How Do You Calculate an Extension Spring's Rate?

You've chosen a spring, but it's too stiff or too weak. Masewera ongoyerekeza awa amabweretsa kusachita bwino, kulephera kwa mankhwala, ndi kukonzanso kokwera mtengo, kuyimitsa polojekiti yanu pamene mukufufuza yankho.

The spring rate is calculated using a formula that considers the material's shear modulus (G), waya awiri[1] (d), kutanthauza coil diameter[^ 2] (D), and the number of active coils (Kale). These physical properties directly determine the spring's stiffness.

I've seen countless projects get delayed simply because the spring rate was an afterthought. Katswiri amapanga gulu lonse ndikuyesa kupeza kasupe wokwanira, kungopeza kuti palibe amene ali ndi mlingo woyenera. Pa LINSPRING, nthawi zonse timayamba ndi mphamvu yofunikira. Powerengera zofunikira Mlingo wa masika[^ 3] choyamba, tikhoza kupanga kasupe yemwe amapereka ntchito yeniyeni yofunikira, kupulumutsa nthawi yamakasitomala athu, ndalama, ndi kukhumudwa kwambiri. Let's look at how this calculation is done.

Kodi Fomula Yaikulu Yowerengera Mtengo wa Spring??

Mukuwona Mlingo wa masika[^ 3] fomula, ndipo zikuwoneka zochititsa mantha. You're worried that if you misinterpret just one of the variables, kuwerengera kwanu konse kudzakhala kolakwika, kumabweretsa kuwononga ma prototypes.

Njira yoyamba ndi: *k = (G d⁴) / (8 D³ Kale)**. Zingawoneke zovuta, but it's just a combination of the spring's material (G), waya wake (d), geometry yake (D), ndi kuchuluka kwake kozungulira (Kale).

Nthawi zambiri ndimauza mainjiniya atsopano pagulu langa kuti asamachite mantha ndi formula iyi. Ganizirani za izo ngati Chinsinsi. Zosakaniza ndi zinthu zanu, waya, ndi miyeso ya coil. Njirayi ndi malangizo omwe amakuuzani momwe zosakanizazo zidzaphatikizire kuti apange "flavor" yomaliza," which is your spring's stiffness. The most important thing I've learned is how powerful the waya awiri[1] (d) ndi. Because it's raised to the fourth power, ngakhale kusintha kwakung'ono mu kukula kwa waya kudzakhudza kwambiri pamtengo womaliza wa masika. It's the most critical ingredient in the entire recipe.

Kumvetsetsa Kusiyanasiyana Kulikonse mu Fomula

Chigawo chilichonse cha chilinganizochi chikuyimira mawonekedwe ake a kasupe. Kuwongolera chilichonse ndikofunikira kuti mupeze zotsatira zolondola. Zinthu ziwiri zomwe zimakhudzidwa kwambiri ndi kuchuluka kwa waya komanso kuchuluka kwa koyilo.

• Modulus of Rigidity (G): Ichi ndi katundu wa zinthu zokha, kuyimira kukana kwake kupotoza. Zachitsulo, it's around 11.5 miliyoni psi.
• Waya Diameter (d): Kukhuthala kwa waya wa masika. Izi zimakhala ndi zotsatira zazikulu pa mlingo.
• Kutanthauza Coil Diameter (D): Avereji awiri a koyilo, yowerengeredwa ngati Diameter Yakunja kuchotsera Waya Diameter imodzi.
• Zogwira Coils (Kale): Chiwerengero cha makola mu thupi la kasupe kuti ndi ufulu kutambasula.

Momwe Mungadziwire Bwino Kuchuluka kwa Ma Coils Ogwira Ntchito??

Munaŵerengera chiŵerengero chonse cha makola kuchokera kumapeto mpaka kumapeto. Koma mukamagwiritsa ntchito nambalayi mu fomula, wanu owerengeka Mlingo wa masika[^ 3] doesn't match the test data.

Ichi ndi cholakwika chofala. Chiwerengero cha ma koyilo ogwira ntchito (Kale) zimangophatikiza zozungulira mu thupi lalikulu la masika. The end hooks or loops are not considered active because they do not contribute to the spring's deflection.

Nthawi ina ndinagwira ntchito ndi kasitomala yemwe anali kupanga kasupe wa leash ya galu yobweza. Anawerengera okha ndi kutitumizira zojambula. Mtengo wa masika omwe adafotokoza unali wambiri, zotsika kwambiri kuposa zomwe fomula idaneneratu za mapangidwe awo. Ndinawaitana, ndipo tinayenda mowerengera limodzi. Zinapezeka kuti adaphatikiza zozungulira zomwe zidapanga mbedza zomaliza mwawo "yogwira koyilo[^ 5]" kuwerenga. Zokowera zilipo kusamutsa katundu, osati kutambasula. Nthawi ina tinakonza nambala imodzi ija, kuwerengera kwathu kumagwirizana bwino. Kenako tinatha kusintha kapangidwe kake kuti tiwathandize kukhala osalala, kukoka mofatsa iwo ankafuna kwa leash.

Body Coils vs. Mapeto a Lupu

Kusiyanitsa pakati pa ma coil omwe akugwira ntchito ndi osagwira ntchito kumatengera ntchito yawo. Makoyilo okhawo omwe ali omasuka kupotoza pansi pa katundu amaonedwa kuti akugwira ntchito.

• Thupi Coils: Izi ndi zozungulira zoyambira zomwe zimapanga kutalika kwa masika. Mukakokera pa kasupe, zozungulira izi zosapindika pang'ono, zomwe ndizomwe zimapangitsa kuwonjezera. Choncho, onse ali okangalika.
• Mapeto Ma Hooks/Loops: Izi zimapangidwa kuchokera ku koyilo yomaliza kapena ziwiri kumapeto kulikonse. Ntchito yawo ndi kulumikiza kasupe ku msonkhano wanu. They transfer force but are not designed to flex or contribute to the spring's travel. Iwo amaonedwa kuti ndi “akufa" kapena muyogwira koyilo[^ 5]. Choncho, kwa kasupe wowonjezera wokhazikika, Na = chiwerengero cha zozungulira m'thupi.

Momwe Mungawerengere Mtengo kuchokera ku Physical Spring?

Muli ndi kasupe, but you don't know its specifications. Muyenera kupeza mlingo wake popanda kukhala ndi zojambula zojambula kapena kudziwa zakuthupi, kupanga kukhala kosatheka kugwiritsa ntchito formula.

Mutha kudziwa kuchuluka kwake moyeserera ndi mayeso osavuta a mfundo ziwiri. Yezerani mphamvu yofunikira kutambasula kasupe mpaka utali wosiyana. The Mlingo wa masika[^ 3] ndi kusintha kwa mphamvu kugawanika ndi kusintha kwa kutalika.

Izi ndi zomwe timachita mu labu yathu yabwino tsiku lililonse. It's the most practical and reliable way to verify a spring's rate. Ndinali ndi kasitomala yemwe amayesa kusintha kasupe wosweka mu chidutswa cha zida zakale zafamu. Wopanga woyambayo analibe bizinesi, ndipo panalibe zojambula. Anatitumizira kasupe wosweka. We couldn't use the design formula because we weren't 100% wotsimikiza za zinthu. M'malo mwake, timayika pa load tester yathu. Tinayeza katunduyo paulendo wa inchi imodzi ndi maulendo awiri. Pochotsa mphamvu ndi utali, tinawerengera ndalama zenizeni za masika. Kuchokera pamenepo, tikhoza kupanga cholowa m'malo mwangwiro.

Njira Yoyesera ya mfundo ziwiri

Njirayi ndi yolunjika ndipo imafuna zida zoyezera zokhazokha.

1. Muyeso Point 1: Tambasulani kasupe mpaka kutalika kodziwika (L1) ndi kulemba mphamvu (F1).
2. Muyeso Point 2: Tambasulani kasupe mpaka kutalika kwachiwiri kodziwika (L2) ndi kulemba mphamvu (F2).
3. Werengani Mlingo (k): Gwiritsani ntchito fomula: k = (F2 - F1) / (L2 - L1).

Mwachitsanzo, ngati kasupe akuwonetsa katundu wa 20 lbs ku 4 inchi ndi 30 lbs ku 6 mainchesi:

• Kusintha kwa Mphamvu = 30 lbs ndi - 20 lbs = 10 lbs ndi
• Kusintha kwa Utali = 6 mainchesi - 4 inchi = 2 mainchesi
• Mtengo wa Spring (k) = 10 lbs ndi / 2 inchi = 5 lbs/inchi

Mapeto

You can calculate an extension spring's rate theoretically using its physical dimensions and material, kapena pochiyesa. Njira zonsezi ndizofunikira pakupanga kolondola kwa masika ndi kutsimikizira.

[1]: Phunzirani momwe ma waya awiriwa amakhudzira kuuma kwamasika komanso magwiridwe antchito.
[^ 2]: Dziwani kufunikira kwa mainchesi a coil pozindikira mawonekedwe a masika ndi magwiridwe antchito.
[^ 3]: Kumvetsetsa chilinganizo cha masika ndikofunikira kuti mupange akasupe ogwira mtima omwe amakwaniritsa zofunikira zinazake.
[^ 4]: Dziwani zambiri za Modulus of Rigidity ndi gawo lake pakusankha zinthu za akasupe.
[^ 5]: Kumvetsetsa ma coil omwe akugwira ntchito ndikofunikira kuti muwerenge molondola komanso kupanga masika.