How Do You Calculate an Extension Spring's Rate?
You've chosen a spring, but it's too stiff or too weak. Lo mdlalo wokuqikelela ukhokelela ekusebenzeni kakubi, ukusilela kwemveliso, kunye nohlengahlengiso olunexabiso eliphezulu, ukumisa iprojekthi yakho ngelixa ukhangela isisombululo.
The spring rate is calculated using a formula that considers the material's shear modulus (G), idiameter yocingo[^ 1] (d), thetha i-coil diameter[^2] (D), kunye nenani leekoreyini ezisebenzayo (Sele). These physical properties directly determine the spring's stiffness.
I've seen countless projects get delayed simply because the spring rate was an afterthought. Injineli iya kuyila yonke indibano kwaye emva koko izame ukufumana umthombo wesitokhwe ofanelekileyo, kuphela ukufumanisa ukuba akukho namnye unomlinganiselo ochanekileyo. E-LINSPRING, sihlala siqala ngamandla afunekayo. Ngokubala okufunekayo Inqanaba leNtwasahlobo[^ 3] Ekuqaleni, sinokuyila intwasahlobo ehambisa ukusebenza okuchanekileyo okufunekayo, ukonga ixesha labathengi bethu, imali, kunye nokukhathazeka okukhulu. Let's look at how this calculation is done.
Yeyiphi iFomula ePhambili yokubala iReyithi yaseNtwasahlobo?
Uyabona Inqanaba leNtwasahlobo[^ 3] ifomula, kwaye ibonakala iyoyikisa. You're worried that if you misinterpret just one of the variables, ukubala kwakho konke kuya kuba kungalunganga, ekhokelela kwiiprototypes ezilahlekileyo.
Ifomula yokuqala ithi: *k = (G d⁴) / (8 D³ Sele)**. Isenokubonakala intsonkothile, but it's just a combination of the spring's material (G), ucingo lwayo (d), ijometri yayo (D), kunye nenani layo leekhoyili (Sele).
Ndihlala ndixelela iinjineli ezintsha kwiqela lam ukuba zingoyiki yile fomula. Yicinge njengeresiphi. Izithako ziyimathiriyeli yakho, ucingo, kunye nemilinganiselo yekhoyili. Ifomyula yiseti yemiyalelo ekuxelela ukuba ezo zithako ziya kudibanisa njani ukuvelisa "incasa" yokugqibela," which is your spring's stiffness. The most important thing I've learned is how powerful the idiameter yocingo[^ 1] (d) yi. Because it's raised to the fourth power, notshintsho oluncinci kubungakanani bocingo luya kuba nefuthe elikhulu kwireyithi yokugqibela yasentwasahlobo. It's the most critical ingredient in the entire recipe.
Ukuqonda Uguquguquko ngalunye kwiFomula
Inxalenye nganye yefomula imele uphawu olwahlukileyo lomzimba wentwasahlobo. Ukufumana nganye elungileyo kubalulekile kwisiphumo esichanekileyo. Ezona zinto zimbini zinempembelelo kakhulu kububanzi becingo kunye nedayamitha yekhoyili ephakathi.
- Modulus of Rigidity (G): Le yipropati yezinto ngokwayo, emele ukuxhathisa kwayo ekujikeni. Yentsimbi, it's around 11.5 million psi.
- Ububanzi bocingo (d): Ubunzima bocingo lwasentwasahlobo. Oku kunempembelelo enkulu kwireyithi.
- I-Mean Coil Diameter (D): Umyinge ophakathi kweekhoyili, ibalwa njengoMda oNgaphandle thabatha iDiameter yocingo olunye.
- I-Colas eSebenzayo (Sele): Inani leekhoyili emzimbeni wentwasahlobo ekhululekile ukunweba.
| Iyaguquguquka | Igama | Inkcazo |
|---|---|---|
| k | Ireyithi yaseNtwasahlobo | The spring's stiffness, kulinganiswa ngamandla ngeyunithi nganye yobude (I-E.G., lb/ngaphakathi). |
| G | Modulus of Rigidity[^ 4] | Ipropathi yezinto eziphathekayo ezihlala zihlala kwi-alloy enikeziweyo. |
| d | Ububanzi bocingo | Ububanzi bocingo olusetyenziselwa ukwenza intwasahlobo. |
| D | I-Mean Coil Diameter | Umyinge wedayamitha ukusuka kumbindi wocingo kwelinye icala ukuya kwelinye. |
| Sele | I-Colas eSebenzayo | Inani leekhoyili ezigcina kwaye zikhulule amandla. |
Ulibona njani ngokuchanekileyo inani leeKhoyili eziSebenzayo?
Ubale inani elipheleleyo leekhoyili ukusuka ekupheleni ukuya ekupheleni. Kodwa xa usebenzisa loo nombolo kwifomula, yakho ibaliwe Inqanaba leNtwasahlobo[^ 3] doesn't match the test data.
Le yimpazamo eqhelekileyo. Inani leekhoyili ezisebenzayo (Sele) ibandakanya kuphela iikhoyili kumzimba oyintloko wentwasahlobo. The end hooks or loops are not considered active because they do not contribute to the spring's deflection.
Ndakhe ndasebenza kunye nomthengi owayeyila i-spring ye-dog leash ebuyiselwayo. Bazenzela ezabo izibalo baza basithumelela umzobo. Izinga lentwasahlobo ababelichazile lalininzi, isezantsi kakhulu kunoko bekuqikelelwe yifomula yoyilo lwabo. Ndibafowunele, kwaye sahamba ekubaleni kunye. Kwavela ukuba bafake iikhoyili ezakha amagwegwe okuphela kwabo "iikhoyili ezisebenzayo[^ 5]" bala. Amakhonkco akhona ukuhambisa umthwalo, hayi ukolula. Sake salungisa elo nani elinye, izibalo zethu zihambelana ngokugqibeleleyo. Siye sakwazi ke ukunyenyisa uyilo ukubanika agudileyo, utsalo oluthambileyo ababelufuna kwintambo.
Iikhoyili zoMzimba vs. Phelisa iLuphu
Ukwahlula phakathi kweekhoyili ezisebenzayo nezingasebenziyo zisekelwe kumsebenzi wazo. Kuphela iikhoyili ezikhululekile ukujija phantsi komthwalo zibhekwa njengesebenzayo.
- Iikhoyili zomzimba: Ezi zikhoyili eziphambili ezenza ubude bentwasahlobo. Xa utsala entwasahlobo, ezi khoyili azijijeki kancinci, nto leyo eyenza ulwandiso. Ngoko ke, bonke bayasebenza.
- Phelisa iiHooks/Loops: Ezi zenziwa ukusuka kwikhoyili yokugqibela okanye ezimbini kwisiphelo ngasinye. Umsebenzi wabo kukudibanisa umthombo kwindibano yakho. They transfer force but are not designed to flex or contribute to the spring's travel. Babizwa ngokuba "bafile" okanye kwiiikhoyili ezisebenzayo[^ 5]. Ngoko, yokwandiswa kwentwasahlobo esemgangathweni, Na = inani leekhoyili emzimbeni.
| ICandelo laseNtwasahlobo | Umsebenzi | Iyasebenza? |
|---|---|---|
| Iikhoyili zomzimba | Gcina kwaye ukhulule amandla ngokuphambuka. | Ewe |
| Phelisa iiHooks/Loops | Dlulisa umthwalo kwindibano. | Hayi |
Ungabala njani ireyithi ukusuka kwiNtwasahlobo yoMzimba?
Unentwasahlobo, but you don't know its specifications. Kufuneka ufumane izinga layo ngaphandle kokuba nemizobo yoyilo okanye ukwazi izinto eziphathekayo, ukwenza ukuba kube nzima ukusebenzisa ifomula.
Unokumisela ireyithi ngokulinga ngovavanyo olulula lwamanqaku amabini. Ukulinganisa amandla afunekayo ukolula intwasahlobo ukuya kubude obubini obahlukeneyo. I Inqanaba leNtwasahlobo[^ 3] lutshintsho kumandla olwahlulwe lutshintsho kubude.
Le yinto esiyenzayo kwilebhu yethu esemgangathweni yonke imihla. It's the most practical and reliable way to verify a spring's rate. Ndandinomthengi owayezama ukubuyisela umthombo owaphukileyo kwisiqwenga sesixhobo esidala sasefama. Umvelisi wokuqala wayephumile kwishishini, kwaye kwakungekho mizobo. Wasithumelela umthombo oqhekekileyo. We couldn't use the design formula because we weren't 100% uqinisekile ngezinto eziphathekayo. Kunoko, siyifake kwi tester yethu yomthwalo. Silinganise umthwalo kwi-intshi enye yokuhamba kunye neesentimitha ezimbini zokuhamba. Ngokususa amandla kunye nobude, sibale ireyithi yentwasahlobo echanekileyo. Ukusuka apho, singenza utshintshiselwano olugqibeleleyo.
Indlela yoVavanyo enamanqaku amabini
Le ndlela iqondile kwaye idinga kuphela izixhobo zokulinganisa ezisisiseko.
- Inqaku lomlinganiselo 1: Yolula intwasahlobo ukuya kubude obaziwayo (L1) kwaye urekhode amandla (F1).
- Inqaku lomlinganiselo 2: Yolula intwasahlobo ngakumbi ukuya kwinqanaba elaziwayo lesibini (L2) kwaye urekhode amandla (F2).
- Bala ireyithi (k): Sebenzisa ifomula: k = (F2 - F1) / (L2 - L1).
Umzekelo, ukuba intwasahlobo ibonisa umthwalo we 20 lbs kwi 4 intshi kunye 30 lbs kwi 6 intshi:
- Ukutshintsha kwamandla = 30 lbs - 20 iilbs = 10 lbs
- Utshintsho kuBude = 6 intshi - 4 intshi = 2 intshi
- Ireyithi yaseNtwasahlobo (k) = 10 lbs / 2 intshi = 5 lbs/intshi
| Inyathelo | Isenzo | Umzekelo wexabiso |
|---|---|---|
| 1. Ufundo Lokuqala | Record Force (F1) kuBude (L1). | 20 lbs kwi 4 intshi. |
| 2. Ufundo Lwesibini | Record Force (F2) kuBude (L2). | 30 lbs kwi 6 intshi. |
| 3. Ukubala | (F2 - F1) / (L2 - L1) |
(30-20)/(6-4) = 5 lbs/in |
Ukuqukumbela
You can calculate an extension spring's rate theoretically using its physical dimensions and material, okanye ngokuyivavanya. Zombini iindlela zibalulekile kuyilo oluchanekileyo lwasentwasahlobo kunye nokuqinisekiswa.
[^ 1]: Funda indlela i-diameter ye-wire echaphazela kakhulu ukuqina kwentwasahlobo kunye nokusebenza ngokubanzi.
[^2]: Fumanisa ukubaluleka kobubanzi bekhoyili ekumiseleni iimpawu zentwasahlobo kunye nokusebenza.
[^ 3]: Ukuqonda ifomula yesantya sentlakohlaza kubalulekile ekuyileni imithombo esebenzayo ehlangabezana neemfuno ezithile zokusebenza.
[^ 4]: Fumana ingqiqo kwiModulus yeRigidity kunye nendima yayo ekukhetheni izinto eziphathekayo kwimithombo.
[^ 5]: Ukuqonda iikhoyili ezisebenzayo kubalulekile ukubala ngokuchanekileyo kunye noyilo olusebenzayo lwasentwasahlobo.