【導讀】用于建筑、水利工程、林業(yè)、礦山、碼頭等的物料升降或平拖。降或平拖，還可作現(xiàn)代化電控自動作業(yè)線的配套設備。其中高于20噸的為大噸位絞車,絞車可以單獨使用，也可作為起重、筑。路和礦井提升等機械中的組成部件，因操作簡單、繞繩量大、移置方便而廣泛應用。絞車主要技術指標有額定負載、支持負載、繩速、容繩量等。絞車按照動力分為手動、電動、液壓三類。按照卷筒分布形式有分為并列雙卷筒和。電動絞車廣泛用于工作繁重和所需牽引力較大的場所。經(jīng)減速機帶動卷筒，電動機與減速器輸入軸之間裝有制動器。一般額定載荷低于10T的絞車。1）了解電動絞車的結構、特點以及工作原理。有合理的強度與剛度，使用可靠，具有很好的經(jīng)濟性，重量輕，制造維修方便。2)確定油壓機的總體方案設計。初步了解電動絞車的發(fā)展及應用。6）用CAD軟件畫出電動絞車的全部設計圖和零件圖。

　　

【正文】 ual inductance between the phase windings. _pma, _pmb and _pmc are the fluxlinkages of the phases due to the permanent mag, and can be assumed to be sinusoid functions of rotor position _ as follow λ pma = λ 1 sin(Nθ ), λ pmb = λ 1 sin(Nθ ? 2 /3), λ pmc = λ 1 sin(Nθ 2 /3), where N is number of rotor teeth. The nonlinearity emphasized in this paper is represented by the above equations, that is, the fluxlinkages are nonlinear functions of the rotor position. By using the q。 d transformation, the frame of reference is changed from the fixed phase axes to the axes moving with the rotor (refer to Figure 2). Transformation matrix from the a。 b。 c frame to the q。 d frame is given by [8] For example, voltages in the q。 d reference are given by In the a。 b。 c reference, only two variables are independent (ia C ib C ic D 0)。 therefore, the above transformation from three variables to two variables is allowable. Applying the above transformation to the voltage equations (1), the transferred voltage equation in the q。 d frame can be obtained as vq = Riq + L1*diq/dt + NL1idω + Nλ 1ω , vd=Rid + L1*did/dt ? NL1iqω , (5) Figure 2. a, b, c and d, q reference frame. where L1 D L CM, and ! is the speed of the can be shown that the motor’s torque has the following form [2] T = 3/2Nλ 1iq The equation of motion of the rotor is written as J*dω /dt = 3/2*Nλ 1iq ? Bfω – Tl , where Bf is the coefficient of viscous friction, and Tl represents load torque, which is assumed to be a constant in this paper. In order to constitute the plete state equation of the motor, we need another state variable that represents the position of the rotor. For this purpose the so called load angle _ [8] is usually used, which satisfies the following equation Dδ /dt = ω ?ω 0 , where !0 is steadystate speed of the motor. Equations (5), (7), and (8) constitute the statespace model of the motor, for which the input variables are the voltages vq and vd. As mentioned before, stepper motors are fed by an inverter, whose output voltages are not sinusoidal but instead are square waves. However, because the nonsinusoidal voltages do not change the oscillation feature and instability very much if pared to the sinusoidal case (as will be shown in Section 3, the oscillation is due to the nonlinearity of the motor), for the purposes of this paper we can assume the supply voltages are sinusoidal. Under this assumption, we can get vq and vd as follows vq = Vmcos(Nδ ) , vd = Vmsin(Nδ ) , where Vm is the maximum of the sine wave. With the above equation, we have changed the input voltages from a function of time to a function of state, and in this way we can represent the dynamics of the motor by a autonomous system, as shown below. This will simplify the mathematical analysis. From Equations (5), (7), and (8), the statespace model of the motor can be written in a matrix form as follows ? = F(X,u) = AX + Fn(X) + Bu , (10) where X D Tiq id ! _UT , u D T!1 TlUT is defined as the input, and !1 D N!0 is the supply frequency. The input matrix B is defined by The matrix A is the linear part of , and is given by , and is given by The input term u is independent of time, and therefore Equation (10) is autonomous. There are three parameters in 。u/, they are the supply frequency !1, the supply voltage magnitude Vm and the load torque Tl . These parameters govern the behaviour of the stepper motor. In practice, stepper motors are usually driven in such a way that the supply frequency !1 is changed by the mand pulse to control the motor’s speed, while the supply voltage is kept constant. Therefore, we shall investigate the effect of parameter !1. 3. Bifurcation and MidFrequency Oscillation By setting ! D !0, the equilibria of Equation (10) are given as and 39。 is its phase angle defined by φ = arctan(ω 1L1/R) . (16) Equations (12) and (13) indicate that multiple equilibria exist, which means that these equilibria can never be globally stable. One can see that there are two groups of equilibria as shown in Equations (12) and (13). The first group represented by Equation (12) corresponds to the real operating conditions of the motor. The second group represented by Equation (13) is always unstable and does not relate to the real operating conditions. In the following, we will concentrate on the equilibria represented by Equation (12).