How Do You Calculate an Extension Spring's Rate?
You've chosen a spring, but it's too stiff or too weak. Qhov kev twv twv ua si no ua rau kev ua haujlwm tsis zoo, cov khoom ua tsis tiav, thiab raug nqi kho dua tshiab, nres koj qhov project thaum koj nrhiav kev daws teeb meem.
The spring rate is calculated using a formula that considers the material's shear modulus (G), txoj kab uas hla[^ 1] (d), txhais tau tias coil diameter[^2] (D), thiab tus naj npawb ntawm active coils (Twb). These physical properties directly determine the spring's stiffness.
I've seen countless projects get delayed simply because the spring rate was an afterthought. Ib tug engineer yuav tsim ib qho kev sib dhos tag nrho thiab tom qab ntawd sim nrhiav lub caij nplooj ntoos hlav uas haum, tsuas yog nrhiav tsis tau tus nqi zoo. Ntawm LINSPRING, peb ib txwm pib nrog lub zog xav tau. Los ntawm kev xam qhov tsim nyog Tus nqi caij nplooj ntoos hlav[^3] ua ntej, peb tuaj yeem tsim lub caij nplooj ntoos hlav uas xa cov kev ua tau zoo uas xav tau, txuag peb cov neeg siv khoom lub sijhawm, nyiaj, thiab ntxhov siab heev. Let's look at how this calculation is done.
Yuav ua li cas yog lub ntsiab Formula rau xam Spring Rate?
Koj pom cov Tus nqi caij nplooj ntoos hlav[^3] qauv, thiab nws zoo li ntshai. You're worried that if you misinterpret just one of the variables, koj qhov kev suav tag nrho yuav tsis raug, ua rau khib nyiab prototypes.
Cov qauv tseem ceeb yog: *k = ib (G d ⁴) / (8 D³ Twb)**. Tej zaum nws yuav zoo li nyuaj, but it's just a combination of the spring's material (G), nws kab (d), nws geometry (D), thiab nws cov coils (Twb).
Kuv feem ntau qhia cov engineers tshiab ntawm kuv pab neeg kom tsis txhob ntshai los ntawm cov qauv no. Xav txog nws zoo li daim ntawv qhia. Cov khoom xyaw yog koj cov khoom, hlau, thiab coil dimensions. Cov mis yog cov txheej txheem qhia uas qhia koj tias cov khoom xyaw yuav muab sib xyaw ua ke los tsim qhov kawg "flavor," which is your spring's stiffness. The most important thing I've learned is how powerful the txoj kab uas hla[^ 1] (d) yog. Because it's raised to the fourth power, txawm tias me me hloov ntawm cov hlau loj yuav muaj kev cuam tshuam loj heev rau lub caij nplooj ntoos hlav zaum kawg. It's the most critical ingredient in the entire recipe.
Nkag siab txhua qhov sib txawv hauv cov qauv
Txhua feem ntawm cov qauv qhia txog qhov txawv ntawm lub cev ntawm lub caij nplooj ntoos hlav. Tau txais txhua txoj cai yog qhov tseem ceeb rau kev ua tau zoo. Qhov thib ob qhov tseem ceeb tshaj plaws yog cov hlau txoj kab uas hla thiab qhov nruab nrab coil txoj kab uas hla.
- Modulus ntawm Rigidity (G): Qhov no yog ib yam khoom ntawm cov khoom nws tus kheej, sawv cev nws tsis kam mus twisting. Rau hlau, it's around 11.5 lab psi.
- Hlau Dia (d): Lub thickness ntawm lub caij nplooj ntoos hlav hlau. Qhov no muaj qhov cuam tshuam loj tshaj plaws ntawm tus nqi.
- Mean Coil Diameter (D): Qhov nruab nrab txoj kab uas hla ntawm cov coils, xam raws li Outer Diameter rho tawm ib Wire Diameter.
- Active Coils (Twb): Tus naj npawb ntawm cov coils nyob rau hauv lub cev ntawm lub caij nplooj ntoos hlav uas pub dawb rau ncab.
| Hloov pauv | Lub npe | Kev piav qhia |
|---|---|---|
| k | Caij nplooj ntoos hlav Rate | The spring's stiffness, ntsuas nyob rau hauv quab yuam ib unit ntawm qhov ntev (E.G., lb/ib). |
| G | Modulus ntawm Rigidity[^4] | Cov khoom vaj khoom tsev uas yog tas mus li rau ib tug muab alloy. |
| d | Hlau Dia | Txoj kab uas hla ntawm cov hlau siv los ua lub caij nplooj ntoos hlav. |
| D | Mean Coil Diameter | Qhov nruab nrab txoj kab uas hla ntawm qhov nruab nrab ntawm cov xaim ntawm ib sab mus rau lwm qhov. |
| Twb | Active Coils | Tus naj npawb ntawm cov coils uas khaws thiab tso tawm lub zog. |
Yuav ua li cas thiaj txiav txim siab tus naj npawb ntawm Active Coils?
Koj suav tag nrho cov coils ntawm qhov kawg mus rau qhov kawg. Tab sis thaum koj siv tus lej ntawd hauv cov qauv, koj xam Tus nqi caij nplooj ntoos hlav[^3] doesn't match the test data.
Qhov no yog ib qho yuam kev. Tus naj npawb ntawm active coils (Twb) tsuas yog suav nrog cov coils hauv lub cev tseem ceeb ntawm lub caij nplooj ntoos hlav. The end hooks or loops are not considered active because they do not contribute to the spring's deflection.
Ib zaug kuv tau ua haujlwm nrog ib tus neeg siv khoom uas tab tom tsim lub caij nplooj ntoo hlav rau cov dev rov qab. Lawv tau ua lawv tus kheej suav thiab xa peb daim duab. Lub caij nplooj ntoos hlav tus nqi lawv teev yog ntau, ntau qis dua li cov qauv kwv yees rau lawv cov qauv tsim. kuv hu lawv, thiab peb tau taug kev los ntawm kev suav ua ke. Nws muab tawm tias lawv tau suav nrog cov coils uas tsim qhov kawg hooks hauv lawv "active coils[^ 5]" suav. Cov hooks nyob ntawd los hloov lub load, tsis txhob ncab. Thaum peb kho tus lej ntawd, peb cov kev suav ua tau zoo kawg nkaus. Tom qab ntawd peb tuaj yeem kho tus qauv tsim kom muab lawv tus du, gentle pull they wanted for the leash.
Body Coils vs. End Loops
The distinction between active and inactive coils is based on their function. Only the coils that are free to twist under load are considered active.
- Body Coils: These are the primary coils that form the length of the spring. When you pull on the spring, these coils un-twist slightly, which is what creates the extension. Therefore, they are all active.
- End Hooks/Loops: These are formed from the last coil or two on each end. Their job is to attach the spring to your assembly. They transfer force but are not designed to flex or contribute to the spring's travel. They are considered "dead" or inactive coils[^ 5]. Yog li, for a standard extension spring, Na = the number of coils in the body.
| Spring Component | Rooj mov | Active? |
|---|---|---|
| Body Coils | Store and release energy by deflecting. | Yog lawm |
| End Hooks/Loops | Transfer load to the assembly. | Tsis muaj |
Yuav ua li cas koj xam tus nqi los ntawm lub cev lub caij nplooj ntoos hlav?
Koj muaj caij nplooj ntoos hlav, but you don't know its specifications. Koj yuav tsum nrhiav nws tus nqi yam tsis muaj kev tsim cov duab kos lossis paub txog cov khoom siv, making it impossible to use the formula.
Koj tuaj yeem txiav txim siab tus nqi sim nrog kev sim ob-point yooj yim. Ntsuas lub zog uas yuav tsum tau ncab lub caij nplooj ntoos hlav mus rau ob qhov ntev sib txawv. Tus Tus nqi caij nplooj ntoos hlav[^3] yog qhov kev hloov ntawm kev quab yuam muab faib los ntawm kev hloov ntawm qhov ntev.
Nov yog qee yam peb ua hauv peb lub chaw kuaj mob zoo txhua hnub. It's the most practical and reliable way to verify a spring's rate. Kuv muaj ib tus neeg siv khoom uas tab tom sim hloov lub caij nplooj ntoo hlav tawg hauv ib daim ntawm cov cuab yeej ua liaj ua teb qub. 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% paub meej ntawm cov khoom. Instead, peb muab tso rau hauv peb lub load tester. Peb ntsuas lub load ntawm ib nti ntawm kev mus los thiab ntawm ob nti ntawm kev mus ncig. Los ntawm rho tawm lub zog thiab qhov ntev, peb suav tus nqi caij nplooj ntoos hlav. From there, peb tuaj yeem tsim qhov hloov pauv zoo meej.
Ob-Point Test Method
Txoj kev no yog ncaj nraim thiab tsuas yog siv cov cuab yeej ntsuas yooj yim xwb.
- Ntsuas Point 1: Stretch lub caij nplooj ntoos hlav kom paub qhov ntev (L1) thiab sau lub zog (F1).
- Ntsuas Point 2: Stretch lub caij nplooj ntoos hlav ntxiv mus rau ib tug thib ob paub ntev ntev (L2) thiab sau lub zog (F2).
- Xam tus nqi (k): Siv cov qauv: k = ib (F2 - F1) / (L2 - L1).
Piv txwv li, yog hais tias lub caij nplooj ntoos hlav qhia ib tug load 20 lbs pe 4 ntiv tes thiab 30 lbs pe 6 ntiv tes:
- Hloov hauv Force = 30 lbs - 20 lbs = 10 lbs
- Hloov hauv Length = 6 ntiv tes - 4 ntiv = 2 ntiv tes
- Caij nplooj ntoos hlav Rate (k) = 10 lbs / 2 ntiv = 5 lbs/inch
| Kauj ruam | Kev ua | Piv txwv tus nqi |
|---|---|---|
| 1. Thawj Kev Nyeem Ntawv | Cov ntaub ntawv Force (F1) ntawm Length (L1). | 20 lbs pe 4 ntiv tes. |
| 2. Kev nyeem thib ob | Cov ntaub ntawv Force (F2) ntawm Length (L2). | 30 lbs pe 6 ntiv tes. |
| 3. Calculation | (F2 - F1) / (L2 - L1) |
(30-20)/(6-4) = 5 lbs/in |
Tag
You can calculate an extension spring's rate theoretically using its physical dimensions and material, los yog xyaum los ntawm kev sim nws. Ob txoj hauv kev yog qhov tseem ceeb rau kev tsim lub caij nplooj ntoos hlav raug thiab pov thawj.
[^ 1]: Kawm paub yuav ua li cas hlau txoj kab uas hla ho cuam tshuam lub caij nplooj ntoos hlav txhav thiab tag nrho functionality.
[^2]: Tshawb nrhiav qhov tseem ceeb ntawm txoj kab uas hla txoj kab uas hla hauv kev txiav txim siab lub caij nplooj ntoos hlav yam ntxwv thiab kev ua tau zoo.
[^3]: Kev nkag siab txog tus nqi caij nplooj ntoos hlav yog qhov tseem ceeb rau kev tsim cov springs zoo uas ua tau raws li cov kev xav tau tshwj xeeb.
[^4]: Tau txais kev nkag siab txog Modulus ntawm Rigidity thiab nws lub luag haujlwm hauv kev xaiv cov khoom siv rau cov springs.
[^ 5]: Nkag siab txog cov coils nquag yog qhov tseem ceeb rau kev suav kom raug thiab tsim lub caij nplooj ntoos hlav zoo.