 33 0 1 110 937 6 83 5 13. 0 449.0 39 5.0 31 1.0 249.0 202.0 167.0 139 .0 9 33 0 000 3 930 000 2 010 000 734 000 492 000 252 000 146 000 74 600 31 500 16 100 9 33 0 5 870 3 930 2 760 5 010 1 510 1 170 917 734 597 492 410 34 5 252 189.0 166.0 146.0 115.0 91.8 74.6 61.5 51 .3 9 230 000 3 890 000 1 990 000 726 000 487 000 249 000 144 000 73 800 31 100 15 900 9 230 ... 00 1.259 840 33 .33 7 50 0. 234 37 5 6.000 00 6 .35 0 00 7 30 31 ⁄ 32 31 .750 00 5.9 53 12 6.5 7⁄ 8 25 0.177 160 6 27⁄ 32 23. 812 50 0.157 480 4.5 3 64 0.047 240 1.984 38 2.778 00 4.000 00 0.046 875 1.200 00 1.587 50 0.025 3 4 Diameter mmb 1 .31 2 500 34 .000 00 1 .33 8 580 1⁄ 4 32 17⁄ 64 34 34 .925 00 1 .37 5 000 9⁄ 32 35 35 .000 00 1 .37 7 950 36 36 .000 00 1.417 32 0 36 .512 50 38 1. 437 500 38 .000 00 15⁄16 13 8 17⁄16 1.496... 8 3 4 7⁄ 8 10 20 55⁄8 33 ⁄4 1 23 4 3 51⁄2 6 11–22 61⁄4 41⁄8 1 13 8 12–24 63 4 41⁄2 11⁄8 11⁄2 3 8 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 3 4 7⁄ 8 7⁄ 8 31 ⁄4 61⁄2 7 13 26 73 8 47⁄8 11⁄4 15⁄8 1 31 ⁄2 14–28 77⁄8 51⁄4 13 8 13 4 1 33 ⁄4 4 71⁄2 8 15 30 55⁄8 6 13 8 16 32 81⁄2 9 11⁄2 17⁄8 2 11⁄4 1 41⁄4 17 34 91⁄2 63 8 15⁄8 21⁄8 13 8 11⁄16 41⁄2 81⁄2 9 18 36 101 ⁄4 63 4 13 4 21⁄4 13 8 11⁄8 43 4 5 91⁄2 10 19 38 1 03 4 71⁄8 13 4 23 8... 060 835 668 5 43 448 37 3 31 4 229 172.0 151.0 133 .0 104 .0 83. 5 67.9 56.0 46.7 8 410 000 3 550 000 1 820 000 662 000 4 43 000 227 000 131 000 67 200 28 400 14 500 8 410 5 290 3 550 2 490 1 820 1 36 0 1 050 826 662 538 4 43 370 31 1 227 171.0 149.0 131 .0 1 03. 0 82.7 67.2 55.4 46.2 8.470 8. 830 14.947 8 35 0 000 8 010 000 4 730 000 3 520 000 3 380 000 2 000 000 1 800 000 1 730 000 1 020 000 657 000 631 000 37 3 000... 13 4 21⁄4 4 11⁄4 23 16 23 4 5 11⁄2 25⁄8 13 4 2 31 ⁄16 33 ⁄8 4 7 31 ⁄2 41⁄2 8 21⁄4 31 5⁄16 51⁄8 9 21⁄2 43 8 55⁄8 10 23 4 3 4 13 16 61⁄4 11 51⁄4 63 4 12 31 ⁄4 511⁄16 13 31⁄2 61⁄8 73 8 8 33 ⁄4 69⁄16 81⁄2 15 6 14 4 7 9 16 41⁄2 5 77⁄8 101 ⁄4 18 83 4 111⁄4 20 83 4 111⁄4 20 101 ⁄2 1 23 8 22 51⁄2 6 61⁄2 7 1 13 8 131 ⁄2 24 121⁄4 145⁄8 26 71⁄2 8 131 ⁄8 14 1 53 4 28 28 81⁄2 9 147⁄8 167⁄8 18 30 1 53 4 191⁄8 31 165⁄8 201⁄4 32 ... 1 810 1 050 659 441 31 0 226 170 131 1 03 82 .3 66.9 55.2 46.0 38 .7 32 .9 28.2 24.4 21.2 18.6 16 .3 14.5 12.9 11.5 10 .3 9.26 8 .37 7.58 6.89 279 224 000 28 000 8 31 0 3 500 1 790 1 040 654 438 30 8 224 169 130 102 81.7 66.5 54.8 45.7 38 .5 32 .7 28.0 24.2 21.1 18.4 16.2 14.4 12.8 11.4 10. 2 9.20 8 .31 7. 53 6.85 2 83 221 000 27 600 8 190 3 460 1 770 1 020 645 432 30 3 221 166 128 101 80.6 65.5 54.0 45.0 37 .9 32 .2... 165⁄8 201⁄4 32 171⁄2 2 13 8 34 91⁄2 10 101⁄2 11 1 83 8 221⁄2 35 191⁄4 235 ⁄8 36 111⁄2 12 201⁄8 21 2 43 4 37 257⁄8 38 E F 11⁄ 16 13 16 15⁄ 16 11⁄16 13 16 15⁄16 17⁄16 19⁄16 111⁄16 1 13 16 115⁄16 21⁄16 21⁄4 21⁄2 23 4 23 4 215⁄16 31 ⁄8 31 ⁄4 37 ⁄16 31 ⁄2 31 1⁄16 33 ⁄4 31 5⁄16 41⁄8 41⁄4 47⁄16 45⁄8 4 13 16 5⁄ 16 3 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3 4 13 16 7⁄ 8 15⁄ 16 G 11⁄2 17⁄8 21⁄4 25⁄8 3 33 8 33 ⁄4 41⁄8 41⁄2 47⁄8 51⁄4... 000 130 000 125 000 73 900 66 800 64 100 37 900 28 200 27 000 16 000 14 400 13 800 8 180 8 35 0 8 010 4 730 5 260 5 040 2 980 3 520 3 380 2 000 2 470 2 37 0 1 400 1 800 1 730 1 020 1 36 0 1 30 0 768 1 040 1 000 592 821 788 465 657 631 37 3 534 5 13 3 03 440 422 250 36 7 35 2 208 30 9 297 175 225 216 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