I-Granite luhlobo lwelitye elitshisiweyo elimbiwa ngenxa yamandla alo agqithisileyo, ubuninzi, ukuqina, kunye nokumelana nokugqwala. Kodwa i-granite ikwanokuguquguquka kakhulu- ayisiyoyezikwere kunye neengxande kuphela! Enyanisweni, sisebenza ngokuzithemba ngezinto ze-granite ezenziwe ngeemilo, ii-engile, kunye nee-curves zazo zonke iintlobo rhoqo-ngeziphumo ezigqwesileyo.
Through our state of the art processing, cut surfaces can be exceptionally flat. These qualities make granite the ideal material to create custom-size and custom-design machine bases and metrology components. Granite is:
■ enokusetyenzwa ngomatshini
■ tyaba ngokuchanekileyo xa isikiwe kwaye igqityiwe
■ ukumelana nomhlwa
■ eqinileyo
■ ihlala ixesha elide
Izinto zegranite nazo kulula ukuzicoca. Xa usenza uyilo olukhethekileyo, qiniseka ukuba ukhetha igranite ngenxa yezibonelelo zayo ezibalaseleyo.
IIMFANELO / IZICELO ZOKUNXIBA OKUPHEZULU
I-granite esetyenziswa yi-ZHHIMG kwiimveliso zethu zeplati zomphezulu ezisemgangathweni inomxholo ophezulu we-quartz, nto leyo enika ukumelana okukhulu nokuguguleka kunye nokonakala. Imibala yethu emnyama ephezulu inezinga eliphantsi lokufunxwa kwamanzi, nto leyo enciphisa amathuba okuba ii-precision gauges zakho zigrule ngelixa zibekwe kwiiplati. Imibala yegranite enikezelwa yi-ZHHIMG ibangela ukukhanya okuncinci, nto leyo ethetha ukuba amehlo angaphantsi kubantu abasebenzisa iiplati. Sikhethe iintlobo zethu zegranite ngelixa sicinga ngokwandiswa kobushushu ukuze sigcine olu phawu luncinci.
CUSTOM APPLICATIONS
Xa usetyenziso lwakho lufuna ipleyiti enemilo eyenzelwe wena, izinto ezifakwe imisonto, iindawo zokufaka okanye ezinye izinto zokulungisa, kuya kufuneka ukhethe izinto ezifana neBlack Jinan Black. Ezi zinto zendalo zinika ukuqina okuphezulu, ukudambisa ukungcangcazela okugqwesileyo, kunye nokuphucula ukusebenza koomatshini.
Kubalulekile ukuqaphela ukuba umbala wodwa awubonisi iimpawu zomzimba zelitye. Ngokubanzi, umbala wegranite unxulumene ngokuthe ngqo nokuba khona okanye ukungabikho kweeminerali, ezinokuthi zingabi nafuthe kwiimpawu ezenza izinto ezilungileyo zepleyiti yomphezulu. Kukho iigranite ezipinki, ezingwevu, nezimnyama ezilungele iipleyiti zomphezulu, kunye neegranite ezimnyama, ezingwevu, nezipinki ezingafanelekiyo kwaphela ekusetyenzisweni ngokuchanekileyo. Iimpawu ezibalulekileyo zegranite, njengoko ziphathelele ukusetyenziswa kwayo njengezinto zepleyiti yomphezulu, azinanto yakwenza nombala, kwaye zezi zilandelayo:
■ Ukuqina (ukuphambuka phantsi komthwalo - kuboniswe yiModulus of Elasticity)
■ Ukuqina
■ Uxinano
■ Ukumelana nokunxitywa
■ Uzinzo
■ Ukufunxa
Sivavanye izinto ezininzi zegranite saza sazithelekisa ezi zinto. Ekugqibeleni sifumana isiphumo, igranite emnyama yaseJinan yeyona nto ibalaseleyo esakha sayazi. Igranite emnyama yaseIndiya kunye negranite yaseMzantsi Afrika zifana neGranite emnyama yaseJinan, kodwa iimpawu zazo zomzimba zincinci kuneGranite emnyama yaseJinan. I-ZHHIMG iya kuqhubeka ikhangela ezinye izinto zegranite ehlabathini kwaye ithelekise iimpawu zazo zomzimba.
Ukuze uthethe ngakumbi ngegranite efanelekileyo kwiprojekthi yakho, nceda unxibelelane nathiinfo@zhhimg.com.
Abavelisi abahlukeneyo basebenzisa imigangatho eyahlukeneyo. Kukho imigangatho emininzi ehlabathini.
I-DIN Standard, i-ASME B89.3.7-2013 okanye i-Federal Specification GGG-P-463c (ii-Granite Surface Plates) njalo njalo njengesiseko seenkcukacha zazo.
Kwaye singavelisa ipleyiti yokuhlola ngokuchanekileyo kwegranite ngokweemfuno zakho. Wamkelekile ukuba unxibelelane nathi ukuba ufuna ukwazi ulwazi oluthe kratya malunga nemigangatho engaphezulu.
Ukuthe tyaba kungathathwa njengokuba onke amanqaku aphezu komhlaba equlethwe kwiiplani ezimbini ezihambelanayo, iplani esisiseko kunye neplani yophahla. Ukulinganiswa komgama phakathi kweplani kukuthe tyaba ngokubanzi komphezulu. Olu linganiso lokuthe tyaba ludla ngokuba nokunyamezelana kwaye lunokubandakanya uphawu lwebanga.
Umzekelo, ukunyamezelana kwe-flatness kwamabakala amathathu asemgangathweni kuchazwa kwinkcazo karhulumente njengoko kumiselwe yile fomyula ilandelayo:
■ Ibanga leLebhu i-AA = (40 + i-diagonal square/25) x .000001" (ecaleni elinye)
■ Uvavanyo lweBanga A = Ilebhu yeBanga AA x 2
■ Igumbi leZixhobo Ibanga B = Ibanga leLebhu AA x 4.
Kwiipleyiti zomphezulu ezinobukhulu obuqhelekileyo, siqinisekisa ukunyamezelana kokuthe tyaba okugqitha iimfuno zale nkcazo. Ukongeza kokuthe tyaba, i-ASME B89.3.7-2013 kunye ne-Federal Specification GGG-P-463c zijongana nezihloko eziquka: ukuchaneka kokulinganisa okuphindaphindiweyo, iimpawu zezinto zegranite zepleyiti yomphezulu, ukugqitywa komphezulu, indawo yenkxaso, ukuqina, iindlela ezamkelekileyo zokuhlola, ukufakwa kwezinto ezifakwe ngemisonto, njl.njl.
Iipleyiti zomphezulu wegranite ze-ZHHIMG kunye neepleyiti zokuhlola igranite ziyahlangabezana okanye zidlule zonke iimfuno ezichazwe kule nkcazo. Okwangoku, akukho nkcazo icacileyo yeepleyiti ze-angle zegranite, ii-parallels, okanye ii-master squares.
Kwaye ungazifumana iifomyula zeminye imigangatho kuKHUPHELA.
Okokuqala, kubalulekile ukugcina ipleyiti icocekile. Uthuli olurhabaxa oluqhutywa ngumoya ludla ngokuba lolona mthombo mkhulu wokukrazuka kwepleyiti, njengoko ludla ngokungena kwiindawo zokusebenza kunye neendawo ezidibanayo zeegeyiji. Okwesibini, gquma ipleyiti yakho ukuze uyikhusele eluthulini nasekonakaleni. Ubomi bokunxiba bunokwandiswa ngokugubungela ipleyiti xa ingasetyenziswa, ngokuyijikelezisa rhoqo ukuze indawo enye ingafumani ukusetyenziswa okugqithisileyo, nangokutshintsha iiphedi zoqhagamshelwano zentsimbi xa zilinganiswa ngeephedi ze-carbide. Kwakhona, kuphephe ukubeka ukutya okanye iziselo ezibandayo kwipleyiti. Qaphela ukuba iziselo ezininzi ezibandayo ziqulethe i-carbonic okanye i-phosphoric acid, enokunyibilikisa iiminerali ezithambileyo kwaye ishiye imingxunya emincinci kumphezulu.
Oku kuxhomekeke kwindlela esetyenziswa ngayo ipleyiti. Ukuba kunokwenzeka, sicebisa ukuba ucoce ipleyiti ekuqaleni kosuku (okanye ishifti yomsebenzi) uze uyicoce kwakhona ekupheleni kwayo. Ukuba ipleyiti ingcola, ingakumbi ngolwelo olunamafutha okanye olunamathelayo, kufuneka icocwe ngoko nangoko.
Coca ipleyiti rhoqo ngesicoci sepleyiti esingenamanzi okanye i-ZHHIMG Waterless surface plate. Ukukhetha izisombululo zokucoca kubalulekile. Ukuba kusetyenziswa isinyibilikisi esiguquguqukayo (i-acetone, i-lacquer thinner, i-alcohol, njl.njl.) ukufuma kuya kupholisa umphezulu, kwaye kuwuphazamise. Kwimeko enjalo, kuyimfuneko ukuvumela ipleyiti ukuba iqheleke ngaphambi kokuba uyisebenzise okanye kuya kwenzeka iimpazamo zokulinganisa.
Ixesha elifunekayo ukuze ipleyiti ihlale ikwimeko entle liya kwahluka ngokobukhulu bepleyiti, kunye nobungakanani bokuphola. Iyure enye mayibe yanele iipleyiti ezincinci. Kunokufuneka iiyure ezimbini kwiipleyiti ezinkulu. Ukuba kusetyenziswa isicoci esisekelwe emanzini, kuya kubakho nokuphola okubangelwa kukufuma.
Ipleyiti iya kugcina amanzi, kwaye oku kunokubangela ukugqwala kweendawo zesinyithi xa zidibene nomphezulu. Ezinye izixhobo zokucoca ziya kushiya intsalela enamathelayo emva kokuba zomile, nto leyo eya kutsala uthuli oluphuma emoyeni, kwaye ngokwenene yonyuse ukuguguleka, endaweni yokunciphisa.
Oku kuxhomekeke ekusetyenzisweni kwepleyiti kunye nendawo engqongileyo. Sicebisa ukuba ipleyiti entsha okanye isixhobo segranite esichanekileyo sifumane uhlengahlengiso olupheleleyo kungekapheli unyaka omnye wokuthengwa. Ukuba ipleyiti yomphezulu wegranite iya kusetyenziswa kakhulu, kungacetyiswa ukuba sinciphise eli xesha liye kwiinyanga ezintandathu. Ukuhlolwa kwenyanga nganye kweempazamo zokulinganisa eziphindaphindwayo kusetyenziswa inqanaba le-elektroniki, okanye isixhobo esifanayo kuya kubonisa naziphi na iindawo zokuguguleka ezikhulayo kwaye kuthatha imizuzu embalwa kuphela ukusebenza. Emva kokuba iziphumo zohlengahlengiso lokuqala zichongiwe, ixesha lohlengahlengiso linokwandiswa okanye lifinyezwe njengoko kuvunyelwe okanye kufunwa yinkqubo yakho yomgangatho wangaphakathi.
Singakunika inkonzo yokukunceda uhlole kwaye ulinganise ipleyiti yakho yomphezulu wegranite.
Kukho izizathu ezininzi ezinokubangela umahluko phakathi kokulinganiswa:
- Umphezulu uhlanjwe ngesicombululo esishushu okanye esibandayo ngaphambi kokulungiswa, kwaye awuzange unikwe ixesha elaneleyo lokulungisa imeko.
- Ipleyiti ayixhaswanga kakuhle
- Utshintsho lobushushu
- Iidrafti
- Ukukhanya kwelanga ngqo okanye olunye ubushushu obukhanyayo kumphezulu wepleyiti. Qiniseka ukuba izibane eziphezulu azifudumezi umphezulu
- Utshintsho kwi-gradient yobushushu obuthe nkqo phakathi kobusika nehlobo (Ukuba kunokwenzeka, yazi i-vertical gradient temperature ngexesha lokwenziwa kwe-calibration.)
- Ipleyiti ayinikwanga ixesha elaneleyo lokulungisa imeko emva kokuthunyelwa
- Ukusetyenziswa gwenxa kwezixhobo zokuhlola okanye ukusetyenziswa kwezixhobo ezingalinganiswanga
- Utshintsho lomphezulu olubangelwa kukuguguleka
Kwiifektri ezininzi, amagumbi okuhlola kunye neelebhu, iipleyiti zomphezulu wegranite ezichanekileyo zixhomekeke kuzo njengesiseko sokulinganisa ngokuchanekileyo. Ngenxa yokuba umlinganiselo ngamnye othe tye uxhomekeke kumphezulu ochanekileyo wereferensi apho kuthathwa khona imilinganiselo yokugqibela, iipleyiti zomphezulu zibonelela ngeyona ndawo ifanelekileyo yokujonga umsebenzi kunye noyilo ngaphambi kokwenziwa kwemishini. Zikwasisiseko esifanelekileyo sokwenza imilinganiselo yobude kunye nokulinganisa umphezulu. Ngaphezu koko, inqanaba eliphezulu lokuthe tyaba, ukuzinza, umgangatho ngokubanzi kunye nomsebenzi osebenzayo kuzenza zibe lukhetho olufanelekileyo lokufaka iinkqubo zokulinganisa ezintsonkothileyo zoomatshini, ze-elektroniki kunye nezokukhanya. Kuzo naziphi na ezi nkqubo zokulinganisa, kubalulekile ukugcina iipleyiti zomphezulu zilinganisiwe.
Repeat Measurements and Flatness
Zombini izilinganiso zokuthe tyaba kunye neziphindaphindwayo zibalulekile ukuqinisekisa umphezulu ochanekileyo. Ukuthe tyaba kungathathwa njengeendawo zonke ezikumphezulu eziqulethwe kwiiplani ezimbini ezihambelanayo, iplani esisiseko kunye neplani yophahla. Ukulinganiswa komgama phakathi kweplani kukuthe tyaba ngokubanzi komphezulu. Olu vavanyo lokuthe tyaba ludla ngokuba nokunyamezela kwaye lunokubandakanya uphawu lwebanga.
The flatness tolerances for three standard grades are defined in the federal specification as determined by the following formula:
Umgangatho we-DIN, Umgangatho we-GB, Umgangatho we-ASME, Umgangatho we-JJS... ilizwe elahlukileyo elinesimo esahlukileyo...
Iinkcukacha ezithe vetshe malunga nomgangatho.
In addition to flatness, repeatability must be ensured. A repeat measurement is a measurement of local flatness areas. It is a measurement taken anywhere on the surface of a plate that will repeat within the stated tolerance. Controlling local area flatness to a tighter tolerance than overall flatness guarantees a gradual change in surface flatness profile, thereby minimizing local errors.
Ukuqinisekisa ukuba ipleyiti yomphezulu ihlangabezana neemfuno ezithe tyaba kunye nemilinganiselo ephindaphindwayo, abavelisi beepleyiti zomphezulu wegranite kufuneka basebenzise i-Federal Specification GGG-P-463c njengesiseko seenkcazo zabo. Lo mgangatho ujongana nokuchaneka kokulinganisa okuphindaphindwayo, iipropati zezinto zegranite yomphezulu wepleyiti, ukugqitywa komphezulu, indawo yenkxaso, ukuqina, iindlela ezamkelekileyo zokuhlola kunye nokufakela izinto ezifakwe ngemisonto.
Checking Plate Accuracy
Ngokulandela izikhokelo ezimbalwa ezilula, utyalo-mali kwipleyiti yomphezulu wegranite lufanele luhlale iminyaka emininzi. Ngokuxhomekeke ekusetyenzisweni kwepleyiti, indawo yevenkile kunye nokuchaneka okufunekayo, amaxesha okujonga ukuchaneka kwepleyiti yomphezulu ayahluka. Umgaqo oqhelekileyo kukuba ipleyiti entsha ifumane uhlengahlengiso olupheleleyo kungekapheli unyaka omnye emva kokuthengwa. Ukuba ipleyiti isetyenziswa rhoqo, kuyacetyiswa ukuba ifinyezwe eli xesha liye kwiinyanga ezintandathu.
Before a surface plate has worn beyond specification for overall flatness, it will show worn or wavy posts. Monthly inspection for repeat measurement errors using a repeat reading gage will identify wear spots. A repeat reading gage is a high-precision instrument that detects local error and can be displayed on a high magnification electronic amplifier.
An effective inspection program should include regular checks with an autocollimator, providing actual calibration of overall flatness traceable to National Institute of Standards and Technology (NIST). Comprehensive calibration by the manufacturer or an independent company is necessary from time to time.
Variations Between Calibrations
Kwezinye iimeko, kukho umahluko phakathi kokulinganiswa kwepleyiti yomphezulu. Ngamanye amaxesha izinto ezifana nokutshintsha komphezulu okubangelwa kukuguguleka, ukusetyenziswa gwenxa kwezixhobo zokuhlola okanye ukusetyenziswa kwezixhobo ezingalinganiswanga zinokubangela olu tshintsho. Nangona kunjalo, ezona zinto zimbini zixhaphakileyo bubushushu kunye nenkxaso.
One of the most important variables is temperature. For instance, the surface might have been washed with a hot or cold solution prior to calibration and not allowed sufficient time to normalize. Other causes of temperature change include drafts of cold or hot air, direct sunlight, overhead lighting or other sources of radiant heat on the surface of the plate.
There also can be variations in the vertical temperature gradient between winter and summer. In some cases, the plate is not allowed sufficient time to normalize after shipment. It is a good idea to record the vertical gradient temperature at the time the calibration is performed.
Another common cause for calibration variation is a plate that is improperly supported. A surface plate should be supported at three points, ideally located 20% of the length in from the ends of the plate. Two supports should be located 20% of the width in from the long sides, and the remaining support should be centered.
Only three points can rest solidly on anything but a precision surface. Attempting to support the plate at more than three points will cause the plate to receive its support from various combinations of three points, which will not be the same three points on which it was supported during production. This will introduce errors as the plate deflects to conform to the new support arrangement. Consider using steel stands with support beams designed to line up with the proper support points. Stands for this purpose are generally available from the surface plate manufacturer.
If the plate is properly supported, precise leveling is only necessary if an application specifies it. Leveling is not necessary to maintain the accuracy of a properly supported plate.
Extend Plate Life
Ukulandela izikhokelo ezimbalwa kuya kunciphisa ukuguguleka kwepleyiti yomphezulu wegranite kwaye ekugqibeleni, kuya kwandisa ubomi bayo.
Okokuqala, kubalulekile ukugcina ipleyiti icocekile. Uthuli olurhabaxa oluqhutywa ngomoya ludla ngokuba lolona mthombo mkhulu wokuguguleka kwepleyiti, njengoko ludla ngokungena kwiindawo zokusebenza kunye neendawo ezidibanayo zeegeyiji.
It also is important to cover plates to protect it from dust and damage. Wear life can be extended by covering the plate when not in use.
Jikelezisa ipleyiti rhoqo ukuze indawo enye ingasetyenziswa kakhulu. Kwakhona, kuyacetyiswa ukuba kutshintshwe ii-contact pads zentsimbi xa kujongwa ii-gauge ngee-carbide pads.
Avoid setting food or soft drinks on the plate. Many soft drinks contain either carbonic or phosphoric acid, which can dissolve the softer minerals and leave small pits in the surface.
Where to Relap
Xa ipleyiti yomphezulu wegranite ifuna ukuphinda ibekwe phezu kwayo, cinga ukuba le nkonzo yenziwe kwindawo okanye kwindawo yokulinganisa. Kuhlala kungcono ukuba ipleyiti ibekwe kwakhona kumzi-mveliso okanye kwindawo enikezelweyo. Nangona kunjalo, ukuba ipleyiti ayigugi kakhulu, ngokubanzi ngaphakathi kwe-intshi eziyi-0.001 yokunyamezela okufunekayo, ingaphinda ibekwe kwakhona kwindawo. Ukuba ipleyiti igugiwe ukuya kwinqanaba apho ingaphezulu kwe-intshi eziyi-0.001 ngenxa yokunyamezela, okanye ukuba igrumbe kakhulu okanye ikrumbekile, kufuneka ithunyelwe kumzi-mveliso ukuze igrumbe ngaphambi kokuba iphindwe.
A calibration facility has the equipment and factory setting providing the optimum conditions for proper plate calibration and rework if necessary.
Kufuneka kusetyenziswe unonophelo olukhulu ekukhetheni ingcali yokulinganisa nokulungisa umphezulu kwindawo leyo. Cela imvume kwaye uqinisekise ukuba izixhobo eziza kusetyenziswa yingcali zinokulinganiswa okulandelekayo. Amava nawo abalulekile, njengoko kuthatha iminyaka emininzi ukufunda indlela yokurhangqa ngokuchanekileyo i-granite.
Critical measurements start with a precision granite surface plate as a baseline. By ensuring a reliable reference by using a properly calibrated surface plate, manufacturers have one of the essential tools for reliable measurements and better quality parts.Q
Checklist for Calibration Variations
1. Umphezulu uhlanjwe ngesicombululo esishushu okanye esibandayo ngaphambi kokulungiswa kwaye awuzange unikwe ixesha elaneleyo lokulungisa imeko.
2. Ipleyiti ayixhaswanga kakuhle.
3. Utshintsho lobushushu.
4. Iidrafti.
5. Ukukhanya kwelanga ngqo okanye olunye ubushushu obukhanyayo kumphezulu wepleyiti. Qiniseka ukuba izibane ezikhanyisa ngaphezulu azifudumezi umphezulu.
6. Utshintsho kwi-gradient yobushushu obuthe nkqo phakathi kobusika nehlobo. Ukuba kunokwenzeka, yazi i-gradient yobushushu obuthe nkqo ngexesha lokulinganisa.
7. Ipleyiti ayivumelekanga ixesha elaneleyo lokulungisa emva kokuthunyelwa.
8. Ukusetyenziswa gwenxa kwezixhobo zokuhlola okanye ukusetyenziswa kwezixhobo ezingalinganiyo.
9. Utshintsho kumphezulu olubangelwa kukuguguleka.
Tech Tips
- Ngenxa yokuba yonke imilinganiselo ethe tye ixhomekeke kumphezulu ochanekileyo wesalathiso apho kuthathwa khona imilinganiselo yokugqibela, iipleyiti zomphezulu zibonelela ngeyona ndawo ilungileyo yesalathiso sokuhlolwa komsebenzi kunye noyilo ngaphambi kokuba kwenziwe i-machining.
- Controlling local area flatness to a tighter tolerance than overall flatness guarantees a gradual change in surface flatness profile, thereby minimizing local errors.
- Inkqubo yokuhlola esebenzayo kufuneka iquke ukujonga rhoqo nge-autocollimator, ebonelela ngokulinganisa ubume obuthe tyaba obunokulandelelwa yi-National Inspection Authority.
Phakathi kwee-minerali ezincinci ezenza i-granite, ngaphezulu kwe-90% yi-feldspar kunye ne-quartz, apho i-feldspar yeyona ininzi. I-feldspar idla ngokuba mhlophe, ngwevu, kwaye ibomvu njengenyama, kwaye i-quartz ikakhulu ayinambala okanye imhlophe ngwevu, nto leyo eyenza umbala osisiseko we-granite. I-Feldspar kunye ne-quartz ziiminerali eziqinileyo, kwaye kunzima ukuzihambisa ngemela yentsimbi. Ngokuphathelele amabala amnyama kwi-granite, ikakhulu i-mica emnyama, kukho ezinye iiminerali. Nangona i-biotite ithambile, amandla ayo okumelana noxinzelelo abuthathaka, kwaye kwangaxeshanye ine-granite encinci, edla ngokuba ngaphantsi kwe-10%. Le yimeko yezinto ezibonakalayo apho i-granite inamandla ngakumbi.
Esinye isizathu sokuba igranite ibe namandla kukuba amasuntswana ayo eeminerali anamathelene ngokuqinileyo kwaye anamathele omnye komnye. Iimbobo zihlala zingaphantsi kwe-1% yomthamo uwonke welitye. Oku kunika igranite amandla okumelana noxinzelelo olunamandla kwaye ayingeni lula kumswakama.
Izinto zegranite zenziwe ngamatye angenawo umhlwa, ukumelana ne-asidi kunye ne-alkali, ukumelana nokuguguleka okuhle kunye nobomi benkonzo ende, akukho londolozo lukhethekileyo. Izinto zegranite ezichanekileyo zisetyenziswa kakhulu kwizixhobo zoshishino loomatshini. Ke ngoko, zibizwa ngokuba zizinto zegranite ezichanekileyo okanye izinto zegranite. Iimpawu zezinto zegranite ezichanekileyo ziyafana nezo zamaqonga egranite. Intshayelelo ekusebenziseni izixhobo kunye nokulinganisa izinto zegranite ezichanekileyo: Umatshini wokulungisa ngokuchanekileyo kunye neteknoloji yoomatshini abancinci zizikhokelo ezibalulekileyo zophuhliso loshishino loomatshini, kwaye ziye zaba luphawu olubalulekileyo lokulinganisa inqanaba lobuchwepheshe obuphezulu. Uphuhliso lwetekhnoloji yanamhlanje kunye neshishini lokhuselo alunakwahlulwa kwiteknoloji yokulungisa ngokuchanekileyo kunye nomatshini omncinci. Izinto zegranite zinokutyibilika kakuhle kumlinganiselo, ngaphandle kokuma. Ukulinganiswa komphezulu womsebenzi, imikrwelo ngokubanzi ayichaphazeli ukuchaneka komlinganiselo. Izinto zegranite kufuneka ziyilwe kwaye ziveliswe ngokweemfuno zecala lemfuno.
Intsimi yesicelo:
Njengoko sonke sisazi, oomatshini abaninzi kunye nezixhobo zikhetha izinto zegranite ezichanekileyo.
Izixhobo zegranite zisetyenziselwa intshukumo enamandla, iimoto ezithe nkqo, i-cmm, i-cnc, umatshini we-laser...
wamkelekile ukuba unxibelelane nathi ukuze ufumane ulwazi oluthe kratya.
Izixhobo zokulinganisa igranite kunye nezixhobo zoomatshini zegranite zenziwe ngegranite emnyama ekumgangatho ophezulu. Ngenxa yokuchaneka kwazo okuphezulu, ixesha elide, uzinzo oluhle kunye nokumelana nokugqwala, ziye zasetyenziswa ngakumbi nangakumbi ekuhlolweni kwemveliso kumashishini anamhlanje nakwiindawo zesayensi ezifana nesithuba se-aero yoomatshini kunye nophando lwesayensi.
Iingenelo
----Iqine kabini kunentsimbi ephosiweyo;
----Utshintsho oluncinci lobukhulu lubangelwa lutshintsho lobushushu;
---- Ayinangxaki yokubhitya, ngoko ke akukho kuphazamiseka komsebenzi;
---- Ayinazo iibherrs okanye iiprotrusions ngenxa yesakhiwo sengqolowa esicolekileyo kunye nokunamathela okuncinci, okuqinisekisa ukuba incinci kakhulu ixesha elide kwaye ayibangeli monakalo kwezinye iindawo okanye izixhobo;
-----Ukusebenza okungenangxaki kokusetyenziswa ngezinto zemagnethi;
----Ihlala ixesha elide kwaye ayinamhlwa, nto leyo ebangela iindleko eziphantsi zokulungisa.
Iipleyiti zomphezulu wegranite ezichanekileyo zinamathele ngokuchanekileyo kumgangatho ophezulu wokuthe tyaba ukuze kufezekiswe ukuchaneka kwaye zisetyenziswa njengesiseko sokufakela iinkqubo zokulinganisa ezintsonkothileyo zoomatshini, ze-elektroniki kunye nezokukhanya.
Ezinye zeempawu ezikhethekileyo zepleyiti yomphezulu wegranite:
Ukufana kwi-Hardness;
Iimeko ezichanekileyo phantsi komthwalo;
Isifunxi sokungcangcazela;
Kulula Ukuyicoca;
Ayikwazi ukusonga;
Ukuxinana okuphantsi;
Ayirhawuzeli;
Ayinamagnethi
Iingenelo zePlate yoMphezulu weGranite
First, the rock after a long period of natural aging, uniform structure, coefficient minimum, the internal stress completely disappear, not deformed, so the precision is high.
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Routine surface plate calibration is necessary to ensure flatness and repeatability over time. The precision measurement group at Cross is ISO 17025 accredited for calibration of surface plate flatness and repeatability. We utilize the Mahr Surface Plate Certification System featuring:
- Moody and Profile Analysis,
- Isometric or Numeric plots,
- Multiple Run Average, and
- Automatic Grading According to Industry Standards.
The Mahr Computer Assisted Model determines any angular or linear deviation from absolute level, and is ideally suited for highly precise profiling of surface plates.
Intervals between calibrations will vary depending on the frequency of use, the environmental conditions where the plate is located, and the specific quality requirements of your company. Properly maintaining your surface plate may allow for longer intervals between each calibration, helps you avoid the added cost of relapping, and most importantly ensures the measurements you obtain on the plate are as accurate as possible. Although surface plates appear robust, they are precision instruments and should be treated as such. Here are some things to consider regarding care of your surface plates:
- Keep the plate clean, and if possible cover it when it is not in use
- Nothing should be placed on the plate other than gages or pieces to be measured.
- Don’t use the same spot on the plate every time.
- If possible, rotate the plate periodically.
- Respect the load limit of your plate
Precision Granite Base Can Improve Machine Tool Performances
Requirements are constantly increasing in mechanical engineering in general and in machine tool construction in particular. Achieving maximum precision and performance values without increasing costs are constant challenges to being competitive. The machine tool bed is a decisive factor here. Therefore, more and more machine tool manufacturers are relying on granite. Due to its physical parameters, it offers clear advantages that cannot be achieved with steel or polymer concrete.
Granite is a so-called volcanic deep rock and has a very dense and homogeneous structure with an extremely low coefficient of expansion, low thermal conductivity and high vibration damping.
Below you will discover why the common opinion that granite is mainly only suitable as machine base for high-end coordinate measuring machines is long outdated and why this natural material as a machine tool base is a very advantageous alternative to steel or cast iron even for high-precision machine tools.
We can manufacture granite components for dynamic motion, granite components for linear motors, granite components for ndt, granite components for xray, granite components for cmm, granite components for cnc, granite precision for laser, granite components for aerospace, granite components for precision stages...
High Added Value Without Additional Costs
The increasing use of granite in mechanical engineering is not so much due to the massive increase in the price of steel. Rather, it is because the added value for the machine tool achieved with a machine bed made of granite is possible at very little or no extra cost. This is proven by cost comparisons of well-known machine tool manufacturers in Germany and Europe.
The considerable gain in thermodynamic stability, vibration damping and long-term precision made possible by granite cannot be achieved with a cast iron or steel bed, or only at relatively high cost. For example, thermal errors can account for up to 75% of the total error of a machine, with compensation often attempted for by software – with moderate success. Due to its low thermal conductivity, granite is the better foundation for long-term precision.
With a tolerance of 1 μm, granite easily meets the flatness requirements according to DIN 876 for the degree of accuracy 00. With a value of 6 on the hardness scale 1 to 10, it is extremely hard, and with its specific weight of 2.8g/cm³ it almost reaches the value of aluminium. This also results in additional advantages such as higher feed rates, higher axis accelerations and an extension of the tool life for cutting machine tools. Thus, the change from a cast bed to a granite machine bed moves the machine tool in question into the high-end class in terms of precision and performance – at no extra cost.
Granite’s Improved Ecological Footprint
In contrast to materials such as steel or cast iron, natural stone does not have to be produced with a great deal of energy and using additives. Only relatively small amounts of energy are required for quarrying and surface treatment. This results in a superior ecological footprint, which even at the end of a machine’s life surpasses that of steel as a material. The granite bed can be the basis for a new machine or be used for completely different purposes such as shredding for road construction.
Nor are there any shortages of resources for granite. It is a deep rock formed from magma within the earth’s crust. It has ‘matured’ for millions of years and is available in very large quantities as a natural resource on almost all continents, including all of Europe.
Conclusion: The numerous demonstrable advantages of granite compared to steel or cast iron justify the increasing willingness of mechanical engineers to use this natural material as a foundation for high-precision, high-performance machine tools. Detailed information about granite properties, which are advantageous for machine tools and mechanical engineering, can be found in this further article.
A repeat measurement is a measurement of local flatness areas. The Repeat Measurement specification states that a measurement taken anywhere on the surface of a plate will repeat within the stated tolerance. Controlling local area flatness tighter than overall flatness guarantees a gradual change in surface flatness profile thereby minimizing local errors.
Most manufacturers, including imported brands, adhere to the Federal Specification of overall flatness tolerances but many overlook the repeat measurements. Many of the low value or budget plates available in the market today will not guarantee repeat measurements. A manufacturer who does not guarantee repeat measurements is NOT producing plates that meet the requirements of ASME B89.3.7-2013 or Federal Specification GGG-P-463c, or DIN 876, GB, JJS...
Both are critical to ensure a precision surface for accurate measurements. Flatness specification alone is not sufficient to guarantee measurement accuracy. Take as an example, a 36 X 48 Inspection Grade A surface plate, which meets ONLY the flatness specification of .000300". If the piece being checked bridges several peaks, and the gage being used is in a low spot, the measurement error could be the full tolerance in one area, 000300"! Actually, it can be much higher if the gage is resting on the slope of an incline.
Errors of .000600"-.000800" are possible, depending upon the severity of the slope, and the arm length of the gage being used. If this plate had a Repeat Measurement specification of .000050"F.I.R. then the measurement error would be less than .000050" regardless of where the measurement is taken on the plate. Another problem, which usually arises when an untrained technician attempts to resurface a plate on-site, is the use of Repeat Measurements alone to certify a plate.
The instruments that are used to verify repeatability are NOT designed to check overall flatness. When set to zero on a perfectly curved surface, they will continue to read zero, whether that surface is perfectly flat or perfectly concave or convex 1/2"! They simply verify the uniformity of the surface, not the flatness. Only a plate that meets both the flatness specification AND the repeat measurement specification truly meets the requirements of ASME B89.3.7-2013 or Federal Specification GGG-P-463c.
Ask us about or flatness specification and repeat measurement promise by calling +86 19969991659 or emailing INFO@ZHHIMG.COM
Yes, but they can only be guaranteed for a specific vertical temperature gradient. The effects of thermal expansion on the plate could easily cause a change in accuracy greater than the tolerance if there is a change in the gradient. In some cases, if the tolerance is tight enough, the heat absorbed from overhead lighting can cause enough of a gradient change over several hours.
Granite has a coefficient of thermal expansion of approximately .0000035 inches per inch per 1°F. As an example: A 36" x 48" x 8" surface plate has an accuracy of .000075" (1/2 of Grade AA) at a gradient of 0°F, the top and bottom are the same temperature. If the top of the plate warms up to the point where it is 1°F warmer than the bottom, the accuracy would change to .000275" convex ! Therefore, ordering a plate with a tolerance tighter than Laboratory Grade AA should only be considered if there is adequate climate control.
A surface plate should be supported at 3 points, ideally located 20% of the length in from the ends of the plate. Two supports should be located 20% of the width in from the long sides, and the remaining support should be centered. Only 3 points can rest solidly on anything but a precision surface.
The plate should be supported at these points during production, and it should be supported only at these three points while in use. Attempting to support the plate at more than three points will cause the plate to receive its support from various combinations of three points, which will not be the same 3 points on which it was supported during production. This will introduce errors as the plate deflects to conform to the new support arrangement. All zhhimg steel stands have support beams designed to line up with the proper support points.
If the plate is properly supported, precise leveling is only necessary if your application calls for it. Leveling is not necessary to maintain the accuracy of a properly supported plate.
Why Choose Granite for Machine Bases and Metrology Components?
The answer is 'yes' for almost every application. The advantages of granite include: No rust or corrosion, almost immune to warping, no compensating hump when nicked, longer wear life, smoother action, greater precision, virtually non-magnetic, low co-efficient of thermal expansion, and low maintenance cost.
Granite is a type of igneous rock quarried for its extreme strength, density, durability, and resistance to corrosion. But granite is also very versatile– it’s not just for squares and rectangles! In fact, Starrett Tru-Stone confidently works with granite components engineered in shapes, angles, and curves of all variations on a regular basis—with excellent outcomes.
Through our state of the art processing, cut surfaces can be exceptionally flat. These qualities make granite the ideal material to create custom-size and custom-design machine bases and metrology components. Granite is:
machineable
precisely flat when cut and finished
rust resistant
durable
long lasting
Granite components are also easy to clean. When creating custom designs, be sure to choose granite for its superior benefits.
STANDARDS / HIGH WEAR APPLICATIONS
The granite utilized by ZhongHui for our standard surface plate products has high quartz content, which provides greater resistance to wear and damage. Our Superior Black and Crystal Pink colors have low water absorption rates, minimizing the possibility of your precision gages rusting while setting on the plates. The colors of granite offered by ZhongHui result in less glare, which means less eyestrain for individuals using the plates. We have chosen our granite types while considering thermal expansion in an effort to keep this aspect minimal.
CUSTOM APPLICATIONS
When your application calls for a plate with custom shapes, threaded inserts, slots or other machining, you’ll want to select a material like Black Diabase. This natural material offers superior stiffness, excellent vibration dampening, and improved machinability.
Yes, if they are not too badly worn. Our factory setting and equipment allow the optimum conditions for proper plate calibration and rework if necessary. Generally, if a plate is within .001" of the required tolerance, it can be resurfaced on-site. If a plate is worn to the point where it is more than .001" out of tolerance, or if it is badly pitted or nicked, then it will need to be sent to the factory for grinding prior to relapping.
Great care should be exercised in selecting an on-site calibration and resurfacing technician. We urge you to use caution in selecting your calibration service. Ask for accreditation and verify the equipment that the technician will use has a National Inspection Institution traceable calibration. It takes many years to learn how to properly lap precision granite.
ZhongHui provides quick turn-around on calibrations performed in our factory. Send your plates in for calibration if possible. Your quality and reputation depend on the accuracy of your measurement instruments including surface plates!
Our black surface plates have a significantly higher density and are up to three times as stiff. Therefore, a plate made of the black does not need to be as thick as a granite plate of the same size to have equal or greater resistance to deflection. Reduced thickness means less weight and lower shipping costs.
Beware of others who use lower quality black granite in the same thickness. As stated above, properties of granite, like wood or metal, vary by material and color, and is not an accurate predictor of stiffness, hardness, or wear resistance. In fact, many types of black granite and diabase are very soft and not suitable for surface plate applications.
No. The specialized equipment and training necessary to rework these items requires that they be returned to the factory for calibration and rework.
Yes. Ceramic and granite have similar characteristics, and the methods used to calibrate and lap granite can be used with ceramic items as well. Ceramics are more difficult to lap than granite resulting in a higher cost.
Yes, provided that the inserts are recessed below the surface. If steel inserts are flush with, or above the surface plane, they must be spot-faced down before the plate can be lapped. If required, we can provide that service.
Yes. Steel inserts with the desired thread (English or metric) can be epoxy bonded into the plate at the desired locations. ZhongHui uses CNC machines to provide the tightest insert locations within +/- 0.005”. For less critical inserts, our locational tolerance for threaded inserts is ±.060". Other options include steel T-Bars and dovetail slots machined directly into the granite.
Inserts that are properly bonded using high strength epoxy and good workmanship will withstand a great deal of torsional and shear force. In a recent test, using 3/8"-16 threaded inserts, an independent testing laboratory measured the force required to pull an epoxy-bonded insert from a surface plate. Ten plates were tested. Out of these ten, in nine cases, the granite fractured first. The average load at the point of failure was 10,020 lbs. for gray granite and 12,310 lbs. for black. In the single case where an insert pulled free of the plate, the load at the point of failure was 12,990 lbs.! If a work piece forms a bridge across the insert and extreme torque is applied, it is possible to generate enough force to fracture the granite. Partially for this reason, ZhongHui gives guidelines for the maximum safe torque that can be applied the epoxy bonded inserts: https://www.zhhimg.com/standard-thread-inserts-product/
Yes, but only at our factory. At our plant, we can restore almost any plate to 'like-new' condition, usually for less than half the cost of replacing it. Damaged edges can be cosmetically patched, deep grooves, nicks, and pits can be ground out, and the attached supports can be replaced. In addition, we can modify your plate to increase its versatility by adding solid or threaded steel inserts and cutting slots or clamping lips, per your specifications.
Why Choose Granite?
Granite is a type of igneous rock formed in the Earth millions of years ago. The composition of igneous rock contained many minerals such as quartz that is extremely hard and wear-resistant. In addition to hardness and wear resistance granite has approximately half the coefficient of expansion as cast iron. As its volumetric weight is approximately one third that of cast iron, granite is easier to manoeuvre.
For machine bases and metrology components, black granite is the colour most used. Black granite has a higher percentage of quartz than other colours and is, therefore, the hardest wearing.
Granite is cost-effective, and cut surfaces can be exceptionally flat. Not only can it be hand lapped to achieve extremes of accuracy, but re-conditioning can be performed without moving the plate or table off-site. It is entirely a hand lapping operation and generally costs much less than re-conditioning a cast iron alternative.
These qualities make granite the ideal material to create custom-size and custom-design machine bases and metrology components such as the granite surface plate.
ZhongHui produces bespoke granite products that are created to support specific measurement requirements. These bespoke items vary from straight edges to tri squares. Due to the versatile nature of granite, the components can be produced to any size required; they are hard wearing and long-lasting.
Advantages of Granite Surface Plates
The importance of measuring on an even surface was established by British inventor Henry Maudsley in the 1800s. As a machine tool innovator, he determined that consistent production of parts required a solid surface for reliable measurements.
The industrial revolution created a demand for measuring surfaces, so engineering company Crown Windley created manufacturing standards. The standards for surface plates were first set by Crown in 1904 using metal. As the demand and cost for metal increased, alternative materials for the measuring surface were investigated.
In America, monument creator Wallace Herman established that black granite was an excellent surface plate material alternative to metal. As granite is non-magnetic and doesn’t rust, it soon became the preferred measuring surface.
A granite surface plate is an essential investment for laboratories and test facilities. A granite surface plate of 600 x 600 mm can be mounted on a support stand. The stands provide a working height of 34” (0.86m) with five adjustable points for levelling.
For reliable and consistent measurement results, a granite surface plate is crucial. As the surface is a smooth and stable plane, it enables instruments to be carefully manipulated.
The main advantages of granite surface plates are:
• Non-reflective
• Resistant to chemicals and corrosion
• Low coefficient of expansion compared with cart iron so less affected by temperature change
• Naturally rigid and hard-wearing
• The plane of the surface is unaffected if scratched
• Will not rust
• Non-magnetic
• Easy to clean and maintain
• Calibration and resurfacing can be done onsite
• Suitable for drilling for threaded support inserts
• High vibration damping
For many shops, inspection rooms and laboratories, precision granite surface plates are relied on as the basis for accurate measurement. Because every linear measurement depends on an accurate reference surface from which final dimensions are taken, surface plates provide the best reference plane for work inspection and layout prior to machining. They also are ideal bases for making height measurements and gaging surfaces. Further, a high degree of flatness, stability, overall quality and workmanship make them a good choice for mounting sophisticated mechanical, electronic and optical gaging systems. For any of these measurement processes, it is imperative to keep surface plates calibrated.
Repeat Measurements and Flatness
Both flatness and repeat measurements are critical to ensure a precision surface. Flatness can be considered as all points on the surface being contained within two parallel planes, the base plane and the roof plane. The measurement of distance between the planes is the overall flatness of the surface. This flatness measurement commonly carries a tolerance and may include a grade designation.
The flatness tolerances for three standard grades are defined in the federal specification as determined by the following formula:
Laboratory Grade AA = (40 + diagonal² / 25) x 0.000001 inch (unilateral)
Inspection Grade A = Laboratory Grade AA x 2
Tool Room Grade B = Laboratory Grade AA x 4
In addition to flatness, repeatability must be ensured. A repeat measurement is a measurement of local flatness areas. It is a measurement taken anywhere on the surface of a plate that will repeat within the stated tolerance. Controlling local area flatness to a tighter tolerance than overall flatness guarantees a gradual change in surface flatness profile, thereby minimizing local errors.
To ensure a surface plate meets both the flatness and repeat measurement specifications, manufacturers of granite surface plates should use Federal Specification GGG-P-463c as a basis for their specifications. This standard addresses repeat measurement accuracy, material properties of surface plate granites, surface finish, support point location, stiffness, acceptable methods of inspection and installation of threaded inserts.
Before a surface plate has worn beyond specification for overall flatness, it will show worn or wavy posts. Monthly inspection for repeat measurement errors using a repeat reading gage will identify wear spots. A repeat reading gage is a high-precision instrument that detects local error and can be displayed on a high magnification electronic amplifier.
Checking Plate Accuracy
By following a few simple guidelines, an investment in a granite surface plate should last for many years. Depending on plate usage, shop environment and required accuracy, frequency of checking the surface plate accuracy varies. A general rule of thumb is for a new plate to receive a full recalibration within one year of purchase. If the plate is used frequently, it is advisable to shorten this interval to six months.
Before a surface plate has worn beyond specification for overall flatness, it will show worn or wavy posts. Monthly inspection for repeat measurement errors using a repeat reading gage will identify wear spots. A repeat reading gage is a high-precision instrument that detects local error and can be displayed on a high magnification electronic amplifier.
An effective inspection program should include regular checks with an autocollimator, providing actual calibration of overall flatness traceable to National Institute of Standards and Technology (NIST). Comprehensive calibration by the manufacturer or an independent company is necessary from time to time.
Variations Between Calibrations
In some cases, there are variations between surface plate calibrations. Sometimes factors such as surface change resulting from wear, incorrect use of inspection equipment or use of noncalibrated equipment can account for these variations. The two most common factors, however, are temperature and support.
One of the most important variables is temperature. For instance, the surface might have been washed with a hot or cold solution prior to calibration and not allowed sufficient time to normalize. Other causes of temperature change include drafts of cold or hot air, direct sunlight, overhead lighting or other sources of radiant heat on the surface of the plate.
There also can be variations in the vertical temperature gradient between winter and summer. In some cases, the plate is not allowed sufficient time to normalize after shipment. It is a good idea to record the vertical gradient temperature at the time the calibration is performed.
Another common cause for calibration variation is a plate that is improperly supported. A surface plate should be supported at three points, ideally located 20% of the length in from the ends of the plate. Two supports should be located 20% of the width in from the long sides, and the remaining support should be centered.
Only three points can rest solidly on anything but a precision surface. Attempting to support the plate at more than three points will cause the plate to receive its support from various combinations of three points, which will not be the same three points on which it was supported during production. This will introduce errors as the plate deflects to conform to the new support arrangement. Consider using steel stands with support beams designed to line up with the proper support points. Stands for this purpose are generally available from the surface plate manufacturer.
If the plate is properly supported, precise leveling is only necessary if an application specifies it. Leveling is not necessary to maintain the accuracy of a properly supported plate.
It is important to keep the plate clean. Airborne abrasive dust is usually the greatest source of wear and tear on a plate, as it tends to embed in workpieces and the contact surfaces of gages. Cover plates to protect them from dust and damage. Wear life can be extended by covering the plate when not in use.
Extend Plate Life
Following a few guidelines will reduce wear on a granite surface plate and ultimately, extend its life.
First, it is important to keep the plate clean. Airborne abrasive dust is usually the greatest source of wear and tear on a plate, as it tends to embed in workpieces and the contact surfaces of gages.
It also is important to cover plates to protect it from dust and damage. Wear life can be extended by covering the plate when not in use.
Rotate the plate periodically so that a single area does not receive excessive use. Also, it is recommended to replace steel contact pads on gaging with carbide pads.
Avoid setting food or soft drinks on the plate. Many soft drinks contain either carbonic or phosphoric acid, which can dissolve the softer minerals and leave small pits in the surface.
Where to Relap
When a granite surface plate needs re-surfacing, consider whether to have this service performed on-site or at the calibration facility. It is always preferable to have the plate relapped at the factory or a dedicated facility. If, however, the plate is not too badly worn, generally within 0.001 inch of the required tolerance, it can be resurfaced on-site. If a plate is worn to the point where it is more than 0.001 inch out of tolerance, or if it is badly pitted or nicked, then it should be sent to the factory for grinding prior to relapping.
A calibration facility has the equipment and factory setting providing the optimum conditions for proper plate calibration and rework if necessary.
Great care should be exercised in selecting an on-site calibration and resurfacing technician. Ask for accreditation and verify the equipment that the technician will use has a NIST-traceable calibration. Experience also is an important factor, as it takes many years to learn how to correctly lap precision granite.
Critical measurements start with a precision granite surface plate as a baseline. By ensuring a reliable reference by using a properly calibrated surface plate, manufacturers have one of the essential tools for reliable measurements and better quality parts.
Checklist for Calibration Variations
- The surface was washed with a hot or cold solution prior to calibration and was not allowed sufficient time to normalize.
- The plate is improperly supported.
- Temperature change.
- Drafts.
- Direct sunlight or other radiant heat on the surface of the plate. Be sure that overhead lighting is not heating the surface.
- Variations in the vertical temperature gradient between winter and summer. If at all possible, know the vertical gradient temperature at the time the calibration is performed.
- Plate not allowed sufficient time to normalize after shipment.
- Improper use of inspection equipment or use of noncalibrated equipment.
- Surface change resulting from wear.
Tech Tips
Because every linear measurement depends on an accurate reference surface from which final dimensions are taken, surface plates provide the best reference plane for work inspection and layout prior to machining.
Controlling local area flatness to a tighter tolerance than overall flatness guarantees a gradual change in surface flatness profile, thereby minimizing local errors.




