Ratio breakdown Tb/Tf 3。2

Slip sb 0。315

Motor constant a 1。711

Motor constant b 1。316

3。1。 Gear reducer powered by an electric motor

Specifications of used induction motor are shown in Table 4。 The transmission is loaded by the pump (Eq。 (14)) having an inertia  moment J22 ¼ 0。0045 Kg  m2。

Using the Euler algorithm for the resolution of Eq。 (15), the rotational speed evolution of induction motor versus time is shown in Fig。 2。 It clearly shows two distinct regimes。 The first one (A) is the transient regime characterized by an increasing rotational speed and the second one is the steady state regime (B) for which the motor reaches its nominal

rotational speed on。 The duration of the transient regime is TL ¼ 0。25 s。

Fig。 3。 shows the evolution of driving and load torques for the studied system。

As a consequence of the variability of speed, one can expect a variability of the mesh period given by Eq。 (2)。

Fig。 4 shows the evolution of the mesh stiffness during the transient regime。 It is shaped (modeled) as a non-periodic function with a decreasing period following the increase in speed。

Fig。 5 shows the dynamic response registered on the pinion bearing。 Two different behaviors are recovered [20]

– Stage A[0 TL] during which the displacement is variable and non-periodic with high vibration amplitudes。 The variation of the motor torque and the mesh stiffness at starting time are described in this area (Fig。  5-1)。

– Stage B[TL Tf] during which the displacement becomes periodic with period Tg。 In this area the motor rotates at its constant nominal frequency and the meshing stiffness becomes periodic with a constant period by consequence。 The response shows periodic behavior with regular vibration level。

Fig。 5-2 shows the frequency spectrum of the linear displacement of the pinion shaft。 The spectrum shows the presence of the meshing frequency fg ¼ 480 Hz and its harmonics n ~ fg surrounded by side-bands。 It shows also the eigenfrequencies f2  and f5  of the system。 The presence of side-bands is induced by the transient regime behavior。

During the steady state regime the displacement is periodic as shown in Fig。 5-3, the mesh frequency and its harmonics dominate the spectrum (Fig。 5-4)。

文章研究了一个单级直齿圆柱齿轮减速器在瞬态中的动态特性，并得 到了该单级直齿圆柱齿轮在不同的转速下的动态响应。

首先，作用于齿轮上的激励除了电机转矩和动态负载，还包括输入转速的变 化引起的啮合刚度的波动。然后，使用 Newmark 算法计算其动态响应。在这之 后，开始对直齿圆柱齿轮中的一个参数进行研究，第一次用电机驱动，第二次用 四缸四冲程柴油机驱动。动态响应的结果证明了齿轮组的瞬态特性对其动态行为 会产生显著的影响，尤其是在发动机非周期运转条件下。

1。 引言 齿轮减速器一般是用来提供从旋转动力源到机械设备之间转速和扭矩变化

的连接，对齿轮组来说有内部和外部的两种激励源。内部激励源是由随时间变化 的啮合刚度产生的。因为起初观察到了噪声和振动，所以许多学者认为这种波动 是系统激励的主要来源。为了研究在它在响应中存在的缺陷，Bartelmus 和 Chaari 等人在一个直齿轮系统的动态模型中引入了这个随时间变化的啮合刚度。在响应 谱中增加频率成分，可以观察到幅度的调制。Bartelmus 和 Walha 等人研究了一 个两级变速箱中的侧隙对其动态响应的影响，他总结出齿的分离发生在瞬态响应 中振动能级增加的时候。