How Do You Calculate an Extension Spring's Rate?
You've chosen a spring, but it's too stiff or too weak. Ko tenei keemu matapae ka arahi ki te ngoikore o te mahi, rahunga hua, me nga hoahoa hou utu nui, te aukati i to kaupapa i a koe e rapu ana i tetahi otinga.
The spring rate is calculated using a formula that considers the material's shear modulus (G), diameter waea[^ 1] (pāt), tikanga diameter porohita[^ 2] (D), me te maha o nga koti kaha (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. Ka hoahoa tetahi miihini i tetahi huihuinga katoa ka ngana ki te kimi i tetahi puna rakau e pai ana, engari ka kitea kaore he reiti tika. I LINSPRING, timata tonu tatou ki te kaha e hiahiatia ana. Ma te tatau i nga mea e tika ana reiti puna[^ 3] tuatahi, ka taea e tatou te hoahoa i tetahi puna e tuku ana i nga mahi tika e hiahiatia ana, te whakaora i te wa o taatau kaihoko, moni, me te nui o te pouri. Let's look at how this calculation is done.
He aha te tauira matua mo te tatau i te reiti o te puna?
Ka kite koe i te reiti puna[^ 3] tātai, me te ahua whakamataku. You're worried that if you misinterpret just one of the variables, ka he to tatauranga katoa, ka arahi ki nga tauira kua moumou.
Ko te tātai tuatahi: *k = (G d⁴) / (8 D³ Na)**. He uaua pea te ahua, but it's just a combination of the spring's material (G), tona waea (pāt), tona āhuahanga (D), me te maha o nga porotaka (Na).
He maha nga wa ka korero ahau ki nga miihini hou o taku roopu kia kaua e mataku ki tenei tikanga. Whakaarohia he tohutaka. Ko nga kai ko to rauemi, waea, me te rahi o nga porohita. Ko te tauira ko te huinga o nga tohutohu e whakaatu ana ki a koe me pehea e whakakotahi ai aua kai ki te whakaputa i te "reka," which is your spring's stiffness. The most important thing I've learned is how powerful the diameter waea[^ 1] (pāt) ko. Because it's raised to the fourth power, ahakoa he iti noa te whakarereketanga o te rahi waea ka whai paanga nui ki te reiti o te puna whakamutunga. It's the most critical ingredient in the entire recipe.
Te Maramatanga ki ia Taurangi o te Tātai
Ko ia wahanga o te tauira e whakaatu ana i tetahi ahuatanga tinana motuhake o te puna. He mea nui kia tika te whiwhinga o ia mea. Ko nga mea e rua e whai mana nui ana ko te diameter waea me te diameter o te porowhita toharite.
- Modulus of Rigidity (G): He taonga tenei o te rawa ake, e tohu ana i tana atete ki te hurihuri. Mo te maitai, it's around 11.5 miriona psi.
- Diameter waea (pāt): Te matotoru o te waea puna. Ko tenei te tino paanga ki te reiti.
- Mean Coil Diameter (D): Ko te diameter toharite o nga coils, ka tatauhia ko te Diamita o waho me te iti o te Waea Waea.
- Ngaiti Hohe (Na): Te maha o nga porotaka kei roto i te tinana o te puna e waatea ana ki te totoro.
| Taurangi | Ingoa | Whakaahuatanga |
|---|---|---|
| k | Te Raru o te Ra | The spring's stiffness, ine i te kaha mo ia waeine roa (E.g., lb/in). |
| G | Modulus of Rigidity[^4] | He taonga toi mo te koranu. |
| pāt | Diameter waea | Te diameter o te waea i whakamahia hei hanga i te puna. |
| D | Mean Coil Diameter | Ko te diameter toharite mai i te pokapū o te waea i tetahi taha ki tetahi taha. |
| Na | Ngaiti Hohe | Te maha o nga coils e penapena me te tuku i te kaha. |
Me Pewhea Te Tautuhi Tika i te Tau o nga Coils Hohe?
I tatauhia e koe te tapeke o nga coils mai i te pito ki te pito. Engari ka whakamahi koe i taua tau i roto i te tauira, to tatau reiti puna[^ 3] doesn't match the test data.
He hapa noa tenei. Te maha o nga coils hohe (Na) kei roto anake nga porowhita i te tinana matua o te puna. The end hooks or loops are not considered active because they do not contribute to the spring's deflection.
I tetahi wa i mahi tahi ahau me tetahi kaihoko e hoahoa ana i tetahi puna mo te here kuri ka taea te tango. I mahia e ratou a ratou ake tatauranga, ka tukuna he tuhi ki a matou. He nui te reiti o te puna i tohua e ratou, he iti ake i ta te tauira i tohu mo to raatau hoahoa. I karanga ahau ki a ratou, a ka haere tahi maua i roto i te tatauranga. Ko te ahua kua whakauruhia e ratou nga porotaka i hanga nga matau mutunga ki roto i o raatau "ngongo hohe[^5]" tatau. Kei reira nga matau hei whakawhiti i te kawenga, kaua e totoro. Kia whakatikahia taua nama kotahi, i tino rite a matou tatauranga. Na ka taea e matou te whakatika i te hoahoa kia pai ai te maeneene, kume ngawari i hiahia ratou mo te here.
Roopu Tinana vs. Koropiko Whakamutunga
Ko te wehewehenga i waenga i nga coils hohe me te hohekore i runga i ta raatau mahi. Ko nga porowhita e waatea ana ki te whiri i raro i te kawenga ka kiia he kaha.
- Nga Roopu Tinana: Ko nga piira tuatahi enei e hanga ana i te roa o te puna. Ka toia e koe te puna, ka wetewete noa enei porotaka, ko te aha te hanga i te toronga. No reira, he kaha ratou katoa.
- Whakamutua Matau/Loops: He mea hanga mai i te porowhita whakamutunga, e rua ranei i ia pito. Ko ta ratou mahi he whakapiri i te puna ki to hui. They transfer force but are not designed to flex or contribute to the spring's travel. Ka kiia ratou "kua mate" i roto raneingongo hohe[^5]. Na, mo te puna toronga paerewa, Na = te maha o nga porowhita o te tinana.
| Wae Puna | Mahi | Hohe? |
|---|---|---|
| Nga Roopu Tinana | Rokiroki me te tuku pūngao mā te whakahuri. | Āe |
| Whakamutua Matau/Loops | Whakawhiti te kawenga ki te huihuinga. | Kao |
Me pehea koe e tatau ai i te reiti mai i te puna tinana?
He puna koe, but you don't know its specifications. Me rapu e koe tona reiti me te kore e whai i nga tuhi hoahoa me te mohio ki nga rauemi, making it impossible to use the formula.
You can determine the rate experimentally with a simple two-point test. Measure the force required to stretch the spring to two different lengths. Ko te reiti puna[^ 3] is the change in force divided by the change in length.
This is something we do in our quality lab every day. It's the most practical and reliable way to verify a spring's rate. I had a customer who was trying to replace a broken spring in a piece of old farm equipment. The original manufacturer was out of business, and there were no drawings. He sent us the broken spring. We couldn't use the design formula because we weren't 100% sure of the material. Engari, we put it on our load tester. We measured the load at one inch of travel and at two inches of travel. By subtracting the forces and lengths, i tatauhia e matou te tere o te puna. Mai i reira, ka taea e taatau te hanga he whakakapinga tino pai.
Te Tikanga Whakamātautau-rua
He ngawari noa tenei tikanga, me nga taputapu inenga taketake anake.
- Ine ine 1: Totoro te puna ki te roa e mohiotia ana (L1) me te tuhi i te kaha (F1).
- Ine ine 2: Totoro atu te puna ki te tuarua e mohiotia ana te roa (L2) me te tuhi i te kaha (F2).
- Tātaihia te Reiti (k): Whakamahia te tātai: k = (F2 - F1) / (L2 - L1).
Hei tauira, ki te whakaatu tetahi puna i te pikaunga o 20 lbs kei 4 inihi me 30 lbs kei 6 inihi:
- Hurihia te Kaha = 30 lbs - 20 lbs = 10 lbs
- Hurihia te Roa = 6 inihi - 4 inihi = 2 inihi
- Te Raru o te Ra (k) = 10 lbs / 2 inihi = 5 lbs/inihi
| Hipanga | Mahi | Tauira Uara |
|---|---|---|
| 1. Panui Tuatahi | Record Force (F1) i te Roa (L1). | 20 lbs kei 4 inihi. |
| 2. Panui Tuarua | Record Force (F2) i te Roa (L2). | 30 lbs kei 6 inihi. |
| 3. Tātaitanga | (F2 - F1) / (L2 - L1) |
(30-20)/(6-4) = 5 lbs/in |
Whakamutunga
You can calculate an extension spring's rate theoretically using its physical dimensions and material, ma te whakamatautau ranei. Ko nga tikanga e rua he mea nui mo te hoahoa puna tika me te manatoko.
[^ 1]: Akohia pehea te awe o te diameter waea i te pakari o te puna me te mahi katoa.
[^ 2]: Tirohia te hiranga o te diameter porowhita toharite hei whakatau i nga ahuatanga o te puna me te mahi.
[^ 3]: Ko te mohio ki te tauira reiti puna he mea nui mo te hoahoa i nga puna whai hua e tutuki ana i nga whakaritenga mahi.
[^4]: Tikina he mohiotanga mo te Modulus of Rigidity me tana mahi ki te whiriwhiri rauemi mo nga puna.
[^5]: He mea nui te mohio ki nga coils hohe mo nga tatauranga tika me te hoahoa puna whai hua.