英文文献及翻译
输送带的二维动态特性
3.1.1非线性梁架（构架）元
如果只有带的纵向变形是主要素，那么梁架元就可用于模型的皮带弹性反应。梁架元组成部分有如图2所示的两个结点， P和Q ，四个位移参数确定部分载体X：
xT = [up vp uq vq] (1)
对平面运动的梁架元有三个独立的刚体运动，因此（这公式）仍然是描述一个变形的参数。
图2 ：梁架元的精确位移
梁架元轴的长度变化， [ 7 ] ：
ε 1 = D1(x) = ∫1 o ds2 - ds2
o
d
ξ
(2) 2ds2o
DSO是限元未变形的长度，DS是限元变形的长度，ξ是沿着有限元轴的无量纲长度。
图3 ：张带的静态凹陷
虽然带呈弯曲状态，但梁架元并没有变形，这可能考虑到带小数值凹陷的静态影
响。静态带凹陷的比率是有定义的（见图3 ）：
K1 = δ/1 = q1/8T (3)
其中q是暴露在外面带和散装物料的重量在竖直方向上分布的荷载， 1是带轮间距，而T是带的张力。，带凹陷的纵向变形影响取决于[ 7 ] ：
εs = 8/3 K2s (4)
产生了非线性梁架元总的纵向变形。
3.1.2梁架元
图4 ：节点的精确位移和旋转的梁架元。
如果带的横向位移是主要因素，那么梁架元就可以用来模拟皮带。同样对于拥有六个位移参数的梁架元的平面运动来说，相当于三个独立的刚体运动。因此就剩下三个变形参数是：纵向变形参数ε 1 ，两个弯曲变形参数ε2和ε 3 。
图5 ：梁架元的弯曲变形的
梁架元弯曲变形的参数可以定义为梁架元的组成载体（见图4 ）：
xT = [up vp μp uq vq μq] (5)
和如图5的变形结构
e2p1pq
ε 2 = D2(x)
=
1o
(6)
ε 3 = D3(x) -eq21pq
= 1o
3.2绕过托辊及带轮的带运动
当绕过托辊或带轮的时候，带运动是受到约束的。为了说明（弄清楚）这些制约因素，影响制约因素（边界）的条件都必须添加到用来代模拟带的有限元中来。这可以通过使用多体动力学进行描述。多体机置动力学的经典描述，建立起由若干约束条件连接起来的刚体或刚性链接。在（变形）输送带的有限元描述里，带被分离成多个有限元，有限元之间的联系是可变形的。有限元是由节点连接的，因此分配了位移参数。要确定带的运动，排除了刚体模型的变形模式。如果一个带绕过托辊，，决定托辊上带的位置（如见图6）的带长度为ξ，被添加到组件矢量，如：式（6），因此产生了7个位移矢量参数。
图6 ：由托辊支撑的带
梁架元有两个独立的刚体运动，因此依然有五个变形参数存在。其中已经在3.1中给出了ε 1 , ε2和ε 3 ，确定了带的变形。剩下ε4和ε 5 ，确定带和托辊之间的相互作用，见图7 。
图7 ：两个约束条件的梁架元有限元。
这些变形参数可以假设成无限刚度的弹性。这意味着：
ε 4 = D4(x) = (rξ + u ξ)e2 - rid.e2 = 0
ε 5 = D5(x) = (r ξ + uξ)e1 - rid.e1 =
0 (7)
如果模拟的是ε 4 > 0的时候，那么带将脱离托辊，而描述带的有限元上的
约束条件也将去除。
3.3滚动阻力
为了使一种模型能应用于带式输送机有限元模型的滚动阻力，已经制定了一种计算滚动阻力的近似公式， [ 8 ] 。带运动中，暴露在带外面的总滚动阻力的组成部分，这三部分是耗能的主要部分，可以区分为包括：压痕滚动阻力，托辊的惯性（加速滚动阻力）和轴承滚动阻力（轴承阻力）。确定滚动阻力因素的参数包括直径和托辊的材料，以及各种带参数，如速度，宽度，材料，紧张状态，环境温度，带横向负荷，托辊间距和槽角。总滚动阻力的因素，可以表示成总滚动阻力和带垂直负荷之间的比例，定义为：
ft = fi + fa + fb (8)
Fi是压痕滚动阻力的系数，FA是加速阻力系数，而FB是轴承阻力系数。这些组成系数由下面的[9]确定：
Fi = CFznzh nhD-nD VbnvK-nk NTnT
Mred ?2u
fa =
Fzb ?t2
(9)
Mf
fb =
Fzbri
FZ是带垂直方向上分布的负载和散装物料的负载的总和， H是带的覆盖厚度，D 是托辊的直径，Vb是带速，KN是带负荷的名义百分之比，T是环境温度，Mred 是托辊的折算质量，B是带的宽度， U是带的纵向位移，MF是总的轴承阻力矩和RI是轴承内部半径。在计算滚动阻力中，皮带的动力性能及机械性能和皮带上覆盖的材料发挥着重要作用。这使得带的选择和带上覆盖材料，尽量减少由动力阻力引起的能源消耗。
3.4带驱动系统
在稳定性的带运动情况下，为了能够测定带式输送机驱动系统的旋转组件的影响，这个带式输送机的总模型必须是含有驱动系统模型。驱动系统的旋转元件，就像一个减速箱，参照了3.2节中所述的约束条件。带有减速比的减速箱，可以
用带两个位移参数的减速元件来代替， μp 和μq ，像一个刚体的（旋转）运动，因此就剩下一个变形参数：
εred = Dred(x) = iμp + μq = 0 (10)
要确定电式扭矩感应式电机，是否适应所谓的两轴式电动机。该相电压的矢量v 可从（11）获得：
v = Ri + ωsGi + L ?i/?t (11)
在（11）式中I 是相电流矢量，R 是模型的相电阻， c 是模型的相电感抗，L 是模型的相感系数而ωs 是电机转子的角速度。电磁转矩等于：
Tc = iTGi (12)
电机模型和驱动系统机械组件是由驱动系统的运动方程联系着的：
Ti = Iij ?2
?j + Cik
??k Kil? (13)
?t 2 ?t
其中T 是扭矩矢量，I 是模型的惯量，C 是模型的阻尼，K 是矩阵刚度和?是电机旋转轴的角速度。
模拟启动或停止程序控制反馈的程序可以添加到带式驱动系统模型中，用来控制驱动扭矩。
3.5运动方程
整个带式输送机模型的运动方程可以得出潜在功率的原则， [ 7 ] ：
fk - Mkl ?2x1 / ?t 2 = ζ1Dik (14)
其中F 是阻力矢量，M 是模型的质量而ζ是拉格朗日乘数的矢量，可能解释为双重压力矢量to 张力矢量ε 。为了解决带有X 这一组方程，方程一体化是必要的。但是一体化的结果，必须确保满足约束条件。如果(8)式中应变为零，那么必须纠正一体化结果，如见[ 7 ] 。可以使用模型的反馈选择，例如限制提升物质垂直方向上的运动。这种违逆动力学的问题可以用下面公式表示。鉴于带模型及其驱动系统的提升运动众所周知，根据系统自由度和它的比例（速度）可以
确定其他元件的运动。它超出了本文所讨论关于此项的所有细节范围。
3.6实例
为了在长距离带式输送机系统设计阶段能够正确设计，应用了有限元法。例如带强度的选择，可以减少的尽量减少，使用模型模拟的结果确定传送带的最大张力。以有限元模型的功能作为例子，应该考虑到在两个托辊位置范围之间稳定移动带的横向振动。在运输机的设计阶段这必须被确定，才得以确保空带的共振。
对于皮带输送机的设计来说，托辊和移动带间相互作用影响是很重要的。托辊的及带轮的几何不完善性，导致带脱离托辊和带轮能支撑的位置，在带和支撑带轮之间产生一种横向振动。这对带施加了一部分的交互轴向应力。如果这部分力是比皮带的预应力小，那么带将在它的固有频率中振动，否则带将被迫振动。皮带是会受迫振动的，例如受托辊的偏心率影响。在输送带返程中，这种振动特别值得注意。由于受迫振动的频率取决于带轮和托辊的角速度，因此对于带的速度，确定在带轮和托辊之间，带在自然频率状况下，横向振动中带速影响，这个是很重要的。如果受迫振动的频率接近于皮带横向振动的固有频率，将发生共振现象。
有限元模型的模拟结果可用于确定稳定移动的带的横向振动频率范围。该频率是利用快速傅立叶技术从时域范围到频域范围，带横向位移变换后得到的结果。除了使用有限元模型外也可以运用近似分析法。
皮带可以模拟成一个预应力梁。如果皮带的弯曲硬度可以被忽略，横向位移比托辊间距还小，Ks << 1 ，并且带增加的长度相对于横向位移的原始长度来说是微不足道，带的横向振动可近似为下列线性微分方程，如见图15 ：
?2
v = (c22 - C2
b) ?2
v
- 2Vb
?2v
(15)
?t 2?x
2
?x?
t
其中V是皮带的横向位移和C2是横向波的波速度，由（16）式定义：c2 = √g1/8Ks (16)
首先，图5中带的横向固有频率范围可从公式（16）获得，如果假定v(O,t)=v(l,t)=0：
fb =
1 c
2 (1 - ?
2) (17)
21 ?是无量纲的速比，由（18）式确定：
? = Vb / c2 (18)
FB 是不同带的各自独立的频率范围，由于输送带长度方向上带张力变化。托辊的受迫振动频率，使托辊产生了一个偏心率等于：
fi = Vb / πD (19)
其中D 是托辊的直径。为了设计一个在托辊间距中无支撑的共振，这受到以下条件限制：
L
≠
πD (
1-?2)
(20) 2? 由线性微分方程（16）所取得的成果不过是只适用于小数值的速比?。对于大数值的速比?来说，如高速运输机或低的带张力，在（16）式中所有非线性条件就显得重要的。因此，数值模拟的运用，有限元模型的开发，都是为了确定带横向振动线性和非线性频率之间的比例范围。这些关系已被确定适合不同的数值的?，例如说一个功能凹陷的比率Ks 。
使用快速傅里叶技术将横向位移结果的转化为频谱。从这些频谱中获得的频率与公式（18）获得的频率相比，其产生了图8所显示的曲线。从这一数字可见，对小于0.3的?来说，计算误差很小。对于大数值的?来说，运用线性近似值法产生的计算误差达到10 ％以上。运用了皮带采用非线性梁架元的有限元模型，因此可以准确地确定大数值?的横向振动。
对于小数值?的横向振动的频率也可以用公式（18）准确地预测。然而，它不能分析，例如带凹陷和纵向波的传播之间的相互作用，或者同样可以看成有限元模型的脱离托辊的皮带。
这决定带应力和横向振动频率之间的关系可以用于皮带张力监测系统。
图8 ：由两个托辊支撑的带的横向振动线性和非线性频率之间的比例。
4 实验验证
为了使模拟的结果能够得到验证，实验中使用了动态试验设备，如图9所示。
图9 ：动态试验设施
使用这试验设施能够确定的两个托辊的间距和卸荷扁带的横向振动，例如返程部分的。声音装置是用来测量皮带的位移。此外，还有在试验中为我们所知的张紧力，带速，电机转矩，托辊转子与托辊的距离。
5 为例
由于最具有成本效益带式输送机的操作条件中出现了宽度范围为0.6m- 1.2m[ 2 ] 的各种皮带，可通过变换不同的带速改变带的输送能力，。然而在带速度被改变之前，应确定带和托辊之间的相互作用，以确保无支撑的带的共振。为了说明稳定移动的带的横向位移这一点，测量了两个托辊的间隔。带的总长度L是52.7m，托辊间距I是3.66m，静态凹陷的比例常数是2.1 ％，?为0.24而带速Vb为 3.57m/ s。
这个信号的后期转化由如图5所示的快速傅里叶技术频谱获得。在图5中出
图10 ：带稳定移动时横向振动频率
现了3个频率。第一频率是由带结合处所引起的：
fs = Vb/L = 0.067 Hz
第二个频率，出现在1.94赫兹，是由皮带的横向振动所造成的。
第三个频率出现在10.5Hz，是由托辊的旋转所造成的，从图11所示的数值模拟获得。
图11 ：计算共振区的不同托辊的直径D.
贯穿实验表明皮带速度和托辊间距。
图11显示的是拖过带与托辊互动引起的共振区可以预测三个托辊的直径。该带式输送机的托辊直径为0.108M，从而可以预测皮带速度邻近0.64M/S的共振现象。为了验证结果，在启动运输机的时候测量了带的最大横向位移跨度。
图12 ：测量横向振动和带静态凹陷幅度的标准差的比例。
在图12中，可以看出横向振动的最大振幅发生在带速为0.64M/S处，正如有限元模型模拟预测的结果一样。因此，带速度不应选择临近0.64米/ s的。虽然是用扁带进行实验和理论的验证的，但是这种应用技术也可运用于槽型带中。
6．结论
带式输送机有限元模型中梁架元的应用，带横向位移的模拟，从而使能够设计出带无支撑的共振。对于小数值的?来说，采用梁架元代替线性微分方程预测共振现象的优势是同样可以预测到皮带纵向和横向位移的之间的相互作用以及从模拟中预见皮带脱离托辊。
The Two-Dimensional Dynamic Behavior of Conveyor Belts 3.1.1 NON LINEAR TRUSS ELEMENT
If only the longitudinal deformation of the belt is of interest then a truss element can be used to model the elastic response of the belt. A truss element as shown in Figure 2 has two nodal points, p and q, and four displacement parameters which determine the component vector x:
xT = [up vp uq vq] (1)
For the in-plane motion of the truss element there are three independent rigid body motions therefore one deformation parameter remains which describes
Figure 2: Definition of the displacements of a truss element the change of length of the axis of the truss element [7]:
ε1 = D1(x) = ∫1 o ds2 - ds2o
dξ (2) 2ds2o
where dso is the length of the undeformed element, ds the length of the deformed element and ξ a dimensionless length coordinate along the axis of the element.
Figure 3: Static sag of a tensioned belt
Although bending, deformations are not included in the truss element, it is possible to take the static influence of small values of the belt sag into account. The static belt sag ratio is defined by (see Figure 3):
K1 = δ/1 = q1/8T (3)
where q is the distributed vertical load exerted on the belt by the weight of the belt and the bulk material, 1 the idler space and T the belt tension. The effect of the belt sag on the longitudinal deformation is determined by [7]:
εs = 8/3 K2s (4)
which yields the total longitudinal deformation of the non linear truss element: 3.1.2 BEAM ELEMENT
Figure 4: Definition of the nodal point displacements and rotations of a beam element.
If the transverse displacement of the belt is being of interest then the belt can be modelled by a beam element. Also for the in-plane motion of a beam element, which has six displacement parameters, there are three independent rigid body motions. Therefore three deformation parameters remain: the longitudinal deformation parameter, ε1, and two bending deformation parameters, ε2 and ε3.
Figure 5: The bending deformations of a beam element The bending deformation parameters of the beam element can be defined with the component vector of the beam element (see Figure 4):
xT = [up vp μp uq vq μq] (5)
and the deformed configuration as shown in Figure 5:
e2p1pq
ε2 = D2(x) =
1o
(6)
-eq21pq
ε3 = D3(x) =
1o
3.2 THE MOVEMENT OF THE BELT OVER IDLERS AND PULLEYS
The movement of a belt is constrained when it moves over an idler or a pulley. In order to account for these constraints, constraint (boundary) conditions have to be added to the finite element description of the belt. This can be done by using multi-body dynamics.
The classic description of the dynamics of multi-body mechanisms is developed for rigid bodies or rigid links which are connected by several constraint conditions. In a finite element description of a (deformable) conveyor belt, where the belt is discretised in a number of finite elements, the links between the elements are deformable. The finite elements are connected by nodal points and therefore share displacement parameters. To determine the movement of the belt, the rigid body modes are eliminated from the deformation modes. If a belt moves over an idler then the length coordinate ξ, which determines the position of the belt on the idler, se e Figure 6, is added to the component vector, e.g. (6), thus resulting in a vector of seven displacement parameters.
Figure 6: Belt supported by an idler.
There are two independent rigid body motions for an in-plane supported beam element therefore five deformation parameters remain. Three of them, ε1, ε2 and ε3, determine the deformation of the belt and are already given in 3.1. The remaining two, ε4 and ε5, determine the interaction between the belt and the idler, see Figure 7.
Figure 7: FEM beam element with two constraint conditions.
These deformation parameters can be imagined as springs of infinite stiffness. This implies that:
ε4 = D4(x) = (rξ + u ξ)e2 - rid.e2 = 0
ε5 = D5(x) = (r ξ + uξ)e1 - rid.e1 = 0 (7)
If during simulation ε4 > 0 then the belt is lifted off the idler and the constraint conditions are removed from the finite element description of the belt.
3.3 THE ROLLING RESISTANCE
In order to enable application of a model for the rolling resistance in the finite element model of the belt conveyor an approximate formulation for this resistance has been developed, [8]. Components of the total rolling resistance which is exerted on a belt during motion three parts that account for the major part of the dissipated energy, can be distinguished including: the indentation rolling resistance, the inertia of the idlers (acceleration rolling resistance) and the resistance of the bearings to rotation (bearing resistance). Parameters which determine the rolling resistance factor include the diameter and material of the idlers, belt parameters such as speed, width, material, tension, the ambient temperature, lateral belt load, the idler spacing and trough angle. The total rolling resistance factor that expresses the ratio between the total rolling resistance and the vertical belt load can be defined by:
ft = fi + fa + fb (8)
where fi is the indentation rolling resistance factor, fa the acceleration resistance factor and fb the bearings resistance factor. These components are defined by:
Fi = CFznzh nhD-nD VbnvK-nk NTnT
(9)
fa =
Mred ?2u
Fzb ?t2
fb =
Mf
Fzbri where Fz is distributed vertical belt and bulk material load, h the thickness of the belt cover, D the idler diameter, Vb the belt speed, KN the nominal percent belt load, T the ambient temperature, mred the reduced mass of an idler, b the belt width, u the longitudinal displacement of the belt, Mf the total bearing resistance moment and ri the internal bearing radius. The dynamic and mechanic properties of the belt and belt cover material play an important role in the calculation of the rolling resistance. This enables the selection of belt and belt cover material which minimise the energy dissipated by the rolling resistance.
3.4 THE BELT'S DRIVE SYSTEM
To enable the determination of the influence of the rotation of the components of
the drive system of a belt conveyor, on the stability of motion of the belt, a model of the drive system is included in the total model of the belt conveyor. The transition elements of the drive system, as for example the reduction box, are modelled with constraint conditions as described in section 3.2. A reduction box with reduction ratio i can be modelled by a reduction box element with two displacement parameters, μp and μq, one rigid body motion (rotation) and therefore one deformation parameter:
εred = Dred(x) = iμp + μq = 0 (10)
To determine the electrical torque of an induction machine, the so-called two axis representation of an electrical machine is adapted. The vector of phase voltages v can be obtained from:
v = Ri + ωsGi + L ?i/?t (11)
In eq. (11) i is the vector of phase currents, R the matrix of phase resistance's, C the matrix of inductive phase resistance's, L the matrix of phase inductance's and ωs the electrical angular velocity of the rotor. The electromagnetic torque is equal to:
Tc = iTGi (12)
The connection of the motor model and the mechanical components of the drive system is given by the equations of motion of the drive system:
Ti = Iij ?2?j
+ Cik
??k
Kil? (13) ?t2?t
where T is the torque vector, I the inertia matrix, C the damping matrix, K the stiffness matrix and ? the angle of rotation of the drive component axis's.
To simulate a controlled start or stop procedure a feedback routine can be added to the model of the belt's drive system in order to control the drive torque.
3.5 THE EQUATIONS OF MOTION
The equations of motion of the total belt conveyor model can be derived with the principle of virtual power which leads to [7]:
fk - Mkl ?2x1 / ?t2 = ζ1Dik (14)
where f is the vector of resistance forces, M the mass matrix and ζ the vector of multipliers of Lagrange which may be interpret as the vector of stresses dual to the vector of strains ε. To arrive at the solution for x from this set of equations, integration is necessary. However the results of the integration have to satisfy the constraint
conditions. If the zero prescribed strain components of for example e.g. (8) have a residual value then the results of the integration have to be corrected, also see [7]. It is possible to use the feedback option of the model for example to restrict the vertical movement of the take-up mass. This inverse dynamic problem can be formulated as follows. Given the model of the belt and its drive system, the motion of the take-up system known, determine the motion of the remaining elements in terms of the degrees of freedom of the system and its rates. It is beyond the scope of this paper to discuss all the details of this option.
3.6 EXAMPLE
Application of the FEM in the desian stage of long belt conveyor systems enables its proper design. The selected belt strength, for example, can be minimised by minimising, the maximum belt tension using the simulation results of the model. As an example of the features of the finite element model, the transverse vibration of a span of a stationary moving belt between two idler stations will be considered. This should be determined in the design stage of the conveyor in order to ensure resonance free belt support.
The effect of the interaction between idlers and a moving belt is important in belt-conveyor design. Geometric imperfections of idlers and pulleys cause the belt on top of these supports to be displaced, yielding a transverse vibration of the belt between the supports. This imposes an alternating axial stress component in the belt. If this component is small compared to the prestress of the belt then the belt will vibrate in it's natural frequency, otherwise the belt's vibration will follow the imposed excitation. The belt can for example be excitated by an eccentricity of the idlers. This kind of vibrations is particularly noticeable on belt conveyor returns. Since the frequency of the imposed excitation depends on the angular speed of the pulleys and idlers, and thus on the belt speed, it is important to determine the influence of the belt speed on the natural frequency of the transverse vibration of the belt between two supports. If the frequency of the imposed excitation approaches the natural frequency of transverse vibration of the belt, resonance phenomena occur.
The results of simulation with the finite element model can be used to determine the frequency of transverse vibration of a stationary moving belt span. This frequency
is obtained after transformation of the results of the transverse displacement of the belt span from the time domain to the frequency domain using the fast fourier technique. Besides using the finite element model also an analytical approach can be used.
The belt can be modelled as a prestressed beam. If the bending stiffness of the belt is neglected, the transverse displacements are small compared to the idler space, Ks << 1, and the increase of the belt length due to the transverse displacement is negligible compared to its initial length, the transverse vibration of the belt can be approximated by the following linear differential equation, also see Figure 5:
?2v
= (c22 - C2b) ?2v
- 2Vb
?2v
(15)
?t2?x2?x?t
where v is the transverse displacement of the belt and c2 the wave speed of the transverse waves defined by, [1]:
c2 = √g1/8Ks (16)
The first natural transverse frequency of the belt span of Figure 5 can be obtained from eq. (16) if it is assumed that v(O,t)=v(l,t)=0:
fb = 1
c2 (1 - ?2) (17) 21
where ? is the dimensionless speed ratio defined by:
? = Vb / c2 (18)
The frequency fb is different for each individual belt span since the belt tension varies over the length of the conveyor. The excitation frequency of an idler which has a single eccentricity is equal to:
fi = Vb / πD (19)
where D is the diameter of the idler. In order to design a resonance free belt support the idler space is subjected to the following condition:
L ≠πD
(1-?2) (20) 2?
The results obtained with the linear differential equation (16) however are valid
only for low values of the ratio ?. For higher values of ?, as is the case for high-speed conveyors or low belt tensions, the non-linear terms in the full form of e.g. (16) become significant. Therefore numerical simulations using, the FEM model have been made in order to determine the ratio between the linear and the non-linear frequency of transverse vibration of a belt span. These relations have been determined for different values of ? as a function of the sag ratio Ks.
The results for the transverse displacements were transformed to a frequency spectrum using a fast-fourier technique. The frequencies obtained from these spectra were compared to the frequencies obtained from e.g. (18) which yielded the curves as shown in Figure 8. From this figure it follows that for ? smaller that 0.3 the calculation errors are small. For higher values of ? the calculation error made by a linear approximation is more than 10 %. Application of a finite element model of the belt which uses non-linear beam elements therefore enables an accurate determination of the transverse vibrations for high values of ?.
For lower values of ? the frequencies of transverse vibration can also be predicted accurate by e.g. (18). However it is not possible to analyse, for example, the interaction between the belt sag and the propagation of longitudinal waves or the lifting of the belt off the idlers as can be done with the finite element model.
The determined relation between the belt stress and the frequency of transverse vibrations can also be used in belt tension monitoring systems.
Figure 8: Ratio between the linear and the non-linear frequency of transverse
vibration of a belt span supported by two idlers.
4. EXPERIMENTAL VERIFICATION
In order to be able to verificate the results of the simulations, experiments have been carried out with the dynamic test facility shown in Figure 9.
Figure 9: Dynamic test facility
With this test facility the transverse vibration of an unloaded flat belt span between two idlers, as for example a return part, can be determined. An acoustic device is used to measure the displacement of the belt. Besides that, also the tensioning force, belt speed, motor torque, idler rotations and idler space were known during the
experiments.
5. EXAMPLE
Since the most cost-effective operation conditions of belt conveyors occur in the range of belt widths 0.6 - 1.2 m [2], the belt's capacity can be varied by varying the belt speed. However before the belt speed is varied the interaction between the belt and the idler should be determined in order to ensure resonance free belt support. To illustrate this the transverse displacement of a stationary moving belt span between two idlers have been measured. The total belt length L was 52.7 m, the idler space I was 3.66 m, the static sag ratio Ks 2.1 %, ? was 0.24 and the belt speed Vb 3.57 m/s.
After transformation of this signal by a fast fourier technique the frequency spectrum of Figure 5 was obtained. In Figure 5 three frequencies appear. The first frequency is
caused by the passage of the belt splice:
fs = Vb/L = 0.067 Hz
The second frequency, which appears at 1.94 Hz, is caused by the transverse vibration
of the belt.
Figure 10: Frequencies of transverse vibration of a stationary moving belt span
supported by two idlers.
The third frequency which appears at 10.5 Hz is caused by the rotation of the idlers.
From the numerical simulations Figure 11 was obtained.
F igure 11: Calculated resonance zone's for different idler diameters D. Cross indicates
belt speed and idler space during experiment.
Figure 11 shows the zone's where resonance caused by the belt/idler interaction may be expected for three idler diameters. The idlers of the belt conveyor had a diameter of 0.108 m thus resonance phenomena may be expected nearby a belt speed of 0.64 m/s. To check this, the maximum transverse displacement of the belt span has been
measured during a start-up of the conveyor.
Figure 12: Measured ratio of the standard deviation of the amplitude of transverse
vibration and the static belt sag.
As can be seen in Figure 12 the maximum amplitude of the transverse vibration occur at a belt speed of 0.64 m/s as was predicted by the results of simulation with the finite
element model. Therefore the belt speed should not be chosen nearby 0.64 m/s. Although a flat belt is used for the experiments and the theoretical verification, the applied techniques can also be used for troughed belts.
6. CONCLUSIONS
Application of beam elements in finite element models of belt conveyors enable the simulation of the transverse displacement of the belt thus enabling the design of resonance free belt supports. The advantage of applying beam elements for small values of ? instead of using a linear differential equation to predict resonance phenomena is that also the interaction between the longitudinal and transverse displacement of the belt and the lifting of the belt off the idlers can be predicted from
simulation.
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南京航空航天大学金城学院 毕业设计（论文）外文文献翻译 系部经济系 专业国际经济与贸易 学生姓名陈雅琼学号2011051115 指导教师邓晶职称副教授 2015年5月
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Inventory management Inventory Control On the so-called "inventory control", many people will interpret it as a "storage management", which is actually a big distortion. The traditional narrow view, mainly for warehouse inventory control of materials for inventory, data processing, storage, distribution, etc., through the implementation of anti-corrosion, temperature and humidity control means, to make the custody of the physical inventory to maintain optimum purposes. This is just a form of inventory control, or can be defined as the physical inventory control. How, then, from a broad perspective to understand inventory control? Inventory control should be related to the company's financial and operational objectives, in particular operating cash flow by optimizing the entire demand and supply chain management processes (DSCM), a reasonable set of ERP control strategy, and supported by appropriate information processing tools, tools to achieved in ensuring the timely delivery of the premise, as far as possible to reduce inventory levels, reducing inventory and obsolescence, the risk of devaluation. In this sense, the physical inventory control to achieve financial goals is just a means to control the entire inventory or just a necessary part; from the perspective of organizational functions, physical inventory control, warehouse management is mainly the responsibility of The broad inventory control is the demand and supply chain management, and the whole company's responsibility. Why until now many people's understanding of inventory control, limited physical inventory control? The following two reasons can not be ignored: First, our enterprises do not attach importance to inventory control. Especially those who benefit relatively good business, as long as there is money on the few people to consider the problem of inventory turnover. Inventory control is simply interpreted as warehouse management, unless the time to spend money, it may have been to see the inventory problem, and see the results are often very simple procurement to buy more, or did not do warehouse departments . Second, ERP misleading. Invoicing software is simple audacity to call it ERP, companies on their so-called ERP can reduce the number of inventory, inventory control, seems to rely on their small software can get. Even as SAP, BAAN ERP world, the field of
10kV小区供配电英文文献及中文翻译
在广州甚至广东的住宅小区电气设计中,一般都会涉及到小区的高低压供配电系统的设计.如10kV高压配电系统图,低压配电系统图等等图纸一大堆.然而在真正实施过程中,供电部门(尤其是供电公司指定的所谓电力设计小公司)根本将这些图纸作为一回事,按其电脑里原有的电子档图纸将数据稍作改动以及断路器按其所好换个厂家名称便美其名曰设计(可笑不?),拿出来的图纸根本无法满足电气设计的设计意图,致使严重存在以下问题:(也不知道是职业道德问题还是根本一窍不通) 1.跟原设计的电气系统货不对板,存在与低压开关柜后出线回路严重冲突,对实际施工造成严重阻碍,经常要求设计单位改动原有电气系统图才能满足它的要求(垄断的没话说). 2.对消防负荷和非消防负荷的供电(主要在高层建筑里)应严格分回路(从母线段)都不清楚,将消防负荷和非消防负荷按一个回路出线(尤其是将电梯和消防电梯,地下室的动力合在一起等等,有的甚至将楼顶消防风机和梯间照明合在一个回路,以一个表计量). 3.系统接地保护接地型式由原设计的TN-S系统竟曲解成"TN-S-C-S"系统(室内的还需要做TN-C,好玩吧?),严格的按照所谓的"三相四线制"再做重复接地来实施,导致后续施工中存在重复浪费资源以及安全隐患等等问题.. ............................(违反建筑电气设计规范等等问题实在不好意思一一例举,给那帮人留点混饭吃的面子算了) 总之吧,在通过图纸审查后的电气设计图纸在这帮人的眼里根本不知何物,经常是完工后的高低压供配电系统已是面目全非了,能有百分之五十的保留已经是谢天谢地了. 所以.我觉得:住宅建筑电气设计,让供电部门走!大不了留点位置,让他供几个必需回路的电,爱怎么折腾让他自个怎么折腾去.. Guangzhou, Guangdong, even in the electrical design of residential quarters, generally involving high-low cell power supply system design. 10kV power distribution systems, such as maps, drawings, etc. low-voltage distribution system map a lot. But in the real implementation of the process, the power sector (especially the so-called power supply design company appointed a small company) did these drawings for one thing, according to computer drawings of the original electronic file data to make a little change, and circuit breakers by their the name of another manufacturer will be sounding good design (ridiculously?), drawing out the design simply can not meet the electrical design intent, resulting in a serious following problems: (do not know or not know nothing about ethical issues) 1. With the original design of the electrical system not meeting board, the existence and low voltage switchgear circuit after qualifying serious conflicts seriously hinder the actual construction, often require changes to the original design unit plans to meet its electrical system requirements (monopoly impress ). 2. On the fire load and fire load of non-supply (mainly in high-rise building in) should be strictly sub-loop (from the bus segment) are not clear, the fire load and fire load of non-qualifying press of a circuit (especially the elevator and fire elevator, basement, etc.
英文文献翻译
中等分辨率制备分离的 快速色谱技术 W. Clark Still,* Michael K a h n , and Abhijit Mitra Departm(7nt o/ Chemistry, Columbia Uniuersity,1Veu York, Neu; York 10027 ReceiLied January 26, 1978 我们希望找到一种简单的吸附色谱技术用于有机化合物的常规净化。这种技术是适于传统的有机物大规模制备分离，该技术需使用长柱色谱法。尽管这种技术得到的效果非常好，但是其需要消耗大量的时间，并且由于频带拖尾经常出现低复原率。当分离的样本剂量大于1或者2g时，这些问题显得更加突出。近年来，几种制备系统已经进行了改进，能将分离时间减少到1-3h，并允许各成分的分辨率ΔR f≥（使用薄层色谱分析进行分析）。在这些方法中，在我们的实验室中，媒介压力色谱法1和短柱色谱法2是最成功的。最近，我们发现一种可以将分离速度大幅度提升的技术，可用于反应产物的常规提纯，我们将这种技术称为急骤色谱法。虽然这种技术的分辨率只是中等（ΔR f≥），而且构建这个系统花费非常低，并且能在10-15min内分离重量在的样本。4 急骤色谱法是以空气压力驱动的混合介质压力以及短柱色谱法为基础，专门针对快速分离，介质压力以及短柱色谱已经进行了优化。优化实验是在一组标准条件5下进行的，优化实验使用苯甲醇作为样本，放在一个20mm*5in.的硅胶柱60内，使用Tracor 970紫外检测器监测圆柱的输出。分辨率通过持续时间（r）和峰宽（w,w/2）的比率进行测定的（Figure 1），结果如图2-4所示，图2-4分别放映分辨率随着硅胶颗粒大小、洗脱液流速和样本大小的变化。
英文文献及中文翻译
毕业设计说明书 英文文献及中文翻译 学院：专 2011年6月 电子与计算机科学技术软件工程
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毕业论文5000字英文文献翻译
英文翻译 英语原文： . Introducing Classes The only remaining feature we need to understand before solving our bookstore problem is how to write a data structure to represent our transaction data. In C++ we define our own data structure by defining a class. The class mechanism is one of the most important features in C++. In fact, a primary focus of the design of C++ is to make it possible to define class types that behave as naturally as the built-in types themselves. The library types that we've seen already, such as istream and ostream, are all defined as classesthat is,they are not strictly speaking part of the language. Complete understanding of the class mechanism requires mastering a lot of information. Fortunately, it is possible to use a class that someone else has written without knowing how to define a class ourselves. In this section, we'll describe a simple class that we canuse in solving our bookstore problem. We'll implement this class in the subsequent chapters as we learn more about types,expressions, statements, and functionsall of which are used in defining classes. To use a class we need to know three things: What is its name? Where is it defined? What operations does it support? For our bookstore problem, we'll assume that the class is named Sales_item and that it is defined in a header named Sales_item.h. The Sales_item Class The purpose of the Sales_item class is to store an ISBN and keep track of the number of copies sold, the revenue, and average sales price for that book. How these data are stored or computed is not our concern. To use a class, we need not know anything about how it is implemented. Instead, what we need to know is what operations the class provides. As we've seen, when we use library facilities such as IO, we must include the associated headers. Similarly, for our own classes, we must make the definitions associated with the class available to the compiler. We do so in much the same way. Typically, we put the class definition into a file. Any program that wants to use our class must include that file. Conventionally, class types are stored in a file with a name that, like the name of a program source file, has two parts: a file name and a file suffix. Usually the file name is the same as the class defined in the header. The suffix usually is .h, but some programmers use .H, .hpp, or .hxx. Compilers usually aren't picky about header file names, but IDEs sometimes are. We'll assume that our class is defined in a file named Sales_item.h. Operations on Sales_item Objects