How Do You Calculate an Extension Spring's Rate?
You've chosen a spring, but it's too stiff or too weak. Ke alakaʻi nei kēia pāʻani kuhi i ka hana maikaʻi ʻole, hemahema huahana, a me nā kumu kūʻai hou, hoʻopaneʻe i kāu papahana ʻoiai ʻoe e ʻimi i kahi hoʻonā.
The spring rate is calculated using a formula that considers the material's shear modulus (ʻO G), anawaena uwea[^1] (d), mean coil anawaena[^ 2] (ʻO D), a me ka nui o nā'āpana ikaika (Ua hala). These physical properties directly determine the spring's stiffness.
I've seen countless projects get delayed simply because the spring rate was an afterthought. E hoʻolālā ka ʻenekinia i kahi hui holoʻokoʻa a laila e hoʻāʻo e ʻimi i kahi puna waiwai kūpono, ʻo ka ʻike wale ʻana ʻaʻole i loaʻa ka uku kūpono. Ma LINSPRING, hoʻomaka mau mākou me ka ikaika i koi ʻia. Ma ka helu ʻana i nā mea e pono ai puna puna[^ 3] ka mua, hiki iā mākou ke hoʻolālā i kahi puna e hāʻawi i ka hana pololei e pono ai, mālama i kā mākou mea kūʻai aku manawa, kālā, a me ka nui o ka pilikia. Let's look at how this calculation is done.
He aha ke kumu kumu no ka helu ʻana i ka helu puna?
ʻIke ʻoe i ka puna puna[^ 3] ʻōhua, a he mea weliweli ke nana aku. You're worried that if you misinterpret just one of the variables, e hewa ana kāu helu holoʻokoʻa, e alakaʻi ana i nā prototypes i hoʻopau ʻia.
ʻO ke kumu mua: *k = (ʻO G d⁴) / (8 D³ Ua hala)**. He paʻakikī paha, but it's just a combination of the spring's material (ʻO G), kona uwea (d), kona geometry (ʻO D), a me kona heluna o na wili (Ua hala).
'Ōlelo pinepine au i nā 'enekinia hou o koʻu hui mai makaʻu i kēia ʻano. E noʻonoʻo iā ia e like me kahi meaʻai. ʻO nā meaʻai kāu mea, uwea, a me nā ana wili. ʻO ka formula ka hoʻonohonoho o nā ʻōlelo kuhikuhi e haʻi iā ʻoe pehea e hui ai kēlā mau meaʻai e hana i ka "flavor" hope loa," which is your spring's stiffness. The most important thing I've learned is how powerful the anawaena uwea[^1] (d) ʻo ia. Because it's raised to the fourth power, even a tiny change in the wire size will have a massive impact on the final spring rate. It's the most critical ingredient in the entire recipe.
Understanding Each Variable in the Formula
Each part of the formula represents a distinct physical characteristic of the spring. Getting each one right is essential for an accurate result. The two most influential factors are the wire diameter and the mean coil diameter.
- Modulus of Rigidity (ʻO G): This is a property of the material itself, representing its resistance to twisting. For steel, it's around 11.5 million psi.
- ʻO ka helu holoi (d): The thickness of the spring wire. This has the largest effect on the rate.
- Mean Coil Diameter (ʻO D): The average diameter of the coils, helu ʻia ma ke ʻano he anawaena o waho me hoʻokahi anawaena Uea.
- Nā kāʻei ikaika (Ua hala): ʻO ka helu o nā wili i loko o ke kino o ka pūnāwai i manuahi ke kikoo.
| Hoʻololi | Inoa | wehewehe |
|---|---|---|
| k | Kāleka kōkuhi | The spring's stiffness, ana i ka ikaika no ka wae o ka loa (E.g., lb/in). |
| ʻO G | Modulus of Rigidity[^4] | He waiwai waiwai i mau no ka hao i haawiia. |
| d | ʻO ka helu holoi | ʻO ke anawaena o ka uea i hana ʻia i ka puna. |
| ʻO D | Mean Coil Diameter | Ka awelika anawaena mai ke kikowaena o ka uwea ma kekahi aoao a i kekahi. |
| Ua hala | Nā kāʻei ikaika | ʻO ka helu o nā coils e mālama a hoʻokuʻu i ka ikehu. |
Pehea ʻoe e hoʻoholo pololei ai i ka helu o nā huila ʻeleu?
Ua helu ʻoe i ka huina o nā wili mai kekahi ʻaoʻao a i hope. Akā, ke hoʻohana ʻoe i kēlā helu i ke ʻano, kāu helu puna puna[^ 3] doesn't match the test data.
He kuhihewa maʻamau kēia. ʻO ka helu o nā wili hana (Ua hala) ʻo nā ʻōwili wale nō i loko o ke kino nui o ka pūnāwai. The end hooks or loops are not considered active because they do not contribute to the spring's deflection.
Ua hana au me kahi mea kūʻai aku e hoʻolālā ana i kahi puna no ka lei ʻīlio hiki ke huki ʻia. Hana lākou i kā lākou helu ponoʻī a hoʻouna mai iā mākou i kahi kiʻi. ʻO ka nui o ka punawai a lākou i ʻōlelo ai he nui, ʻoi aku ka haʻahaʻa ma mua o ka mea i wānana ʻia no kā lākou hoʻolālā. Ua kāhea au iā lākou, a hele pū mākou ma ka helu ʻana. Ua ʻike ʻia ua hoʻokomo lākou i nā ʻōwili i hana i nā makau hope i loko o kā lākou "nā kāʻei ikaika[^5]" helu. Aia nā makau e hoʻoili i ka ukana, aole e kikoo. Ke hoʻoponopono mākou i kēlā helu hoʻokahi, ua pili pono kā mākou helu ʻana. A laila hiki iā mākou ke hoʻoponopono i ka hoʻolālā e hāʻawi iā lākou i ka maʻalahi, huki mālie lākou i makemake ai no ke kaula.
Kino Coils vs. Hoʻopau Loops
ʻO ka ʻokoʻa ma waena o nā coils hana a me ka hana ʻole e pili ana i kā lākou hana. ʻO nā ʻōwili manuahi wale nō e wili ma lalo o ka ukana i manaʻo ʻia he ʻeleu.
- Nā ʻōʻili kino: ʻO kēia nā ʻōwili kumu mua i hana i ka lōʻihi o ka pūnāwai. Ke huki ʻoe i ka pūnāwai, wehe iki keia mau wiliwili, ʻo ia ka mea e hoʻonui ai. No laila, eleu lakou a pau.
- Hoʻopau Hooks/Loops: Hoʻokumu ʻia kēia mai ka wili hope a ʻelua paha ma kēlā me kēia hopena. ʻO kā lākou hana ka hoʻopili ʻana i ka puna i kāu hui. They transfer force but are not designed to flex or contribute to the spring's travel. Ua manaʻo ʻia lākou he "make" aiʻole i lokonā kāʻei ikaika[^5]. No laila, no kahi puna hoʻonui maʻamau, Na = ka helu o nā wili i loko o ke kino.
| Mea Puna | Hana | ʻeleu? |
|---|---|---|
| Nā ʻōʻili kino | E mālama a hoʻokuʻu i ka ikehu ma ka pale ʻana. | ʻAe |
| Hoʻopau Hooks/Loops | E hoʻoili i ka ukana i ka hui. | ʻAʻole |
Pehea ʻoe e helu ai i ka helu mai kahi pūnāwai kino?
He puna kāu, but you don't know its specifications. Pono ʻoe e ʻimi i kāna helu me ka ʻole o nā kiʻi hoʻolālā a ʻike ʻole paha i ka mea, ʻaʻole hiki ke hoʻohana i ke ʻano.
Hiki iā ʻoe ke hoʻoholo i ka helu ma ka hoʻokolohua me ka hoʻāʻo maʻalahi ʻelua. E ana i ka ikaika e pono ai ke kikoo aku i ka punawai i elua mau loihi. 'Ōlelo puna puna[^ 3] ʻo ka hoʻololi ʻana i ka ikaika i puʻunaue ʻia me ka hoʻololi ʻana i ka lōʻihi.
He mea kēia a mākou e hana ai i kā mākou lab maikaʻi i kēlā me kēia lā. It's the most practical and reliable way to verify a spring's rate. Loaʻa iaʻu kahi mea kūʻai aku e hoʻāʻo nei e pani i kahi pūnāwai haki i kahi ʻāpana o nā lako mahiʻai kahiko. ʻAʻole ʻoihana ka mea hana mua, aohe kii. Ua hoʻouna mai ʻo ia iā mākou i ka pūnāwai naha. We couldn't use the design formula because we weren't 100% maopopo o ka mea. aka, kau mākou ma luna o kā mākou hōʻike haʻahaʻa. Ua ana mākou i ka ukana ma hoʻokahi ʻīniha o ka huakaʻi a ma ʻelua ʻīniha o ka hele ʻana. Ma ka unuhi ʻana i nā ikaika a me nā lōʻihi, ua helu mākou i ka helu puna pololei. From there, hiki iā mākou ke hana i kahi pani kūpono.
ʻO keʻano ho'āʻoʻelua
He mea maʻalahi kēia ʻano hana a koi wale i nā mea hana maʻamau.
- Lae ana 1: E kīkoʻo i ka pūnāwai i kahi lōʻihi i ʻike ʻia (L1) a hoʻopaʻa i ka ikaika (F1).
- Lae ana 2: E hoʻolōʻihi i ka pūnāwai i kahi lua i ʻike ʻia (L2) a hoʻopaʻa i ka ikaika (F2).
- E helu i ka uku (k): E hoʻohana i ke ʻano: k = (F2 - F1) / (L2 - L1).
ʻo kahi laʻana, inā hōʻike kahi pūnāwai i kahi haʻahaʻa o 20 lbs ma 4 iniha a 30 lbs ma 6 iniha:
- Hoʻololi i ka ikaika = 30 lbs - 20 paona = 10 lbs
- Hoʻololi i ka lōʻihi = 6 iniha - 4 iniha = 2 iniha
- Kāleka kōkuhi (k) = 10 lbs / 2 iniha = 5 lbs/inihi
| ʻanuʻu | Hana | Laʻana Waiwai |
|---|---|---|
| 1. Heluhelu Ekahi | Puhi Hoʻopaʻa (F1) ma Length (L1). | 20 lbs ma 4 iniha. |
| 2. Heluhelu Elua | Puhi Hoʻopaʻa (F2) ma Length (L2). | 30 lbs ma 6 iniha. |
| 3. Heluhelu | (F2 - F1) / (L2 - L1) |
(30-20)/(6-4) = 5 lbs/in |
Hopena
You can calculate an extension spring's rate theoretically using its physical dimensions and material, a i ʻole ma ka hoʻāʻo ʻana. Pono nā ʻano ʻelua no ka hoʻolālā ʻana i ka puna a me ka hōʻoia.
[^1]: E aʻo i ka hopena o ke anawaena uea i ka ʻoʻoleʻa puna a me ka hana holoʻokoʻa.
[^ 2]: E ʻike i ke koʻikoʻi o ke anawaena coil mean i ka hoʻoholo ʻana i nā ʻano puna a me ka hana.
[^ 3]: He mea koʻikoʻi ka hoʻomaopopo ʻana i ke ʻano o ka punawai no ka hoʻolālā ʻana i nā pūnāwai kūpono e kū pono ana i nā koi pono hana.
[^4]: Loaʻa nā ʻike i ka Modulus of Rigidity a me kāna kuleana i ke koho ʻana i nā mea no nā puna.
[^5]: He mea nui ka hoʻomaopopo ʻana i nā coils ʻeleu no ka helu pololei ʻana a me ka hoʻolālā punawai kūpono.