5.2 Calculation example of cylindrical spiral torsion spring
Table 12-2-30
| Parameter | Unit | Corporate and data | |
| Original conditions | Minimum working torque T1 Maximum working torque Tn Working torsion angle φ Spring category End structure Free angle |
N.mm N.mm (°)(°) |
2000 6000 40 N<103 Outer arm torsion 120 |
| Parameter calculation | Selection of materials and allowable bending stress σBp | MPa | According to the design requirements, it is a Sichuan type elastic material. The carbon yellow tensile steel wire of Grade C is selected, and the preliminary assumption is that the diameter of the steel wire is d=4~5.5mm. According to Table 12-2-3, it is found that σb=1520~1470Mpa ,take σb=1500Mpa
According to table 12-2-6,the Allowable bending stress σBp=0.8σb=0.8*1500=1200 |
| Primary winding ratio C | To make the structure compact, temporarily C=6 | ||
| Curvature coefficient K1 | K1=(4C-1)/(4C-4)=(4*6-1)/(4*6-4)=1.15 | ||
| Diameter of steel wire d | mm | d=³√ 32TnK1/πσBp=³√ 32*6000*1.15/3.14*1200=3.88
take d=4,according to table 12-2-3,d=4,Class C,take σb=1520Mpa,Greater than the original tentative value, so it is safe |
|
| Spring pitch diameter D and winding ratio C | mm | D=C*d=6*4=24
take D=25, so C=D/d=35/4=6.25 |
|
| Spring coils | coil | n=Ed4φ/3667D(Tn-T1)=206*103*44*40/3667*25*(6000-2000)=5.75, take n=6 | |
| Stiffness T’ | N.mm/(°) | T’=Ed4φ/3667Dn=206*103*44/3667*25*6=95.87 | |
| Torsion angle at maximum working torque φn | (°) | φn=Tn/T’=6000/95.87=62.58 | |
| Torsion angle at minimum operating torque φ1
Actual minimum operating torque T1 Working ultimate bending stress σj |
(°)
N.mm/(°) MPa |
φ1=φn-φ=62.58-40=22.58
T1=T’φ1=95.87*22.58=2164.7 σj=0.8*σb=0.8*1520=1216 |
|
| Working limit torque Tj | N.mm | Tj=πd3σj/32K1=3.14*43*1216/32*1.15=6640.4 | |
| Working limit torsion angle φj | (°) | φj=Tj/T’=6640.4/95.87=69.26 | |
| Torsion Spring Pitch t | mm | t=d+ δ,δ=0.5 without special request,t=4+0.5=4.5 | |
