How Do You Calculate an Extension Spring's Rate?
You've chosen a spring, but it's too stiff or too weak. Wannan wasan hasashe yana haifar da mummunan aiki, gazawar samfur, da sake fasalin tsada, dakatar da aikinku yayin da kuke neman mafita.
The spring rate is calculated using a formula that considers the material's shear modulus (G), diamita waya[^1] (d), ma'ana diamita na nada[^2] (D), da adadin coils masu aiki (Na). These physical properties directly determine the spring's stiffness.
I've seen countless projects get delayed simply because the spring rate was an afterthought. Injiniyan zai tsara taron gabaɗaya sannan ya yi ƙoƙarin nemo maɓuɓɓugar ruwa da ta dace, kawai don gano babu wanda ke da daidai adadin. A LINSPRING, koyaushe muna farawa da ƙarfin da ake buƙata. Ta hanyar ƙididdige abin da ake bukata yawan bazara[^3] na farko, za mu iya tsara maɓuɓɓugar ruwa wanda ke ba da ainihin aikin da ake bukata, ceton abokan cinikinmu lokaci, kudi, da yawan takaici. Let's look at how this calculation is done.
Menene Babban Tsari don ƙididdige ƙimar bazara?
Kuna ganin yawan bazara[^3] dabara, kuma ga alama ban tsoro. You're worried that if you misinterpret just one of the variables, Duk lissafin ku zai yi kuskure, haifar da ɓata samfurori.
Tsarin farko shine: *ku = (G d) / (8 D³ Na)**. Yana iya zama kamar hadaddun, but it's just a combination of the spring's material (G), wayansa (d), geometry ta (D), da adadin nadawa (Na).
Sau da yawa nakan gaya wa sababbin injiniyoyi a ƙungiyara cewa kada su ji tsoro da wannan dabarar. Yi la'akari da shi kamar girke-girke. Abubuwan sinadaran sune kayan ku, waya, da girman nada. Tsarin tsari shine saitin umarnin da ke gaya muku yadda waɗannan sinadarai za su haɗu don samar da dandano na ƙarshe," which is your spring's stiffness. The most important thing I've learned is how powerful the diamita waya[^1] (d) shine. Because it's raised to the fourth power, ko da ɗan ƙaramin canji a girman waya zai yi tasiri mai yawa akan ƙimar bazara ta ƙarshe. It's the most critical ingredient in the entire recipe.
Fahimtar Kowane Canje-canje a cikin Formula
Kowane bangare na dabara yana wakiltar siffa ta zahiri ta yanayin bazara. Samun kowane daidai yana da mahimmanci don ingantaccen sakamako. Abubuwa biyu mafi tasiri sune diamita na waya da matsakaicin diamita na coil.
- Modulus na Rigidity (G): Wannan dukiya ce ta kayan kanta, wakiltar juriya ga karkatarwa. Don karfe, it's around 11.5 miliyan psi.
- Diamita waya (d): A kauri daga cikin spring waya. Wannan yana da tasiri mafi girma akan ƙimar.
- Ma'ana Diamita na Coil (D): Matsakaicin diamita na coils, lissafta azaman Diamita na Wuta a debe Diamita Waya ɗaya.
- Coils mai aiki (Na): Yawan coils a cikin jiki na bazara wanda ke da kyauta don shimfiɗawa.
| Mai canzawa | Suna | Bayani |
|---|---|---|
| Kr | Ƙididdigar bazara | The spring's stiffness, an auna da ƙarfi a kowace raka'a tsawon tsayi (E.g., lb/in). |
| G | Modulus na Rigidity[^4] | Dukiyar kayan da ke dawwama ga abin da aka ba da gami. |
| d | Diamita waya | Diamita na waya da aka yi amfani da shi don yin bazara. |
| D | Ma'ana Diamita na Coil | Matsakaicin diamita daga tsakiyar waya a gefe ɗaya zuwa wancan. |
| Na | Coils mai aiki | Yawan coils da ke adanawa da sakin kuzari. |
Yaya Kuka Daidaita Ƙayyadaddun Adadin Ƙwayoyin Ƙwaƙwalwa?
Kun ƙidaya jimlar adadin coils daga ƙarshe zuwa ƙarshe. Amma lokacin da kake amfani da wannan lambar a cikin dabara, lissafin ku yawan bazara[^3] doesn't match the test data.
Wannan kuskure ne gama gari. Yawan coils masu aiki (Na) kawai ya haɗa da coils a cikin babban jikin bazara. The end hooks or loops are not considered active because they do not contribute to the spring's deflection.
Na taɓa yin aiki tare da abokin ciniki wanda ke tsara maɓuɓɓugar ruwa don leshin kare mai ja da baya. Sun yi lissafin kansu sun aiko mana da zane. Adadin bazara da suka ayyana ya yi yawa, ya yi ƙasa da abin da dabarar ta annabta don ƙirar su. Na kira su, kuma tare muka yi ta lissafin lissafi. Ya zama sun haɗa da coils ɗin da suka kafa ƙugiya na ƙarshe a cikin su "aiki coils[^5]" ƙidaya. Ƙigiyoyin suna can don canja wurin kaya, kada a mike. Da zarar mun gyara wannan lamba daya, lissafin mu yayi daidai daidai. Sannan mun sami damar daidaita zane don ba su santsi, a hankali ja suka so domin leash.
Jiki Coils vs. Ƙarshen madaukai
Bambanci tsakanin coils masu aiki da marasa aiki ya dogara ne akan aikin su. Sai kawai coils waɗanda ke da 'yanci don murɗawa ƙarƙashin kaya ana ɗaukar aiki.
- Murfin Jiki: Waɗannan su ne naɗaɗɗen farko waɗanda ke samar da tsawon lokacin bazara. Lokacin da ka ja a kan bazara, waɗannan naɗaɗɗen baya karkata kaɗan, wanda shine abin da ke haifar da tsawo. Saboda haka, duk suna aiki.
- Ƙarshen ƙugiya/Madauki: Ana yin waɗannan daga coil na ƙarshe ko biyu akan kowane ƙarshen. Ayyukan su shine haɗa ruwa zuwa taron ku. They transfer force but are not designed to flex or contribute to the spring's travel. An dauke su "matattu" ko inaiki coils[^5]. Don haka, don daidaitaccen tsawaita bazara, Na = adadin coils a jiki.
| Bangaren bazara | Aiki | Mai aiki? |
|---|---|---|
| Murfin Jiki | Ajiye da saki makamashi ta hanyar karkata. | Ee |
| Ƙarshen ƙugiya/Madauki | Canja wurin kaya zuwa taro. | A'a |
Ta Yaya Zaku Iya Ƙididdiga Ƙimar Daga Tsarin Jiki?
Kuna da bazara, but you don't know its specifications. Kuna buƙatar nemo ƙimar sa ba tare da yin zanen zane ko sanin kayan ba, yana sa ba zai yiwu a yi amfani da dabarar ba.
Kuna iya ƙididdige ƙimar ta gwaji tare da gwaji mai sauƙi biyu. Auna ƙarfin da ake buƙata don shimfiɗa bazara zuwa tsayi daban-daban guda biyu. The yawan bazara[^3] shine canjin ƙarfi ya raba da canjin tsayi.
Wannan wani abu ne da muke yi a cikin dakin gwaje-gwaje masu inganci kowace rana. It's the most practical and reliable way to verify a spring's rate. Ina da abokin ciniki wanda ke ƙoƙarin maye gurbin ɓataccen marmaro a cikin wani tsohon kayan aikin gona. Asalin masana'anta ya fita kasuwanci, kuma babu zane-zane. Ya aiko mana da karyewar ruwa. We couldn't use the design formula because we weren't 100% tabbata ga kayan. A maimakon haka, mun sanya shi a kan ma'aunin gwajin mu. Mun auna nauyin da inci ɗaya na tafiya da kuma inci biyu na tafiya. Ta hanyar rage ƙarfi da tsayi, mun ƙididdige ainihin ƙimar bazara. Daga nan, za mu iya ƙera cikakkiyar maye.
Hanyar Gwajin Maki Biyu
Wannan hanya madaidaiciya ce kuma tana buƙatar kayan aikin awo na asali kawai.
- Matsayin Auna 1: Mika maɓuɓɓugar ruwa zuwa tsayin da aka sani (L1) kuma rikodin karfi (F1).
- Matsayin Auna 2: Miƙa maɓuɓɓugar ruwa zuwa tsayin sananniya na biyu (L2) kuma rikodin karfi (F2).
- Yi lissafin Rate (Kr): Yi amfani da dabarar: ku = (F2 - F1) / (L2 - L1).
Misali, idan ruwa ya nuna kaya 20 lbs ku 4 inci kuma 30 lbs ku 6 inci:
- Canji a Ƙarfi = 30 lbs - 20 lbs = 10 lbs
- Canji a Tsawon = 6 inci - 4 inci = 2 inci
- Ƙididdigar bazara (Kr) = 10 lbs / 2 inci = 5 lbs/inch
| Mataki | Aiki | Misalin Ƙimar |
|---|---|---|
| 1. Karatun Farko | Ƙarfin Rikodi (F1) a Tsawon (L1). | 20 lbs ku 4 inci. |
| 2. Karatu Na Biyu | Ƙarfin Rikodi (F2) a Tsawon (L2). | 30 lbs ku 6 inci. |
| 3. Lissafi | (F2 - F1) / (L2 - L1) |
(30-20)/(6-4) = 5 lbs/in |
Ƙarshe
You can calculate an extension spring's rate theoretically using its physical dimensions and material, ko kuma a zahiri ta hanyar gwada shi. Duk hanyoyin biyu suna da mahimmanci don ingantaccen ƙirar bazara da tabbatarwa.
[^1]: Koyi yadda diamita na waya ke tasiri sosai ga taurin bazara da aikin gaba ɗaya.
[^2]: Gano mahimmancin ma'anar diamita na coil wajen tantance halayen bazara da aiki.
[^3]: Fahimtar tsarin ƙimar bazara yana da mahimmanci don zayyana ingantattun maɓuɓɓugan ruwa waɗanda suka cika takamaiman buƙatun aiki.
[^4]: Sami fahimtar Modulus na Rigidity da rawar da yake takawa a zaɓin kayan aiki don maɓuɓɓugan ruwa.
[^5]: Fahimtar coils masu aiki yana da mahimmanci don ingantattun ƙididdiga da ingantaccen ƙirar bazara.