Expanded self-excited overrunning spring clutch structure simple 11 drive shaft 21 key 31 active housing 41 spring 51 seal ring 61 passive housing 71 passive shaft to establish constraints (1) strength reliability constraints by the literature <1>, spring wire The mathematical expectation of the compressive stress Ls=4(D/d)-14(D/d)-432T(e2PNf-1)Pd3+8TPd2D(2) The torque transmitted by the T-clutch; f spring and two-shell The coefficient of friction between.

In order to calculate the reliability of the spring, firstly, the mathematical expectation of the bearing capacity of the Lc spring wire in the reliability coefficient ZR=Lc-nLsR2c+R2s(3) is required; the load-carrying capacity of the Rc spring wire is squared; the compressive stress of the Rs spring wire is Variance; n-intensity reserve coefficient, generally take n=1111125.

From the literature <2>, Rc=CkLc; Rs=SkLs, Ck and Sk are the coefficient of variation of material and stress respectively. For carbon spring, Ck=0114, Sk=0108. Equation (3) is the coupling equation. The equation, which is then constrained by reliability, can be linked to the optimized design, thereby constituting a reliability-optimized design calculation.

Substituting the relationship between equation (2) and Rc, Rs and coefficient of variation into equation (3), the spring reliability coefficient ZR=2(4) According to the literature <2>, the reliability RZ= can be obtained from ZR according to the following formula. 12PQ>-ZRe-t2dt(5) Obviously, the spring has a strength reliability greater than the allowable strength reliability. Substituting equation (4) into equation (5), and substituting d, D, and N with corresponding design variables x1, x2, and x3, and obtaining the strength reliability constraint condition is g1(x)=12 (6) The integral in equation (6) is a generalized integral. It is very difficult to calculate by hand. It can be calculated by computer using the parabola method <3> in the numerical integration of Simpson, and it is convenient for the dynamic observation of the optimization process.

(2) Structural parameters constraint conditions Structural parameters d, D, N are determined according to structural requirements and design experience: an extended self-excited overrunning spring clutch, transmitting torque T = 452 Nmm, requiring spring reliability RZ not less than 99%, test Determine the optimal structural parameters for the clutch.

Solution: spring material selected carbon spring steel wire, specific gravity C=010078g/mm3, take Lc=538N/mm2, strength reserve coefficient n=1125, coefficient of variation of spring material Ck=0114, stress coefficient of variation Sk=0108; clutch The two shell materials are 45 steel, the friction coefficient between the spring and the two shells f=011; the lower and upper limits of the main structural parameters d, D, N are dmin=012mm, dmax=1mm; Dmin=10mm, Dmax= 30mm; Nmin=5, Nmax=10, the above parameters and conditions are substituted into equations (1), (6) and (10) (15), and then loaded into the random optimization program together with the numerical integration program <3> <4>, the results obtained after the operation are rounded to obtain d=018mm, D=25mm, N=6, RZ=01999.

Conclusion This article provides an effective design method for this new type of clutch, which is convenient for popularization and application.