Crossed Roller Ways. Description of each series and Table of dimensions. Anti-Creep Cage Crossed Roller Way. Anti-Creep Cage Crossed Roller Way Unit
|
|
- Phyllis Powers
- 6 years ago
- Views:
Transcription
1 Crossed Roller ays Descripion of each series and Table of dimensions Ani-Creep Cage Crossed Roller ay Page - o -1 Ani-Creep Cage Crossed Roller ay Uni Page -1 o - Crossed Roller ay Page - o -1 Crossed Roller ay Uni Page - o -9 In he able of dimensions, sandard producs are referred o using idenificaion numbers marked wih. The idenificaion numbers marked wih refer o our semi-sandard producs.
2 U.S. PATNTD Ani-Creep Cage Crossed Roller ay CRG Ani-Creep Cage Crossed Roller ay series Shape odel code Ani-Creep Cage Crossed Roller ay is he produc wih a cage creep proof funcion using a rack and pinion mechanism originaed from Crossed Roller ay, feauring smooh linear moion wih super high accuracy. Reliable running performance Perfec soluion for cage creeping problems by a buil in rack and pinion mechanism as an original design. Freedom in mouning This series is reliable for applicaions such as a verical axis for which he exising Crossed Roller ay is no easy o use. Applicable o high-speed operaion Any correcive operaion for cage creeping is no necessary even for a long-ime operaion. Inerchangeable in dimensions I has full inerchangeabiliy wih he exising Crossed Roller ay in mouning dimension. Since he series has he same exernal dimensions o hose of he exising Crossed Roller ay and can be easily replaced wihou any modificaion on he machine or equipmen using he exising Crossed Roller ay. nergy-saving in operaion Any correcive operaion for cage creeping is no necessary even for a long-ime operaion. Smooh operaion Precisely finished raceways are combined wih roller cages, in which he lengh of super precise roller is accuraely conrolled o avoid skewing. Very smooh linear moion wih very lile fricional resisance and free from sick-slip can be achieved. asy mouning The mouning holes of he ways are female hread holes wih a couner bore. So he mouning mehod is flexible, allowing he ways o be mouned eiher by insered hrough he holes prepared on machines. ouning srucure can be designed freely. Ani-Creep Cage Crossed Roller ay CRG U.S. PATNT No.,,1 nd screw Pinion ay CRG Rack ay Rack Cage Roller cage Cylindrical roller Srucure of Ani-Creep Cage Crossed Roller ay Noe : One se consiss of four ways and wo roller cages. - 1=0.09inch -
3 Idenificaion number and specificaion The specificaion of Ani-Creep Cage Crossed Roller ay is indicaed by he idenificaion number. Indicae each specificaion by using a model code, size, par code, classificaion symbol, and supplemenal codes. The ordering uni is a se of he combinaion of four ways and wo roller cages. 1 Series Sandard ype CRG Applicable ype and size are shown in Table 1. Sandard ype CRG SP /B Size 1 Series odel code Table 1 Type and size Size of rolling guide engh of way Accuracy class Size Par code Classificaion symbol Size Type Carbon seel CRG Special specificaion Supplemenal code engh of way The lengh of way is indicaed in millimeers. For applicable way lenghs, please refer Table1. Table 1 engh of way engh of way CRG CRG CRG CRG Accuracy class Sandard Super precision No symbol SP For he allowable values of parallelism of he raceway o he reference mouning surface, see Fig.1. CRG A B A CRG B Parallelism m 1 0 Fig.1 Accuracy of Ani-Creep Cage Crossed Roller ay Sandard Super precision(sp) ay lengh - 1=0.09inch -
4 Special specificaion Special mouning screw B Deail of special specificaion of Crossed Roller ay is shown below. Indicae any specificaion by adding he supplemenal code o he end of he idenificaion number. The way on he preload adjusmen side is moved when he preload is adjused. There should be some allowance for movemen beween he way fixing screw and he mouning hole. hen such allowance cannno be provided or when he fixing screw is insalled from he way side as shown in Fig., i is convenien o use he aached special mouning screws. This special mouning screw is also available when he posiional accuracy of he mouning holes and female hread of he machine on which he fixed side ways are mouned is no sufficien. oad Raing and Allowable oad For he load raing and allowable load of Ani-Creep Cage Crossed Roller ay, values for a downward load provided when a combinaion of four ways and wo roller cages is used in parallel are indicaed. An ouline of hem is described below. The load raings and allowable load of Ani-Creep Cage Crossed Roller ay are designed for equal load capaciy in downward, upward, and laeral direcions. Basic dynamic load raing C The basic dynamic load raing is defined as a consan load boh in direcion and magniude under which a group of idenical Crossed Roller ay are individually operaed and 90% of hose in he group can ravel 0 x meers free from maerial damage due o rolling conac faigue. Table Dimensions of special mouning screws S d H Basic saic load raing C 0 The basic saic load raing is defined as he saic load ha gives a prescribed consan conac sress a he cener of he conac area beween a rolling elemen and raceways receiving he maximum load. Size of CRG Remark : No applicable o size Screw size Screw size d D H S..1.9 D uni : Allowable load F The allowable load is a load under which he sum of elasic deformaions of he rolling elemen and he raceways in he conac area subjeced o he maximum conac sress is small enough o guaranee accuracy and smooh rolling movemen. Therefore, where very smooh and highly accurae linear moion is required, make sure o use an Ani-Creep Cage Crosse Roller ay well wihin he allowable load values. C, C0, F Fig. Direcion of load raing CRG Fig. ouning example wih special mouning screw - 1=0.09inch -
5 ubricaion and dus proecion Precauions for use Oil or grease is used as a lubrican for Ani-Creep Cage Crossed Roller ay. Oil is generally used for high speed or low fricion operaion. On he oher hand, grease is used when operaing speed is low. In case of grease lubricaion, good qualiy lihium-soap base grease is recoended. hen operaion speed is low and load is ligh, coa he raceways wih grease before use and rubricae periodically. Srucure show in Fig. makes he lubricaion easy. Ani-Creep Cage Crossed Roller ay is finished in producion very accuraely. If harmful foreign maerials such as dus or chips ener inside he ways, his will shoren he life or lower he accuracy. ih he objec of prevening exernal harmful foreign maerials such as dus, chips and waer from enering inside, i is recoended o insall a non-conac-ype labyrinh seal shown in Fig. or a conac ype wiper seal shown in Fig. on boh side faces. 1 Specificaions of Ani-Creep Cage Crossed Roller ay Check wheher he operaing characerisics of he seleced Ani-Creep Cage Crossed Roller ay are suiable for he applicaion of he machine or equipmen. Handling of Ani-Creep Cage Crossed Roller ay Ani-Creep Cage Crossed Roller ays are finished in producion very accuraely, so handle carefully. A pinion is assembled in he roller cage. If he cage is dropped or handled roughly, he pinion may come off. As cuing off he cage may cause he pinion coming off or damage o he pinion mouning par, so please avoid cuing off he cage. A rack is assembled in he way and fixed is posiion wih he end screws. hen assembling, he rack may come ou from he way by removing he end screws. Accuracy of he mouning par The general configuraion of maing mouning surfaces for Ani-Creep Cage Crossed Roller ay is shown Fig.. Accuracy of he maing mouning surfaces are, in general, as shown in Table. The accuracy of he maing mouning surfaces direcly affecs he operaing accuracy and performance of Ani-Creep Cage Crossed Roller ay. If very precise operaing accuracy is required, higher accuracy of maing mouning surfaces han he values shown in Table may be needed. Fig. xample of lubricaion mehod C A A A B B A Fig. xample of he maing mouning surfaces Fig. xample of labyrinh seal Table Accuracy of maing mouning surfaces This accuracy direcly affecs he operaing accuracy. A surface Flaness of A surface (four places) should be equal or nearly equal o he value of parallelism in Fig. 1 on page -. CRG B and C surfaces Flaness Flaness of hese surfaces direcly affecs preload. The value of flaness should be equal or nearly equal o he value of parallelism in Fig. 1 on page -1. Squareness Squareness o A surface affecs he rigidiy of assembled uni in he preload direcion. Consequenly, a high accuracy finish is necessary. Fig. xample of wiper seal - 1=0.09inch -9
6 Shape of he mouning par I is recoended o make a relieved fille a he corner of he maing mouning surfaces as shown in Fig.. Allow a clearance of 0. or more beween he way and he maing maerial of he oher side. Preload mehod Preload adjusing screws are generally used for seing preload, as shown in Fig.9. The size of he preload adjusing screws are he same as ha of he mouning screws for he ways. The posiion of he preload adjusing screws is a he same posiion as he mouning screws of he ways. For cenering, use half of way heigh H. Preload amouns differ according o he applicaion of machine or equipmen. xcessive preloads deeriorae life and ofen damage he raceways. Therefore, zero or minimal preload is recoended in general. If accuracy and rigidiy are imporan, a seing plae as shown in Fig..1 or a apered jib as shown in Fig.. may be used. 0. or more Fig. Shape of he mouning par Fig. 9 General example of preload 0. or more Ani-Creep Cage Crossed Roller ay conains synheic resin pars. Accordingly, he maximum operaing emperaure is C. In case of coninuous operaion, operaing emperaure should no exceed 0C. The operaing speed of Ani-Creep Cage Crossed Roller ay should no exceed 0m/min. aximum operaing emperaure aximum speed Tighening orque of mouning screws Tighening orque of mouning screws is shown in Table. If vibraion or shock is large, or momen load is applied, i is recoended o ighen he screws o abou 1. imes he values shown in Table. If vibraion and shock are no presen and high operaing accuracy is needed, a lower ighening orque han he values shown in Table is suggesed. In his case, adhesive or lock-screws may be used o preven any subsequen loosening of he mouning screws. Table Tighening orque of screws Screw size Tighening orque Remark : If he screw sizes on able side and bed side are differen, use he ighening orque of he smaller screw size for boh screws. Fig..1 xample of seing plae CRG Fig.. xample of apered jib - 1=0.09inch -11
7 A general mehod of Ani-Cage Creep Crossed Roller ay is shown in Fig.11. The general procedure is as follows. 1 ay a fixed side ay a bed side ay a bed side ay a preload adjusing side Preparaion for mouning CRG is delivered as an individual package conaining four ways and wo roller cages. The ways in each package are no inerchangeable wih ways in oher packages, so do no mix hem. Separae he end screws or end soppers and wash he ways wih a clean cleaning agen. Afer cleaning, apply rus prevening oil or lubricaing oil. Cleaning of mouning surfaces of able and bed Remove burrs and blemishes from mouning surfaces of able and bed wih an oil-sone, ec. During his process, also pay aenion o he corner grooves of he mouning surfaces. ipe off dus wih clean cloh and apply rus prevenive oil or lubricaing oil. ouning Fig.11 ouning example of CRG Corner groove ouning surface C ouning surface B ouning surface A Preload adjusing screw ouning surface A Corner groove Corner groove Fig.1 ouning surface for CRG ouning surface A ouning surface B ouning surface A ouning of ways a bed side (Fig.1) Afer fiing mouning surface of ways ono he maing mouning surfaces of bed, emporally ighen he mouning screws wih uniform ighening orque. Afer closely fiing he ways o B surfaces (See Fig.1), ighen mouning screws uniformly o he prescribed ighening orque. If high accuracy is required, ighen he mouning screws uniformly o he prescribed ighening orque while checking he parallelism of he wo ways along he overall way lengh. General ighening orque of mouning screws is shown in Table on page -. ouning of ways a able side (Fig.1) Afer fiing he mouning surfaces of he way a he fixed side o he maing mouning surfaces of able, emporally ighen he mouning screws a he fixed side wih uniform ighening orque. Afer closely fiing he way a he fixed side o C surface, ighen he mouning screws a he fixed side uniformly o he prescribed ighening orque. oosen he preload adjusing screws and emporally ighen he mouning screws of he way a adjusing side wih uniform and ligh ighening orque. Assembling of able and bed Remove end screws from he way a able side and way a he bed-side in he side o which he cylindrical rollers wih a reainer are insered. (See Fig.1.1) Place he cylindrical rollers wih a reainer on he way a bed-side wih he cener of he pinion gear in he cener of he reainer engaged wih he end of he rack gear of he way. (See Fig.1.) Do no bend he reainer. A A A Fig.1 ouning accuracy of ways ay a fixed side Surface C ay a adjusing side Preload adjusing screw Fig.1 ouning of ways a able side Fig 1.1 CRG Fig =0.09inch -1
8 ngage he end of he rack gear of he way a able side wih he pinion gear while adjusing he longiudinal and raverse posiions of he way a able-side and pushing he reainer o secure. Do no give any excessive force o he cage. (See Fig.1.) Slide he able on he base. Do no apply any offse load o he rack gear and he pinion gear and do no deform he cage. Check and make sure he rack gear is over he end of he way. If he rack gear is over he end of he way, genly push he rack gear ino he way while moving he able a a lile sroke. (See Fig.1.) Slide he able o he cener of he sroke and ighen he end screws. (See Fig.1.) Fig.1. Fig.1. Fig.1. Preload adjusmen Preload adjusmen is done only when mouning screws for he way a he adjusing side are emporally ighened. Preload adjusmen is sared from he adjusing screw a he cener of he way lengh, proceeding alernaely o he lef and righ. hile checking he clearance (deflecion) a he side surface of able, ighen each Fig.1 xample of preload adjusmen amoun, hen repea he same process applying a higher ighening orque unil a dial gauge indicaes zero-clearance. (No more change in deflecion) Record he ighening orque of he adjusing screws a zero-clearance. hen adjusing he screws close o he end of he way, gradually sroke he able and ensure ha he roller cage is posiioned a he adjusing screws. Using he above process, he inernal clearance becomes zero or minimal amoun of preload, bu he preload amoun is no uniform along he way lengh. Therefore, repea he same process and ighen all adjusing screws uniformly o he recorded ighening orque. Final fixing of he way a adjusing side The mouning screws have been ighened lighly o a uniform orque. Similar o he adjusmen of he preload adjusing screws, emporally ighen he mouning screws a he adjusing side o a slighly lower ighening orque han he prescribed value. Sar from he cener screw of he way lengh and proceed alernaely o he lef and righ. hen ighening he mouning screws close o he end of he way, gradually sroke he able and ensure ha he roller cage is posiioned a he mouning screw. Finally, ighen all mouning screws a he adjusing side uniformly o he prescribed orque similar o he adjusmen of he preload adjusing screws. Final checking (Fig.1) Sroke he able gradually ill is full sroke lengh, ensuring ha he sroke is smooh and quie. Check he operaing accuracy by measuring he upper and side faces of able wih a dial gauge. Genly move he able a a full sroke and make sure ha he cylindrical roller a each end of he reainer does no hi he end screw of he rack base wihin he sroke. If he roller his he reainer end, repea he above seps from he firs. (See Fig.1.) Fig.1 Final check of operaing accuracy CRG Fig.1. Afer checking he sroke movemen, adjus he preload, check he slide movemen of he able and check he accuracy. ih his, he mouning procedure of he CRG crossed roller way is compleed. -1 1=0.09inch -1
9 Ani-Creep Cage Crossed Roller ay CRG F nf H e p R Z(Number of rollers) D d A 0. 0 h d1 g CRG - 0 CRG - CRG - 0 CRG - CRG - 90 CRG - CRG - CRG -1 CRG - CRG - 0 CRG - CRG -0 CRG -1 CRG - CRG -1 CRG -00 CRG - CRG -0 CRG - 0 CRG - CRG - CRG -00 CRG -0 CRG -0 CRG -0 CRG -0 CRG - CRG -00 CRG -0 CRG -00 CRG -0 ass (Ref.) ay( 1 ) g Roller cage( ) g Boundary dimensions Nominal dimensions Dimension of roller cage ouning dimensions A H nf Dw R Z p e g d1 d h aximum sroke lengh Basic dynamic load raing( ) C Basic saic load raing( ) C Allowable load( ) F CRG - 0 CRG - CRG - 0 CRG - CRG - 90 CRG - CRG - CRG -1 CRG - CRG - 0 CRG - CRG -0 CRG -1 CRG - CRG -1 CRG -00 CRG - CRG -0 CRG - 0 CRG - CRG - CRG -00 CRG -0 CRG -0 CRG -0 CRG -0 CRG - CRG -00 CRG -0 CRG -00 CRG -0 CRG Noe( 1 ) : The value shows he mass of one piece of way. ( ) : The value shows he mass of one roller cage. ( ) : Direcion of basic dynamic load raing (C), basic saic load raing (C0) and allowable load (F) is shown in below. C, C 0, F xample of idenificaion number CRG SP /B odel code CRG Size,,, engh of way Accuracy class Sandard No symbol Super Precision SP Special specificaion Special mouning screw -1 1=0.09inch -1
10 CRUG U.S. PATNTD Ani-Creep Cage Crossed Roller ay Uni Ani-Creep Cage Crossed Roller ay Uni series Shape odel code Ani-Creep Cage Crossed Roller ay Uni is he produc wih a cage creep proof funcion using a rack and pinion mechanism originaed from Crossed Roller ay, feauring smooh linear moion wih super high accuracy. Freedom in mouning This series is reliable for applicaions such as a verical axis where Crossed Roller ay Uni may have chances of cage creep. High-speed operaion Any correcive operaion for cage creep is no necessary even for a longime operaion. nergy saving in he operaion is possible. Inerchangeable in dimensions CRUG are dimensionally inerchangeable o Crossed Roller ay Uni. Since hey have he same exernal dimensions o hose of he exising Crossed Roller ay Uni, exising Crossed Roller ay Uni can be replaced wihou any modificaion. Smooh and accurae operaion Combinaion of precisely finished raceways and nonrecirculaing cages wih super high precision rollers provides superbly smooh moion wih very high accuracy. Ani-Creep Cage Crossed Roller ay Uni CRUG U.S. PATNT No.,9,9,,1 CRUG Srucure of Ani-Creep Cage Crossed Roller ay Uni -1 1=0.09inch -19
11 Idenificaion Number of Ani-Creep Cage Crossed Roller ay Uni The specificaion of Ani-Creep Cage Crossed Roller ay Uni is indicaed by he model number. Indicae each specificaion by using a model code and size. xample of idenificaion number CRUG 0 oad Raing and Allowable oad Suarized descripions of load raings of Ani-Creep Cage Crossed Roller ay Uni are given below. For deails of load raing definiions and load calculaions, see "General descripion". The load raings for upward and laeral loads of Ani-Creep Cage Crossed Roller ay Uni are he same as hose for downward load. 1 Series idh odel code Size Basic dynamic load raing C The basic dynamic load raing is defined as he consan load boh in direcion and magniude under which a group of idenical Ani-Creep Cage Crossed Roller ay Unis are individually operaed and 90% of he unis in he group can ravel 0 x meers free from maerial damage due o rolling conac faigue. engh Basic saic load raing C 0 The basic saic load raing is defined as he saic load ha gives a prescribed consan conac sress a he cener of he conac area beween he rolling elemen and raceway receiving he maximum load. 1 Series CRUG Allowable load F idh 0,0,0 Indicae he widh of able uni in. The allowable load is a load under which he sum of elasic deformaions of he rolling elemen and he raceway in he conac area subjeced o he maximum conac sress is small enough o guaranee accuracy and smooh rolling movemen. Therefore, when very smooh and highly accurae linear moion is required, make sure ha he applied load on Ani-Creep Cage Crossed Roller ay Uni is well wihin he allowable load value. engh Indicae he lengh of able uni in. For applicable lenghs, please refer o Table 1. Saic momen raing T 0 The saic momen raing is defined as he saic momen load ha gives a prescribed consan conac sress a he cener of he conac area beween he rolling elemen and raceway receiving he maximum load when a momen is loaded. Table 1 engh of able uni engh C, C0 T0 CRUG CRUG CRUG CRUG Fig. 1 Direcion of load raing Fig. Direcion of saic momen raing -0 1=0.09inch -1
12 Accuracy The accuracy of Ani-Creep Cage Crossed Roller ay Uni is shown in Table. Parallelism a he able cener shows he difference beween he maximum and he minimum of able heigh when he able is sroked. Parallelism a able side shows he difference beween he maximum and he minimum of measured values a he able side (opposie o adjusing side) when he able is sroked. The sandard heigh olerance of he uni is 0.1. If several unis are used on he same mouning surface and he heigh of hose unis require a limied heigh variaion, unis wih a heigh variaion of less han 0.01 among he several unis o be used on he same mouning surface can be supplied on reques. If a special accuracy oher han hose shown in Table is required, consul. Table Accuracy of Ani-Creep Cage Crossed Roller ay Uni Preload re-adjusmen Preload of Ani-Creep Cage Crossed Roller ay Uni is adjused o zero or minimal amoun of preload in he delivery. Preload adjusmen is done only when mouning screws for he way a he adjusing side are emporally ighened lighly. Preload adjusmen is sared from he adjusing screw a he cener of he way lengh, proceeding alernaely o he lef and righ. hile checking he clearance (deflecion) a he side surface of able, ighen each amoun, hen repea he same process applying a higher ighening orque unil a dial gauge indicaes zero-clearance. (No more change in deflecion) Record he ighening orque of he adjusing screws a zero-clearance. hen adjusing he screws close o he end of he way, gradually sroke he able and ensure ha he roller cage is posiioned a he adjusing screws. Using he above process, he inernal clearance becomes zero or minimal amoun of preload, bu he preload amoun is no uniform along he way lengh. Therefore, repea he same process ighen all adjusing screws uniformly o he recorded ighening orque. Fig. xample of preload adjusmen uni : m Uni lengh over incl. Parallelism a able cener Parallelism a able side aximum operaing emperaure Ani-Creep Cage Crossed Roller ay Uni conains synheic resin pars. Accordingly, he maximum operaing emperaure is C. In case of coninuous operaion, operaing emperaure should no exceed 0 C. Precauions for ouning and Use aximum speed The operaing speed of Ani-Creep Cage Crossed Roller ay Uni should no exceed 0m/min. 1 Specificaions of produc Check if he operaing characerisics of he seleced Ani-Creep Cage Crossed Roller ay Uni are suiable for he applicaion of he machine or equipmen. Handling Ani-Creep Cage Crossed Roller ay Uni are finished in producion very accuraely, so handle carefully. A pinion is assembled in he roller cage. If he cage is dropped or handled rougly, he pinion may come off. As cuing off he cage may cause he pinion coming off or damage o he pinion mouning par, so please avoid cuing off he cage. A rack is assembled in he way and fixed is posiion wih he and screws. hen assembling, he rack may come ou from he way by removing he and screws. Tighening orque of mouning screws Tighening orque of mouning screws is shown in Table. If vibraion or shock is large, or momen load is applied, i is recoended o ighen he screws by abou 1. imes he values shown in Table. If vibraion and shock are no presen and high operaing accuracy is needed, a lower ighening orque han he values shown in Table is suggesed. In his case, adhesive or lockscrews may be used o preven any subsequen loosening of he mouning screws. Table Tighening orque of screws Screw size Tighening orque Nm CRUG Remark : If he screw sizes on able side and bed side are differen, use he ighening orque of he smaller screw size for boh screws. - 1=0.09inch -
13 CRUG Ani-Creep Cage Crossed Roller ay Uni CRUG CRG mouning screw H 1 1 Sopper posiion NP 1 CRG mouning screw d 1 d 1 d d 9 h r d np h 1 9 n 1 p 1 d ass (Ref.) Kg H Tolerance Tolerance Boundary dimensions Nominal dimensions aximum 1 sroke NP 1 1 d1 lengh CRUG 0- CRUG 0-0 CRUG CRUG CRUG 0-9 CRUG 0-1 CRUG CRUG 0- CRUG CRUG CRUG 0- CRUG 0-1 CRUG 0- CRUG CRUG CRUG Noe( 1 ) : Direcions of basic dynamic load raiing (C), basic saic load raiing (C0), allowable load (F) and saic momen raiing (T0) are shown in below. Table Bed Sopper and CRG mouning dimension Table Bed d h1 h np d r 9 n1p1 9 xample of idenificaion number CRUG d 0 Basic dynamic load raing( 1 ) C Basic saic load raing( 1 ) C Allowable load( 1 ) F Saic momen raing( 1 ) T CRUG 0- CRUG 0-0 CRUG 0- CRUG 0-0 CRUG 0-9 CRUG 0-1 CRUG 0-1 CRUG 0- CRUG 0-0 CRUG 0- CRUG 0- CRUG 0-1 CRUG 0- CRUG 0-1 CRUG 0-1 CRUG 0-0 CRUG C, C 0, F T 0 Series CRUG idh of able 0, 0, 0 engh of able - 1=0.09inch -
14 Crossed Roller ay CRCR U.S. PATNTD Crossed Roller ay is a linear moion rolling guide in which a roller cage is incorporaed beween wo ways wih V-shaped raceways. As he cylindrical rollers are alernaely crossed, Crossed Roller ay can receive loads in any direcion and can achieve very smooh linear moion wih very high accuracy. ide variaions in size are available for selecions suiable for each applicaion. Crossed Roller ay series Shape Sandard ype odel code CR CRS Sandard ype and module ype Two ypes are available: he sandard ype and he module ype. In he sandard ype four ways and wo roller cages are used as one se, while in he module ype wo inner ways are inegraed ino a single piece. Very smooh operaion Precisely finished raceways are combined wih roller cages, in which he lengh of super precise rollers is accuraely conrolled o avoid skewing. Very smooh linear moion wih very lile fricional resisance and free from sick-slip can be achieved. High carbon chromium bearing seel ype and sainless seel ype Sandard ypes include high carbon chromium bearing seel ype and sainless seel ype. asy mouning The mouning holes of he ways are female hread holes wih a couner bore. So he mouning mehod is flexible, allowing he ways o be mouned eiher by using he female hreads of he ways ogeher wih bols insered hrough he holes prepared on machines or by using he female hreads prepared on machines. ouning srucure can be designed freely. Two inner ways of module ype are inegraed ino a single piece. The mouning srucure can be made simple and, furhermore, as errors from exra machining of he mouning pars can be avoided, accuracy of linear moion can be improved. Crossed Roller ay odule ype CR nd screw ay nd screw Cener way U.S. PATNT No.,9,9 CR, CR Cage Cylindrical roller ay Cage Cylindrical roller ay Roller cage Roller cage Noe : One se consiss of four ways and wo roller cages. CR Noe : One se consiss of one cener way, wo ways and wo roller cages. CR Srucure of Crossed Roller ay Remark : odels wih "S" are sainless seel ype. - 1=0.09inch -
15 Idenificaion number and specificaion The specificaion of Crossed Roller ay is indicaed by he idenificaion number, consising of a model code, a size, a par code, a maerial symbol, a classificaion symbol and any supplemenal codes. 1 Series Sandard ype odule ype CR CR For available models and sizes, see Table 1. Sandard ype CR C0 S SP /U Size of rolling guide Sandard ype CR 000 C S SP /U odule ype CR C0 SP /U engh of way Indicae he lengh of way in. ays wih differen lenghs can be combined. For he lenghs of ways, see he able of dimensions. To indicae a combinaion of ways wih differen lenghs, see "Combinaion of way lenghs ". 1 odule ype CR 00 C0 SP /U Series odel code Number of cylindrical rollers No symbol C The number of cylindrical rollers incorporaed in one cage is indicaed. hen his number is no indicaed, he number of cylindrical rollers shown in he able of dimensions are incorporaed in one cage. Size of rolling guide Size Combinaion of way lenghs engh of way Par code Number of cylindrical rollers aerial aerial symbol Combinaion for he sandard ype One se consiss of wo shor ways and wo long ways ogeher wih wo roller cages. As sandard, he number of rollers in one cage is he number of rollers for he shorer of he wo way lenghs shown in he dimension ables. If a differen number of rollers is required, indicae i in he idenificaion number. Combinaion for he module ype One se consiss of one cener way, wo ways ogeher wih wo roller cages. As sandard, he number of rollers in one cage is he number of rollers for he shorer of he wo way lenghs shown in he dimension ables. If a differen number of rollers is required, indicae i in he idenificaion number. Accuracy class Classificaion symbol Special specificaion Supplemenal code xample CR 00 00C pcs. of rollers incorporaed in one cage ong way lengh : 00 Shor way lengh : 00 xample CR 00 C0 0pcs. of rollers incorporaed in one cage ay lengh : Cener way lengh : 00 CR, CR - 1=0.09inch -9
16 aerial High carbon seel made Sainless seel made : No symbol : S For applicable maerial ypes, see Table 1. Special specificaion For applicable special specificaions, see Table. hen several special specificaions are required, see Table. For deails of special specificaions, see page -. Table 1 Types and sizes Size Type Sandard ype High carbon seel made Sainless seel made odule ype High carbon seel made Table Special specificaions Special specificaion Special mouning screws High rigidiy roller cage nd sopper SA nd sopper SB iper seal Supplemenal code B SA SB U ( 1 ) ( ) ( ) ( ) ( ) Noe( 1 ) : No applicable o size 1 and models. ( ) : No applicable o size 1,, and models. ( ) : No applicable o size 1 models. Sandard ype High carbon seel made Sainless seel made ( ) ( ) ( ) ( ) odule ype High carbon seel made ( 1 ) ( ) ( ) ( ) Accuracy class Sandard Super precision A : No symbol : SP For he allowable values of parallelism of he raceway o he reference mouning surface and of parallelism beween wo raceways of CR, see Fig. 1. Table Combinaions of special specificaions SA SB U B SA SB A A Remark 1 : In he able, he mark -- indicaes ha his combinaion can no be made. : hen several special specificaions are required, arrange he supplemenal codes alphabeically. A B CR B CR A CR, CR Parallelism SP ay lengh Fig. 1 Accuracy of Crossed Roller ay -0 1=0.09inch -1
17 Special specificaions Deails of special specificaions of Crossed Roller ay are shown below. Indicae any specificaion by adding he supplemenal code o he end of he idenificaion number. Special mouning screws B Since he way a he adjusing side moves when he preload is se, some clearance beween he mouning screw and he mouning hole is necessary. However, if sufficien clearance can no be provided or if he mouning screw is fixed from he way side o he able as shown in Fig., special mouning screws may be needed. Furher, if he posiioning accuracy of mouning holes in able or bed are no good, special screws can also be used. The special mouning screws are delivered as appended pars upon reques, bu available in carbon seel ype only. High rigidiy roller cage High rigidiy cages made of copper alloy, which are suiable for use in verical applicaions, are opionally available. This cage is designed o preven rollers from falling ou in one direcion. (See Fig..) For verical usage, i is recoended o use his cage ogeher wih he end sopper SB. Fig. High rigidiy cage Table Dimensions of special mouning screws S d H D nd sopper SA SA hen he cage is sroked frequenly or subjeced o vibraion or unevenly disribued load, he cage posiion may shif while in operaion. I is recoended, in such cases, o replace he end screw wih he end sopper SA. Size 1 models are assembled wih soppers similar o he SA end sopper as sandard. Screw size uni : Table Dimensions of end sopper SA Size Screw size d D H S Size 9 uni : 1 Size CR, CR Fig. ouning example wih special mouning screw - 1=0.09inch -
18 nd sopper SB SB hen he high rigidiy cage is used on a verical axis, he end screw is replaced wih he end sopper SB o limi he sroking of he cage a he way end. The end sopper SB can no be mouned on all ends of he ways in he assembly. Fig. shows he sandard mouning arrangemen. The mouning arrangemen can be changed by loosening screws and reseing he end soppers. iper seal U The end screw is replaced wih he wiper seal o preven foreign paricles from inruding ino he raceways. The wiper seal also serves as he end sopper providing he same funcion as he end sopper SB. The wiper seal canno be mouned on every way end. Fig. shows he sandard mouning arrangemen. The mouning arrangemen can be changed by loosening screws and reseing he wiper seals. Table Dimensions of end sopper SB Table Dimensions of wiper seal 1 1 uni : Size 9 uni : 1 Size Size 9 1 Size Fig. Arrangemen of end soppers SB Fig. Arrangemen of wiper seals CR, CR - 1=0.09inch -
19 oad Raing and Allowable oad Table.1 Calculaion formulae for load raings and allowable loads of CR Upward/downward load 1 aeral load Suarized descripions of load raings of Crossed Roller ay are given below. For deails of load raing definiions and load calculaions, see "General descripion". oad condiion oad oad oad Basic dynamic load raing C The basic dynamic load raing is defined as he consan load boh in direcion and magniude under which a group of idenical Crossed Roller ays are individually operaed and 90% of he unis in he group can ravel 0 x meers free from maerial damage due o rolling conac faigue. Basic saic load raing C 0 The basic saic load raing is defined as he saic load ha gives a prescribed consan conac sress a he cener of he conac area beween he rolling elemen and raceway receiving he maximum load. Allowable load F The allowable load is a load under which he sum of elasic deformaions of he rolling elemen and he raceway in he conac area subjeced o he maximum conac sress is small enough o guaranee accuracy and smooh rolling movemen. Therefore, when very smooh and highly accurae linear moion is required, make sure ha he applied load is well wihin he allowable load value. Basic dynamic load raing C N Basic saic load raing C0 Allowable load F eaning of symbols N N Z Z Cr p CU C0r Z Z Fr oad C0U FU Fa Z C0a Z C0U FU Cr : Basic dynamic load raing for upward / downward load, N Ca : Basic dynamic load raing for laeral load, N C0r : Basic saic load raing for upward / downward load, N C0a : Basic saic load raing for laeral load, N Fr : Allowable load for upward / downward load, N Fa : Allowable load raing for laeral load, N Z : Number of cylindrical rollers incorporaed in one roller cage (Disregard any decimal for Z/) p : Pich beween cylindrical rollers, CU : Basic dynamic load raing per one roller, N C0U : Basic saic load raing per one roller, N FU : Allowable load per one roller, N Noe( 1 ) : hen using one se of CR ype (four ways and wo roller cages) in parallel in his load direcion, use formulae (), () and (9) in Table.. Z Z Ca p CU Calculaion of load raings and allowable load In Crossed Roller ay, he number of cylindrical rollers sharing a load differs according o he load direcion. Therefore, i is necessary o obain load raings and allowable load for each direcion. The basic dynamic load raing CU, basic saic load raing C0U and allowable load FU shown in he able of dimensions indicae values per one roller. The basic dynamic load raing C, basic saic load raing C0 and allowable load F of Crossed Roller ay are obained from he formulae shown in Tables.1 and.. Table. Calculaion formulae for load raings and allowable loads of CR oad condiion Basic dynamic load raing C N Basic saic load raing C0 Allowable load F eaning of symbols N N Z Upward/downward load /oad oad Z /oad Cr p CU Z C0r C0U Z Fr FU oad Cr : Basic dynamic load raing for upward / downward load, N Ca : Basic dynamic load raing for laeral load, N C0r : Basic saic load raing for upward / downward load, N C0a : Basic saic load raing for laeral load, N Fr : Allowable load for upward / downward load, N Fa : Allowable load raing for laeral load, N Z : Number of cylindrical rollers incorporaed in one roller cage (Disregard any decimal for Z/) p : Pich beween cylindrical rollers, CU : Basic dynamic load raing per one roller, N C0U : Basic saic load raing per one roller, N FU : Allowable load per one roller, N Z Z C a p CU Z C0a Z Fa aeral load oad C0U FU CR, CR - 1=0.09inch -
20 Selecion of Specificaion hen selecing he specificaion of Crossed Roller ay, sroke lengh and number of rollers should be considered as well as he accuracy, load raings and allowable load. Sroke lengh and number of rollers Sroke lengh of Crossed Roller ay is relaed o he way lengh and number of rollers in a roller cage, ec. Therefore, selecion procedure is as follows while considering he operaing sroke lengh and applied loads. Number of rollers in one cage is obained from he following formula. RD Z 1 p 1 where, Z: Number of rollers in one cage (Disregard any decimal.) R: Allowable disance beween rollers a boh ends in one cage, D: Roller diameer (See dimension ables.), p : Roller pich (See dimension ables.), () In case of size 1 models Sroke lengh is limied by he cage and end soppers. The cage lengh is obained from he following formula. S1/ S1 Calculaion of way lengh ay lengh is generally more han 1. imes of operaing sroke lengh and is obained from he following formula. 1.S where, : ay lengh, S: Operaing sroke lengh, 1.S S S1 R 1 where, R : Allowable cage lengh, : ay lengh, S1 : aximum sroke lengh, Number of rollers in one cage is obained from he following formula. R S1/ Calculaion of maximum sroke lengh I is suggesed ha he operaing sroke lengh is 0% or less of he maximum sroke lengh. The maximum sroke lengh is obained from he following formula. 1 S1 S where, S1: aximum sroke lengh, S: Operaing sroke lengh, Calculaion of cage lengh and number of rollers Cage lengh is deermined by he way lengh and maximum sroke lengh. In calculaion of cage lengh, he calculaion mehod is differen according o he specificaion of end screws, end soppers, ec. (1) ih sandard end screws or end soppers SA (excep size 1 models) The disance beween rollers a boh ends in one cage is ha way lengh minus half of maximum sroke lengh as in he following formula. S1 S1 R 1 S1/ Re Z 1 1 p where, where, Z : Number of rollers in one cage (Disregard any decimal.) R : Allowable cage lengh, e: nd dimension of cage (See dimension ables.), p : Roller pich (See dimension ables.), () ih end soppers SB or wiper seals Sroke lengh is limied by he cage and end soppers or wiper seals. The cage lengh is obained from he following formula. R S1 1 R : Allowable cage lengh, : ay lengh, S1 : aximum sroke lengh, : Thickness of end sopper SB or wiper seal, (See Table on page - or Table on page -.) The number of rollers in a roller cage is obained from formula (1) in he same way as size 1 models. R S1 CR, CR where, R: Allowable disance beween rollers a boh ends in one cage, : ay lengh, S1: aximum sroke lengh, R S1/ - 1=0.09inch -9
21 1 Calculaion example odelcr Applied loadp 000 N Sroke lenghs 19 For parallel use of Crossed Roller ays under he above specified condiions (See Fig. 1 on page -.), selec he suiable specificaion. Calculaion of way lengh From formula (), way lengh is; 1.S ubricaion and Dus Proecion Oil or grease is used as a lubrican for Crossed Roller ay. Oil is generally used for high speed or low fricion operaion. On he oher hand, grease is used when operaing speed is low. In case of grease lubricaion, a good qualiy lihium-soap base grease is recoended. hen operaion speed is low and load is ligh, coa he raceways wih grease before use and relubricae periodically. Srucure shown in Fig. makes he relubricaion easy. Crossed Roller ays are finished very accuraely. However, if dus or foreign paricles inrude, life and accuracy will be adversely affeced. In order o preven he inrusion of dus, dir, waer, ec., i is recoended o use non-conac ype shields (labyrinh seal) as shown in Fig. or conac ype wiper seals shown in Fig. a he ouside of insalled uni. Therefore, sandard way lengh = 00 is seleced from dimension ables. Calculaion of maximum sroke lengh From formula (11), maximum sroke lengh S1 is; 1 1 S1 S From formula (1), allowable disance beween rollers a boh ends in one cage R is; S1 R 00 1 Calculaion of number of rollers Fig. xample of lubricaion mehod From formula (1), number of rollers in one cage is; (D = and p = 9 from dimension ables) RD 1 Z 1 p Therefore, number of rollers Z = 0 in one cage is obained by disregarding any decimal. Calculaion of allowable load From formula (9) in Table. on page -1, allowable load F in parallel usage is; (allowable load per one roller FU = N from dimension ables) Z 0 F FU 9 10 Fig. xample of non-conac ype shield (abyrinh seal) CR, CR In he calculaion resul, he allowable load F is larger han he applied load P = 000 N. Therefore, his model can be used wihin he allowable load. If he applied load exceeds he calculaed allowable load, i is necessary o consider increasing he way lengh and number of rollers, or o selec a model wih larger diameer rollers. Deerminaion of specificaion As a resul of he above calculaions, CR -00 wih 0 rollers is suiable. The seleced model number is CR -00 C0. Fig. xample of wiper seal -0 1=0.09inch -1
22 1 Specificaion of Crossed Roller ay Check wheher he specificaion of seleced Crossed Roller ay mees he requiremens for he applicaion of he machine or equipmen. Handling of Crossed Roller ay Precauions for Use Crossed Roller ay is a high precision produc, so handle i wih care. The cage can be modified by cuing i o he required cage lengh. hen cuing, do no deform he cage. Preload mehod Preload adjusing screws are generally used for seing preload, as shown in Fig.. The size of he preload adjusing screws are he same as ha of he mouning screws for he ways. The posiion of he preload adjusing screws is a he same posiion as he mouning screws of he ways. For cenering, use half of way heigh H. Preload amouns differ according o he applicaion of machine or equipmen. xcessive preloads deeriorae life and ofen damage he raceways. Therefore, zero or minimal preload is recoended in general. If accuracy and rigidiy are imporan, a seing plae as shown in Fig or a apered jib as shown in Fig. 11. may be used. Accuracy of maing mouning surfaces The general configuraions of maing mouning surfaces for CR and CR are shown in Figs. 9.1 and 9., respecively. Accuracy of he maing mouning surfaces is, in general, as shown in Table 9. The accuracy of maing mouning surfaces direcly affecs he operaing accuracy and performance of Crossed Roller ay. If very high operaing accuracy is required, higher accuracy of maing mouning surfaces han he values shown in Table 9 may be needed. Fig. General example of preload C A A A A B B A C A Fig. 9.1 xample of maing mouning surfaces for CR Fig. 9. xample of maing mouning surfaces for CR Table 9 Accuracy of maing mouning surfaces Fig xample of seing plae CR, CR A surface This accuracy direcly affecs he operaing accuracy. Flaness of A surface (four places) should be equal or nearly equal o he value of parallelism in Fig. 1 on page -. B and C surfaces Flaness Flaness of hese surfaces direcly affecs preload. The value of flaness should be equal or nearly equal o he value of parallelism in Fig. 1 on page -. Squareness Squareness o A surface affecs he rigidiy of assembled uni in he preload direcion. Consequenly, a high accuracy finish is necessary. Fig. 11. xample of apered jib - 1=0.09inch -
23 Crossed Roller ay does no conain synheic resin pars and can be operaed a high emperaures. Bu, when he emperaure exceeds 0 C, consul. The operaing speed of Crossed Roller ay should no exceed 0 m/min. Tighening orque of mouning screws Tighening orque of mouning screws is shown in Table. If vibraion or shock is large, or momen load is applied, i is recoended o ighen he screws o abou 1. imes he values shown in Table. If vibraion and shock are no presen and high operaing accuracy is needed, a lower ighening orque han he values shown in Table is suggesed. In his case, adhesive or lock-screws may be used o preven any subsequen loosening of he mouning screws. ouning of CR A general mehod for mouning CR is shown in Fig. 1. The general procedure is as follows. ay a fixed side ay a bed side ouning ay a bed side ay a adjusing side Table Tighening orque of screws Screw size Tighening orque Nm Remark : If he screw sizes on able side and bed side are differen, use he ighening orque of he smaller screw size for boh screws. 1 Preparaion for mouning CR is delivered as an individual package conaining four ways and wo roller cages. The ways in each package are no inerchangeable wih ways in oher packages, so do no mix hem. Separae he end screws or end soppers and wash he ways wih a clean cleaning agen. Afer cleaning, apply rus prevenive oil or lubricaing oil. Fig. 1 ouning example of CR Corner groove ouning surface C ouning surface B Preload adjusing screw ouning surface A Corner groove ouning surface A ouning surface B Cleaning of mouning surfaces of able and bed Remove burrs and blemishes from mouning surfaces of able and bed wih an oil-sone, ec. During his process, also pay aenion o he corner grooves of he mouning surfaces. ipe off dus wih clean cloh and apply rus prevenive oil or lubricaing oil. ouning surface A Corner groove Fig. 1 ouning surfaces for CR ouning surface A CR, CR - 1=0.09inch -
24 ouning of ways a bed side (Fig. 1) Afer fiing he mouning surfaces of ways ono he maing mouning surfaces of bed, emporarily ighen he mouning screws wih uniform ighening orque. Afer closely fiing he ways o B surfaces (See Fig. 1.), ighen he mouning screws uniformly o he prescribed ighening orque. If high accuracy is required, ighen he mouning screws uniformly o he prescribed ighening orque while checking he parallelism of he wo ways along he overall way lengh. General ighening orque of mouning screws is shown in Table on page -0. ouning of ways a able side (Fig. 1) Afer fiing he mouning surfaces of he way a he fixed side o he maing mouning surfaces of able, emporarily ighen he mouning screws a he fixed side wih uniform ighening orque. Afer closely fiing he way a he fixed side o C surface, ighen he mouning screws a he fixed side uniformly o he prescribed ighening orque. oosen he preload adjusing screws and emporarily ighen he mouning screws of he way a adjusing side wih uniform and ligh ighening orque. Assembling of able and bed (Fig. 1) Adjus he posiions of able and bed in heigh and widh direcions in order o inser roller cages beween he ways a able side and bed side. Inser he roller cages gradually and genly unil he cages posiion roughly a he cener of way lengh. In his process, do no deform he cages. Assemble end screws or end soppers. Push he able o he preload adjusing side, and emporarily ighen he preload adjusing screws unil he clearance a raceways is near zero. Genly sroke he able is full sroke lengh o posiion he roller cage a he cener of he sroke. A A A Fig. 1 ouning accuracy of ways ay a fixed side Surface C ay a adjusing side Preload adjusing screw Fig. 1 ouning of ways a able side Fig. 1 Posiioning of able and bed in assembling ime Preload adjusmen (Fig. 1) Preload adjusmen is done only when mouning screws for he way a he adjusing side are emporarily ighened. Preload adjusmen is sared from he adjusing screw a he cener of he way lengh, proceeding alernaely o he lef and righ. hile checking he clearance (deflecion) Fig. 1 xample of preload adjusmen a he side face of able, ighen each adjusing screw lighly o a uniform amoun, hen repea he same process applying a higher ighening orque unil a dial gauge indicaes zero-clearance (no more change in deflecion). Record he ighening orque of he adjusing screws a zero-clearance. hen adjusing he screws close o he end of he way, gradually sroke he able and ensure ha he roller cage is posiioned a he adjusing screw. Using he above process, he inernal clearance becomes zero or minimal preload, bu he preload amoun is no uniform along he way lengh. Therefore, repea he same process and ighen all adjusing screws uniformly o he recorded ighening orque. Final fixing of way a adjusing side The mouning screws have been ighened lighly o a uniform orque. Similar o he adjusmen of he preload adjusing screws, emporarily ighen he mouning screws a he adjusing side o a slighly lower ighening orque han he prescribed value. Sar from he cener screw of he way lengh and proceed alernaely o he lef and righ. hen ighening he mouning screws close o he end of he way, gradually sroke he able and ensure ha he roller cage is posiioned a he mouning screw. Finally, ighen all mouning screws a he adjusing side uniformly o he prescribed orque similar o he adjusmen of he preload adjusing screws. Final check (Fig. 1) Sroke he able gradually is full sroke lengh, ensuring ha he sroke is smooh and quie. Check he operaing accuracy by measuring he upper and side faces of able wih a dial gauge. Fig. 1 Final check of operaing accuracy CR, CR - 1=0.09inch -
IB Physics Kinematics Worksheet
IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?
More information2002 November 14 Exam III Physics 191
November 4 Exam III Physics 9 Physical onsans: Earh s free-fall acceleraion = g = 9.8 m/s ircle he leer of he single bes answer. quesion is worh poin Each 3. Four differen objecs wih masses: m = kg, m
More informationKINEMATICS IN ONE DIMENSION
KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec
More informationStructural Dynamics and Earthquake Engineering
Srucural Dynamics and Earhquae Engineering Course 1 Inroducion. Single degree of freedom sysems: Equaions of moion, problem saemen, soluion mehods. Course noes are available for download a hp://www.c.up.ro/users/aurelsraan/
More informationHall effect. Formulae :- 1) Hall coefficient RH = cm / Coulumb. 2) Magnetic induction BY 2
Page of 6 all effec Aim :- ) To deermine he all coefficien (R ) ) To measure he unknown magneic field (B ) and o compare i wih ha measured by he Gaussmeer (B ). Apparaus :- ) Gauss meer wih probe ) Elecromagne
More informationAt the end of this lesson, the students should be able to understand
Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress concenraion facor; experimenal and heoreical mehods.
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan
Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure
More information2001 November 15 Exam III Physics 191
1 November 15 Eam III Physics 191 Physical Consans: Earh s free-fall acceleraion = g = 9.8 m/s 2 Circle he leer of he single bes answer. quesion is worh 1 poin Each 3. Four differen objecs wih masses:
More information15210 RECORDING TIMER - AC STUDENT NAME:
CONTENTS 15210 RECORDING TIMER - AC STUDENT NAME: REQUIRED ACCESSORIES o C-Clamps o Ruler or Meer Sick o Mass (200 g or larger) OPTIONAL ACCESSORIES o Ticker Tape Dispenser (#15225) o Consan Speed Vehicle
More informationLINEAR SLOT DIFFUSERS
Supply, Reurn, Dummy Linear Slo Diffusers A OSLD OTIMA model OSLD is a supply linear slo diffuser wih inegral volume conrol damper and hi and miss air sraighening deflecors. h Hi and miss air sraigheners
More informationInvolute Gear Tooth Bending Stress Analysis
Involue Gear Tooh Bending Sress Analysis Lecure 21 Engineering 473 Machine Design Gear Ineracion Line of Ceners Line Tangen o s Line Normal o Line of Ceners 1 s Close Up of Meshed Teeh Line of Conac W
More information15. Vector Valued Functions
1. Vecor Valued Funcions Up o his poin, we have presened vecors wih consan componens, for example, 1, and,,4. However, we can allow he componens of a vecor o be funcions of a common variable. For example,
More informationLecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.
Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in
More informationAnalogue amplifier card
Analogue amplifier card RE 30110/06.05 replaces: 10.04 1/10 Type VT-VSPA-1-X/ H/A/D 6641/00 Table of conens Conens Page Feaures 1 Ordering deails, accessories Funcion 3 Block circui diagram and connecion
More informationPhysics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle
Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,
More informationCHAPTER 12 DIRECT CURRENT CIRCUITS
CHAPTER 12 DIRECT CURRENT CIUITS DIRECT CURRENT CIUITS 257 12.1 RESISTORS IN SERIES AND IN PARALLEL When wo resisors are conneced ogeher as shown in Figure 12.1 we said ha hey are conneced in series. As
More information0 time. 2 Which graph represents the motion of a car that is travelling along a straight road with a uniformly increasing speed?
1 1 The graph relaes o he moion of a falling body. y Which is a correc descripion of he graph? y is disance and air resisance is negligible y is disance and air resisance is no negligible y is speed and
More informationSuggested Practice Problems (set #2) for the Physics Placement Test
Deparmen of Physics College of Ars and Sciences American Universiy of Sharjah (AUS) Fall 014 Suggesed Pracice Problems (se #) for he Physics Placemen Tes This documen conains 5 suggesed problems ha are
More informationMECHANICS OF MATERIALS Poisson s Ratio
Poisson s Raio For a slender bar subjeced o axial loading: ε x x y 0 The elongaion in he x-direcion i is accompanied by a conracion in he oher direcions. Assuming ha he maerial is isoropic (no direcional
More informationPhysics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs.
Physics 180A Fall 2008 Tes 1-120 poins Name Provide he bes answer o he following quesions and problems. Wach your sig figs. 1) The number of meaningful digis in a number is called he number of. When numbers
More information1. VELOCITY AND ACCELERATION
1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under
More informationCLASS XI SET A PHYSICS. 1. If and Let. The correct order of % error in. (a) (b) x = y > z (c) x < z < y (d) x > z < y
PHYSICS 1. If and Le. The correc order of % error in (a) (b) x = y > z x < z < y x > z < y. A hollow verical cylinder of radius r and heigh h has a smooh inernal surface. A small paricle is placed in conac
More informationModule 2 F c i k c s la l w a s o s f dif di fusi s o i n
Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms
More information1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a
Kinemaics Paper 1 1. The graph below shows he ariaion wih ime of he acceleraion a of an objec from = o = T. a T The shaded area under he graph represens change in A. displacemen. B. elociy. C. momenum.
More informationConstant Acceleration
Objecive Consan Acceleraion To deermine he acceleraion of objecs moving along a sraigh line wih consan acceleraion. Inroducion The posiion y of a paricle moving along a sraigh line wih a consan acceleraion
More informationd = ½(v o + v f) t distance = ½ (initial velocity + final velocity) time
BULLSEYE Lab Name: ANSWER KEY Dae: Pre-AP Physics Lab Projecile Moion Weigh = 1 DIRECTIONS: Follow he insrucions below, build he ramp, ake your measuremens, and use your measuremens o make he calculaions
More informationPhys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole
Phys 221 Fall 2014 Chaper 2 Moion in One Dimension 2014, 2005 A. Dzyubenko 2004 Brooks/Cole 1 Kinemaics Kinemaics, a par of classical mechanics: Describes moion in erms of space and ime Ignores he agen
More informationPhys1112: DC and RC circuits
Name: Group Members: Dae: TA s Name: Phys1112: DC and RC circuis Objecives: 1. To undersand curren and volage characerisics of a DC RC discharging circui. 2. To undersand he effec of he RC ime consan.
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationPhysics 221 Fall 2008 Homework #2 Solutions Ch. 2 Due Tues, Sept 9, 2008
Physics 221 Fall 28 Homework #2 Soluions Ch. 2 Due Tues, Sep 9, 28 2.1 A paricle moving along he x-axis moves direcly from posiion x =. m a ime =. s o posiion x = 1. m by ime = 1. s, and hen moves direcly
More informationChapters 6 & 7: Trigonometric Functions of Angles and Real Numbers. Divide both Sides by 180
Algebra Chapers & : Trigonomeric Funcions of Angles and Real Numbers Chapers & : Trigonomeric Funcions of Angles and Real Numbers - Angle Measures Radians: - a uni (rad o measure he size of an angle. rad
More informationCombined Bending with Induced or Applied Torsion of FRP I-Section Beams
Combined Bending wih Induced or Applied Torsion of FRP I-Secion Beams MOJTABA B. SIRJANI School of Science and Technology Norfolk Sae Universiy Norfolk, Virginia 34504 USA sirjani@nsu.edu STEA B. BONDI
More information1. Kinematics I: Position and Velocity
1. Kinemaics I: Posiion and Velociy Inroducion The purpose of his eperimen is o undersand and describe moion. We describe he moion of an objec by specifying is posiion, velociy, and acceleraion. In his
More informationCurling Stress Equation for Transverse Joint Edge of a Concrete Pavement Slab Based on Finite-Element Method Analysis
TRANSPORTATION RESEARCH RECORD 155 35 Curling Sress Equaion for Transverse Join Edge of a Concree Pavemen Slab Based on Finie-Elemen Mehod Analysis TATSUO NISHIZAWA, TADASHI FUKUDA, SABURO MATSUNO, AND
More informationReading from Young & Freedman: For this topic, read sections 25.4 & 25.5, the introduction to chapter 26 and sections 26.1 to 26.2 & 26.4.
PHY1 Elecriciy Topic 7 (Lecures 1 & 11) Elecric Circuis n his opic, we will cover: 1) Elecromoive Force (EMF) ) Series and parallel resisor combinaions 3) Kirchhoff s rules for circuis 4) Time dependence
More informationDisplacement ( x) x x x
Kinemaics Kinemaics is he branch of mechanics ha describes he moion of objecs wihou necessarily discussing wha causes he moion. 1-Dimensional Kinemaics (or 1- Dimensional moion) refers o moion in a sraigh
More informationSensing distance. 2 mm (slot width)
Phoomicrosensor (Transmissive) EE-SX3 Ulra-Compac Slo / SMD Type (Slo widh: mm) PCB surface mouning ype. High resoluion wih a.3-mm-wide aperure. Be sure o read Safey Precauions on page 3. Ordering Informaion
More informationWEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x
WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile
More informationNEWTON S SECOND LAW OF MOTION
Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during
More informationMOMENTUM CONSERVATION LAW
1 AAST/AEDT AP PHYSICS B: Impulse and Momenum Le us run an experimen: The ball is moving wih a velociy of V o and a force of F is applied on i for he ime inerval of. As he resul he ball s velociy changes
More information9. Alternating currents
WS 9. Alernaing currens 9.1 nroducion Besides ohmic resisors, capaciors and inducions play an imporan role in alernaing curren (AC circuis as well. n his experimen, one shall invesigae heir behaviour in
More informationTwo Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
More informationMicrologic Control units 2.0 and 5.0 Low Voltage Products
Micrologic Conol unis.0 and 5.0 Low Volage Producs User manual We do more wih eleciciy. Micrologic Conol unis.0 and 5.0 Discovering your conol uni Idenifying your conol uni Overview of funcions 4 Seing
More informationLAB 5 - PROJECTILE MOTION
Lab 5 Projecile Moion 71 Name Dae Parners OVEVIEW LAB 5 - POJECTILE MOTION We learn in our sudy of kinemaics ha wo-dimensional moion is a sraighforward exension of one-dimensional moion. Projecile moion
More informationDESIGN OF TENSION MEMBERS
CHAPTER Srcral Seel Design LRFD Mehod DESIGN OF TENSION MEMBERS Third Ediion A. J. Clark School of Engineering Deparmen of Civil and Environmenal Engineering Par II Srcral Seel Design and Analysis 4 FALL
More information236 CHAPTER 3 Torsion. Strain Energy in Torsion
36 CHAPER 3 orsion Srain Energy in orsion Problem 3.9-1 A solid circular bar of seel (G 11. 1 6 psi) wih lengh 3 in. and diameer d 1.75 in. is subjeced o pure orsion by orques acing a he ends (see figure).
More informationElectronic Flow Meter FC04 (compressed air/gases)
Elecronic Flow Meer FC0 (compressed air/gases) Descripion The miniaure Flow Meer FC0 is designed o operae wih air, compressed air, oxygen and nirogen. Sensor head inegral wih elecronic circuiry. When used
More informationSPH3U: Projectiles. Recorder: Manager: Speaker:
SPH3U: Projeciles Now i s ime o use our new skills o analyze he moion of a golf ball ha was ossed hrough he air. Le s find ou wha is special abou he moion of a projecile. Recorder: Manager: Speaker: 0
More informationLearning Objectives: Practice designing and simulating digital circuits including flip flops Experience state machine design procedure
Lab 4: Synchronous Sae Machine Design Summary: Design and implemen synchronous sae machine circuis and es hem wih simulaions in Cadence Viruoso. Learning Objecives: Pracice designing and simulaing digial
More informationProgram: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro. Category: Isotropic Linear Elasticity, Dynamics, Member
Verificaion Example Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro Caegory: Isoropic Linear Elasiciy, Dynamics, Member Verificaion Example: 0104 Canilever Beam wih Periodic Exciaion 0104 Canilever Beam
More informationVehicle Arrival Models : Headway
Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where
More informationKriging Models Predicting Atrazine Concentrations in Surface Water Draining Agricultural Watersheds
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Kriging Models Predicing Arazine Concenraions in Surface Waer Draining Agriculural Waersheds Paul L. Mosquin, Jeremy Aldworh, Wenlin Chen Supplemenal Maerial Number
More informationk 1 k 2 x (1) x 2 = k 1 x 1 = k 2 k 1 +k 2 x (2) x k series x (3) k 2 x 2 = k 1 k 2 = k 1+k 2 = 1 k k 2 k series
Final Review A Puzzle... Consider wo massless springs wih spring consans k 1 and k and he same equilibrium lengh. 1. If hese springs ac on a mass m in parallel, hey would be equivalen o a single spring
More informationMATHEMATICAL MODELING OF THE TRACTOR-GRADER AGRICULTURAL SYSTEM CINEMATIC DURING LAND IMPROVING WORKS
Bullein of he Transilvania Universiy of Braşov Series II: Foresry Wood Indusry Agriculural Food Engineering Vol. 5 (54) No. 1-2012 MATHEMATICA MODEING OF THE TRACTOR-GRADER AGRICUTURA SYSTEM CINEMATIC
More informationCHEAPEST PMT ONLINE TEST SERIES AIIMS/NEET TOPPER PREPARE QUESTIONS
CHEAPEST PMT ONLINE TEST SERIES AIIMS/NEET TOPPER PREPARE QUESTIONS For more deails see las page or conac @aimaiims.in Physics Mock Tes Paper AIIMS/NEET 07 Physics 06 Saurday Augus 0 Uni es : Moion in
More informationIn this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should
Cambridge Universiy Press 978--36-60033-7 Cambridge Inernaional AS and A Level Mahemaics: Mechanics Coursebook Excerp More Informaion Chaper The moion of projeciles In his chaper he model of free moion
More informationOptimal Path Planning for Flexible Redundant Robot Manipulators
25 WSEAS In. Conf. on DYNAMICAL SYSEMS and CONROL, Venice, Ialy, November 2-4, 25 (pp363-368) Opimal Pah Planning for Flexible Redundan Robo Manipulaors H. HOMAEI, M. KESHMIRI Deparmen of Mechanical Engineering
More informationPhysics 30: Chapter 2 Exam Momentum & Impulse
Physics 30: Chaper 2 Exam Momenum & Impulse Name: Dae: Mark: /29 Numeric Response. Place your answers o he numeric response quesions, wih unis, in he blanks a he side of he page. (1 mark each) 1. A golfer
More information11a Flow Monitor FS10-EX. Description
Flow Monior FS0-EX Descripion Compac single poin flow monior for use in zone (gases) and zones, (dus), MIN or MX monioring opions, suiable for air, gases, waer, aqueous liquids, oil. Wih screw-in or plug-in
More information15. Bicycle Wheel. Graph of height y (cm) above the axle against time t (s) over a 6-second interval. 15 bike wheel
15. Biccle Wheel The graph We moun a biccle wheel so ha i is free o roae in a verical plane. In fac, wha works easil is o pu an exension on one of he axles, and ge a suden o sand on one side and hold he
More informationx(m) t(sec ) Homework #2. Ph 231 Introductory Physics, Sp-03 Page 1 of 4
Homework #2. Ph 231 Inroducory Physics, Sp-03 Page 1 of 4 2-1A. A person walks 2 miles Eas (E) in 40 minues and hen back 1 mile Wes (W) in 20 minues. Wha are her average speed and average velociy (in ha
More informationAP CALCULUS AB 2003 SCORING GUIDELINES (Form B)
SCORING GUIDELINES (Form B) Quesion A blood vessel is 6 millimeers (mm) long Disance wih circular cross secions of varying diameer. x (mm) 6 8 4 6 Diameer The able above gives he measuremens of he B(x)
More informationSintered Metal Element
Sinered Meal Elemen E /ES Series ronze/sainless Seel FGD FGE FGG FG FGC FGF FGH FQ FN E ES ronze elemens Sainless seel elemens 4 Hex idh across flas C Hex idh across flas C Hex idh across flas C Hex idh
More information4. Electric field lines with respect to equipotential surfaces are
Pre-es Quasi-saic elecromagneism. The field produced by primary charge Q and by an uncharged conducing plane disanced from Q by disance d is equal o he field produced wihou conducing plane by wo following
More informationLab 10: RC, RL, and RLC Circuits
Lab 10: RC, RL, and RLC Circuis In his experimen, we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors. We will sudy he way volages and currens change in
More informationTraveling Waves. Chapter Introduction
Chaper 4 Traveling Waves 4.1 Inroducion To dae, we have considered oscillaions, i.e., periodic, ofen harmonic, variaions of a physical characerisic of a sysem. The sysem a one ime is indisinguishable from
More informationChapter 12: Velocity, acceleration, and forces
To Feel a Force Chaper Spring, Chaper : A. Saes of moion For moion on or near he surface of he earh, i is naural o measure moion wih respec o objecs fixed o he earh. The 4 hr. roaion of he earh has a measurable
More informationLecture 4 Kinetics of a particle Part 3: Impulse and Momentum
MEE Engineering Mechanics II Lecure 4 Lecure 4 Kineics of a paricle Par 3: Impulse and Momenum Linear impulse and momenum Saring from he equaion of moion for a paricle of mass m which is subjeced o an
More informationFinal Spring 2007
.615 Final Spring 7 Overview The purpose of he final exam is o calculae he MHD β limi in a high-bea oroidal okamak agains he dangerous n = 1 exernal ballooning-kink mode. Effecively, his corresponds o
More informationDecimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0.
PHYSICS 20 UNIT 1 SCIENCE MATH WORKSHEET NAME: A. Sandard Noaion Very large and very small numbers are easily wrien using scienific (or sandard) noaion, raher han decimal (or posiional) noaion. Sandard
More information10.6 Parametric Equations
0_006.qd /8/05 9:05 AM Page 77 Secion 0.6 77 Parameric Equaions 0.6 Parameric Equaions Wha ou should learn Evaluae ses of parameric equaions for given values of he parameer. Skech curves ha are represened
More informationNumerical Dispersion
eview of Linear Numerical Sabiliy Numerical Dispersion n he previous lecure, we considered he linear numerical sabiliy of boh advecion and diffusion erms when approimaed wih several spaial and emporal
More informationWORK, ENERGY AND POWER NCERT
Exemplar Problems Physics Chaper Six WORK, ENERGY AND POWER MCQ I 6.1 An elecron and a proon are moving under he influence of muual forces. In calculaing he change in he kineic energy of he sysem during
More informationChapter 3 Kinematics in Two Dimensions
Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Two-dimensional moion includes objecs which are moing in wo direcions a he same ime, such as a projecile, which has boh horizonal and erical moion. These wo
More informationd 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3
and d = c b - b c c d = c b - b c c This process is coninued unil he nh row has been compleed. The complee array of coefficiens is riangular. Noe ha in developing he array an enire row may be divided or
More informationContent-Based Shape Retrieval Using Different Shape Descriptors: A Comparative Study Dengsheng Zhang and Guojun Lu
Conen-Based Shape Rerieval Using Differen Shape Descripors: A Comparaive Sudy Dengsheng Zhang and Guojun Lu Gippsland School of Compuing and Informaion Technology Monash Universiy Churchill, Vicoria 3842
More informationKinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8.
Kinemaics Vocabulary Kinemaics and One Dimensional Moion 8.1 WD1 Kinema means movemen Mahemaical descripion of moion Posiion Time Inerval Displacemen Velociy; absolue value: speed Acceleraion Averages
More information8. Basic RL and RC Circuits
8. Basic L and C Circuis This chaper deals wih he soluions of he responses of L and C circuis The analysis of C and L circuis leads o a linear differenial equaion This chaper covers he following opics
More informationdt = C exp (3 ln t 4 ). t 4 W = C exp ( ln(4 t) 3) = C(4 t) 3.
Mah Rahman Exam Review Soluions () Consider he IVP: ( 4)y 3y + 4y = ; y(3) = 0, y (3) =. (a) Please deermine he longes inerval for which he IVP is guaraneed o have a unique soluion. Soluion: The disconinuiies
More informationFlow-Induced Vibration Analysis of Supported Pipes with a Crack
Flow-Induced Vibraion Analsis of Suppored Pipes wih a Crack Jin-Huk Lee, Samer Masoud Al-Said Deparmen of Mechanical Engineering American Universi of Sharjah, UAE Ouline Inroducion and Moivaion Aeroacousicall
More informationSection 3.8, Mechanical and Electrical Vibrations
Secion 3.8, Mechanical and Elecrical Vibraions Mechanical Unis in he U.S. Cusomary and Meric Sysems Disance Mass Time Force g (Earh) Uni U.S. Cusomary MKS Sysem CGS Sysem fee f slugs seconds sec pounds
More informationLet us start with a two dimensional case. We consider a vector ( x,
Roaion marices We consider now roaion marices in wo and hree dimensions. We sar wih wo dimensions since wo dimensions are easier han hree o undersand, and one dimension is a lile oo simple. However, our
More informationSolution: b All the terms must have the dimension of acceleration. We see that, indeed, each term has the units of acceleration
PHYS 54 Tes Pracice Soluions Spring 8 Q: [4] Knowing ha in he ne epression a is acceleraion, v is speed, is posiion and is ime, from a dimensional v poin of view, he equaion a is a) incorrec b) correc
More information2. Nonlinear Conservation Law Equations
. Nonlinear Conservaion Law Equaions One of he clear lessons learned over recen years in sudying nonlinear parial differenial equaions is ha i is generally no wise o ry o aack a general class of nonlinear
More information3 at MAC 1140 TEST 3 NOTES. 5.1 and 5.2. Exponential Functions. Form I: P is the y-intercept. (0, P) When a > 1: a = growth factor = 1 + growth rate
1 5.1 and 5. Eponenial Funcions Form I: Y Pa, a 1, a > 0 P is he y-inercep. (0, P) When a > 1: a = growh facor = 1 + growh rae The equaion can be wrien as The larger a is, he seeper he graph is. Y P( 1
More informationCalculation of the Two High Voltage Transmission Line Conductors Minimum Distance
World Journal of Engineering and Technology, 15, 3, 89-96 Published Online Ocober 15 in SciRes. hp://www.scirp.org/journal/wje hp://dx.doi.org/1.436/wje.15.33c14 Calculaion of he Two High Volage Transmission
More informationElectrical and current self-induction
Elecrical and curren self-inducion F. F. Mende hp://fmnauka.narod.ru/works.hml mende_fedor@mail.ru Absrac The aricle considers he self-inducance of reacive elemens. Elecrical self-inducion To he laws of
More informationNon-uniform circular motion *
OpenSax-CNX module: m14020 1 Non-uniform circular moion * Sunil Kumar Singh This work is produced by OpenSax-CNX and licensed under he Creaive Commons Aribuion License 2.0 Wha do we mean by non-uniform
More informationSome Basic Information about M-S-D Systems
Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,
More informationSub Module 2.6. Measurement of transient temperature
Mechanical Measuremens Prof. S.P.Venkaeshan Sub Module 2.6 Measuremen of ransien emperaure Many processes of engineering relevance involve variaions wih respec o ime. The sysem properies like emperaure,
More informationCoulomb Balance. Important Information. 1 Introduction
Coulomb Balance Equipmen: Coulomb balance apparaus, 5 5 inch plasic plae, vernier calipers, power supply, se of fracional weighs (less han 500 mg) wih weezers, resisance box se a 1 MΩ, 5 leads, index cards,
More informationI. OBJECTIVE OF THE EXPERIMENT.
I. OBJECTIVE OF THE EXPERIMENT. Swissmero raels a high speeds hrough a unnel a low pressure. I will hereore undergo ricion ha can be due o: ) Viscosiy o gas (c. "Viscosiy o gas" eperimen) ) The air in
More information20. Applications of the Genetic-Drift Model
0. Applicaions of he Geneic-Drif Model 1) Deermining he probabiliy of forming any paricular combinaion of genoypes in he nex generaion: Example: If he parenal allele frequencies are p 0 = 0.35 and q 0
More informationKinematics. See if you can define distance. We think you ll run into the same problem.
Kinemaics Inroducion Moion is fundamenal o our lives and o our hinking. Moving from place o place in a given amoun of ime helps define boh who we are and how we see he world. Seeing oher people, objecs
More informationPHYSICS 149: Lecture 9
PHYSICS 149: Lecure 9 Chaper 3 3.2 Velociy and Acceleraion 3.3 Newon s Second Law of Moion 3.4 Applying Newon s Second Law 3.5 Relaive Velociy Lecure 9 Purdue Universiy, Physics 149 1 Velociy (m/s) The
More informationAcceleration. Part I. Uniformly Accelerated Motion: Kinematics & Geometry
Acceleraion Team: Par I. Uniformly Acceleraed Moion: Kinemaics & Geomery Acceleraion is he rae of change of velociy wih respec o ime: a dv/d. In his experimen, you will sudy a very imporan class of moion
More informationThe Paradox of Twins Described in a Three-dimensional Space-time Frame
The Paradox of Twins Described in a Three-dimensional Space-ime Frame Tower Chen E_mail: chen@uguam.uog.edu Division of Mahemaical Sciences Universiy of Guam, USA Zeon Chen E_mail: zeon_chen@yahoo.com
More informationLogic in computer science
Logic in compuer science Logic plays an imporan role in compuer science Logic is ofen called he calculus of compuer science Logic plays a similar role in compuer science o ha played by calculus in he physical
More information9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for he May/June series 9 FURTHER MATHEMATICS 9/ Paper, maximum raw mark This mark scheme is published as an aid o eachers and candidaes,
More information