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本文将圆盘式振动上料器简化为一个单自度系统,根据拉格兰日方程可求得广义坐标为q的自由振动的运动方程式,即m(ρ~2+R_n~2tg~2ψ)q+k_2R_n~2+g~2ψq=0 m(1+ρ~2/R_n~2tg~2ψ)q+k_zq=0其中:q——广义坐标; ρ——惯性半径; R_n——弹簧分布圆半径; ψ——弹簧侧斜角。对于往复振动,其振动运动方程式为: 对于扭转振动,其振动运动方程式为: 其中:等效质量m_(eq)=m(1+ρ~2/R_n~2tan~2ψ)=m+j/R_n~2tan~2ψ; 等效惯性矩j_(eq)=m(1+ρ~2/R_n~2tan~2ψ)=m+j/R_n~2tan~2ψ; 等效弹性系数k_(eq)=k_z=k_ψ。板簧的等效刚度及其最佳长度为: 其中: 圆杆弹簧的等效刚度及其最佳长度为: 其中:ε=R_n/L=0.65～0.75;η=b/h =6～8; Z_(max)——最大单振幅,一般Z_(max)=0.05～0.1cm;f——激振频率; E——弹性模数,钢的E=2×10~6(kgf/cm~2); [σ_(-1)]——许用应力,一般[σ_(-1)]=2 ×10~3(kgf/cm~2);根据建立的精确数学模型,用计算机进行辅助设计,发挥人和机的优点,从而优化结构参数。
In this paper, the disk-type vibrating feeder is simplified as a single-degree-of-freedom system. According to Lagrange’s equation, the free-vibration equation of motion with generalized coordinate q can be obtained, ie m (ρ ~ 2 + R_n ~ 2tg ~ 2ψ) q + k_2R_n ~ 2 + g ~ 2ψq = 0m (1 + ρ ~ 2 / R_n ~ 2tg ~ 2ψ) q + k_zq = 0 where: q - generalized coordinates; ρ - inertia radius; R_n - spring distribution circle Radius; ψ - spring side bevel. For the reciprocating vibration, the vibration equation of motion is: For the torsional vibration, the vibration equation of motion is: where: equivalent mass m eq = m 1 + ρ ~ 2 / R_n ~ 2 tan ~ 2ψ = m + j / R_n ~ 2tan ~ 2ψ; equivalent moment of inertia j_eq = m 1 + ρ ~ 2 / R_n ~ 2tan ~ 2ψ = m + j / R_n ~ 2tan ~ 2ψ; equivalent elastic coefficient k_eq = k_z = k_ψ. The equivalent stiffness of the leaf spring and its optimal length are: Where: The equivalent stiffness of round rod spring and its optimal length are: where: ε = R_n / L = 0.65-0.75; η = b / h = ; Z - (max) - the largest single amplitude, the general Z max (max) = 0.05 ~ 0.1cm; f - excitation frequency; E - modulus of elasticity, E = 2 × 10-6 steel (kgf / 2]; [σ _ (- 1)] - allowable stress, generally [σ _ (-1)] = 2 × 10 ~ 3 (kgf / cm ~ 2); according to the established accurate mathematical model, , Play the advantages of people and machines, thereby optimizing the structural parameters.