This standard is applicable to couplings as defined in ANSI/AGMA 9009-D02, Flexible Couplings - Nomenclature for Flexible Couplings, with metric bores and keyways. Total Height (X) = Depth (Y) = Return to broaching : 2388 State Route 726 Eaton, Ohio 45320 (937) 456-2232 Fax (937) 456-2282 [email protected] to 3. Design of Square Key and Keyway (Wood Ruff) Stress, Shear and Torque. The intention of the keys/keyways is to allow axial motion of a female sleeve to which the keys are mounted while preventing rotational motion. The invention is directed to an adaptor device suitable for use with a measuring apparatus to determine the centrality to the centerline of a Woodruff keyway in a shaft. EN Standard. Metric keyways are dimensioned by width and depth as measured from the radius of the shaft to the center of the keyway. Coupling in mechanical engineering is a device used to connect two shafts together at their ends for the purpose of transmitting power or torque. 3 mm) in diameter with a standard bar clamp. ). In this comprehensive guide, we will discuss seven popular internal keyway cutting methods. The hollow saddle key is a taper key that fits in a keyway in the hub. Keyway Radius “R”† Over Thru Nominal Min Max Min Max Min Max Hub “W” Over Thru Min Max Min Max Keyways will be furnished with P9 width tolerance only upon request. W width. ** earcneaear r l c oFr Information DIN 6885 page 1 and page 2 differ mainly in the radial position of the parallel key (see sketch). The second is a P9 tolerance. any shaft from 1. The following table includes standard rectangular shaft key sizes for shaft diameters ranging from 5/16" to 9": Standard rectangular key stock is readily available from most Gates Industrial Distributors. We can provide keyed shafts in any length up to 20 foot. Referencing Figure 1, the keyway dimension is W x T1. The essential data for this standard have been extracted from ISO Recommendations R 7731) and R 7742). com The bottom of the key is shaped to fit the curved surface of the shaft. In stock and ready to ship. The adaptor allows the measuring apparatus to rest on the top surface or outside diameter of the shaft so that the measuring apparatus can be used to measure the centrality of the side walls. Standard Metric Keys Keyways for Metric Bores with One Key. For shafts, the standard lengths are 5m, 6m and 7m but generally taken as 1m to 2m. International Standard IS0 3912 was developed by Technical Committee ISO/TC 14, Shafts for machinery and accessories, and was circulated to the member. clearance fit bores with set screws. still see lots of ordinary keyways in bigger shafts. TruKey® Shafting from Keystone is designed to provide the straightest, most accurate keyed shafting, in the industry. Standard keyways provide added torque capacity and fixed shaft phasing. The key and key seat cross section are ISO standardized. Shaft Diameter. Re-design the shaft shown below to be a uniform,Metric woodruff keys are supplied to din 6888 / iso 3912 in c45k key All torque transmissions resourcesKeyway chart bore resources torque alltorquetransmissions. 3mm 5mm 5mm 5mm 5mm 6mm 6mm 6mm 8mm 8mm 22mm 24mm 16mm 17mm 19mm 20mm 25mm Keyway Width (w) 10mm 3mm 3mm 1. Specifications Met. Referencing Figure 1, the keyway dimension is W x T 1. - Series F couplings supplied with 4) All dimensions per AGMA 9002-A86 The hub keyway is dimensioned by its width and depth on the shaft – keyway sides. There are tables for this in "Machinery's Handbook". xx / -0. TruKey® Shafting from Keystone is designed to provide the straightest, most accurate keyed shafting, in the industry. A key cutter, also known as a keyseat cutter, keyway cutter, or woodruff cutter, is a versatile tool that can be used to cut several different types of keyways. Dimensions: Shaft Diameter (A): 2" Keyway Width (B): 1/2" Keyway Depth (C): 1/4" Shaft Material: 1018 Steel; Phone: (407) 347-3519 Email: [email protected] using a key it should firstly be fitted in the shaft Keyway. If the enduser is using oversize plated keystock, then the properly centered keyway is more important. Cut keys to custom lengths. NOMINAL SHAFT DIAMETER BOTTOM OF SHAFT TO BOTTOM OF KEYWAY WIDTH. They conform to ANSI B17. In Figure 2-22 a, the fillet in one corner of the keyway was radiused. Drive shaft Design, key and Keyways. In order to transmit rotation from the shaft to the hub of gear wheels, pulleys, sprockets, couplings, flanges and other coaxial parts, rigid and frictional joints of various types are used. 002 −0 Hub keyway w −0 Shaft keyseat h +0. A flat saddle key is a taper key which fits in a keyway in the hub and is flat on the shaft as shown in Fig. When selecting a keyway tolerance, there are two common selec-tions in the metric system. 2 Exceptions . Hollow saddle keys. Check Details. Metric key keyway dimensions per iso/r773. I would specify location tolerances separately on the length of your first keyway, and on the width and length of your second keyway. Straight Sided Spline Dimensions. So let’s discuss. 46 : Part 1 : 1958 DLMENSIONS OP TANGENTIAL KEYS AND KEYWAYS. 6. Keyways Index KeyWay & Key Dimensions. Hub keyway depth is one-half the nominal height of the key and measured from the side corner. 5 in (170 mm). 010". Appropriate fits can be established for each shaft size and published in a standard. 5 - 4. DIN-Keys & Keyways to ISO Diameter d in accordance to DIN 6885/1 in accordance to DIN 6885/3 above to Width b 1) Depth h Shaft Keyway Depth t₁ Hub Keyway Depth d = t₂ Width b 2) Depth h Shaft Keyway Depth t₁ Hub Keyway Depth d = t₂ mm mm mm mm mm mm mm. Parallel keys are the most widely used machine key. Gib head keys. Because they're usually shorter than. BS ISO 4156:2005_1: Straight cylindrical involute splines. The width of the key (W) is 350 (0. 2515 0. 1890 0. Keyway misumiKey and keyway dimensions (control in motion) Keyway sizing chartMetric key keyway dimensions. Stock lengths from 3 feet to 24 feet. - If a part is 6 inches thick, the Wire-cut EDM machine will be able to cut two inches deep per hour. 002 inch for keyseat length up to and including 4 inches; 0. 8M high quality products and 80 sextillion configurable parts available with fast shipping and low pricing. BOTTOM OF SHAFT TO BOTTOM OF KEYWAY. Functional key length: 267,5mm (= length - (0,5x width)) Shaft material S355J2G3 (St52. Keyway Cutter Hole Keyway Dimensional Data for MIlling Centers and Arbors - ANSI/ASME B94. 5 SHAPE, DIMENSIONS AND TOLERANCES OF KEYWAYS 8 -4 X Sect ion X-X Detail A Vaiues in millimetres Shaft Keyl ) Keyway Diameter d Width b Depth*) Sect ion bXh Radius r Tolerante for class fit Free Normal Close Shaft tl Shaft Hub Hub and hub H9 DIO IV9 Js9 P9 nom. Check out our shaft keyway size chart as well to help you identify your needs. Page 1 of 3. 2-1967. 4: Shaft with overhung gear Example -Homework Problem 9-2 5 9. Keys with greater width tolerance. Machine keys – also called shaft keys or key seats - are removable machine elements installed between shaft key seats and hub keyways to transmit torque in power transmission assemblies. As seen by the image, the top part of the key is also rounded. A list of standard keyway and corresponding key sizes for English shafts are listed below in Table 1. The taper is 1/8” per foot. Keys and keyways BS 46 Part 1 : 1958 Keys and keyway Dimensions-Parallel Rectangular Adve Radius 0. I am designing a part that has two keyways 180 degrees apart on a single large diameter shaft. The table above shows the dimension of the keyway / keyseat for each available hub bore diameter. The standard dimensioning of the keyway is like above. ASME standard B17. sometimes referred to as a keyway. 1 mm. Ann from the top of the shaft, the keyway is shown. BS 46 Part 1 : 1958 Square Keys and keyway Dimensions. Refer to Figures 4 and 5 and Tables 6 and 7 for recommended setscrew location and size. Mechanical & Motion Systems. The standard keyway (USA Standard ANSI B17. These shafts have keyways only on the ends, leaving a plain shaft in the center. ANSI/AGMA 9002-A86 was based upon the design criteria related to bores and keyways in coupling hubs that had evolved over many years of successful industry practice. One could have skipped the step. 1. We stock pre keyed shafting in many diameters, including metric diameters, with standard keyways. 1 to 114. Ansi B17 1 Standard Keyway. Only informative sections of standards are publicly available. The keyway on the. n When referencing the Lovejoy UPC number in this table, include 685144 as a prefix to the number shown. 2 To facilitate the cutting of keyways on the shaft and in the hub, they may be located 180” apart, by agreement between the interested Parties. Standard Type: 20. 015-0. We stock pre keyed shafting in many diameters, including metric diameters, with standard keyways. 1890 0. f7 (shaft) tolerance range = −0. For more information, to get a formal quote on 2" keyed shaft, or for pricing on any of its accompanying components/ accessories please contact us and we will be happy to assist you. 6 %âãÏÓ 105548 0 obj >stream hÞ¼“moÛ6 Ç?A¿ _¦ ‚¿ ?Å@aÀŽë¦[šu±ÛdMó‚–N ŠRHÚ ûéw¤ ¯ ¶,y3H" ÷@ ¿ ô’þH$bÐK ‰HÓ4J©HÇã. Find the depths to cut in keyway and keyseat. In stock and ready to ship. 46 : PART 1 : 1958. Transeals - Keyway Chart. This technique is used for parts like a gear, hub or pulley. Same deal if using a pulley/shaft/sprocket with a taper lock hub. 25. Shaft Keyway Shear and Yield Strength Formulae and Calculator. Rectangular or square parallel keys. 18 3. In the English system, it is standard practice to dimension keyways. Unless otherwise specified, the shaft keyway is assumed to be standard. BS 4235-2:1977, ISO 3912-1977: Specification for metric keys and keyways - Woodruff keys and keyways. One of the following methods should be used to specify keyways: Metric: WxH Key W x T2 Keyway British: WxH12 Key W x H Keyway ISO Standard-mm Imperial -Inches Standard keyway dimensionsStandard shaft sizes key bushing table qd non bore keys shallow range gates includes specific each also Keyway chartShaft and hub keyway dimensions. This is an undersized clearance. The gib head makes them easy to remove when parts need to be taken apart frequently, such as for maintenance or prototyping. Shaft keyway keyways bores t2 chains wxh. Unless otherwise specified, the shaft keyway is assumed to be standard. The dimension from the top of the keyway to the opposite bore side. Click here to purchase the full version from the ANSI store. 5 times the shaft diameter to ensure a good load distribution over the entire key length when the shaft loaded in torsion. 2(w/d)-1. In stock and ready to ship. 1 1. Machine Key Comprehensive Guide. BS 46 Part 1 : 1958 Square Keys and keyway Dimensions. To confirm the status of any standard, identify the replacement standard if it is obsolete and/or purchase the standard please use. They have a square or rectangular cross section. Title: Tables. finished steel stock for parallel keys. o 65. The gib head makes them easy to remove when parts need to be taken apart frequently, such as for maintenance or prototyping. 921 Woodruff Key curvature as that of the key. Woodruff keys work well near shaft shoulders, where a standard open keyway would create too much stress. 000 Min. +35 0. Unless otherwise specified, the shaft keyway is assumed to be standard. If a key is to be fitted place it in the shaft keyway before fitting the bush. One from our supplier is requesting that shaft keys and keyways be toleranced on our prints in such a way that the keyways would *always* be bigger than the keys. Shop Universal Joints - Keyway, Set Screw from MISUMI. This Standard covers the size, type and tolerances of parallel and taper keys and keyseats, and their relationship to shaft diameters and bore diameters. Contact. 3mm 2. A shaft narrower than the applicable shaft diameter should not be used. It other words, the torsional strength of the shaft is reduced. They are also designed to protect a power transmission application by failing first, which protects other component. 5000 2. They can be made using a standard stock material such as key stock or custom machined to suit the application. Keyways are generally used in fastening gears to a shaft, and they should be secured by applying drilled holes for set screws, or applying flats to the shaft, in case of fastening only with set screws. Standard keyway dimensionsStandard shaft sizes key bushing table qd non bore keys shallow range gates includes specific each also Keyway chartShaft and hub keyway dimensions. All Keyways are parallel and to British Standard 46: Part 1: 1958, with the exception of those marked* which are shallower. To use a key as a sacrificial part, choose a softer key that will shear off. 000. The same dimensions as our Clamp-Type Shaft Couplings, these Clamp-Type Couplings with keyways are available from stock with standard keyways. . Notes: n Tolerances for bore and keyways are found in Engineering Data section (pages ED-10 and ED-11). S. 0000 /. The end of a keyway has two standard designs, shown in Figure 1. These values are to be reduced by 25% for the presence of keyways. 001/-0. Where a key is to be used it should be side fitting with top clearance. 8 6. keyways in the shaft members than to keyways in coupling hub bores. . . The projecting part of Woodruff key fits in the keyway in the hub. Dimensions: Shaft Diameter (A): 3-7/16" Keyway Width (B): 7/8" Keyway Depth (C): 7/16" Shaft Material: 1018 Steel; Phone: (407) 347-3519 Email: sales. Check Details. COMPONENTS PowerDrive LLC Bore Tolerance 0 to 2 2 to 3 3 to 4 Over 4 +. 95 6. 3) Keyway fillet radius to be specified by customer. The corresponding shaft tolerance needs to be determined based on whether the fit between the gear and shaft is to be an interfer-ence fit, a transition fit, or a clearance fit. 6. While a designer is free to specify any keyway they wish, straying from the standard option is likely to increase the cost, time, and complexity of the part. 1/4" & 3/8" — 3/32" x 3/64" 1/2" & 9/16" — 1/8" x 3/64"keyways in shaft-hub connection is the shear stress, so the focus is done on it. 062 0. a) PSfrag replacements b) Figure 1: The two standard keyway ends for parallel keys. This specification includes index tolerances for multiple keyways. G&G Manufacturing Company 4432 McKinley Street P. Keyway dimensionsMetric key keyway dimensions per iso/rtt3 js9 width Inch keyway chart ansi agma shaft key width b4 dimensions diameter nominal reference motor electricKeys keyway metric standard keyways sizes engineering shaft key parallel square fit fits mechanical data rectangular british limits figure. ASTM Standard. corresponding keyways for Metric shafts are listed below in Table 2. Undersized Machine Key Assortments. Choose from our selection of 1 15/16" shafts in a wide range of styles and sizes. The shaft's diameters that can be used are 3-inch, 4-inch and 4 5/16-inches. 1) Unless specified by the customer: 2) Actual shaft fit will vary depending on - Series S couplings supplied with actual shaft diameters. depth tol. 3. This standard covers the size, type and tolerances of parallel and taper keys and keyseats, and their relationship to shaft diameters and bore diameters. 4. Keyway toleranceKeyway-and-key-size-dimensions. Top. BS 46 Rectangular Taper & Gib Head KeyWay & Key Dimensions All Dimensions in inches. 3. Also, applications can be in two directions. Home; Metric Keyways Index page; Parallel Keys and keyway Dimensions; Parallel Keys and keyway Dimensions to BS 4235-1:1972 KeyWay & Key Dimensions. The centre of the pair should be opposite the keyway if a key is used with the set screws bearing on a slight relief turned in the shaft or a pair of flats. Standard Keyway Size Chart. 1 - 114. 8mm 3. The common specification dimension, Key Size, is highlighted. 2500 0. Unless otherwise specified, the shaft keyway is assumed. When a keyway is damaged, cut a new, wider one. The centuries-old industry standard shaft-to-hub mounting technique is the key and keyway. Further, shafts, along with any other required drive elements, can be made smaller once the keyway notch factor is removed. Shaft Keys 101 | Machine Design. The hub keyway is dimensioned by its width and depth on the shaft – keyway sides. Keyways Index. Metric Shaft Size Keyway Width Keyway Depth Stock Lengths 5/8" 3/16" 3/32" 13mm: 5mm: 2. Standard keyways run full length. These keys have a tapered body that wedges in to the keyway for a more secure fit than standard machine keys. 28. TruKey® Shafting from Keystone is designed to provide the straightest, most accurate keyed shafting, in the industry. 94 inch. The standard sizes of machine shafts are up to 25 mm with a 5 mm step. js9 widt. . com. Keyways cut in certain area’s on the shaft. Cutting an internal keyway can be a challenging task, but with the right method and tools, it can be done with precision and efficiency. 2 MATHEMATICAL FORMULATION AND FE The torsional moment is given by M t~GJ w l ð1Þ Fig. 06-20-2011, 11:07 AM. The shafts revolutions range from 17 to 54 per minute (rpm). 57 inch;Install in a keyway to transmit torque from shafts to gears and other components. Because this key stock is slightly larger than standard key stock, keys will fit tightly in worn keyways. 5 in (170 mm). Open the catalog to page 11The development of these relations can be found in standard texts. Width. 2-1967 Specification for metric keys and keyways – Parallel and taper keys BS 4235. DIN 6885-1 :- Key, Hub Keyway, Shaft Keyway Details and Dimensions. BS ISO 4156:2005_1: Straight cylindrical involute splines. Figure 2 — Types of key and position of keyway in shaft 18 Table 1 — Rectangular parallel keys, keyways and keybars 4 Table 2 — Square parallel keys, keyways and keybars 6 Table 3 — Rectangular taper keys and keyways, gib-head or plain 9 Table 4 — Square taper keys and keyways, gib-head or plain 10 Table 5 — Woodruff keys and keyways 12 1) Unless specified by the customer: 2) Actual shaft fit will vary depending on - Series S couplings supplied with actual shaft diameters. 21. 5 3. Coping with foreign bore and keyway standards | Machine Design. In general, also, we use this type in low-speed applications. pdf Gates belts, hoses, and applications: standard & non-standard shaft keyMetric keyway. Hollow saddle key. The center of the keyway is typically located 1/3 of the. standard keyseat be used in the shaft in all cases. Pul1 up on. The keyways correspond to the ASME USAS B17. 110 mm to 140 mm – 15 mm step. DIN 6885/2 Keyways d b P9/JS9 Hub keyway b P9/N9 Shaft keyway h t1 = d + t2 t2 t3 = d - t4 t4 11 4 4 4 12. 477 Maximum 2. Motors and gearboxes that generate high torque and acceleration may make shaft keys obsolete. The keyway in the shaft is in the form Of a semicircular recess with the same Fig. There are five main types of shaft keys: sunk, saddle, tangent, round, and spline Sunk Keys Rectangular & square keys. International Standard ISO 3117 was developed by Technical Committee ISO/TC 14, Shafts for machinery and accessories, and was circulated to the member. Locate keyways per Figure 6 and Table 8. The introduction of a DIN or ANSI standard keyway into a shaft normally reduces the shaft radius by 20 to 25%, and often as much as 50%. 1 +0. For a key to function, there must be a keyway on the shaft and a keyseat on the rotating machine element. 1. pdf. Regular. This is useful when the hub/pulley has to slide axially on the shaft to. S. For use on standard hardened round shafts, Shaft Adapters are precision machined, non-marring, easy to adjust, with high clamping power. 3 1. n Non-standard bores available – consult Lovejoy Engineering. ). All keyed Shafting is guaranteed to fit on a bearing, and the ends can be chamfered. Coupling Diameter: 6. Standard keyways provide added torque capacity and fixed shaft phasing. 3 N) When I calculate with this data I reach a safety factor of 1,08. ANSI Woodruff Keys. Recommended Hub Keyway Dimensions (mm) Reference AGMA 9112-A04 Standard metric keyway width tolerance per Js9 Imperial Standard Bore and Keyway Info Recommended Bore Tolerance for Imperial Shafts (Inches) Nominal Shaft Range Shaft Tol. Metric – Rectangular B. 53. Install them in keyways to transmit torque from shafts to gears and other components. Metric External Table Chart Thread Designations Sizes M 1. And the dimension is added from the bottom of the keyway to the bottom perimeter of. 4235 : PART 1 : 1972 Shaft key selection is crucial in avoiding premature failure on keyed joints. Inch (ANSI/AGMA 9002-B4) Metric (ISO/R773) corresponding keyways for Metric shafts are listed below in Table 2. Since they fit more loosely than standard keys, these undersized keys are best for uneven keyways or when you need to disassemble parts frequently, such as during maintenance or prototyping. 018 0RoyMech Resources Keyways BS 46 :1958 Parallel Keys and Keyway Dimensions These Pages include various standards. Re-design the shaft shown below to be a uniform,Keyway chart Shaft standard key sizes rectangular gates keys diameters most. Key dimension Keyway dimension Reference b h C l Basic Basic dimension b of b1 and b2 Sliding type Normal type Fastening type r1 and r2 Basic dimension of t1 Basic dimension of t2. 6 1. Dimensions standard keyseat keyway shaft shafts diameter nominal. 25. Page Count: 34. Shaft Keyseats/Hub Keyways Standard Keyseats/Keyways. That is, for a 1/2" key the depth of the keyway would be . ANSI/AGMA 9002-A86 was based upon the design criteria related to bores and keyways in coupling hubs that had evolved over many years of successful industry. Width. 05 0Unlike clearance fit hubs (which must have either a keyway, square bore, or spline to keep them from rotating), interference fit hubs also have the option of not necessarily having a keyway (or keyways) to transmit shaft toque (though many still will). 2 mm. 18 3. 88 Lecture1: Design of Shaft 33. Check Details. This British Standard is the first of a series for metric keys and keyways and has been prepared under the authority of the Mechanical Engineering Industry Standards Committee. Shallow keyway depths must exceed 2/3 of the full keyway depth of the square keys shown above. Transmission shafts standard sizes or lengths (according to steps). Technical Data: rated torque from 10 - 800 Nm shaft diameter from 5 - 72 mm. This is a +/- band clearance; the value of the tolerance is equally oversized or undersized. This shaft key installation requires a keyway on the hub and it does not require any keyway on the shaft. It helps to transmit torque. − S2 − S1 b 25 25 ℓ 1. 25 - M 1. 2 TECHNICAL INFORMATION Imperial Standards BS 46: Part 1: 1958 1/4 1/2 1/8 x 1/8Install them in keyways to transmit torque from shafts to gears and other components. Standard shaft sizes Standard shaft materials Design of shaft based on strength 8. Shaft couplings shall be so constructed as to present no hazard from bolts, nuts, setscrews, or revolving. These frictionalAccording to OSHA Standard 1910. Lots of times it's a pin or a bolt . (2000+HP) shafts had their keyways worn to the point the shaft needed to be turned from solid 4140 anew. 350 Maximum 2. A Key goes into the Keyway to lock things up. 5. 3) Keyway fillet radius to be specified by customer. It is desired that there is a minimum amount of rotational play. 01~50. . 1-1943 standard. These keys have a tapered body that wedges in to the keyway for a more secure fit than standard machine keys. The introduction of a DIN or ANSI standard keyway into a shaft normally reduces the shaft radius by 20 to 25%, and often as much as 50%. KeyWay /Key Dimensions. Keys and keyways. The shaft is supported on bearings and it rotates a set of gears orshown in Fig. 3D Printing & CAD. Clean and degrease the shaft. Inc. 003, -. A method is included for the photo elastic. S. Rounded Machine Keys. 060 +0. Key dimensions: Parallel keys are most commonly used. 18-8 stainless steel key stock offers a balance of strength and corrosion resistance. metric bores with metric keyways, or shaft keyseat tolerances. the depth of a keyway is an important taken every Shaft keyway depth calculatorKeyway misumi. It also gives the relation to be observed between the diameter of the shaft and the section of the key. b x h width x thck. 1 Shaft Shaft is a common and important machine element. N = Number of splines. 0 2 2 9 10 3 1. 002 -0. A list of standard keyway and corresponding. 4 Splines 9. It is ideal for overhung or unsupported shafts and is an excellent way to attach items such as mixer paddles and shaft Bore Diameter 1: 1. 16-0. KEYSHAFT Keyed Shaft, Diameter 3/4 in, Keyway 3/16 in x 3/32 in. We can provide keyed shafts in any length up to 20 foot. This material is precision ground to offer tighter tolerances than standard 316. 180. 25 mm to 60 mm – 5 mm step. 2-Piece Clamp-Type Shaft Collars with Keyways are for use on standard round shafts, hard or soft, as well as on thin wall tube or over a split hub. 14 mm. This shaft key installation necessitates the use of a keyway on the hub but does not need the use of a keyway on the shaft. The gib head makes them easy to remove when parts need to be taken apart frequently, such as for maintenance or prototyping. 2. Metric – Rectangular B. 414 Maximum 2. (5). . The keyways are dimensioned for use with a stock key class 2 in order to get a tight fit combination. Keyway metric key dimensions standard keyways keys bores shaft hub depth iso diameter engineering table edge width millimetersWoodruff ansi fasteners nominal Woodruff ansi metric keyway fasteners nominalParallel dimensions metric keyway key keys 1972. This is a +/- band clearance; the value of the.