伺服系统设计计算

PEN

蜻蜓，你的峰值加速计算是正确的。

以1 Hz加速5Kg很容易。然而活塞和杆的重量可能比这更重。

我用自然频率的简单公式来计算平均活塞面积。
AreaAvg = 16 * PI ^ 2_Hz ^ 2 * CylLen *质量/ b
AreaAvg是平均活塞面积。取整到下一个圆柱体大小。
Cylen是圆柱体长度
b是石油的大块模量。

当执行器是变形部件时，必须将其视为机械弹簧。
如果您认为机械弹簧是线性的，则会有一个反作用力F（x）= k * x，其中x是弹簧被推动的距离。春天也有质量。必须计算机械弹簧的质量。压缩机械弹簧的经验法则是使用1/3的机械弹簧质量，因为并非所有的弹簧都以相同的速度移动。如果弹簧是线性的，这个假设是完美的。

最初的问题是关于确定缸体的大小。圆柱体的大小将由所需的力决定。

我将Mathcad工作表从英式转换为公制单位。

简单的答案是肯定的，RMC75可以很容易地测试更高的频率。
最近有一个关于RMC被用于测试的话题。
RMC75可以在4Khz下更新。这些计算在理论上是完美的。电子几乎以光速移动。限制只限于液压和机械设计。

有时我应该写一个小程序来播放音乐。这需要产生非常高的频率。音频扬声器可以比液压阀移动得更快。
我认为'欢乐颂'会是一个好的开始，因为时间很简单。

dragonfly, your calculation for peak acceleration is correct.

Accelerating 5Kg at 1 Hz is easy.   However the piston and rod probably weight more than that.

I use the simple formula for natrual frequency to calculate the average piston area.
AreaAvg =  16*PI^2_Hz^2*CylLen*mass/b
AreaAvg is the average piston area.  Round up to the next cylinder size.
Cylen is the cylinder length
b is the bulk moduls of oil.

When the actuator is the part that is being deformed it must be treated as a mechanical spring.
If you assume the mechanical spring is linear there will be an opposing force F(x)=k*x where x is the distance the spring is being pushed.   The spring also has mass.  The mass of the mechanical spring must be calculated.   A good rule of thumb for compressing mechanical springs is to use 1/3 the mechanical spring mass because not all the spring is being moved at the same rate.  This assumption is perfect if the spring is linear.

Iinitially the question was about sizing the cylinder.   The cylinder size will be determined by the required force.

I am converting Mathcad worksheets from British to metric units.

The simple answer is yes, the RMC75 can easily test at much higher frequencys.
There is a recent topic about the RMC being used for testing.
The RMC75 can update at 4Khz.  The calculations are theoretically perfect.  The electrons move at almost the speed of light.  The limitations are only in the hydraulic and mechanical design.

Sometime I should write a small program to play music.  That requires generating very high frequencies.  Audio speakers can move faster than hydraulic valves.
I think 'Ode to Joy' would be a good start because the timing is easy.

蜻蜓

谢谢游侠和pen大侠

请教泵流量和蓄能器流量

以正弦加载为例，油缸需求的流量是正弦变化的，那么油泵流量如何确定比较合理。是按油缸峰值流量选取还是按平均流量选取？油泵流量占比油缸峰值流量的百分比为多少是合理的？如果油泵流量小于油缸峰值流量，那么这就变成一个蓄能器容量合理选择问题。

一个数学问题：

以我开始提出的数据，计算泵流量及蓄能器容量（或者说流量），使系统溢流阀可以按最小溢流量维持系统压力恒定。（多大的泵流量和蓄能器流量，可以使系统溢流阀在一个循环内溢出的流量最少，而且要保证系统压力恒定。）

Thanks to the rangersand the pen warrior.

Consult pump flow andaccumulator flow.

Taking sinusoidalloading as an example, the flow of oil cylinder demand is sinusoidal change, sohow to determine the pump flow is reasonable. Is it selected according to thepeak flow rate of the oil cylinder or the average flow? What is the percentageof the oil pump's flow rate of oil cylinder peak flow? If the pump flow is lessthan the peak flow rate of the oil cylinder, then this becomes a reasonablechoice of accumulator capacity.

A math problem:

Based on the datathat I started to put forward, calculate pump flow and accumulator capacity (orflow rate), so that the system overflow valve can maintain system pressureconstant according to minimum overflow flow. (how much pump flow andaccumulator flow can make the system overflow valve overflow in a loop atleast, and keep the system pressure constant.)

Thanks for theRangers and pen

Ask for pump flow andaccumulator flow

Taking sinusoidalloading as an example, the flow rate of oil cylinder is sinusoidal, so how todetermine the flow rate of oil pump is reasonable. Is it selected according tothe peak flow of oil cylinder or by the average flow rate? How much is thepercentage of the oil pump flow to the peak flow rate of the oil cylinder? Ifthe flow rate of the oil pump is less than the peak flow rate of the cylinder,this will become a reasonable choice of the accumulator capacity.

A mathematicalproblem:

At the beginning ofthe data, the pump flow and accumulator capacity (or flow) are calculated, sothat the system overflow valve can maintain the constant pressure of the systemaccording to the minimum flow rate. (how much pump flow and accumulator flowcan make the overflow valve of the system minimum flow in a cycle, and ensurethe constant pressure of the system).

补充一点

负载力就像压缩弹簧一样, 在接触时，弹簧施加零力，当弹簧被压缩时，它施加10吨力。

Add a little bit

the load force is like compressing aspring,, At contact the spring exerts zero force and when the spring iscompressed it exerts 10 tons of force。

蜻蜓

PEN 发表于 2018-4-25 05:51
蜻蜓，你的峰值加速计算是正确的。

以1 Hz加速5Kg很容易。然而活塞和杆的重量可能比这更重。

Pen teacher

I have seen large loading testing machines.The quality of samples is very large and the quality cannot be ignored.

In the loading system, how to estimate theload quality m?

What is the mechanical spring?

1 third of the total mass of the spring,right?

2. 1/3 of the mass of x part of thecompression?

3. The mass of the compression quantity xpart?

1/3 the mechanical spring does not show thedifference in compression. Suppose the linear spring compresses the spring by1mm and compresses 1cm, does it have the same load mass?

Teacher Pen

I have seen large loading test machine, thequality of sample is very large, and the quality can not be ignored.

How can the load quality m be estimated inthe loading system?

What is 1/3 the mechanical spring?

1 1/3 of the total mass of spring?

2 1/3 of partial mass of X compressionquantity?

3 the mass of the X portion of thecompression quantity?

1/3 the mechanical spring does not reflectthe difference in compression. Suppose that the linear spring will compress thespring 1mm with the compression 1cm and the load mass m?

PEN

设计师应该知道质量。
如果系统没有障碍地移动，那么质量就是执行器的质量和被移动的质量。
如果执行器遇到可压缩阻塞（机械弹簧，测试片），则必须将F（x）= ks * x添加到微分方程中。 :(
如果振幅是5mm，那么运动从-5mm到5mm
IF（x <= x0）
     m*x''+d*x'+k*x=Pa(t)*Aa-Pb(t)*Ab                            // actuator is moving freely
ELSE    (m+ms/3)*x''+d*x'+k*x=Pa(t)*Aa-Pb(t)*Ab - ks(x-x0)   // actuator is obstructed
END_IF
哪里：
x“是加速度
x'是速度
x是位置。
m是质量
d是阻尼
k是液压弹簧常数
Pa是盖侧的压力
Pb是杆侧的压力
Aa是盖侧活塞的面积
Ab是杆侧活塞的面积
毫秒是被压缩的机械弹簧的质量。
ks是机械弹簧或变形负载
x0是杆撞击机械弹簧或负载的位置

使用机械弹簧（试件）质量1/3的原因是因为只有机械弹簧与致动器收缩的那部分以致动器的速度和加速度运动。

解决这个问题需要编写仿真代码，因为微分方程会在遇到阻塞时发生变化。
我的Python模拟器只能模拟自由移动的质量。
简单的公式假设质量在自由移动。
我的Mathcad模拟器可以模拟这个是一两个小时。

蜻蜓

PEN 发表于 2018-4-26 01:51
设计师应该知道质量。
如果系统没有障碍地移动，那么质量就是执行器的质量和被移动的质量。
如果执行器遇 ...

谢谢，可以理解，如果知道K 或者d中的一个，我应该能够通过实验测算出这个m。
蜻蜓22#的问题是我想知道的主题，伺服加载系统泵和蓄能器流量如何匹配，是合理的？是节能的？
Thank you, you can understand, if you know one of the K's or d's, I should be able to figure out the m by the experiment.
The question of dragonfly 22# is the theme I want to know. How does the servo load system pump and the accumulator flow match? Is it energy efficient?

Thank you, Mr. pen. You can understand that if I know one of K or D, I should be able to calculate this m by experiment.
The problem of dragonfly 22# is the theme I want to know. How does the servo loading system match the pump and accumulator flow? Is it reasonable? Is it energy efficient?

back2049

蜻蜓 发表于 2018-4-26 07:18
谢谢，可以理解，如果知道K 或者d中的一个，我应该能够通过实验测算出这个m。
蜻蜓22#的问题是我想知道 ...

为什么加速度不是160,270?

PEN

气缸尺寸必须在蓄能器和阀门尺寸之前计算。

泵需要提供比平均需求更多的流量。
蓄能器将平衡泵上的流量需求。在正弦运动期间，有流量小于平均值的时期。在此期间，蓄电池将充满。有些时候泵不能提供足够的油，因此蓄能器将供应泵不提供的油。蓄能器中的油或气量将在一个周期内变化。蓄电池必须充电，以使气体体积不超过10％，因此压力保持在10％以内。

蓄能器允许泵以更恒定的速度运行。
在＃1中，系统压力为160巴。通过转动压缩泵中弹簧的螺钉调节压力。泵在160巴时不会产生流量。在泵将提供全流量之前，压力必须下降10％-20％。泵基本上只有P控制，并且响应时间很慢。该泵可以产生160 bar的0 LPM，150 bar的50 LPM和140 bar的100 LPM。如果流量需要75 bar，压力将从160 bar降至145 bar。

160 bar的操作压力还是无流量压力？

The cylinder size must be calculated before the accumulator and valve size.

The pump needs to supply just a little more flow than the average requirement.
The accumulator will even out the flow demand on the pump.  During the sinusoidal motion there are periods when the flow is less than average.  During this time the accumulator will fill.   There are also times when the pump will not supply enough oil so the accumulator will supply the oil the pump does not.   The volume of oil or gas in the accumulator will change during a cycle.   The accumulator must be charged so the volume of gas does not change by more than 10% so the pressure stays constant within 10%.

The accumulator allows the pump to run at a more constant speed.
In the #1 the system pressure is 160 bar.   The pressure is adjust by turning a screw that compresses a spring in the pump.   The pump will generate no flow at 160 bar.  The pressure must drop by 10%-20% before the pump will supply full flow.   The pump is basicly P only control and has a slow response time.   The pump may generate 0 LPM at 160 bar,  50 LPM at 150 bar, and 100 LPM at 140 bar.   If the flow require ment is 75 bar the pressure will drop from 160 bar to 145 bar.

So is 160 bar the operational pressure or the no flow pressure?

PEN

以下等式计算活塞的面积。这个计算需要针对每个方向进行一次。
气缸面积必须满足两个条件。力必须足够高，才能以所需的速度和加速度移动物体。固有频率应该是加速频率的4倍左右。应该使用最大面积来查看表格以找到下一个最大的圆柱体尺寸。
面积= max（（（v2 ^ 2 * F1-V1 ^ 2 * F2）/（v2 ^ 2-v1 ^ 2））/ Ps，16 * PI ^ 2 * Hz ^ 2 * CylLen *质量/β）
方程的第一部分使用运动过程中两点的速度和力来计算所需面积。供应压力也是必需的。太多液压设计者试图通过增加供给压力来减小活塞的面积。方程的第二部分计算实现固有频率比加速频率高4倍所需的面积。

如果运动没有任何障碍，则此公式有效。
计算运动曲线中两点的速度和加速度很容易。
对于正弦波，计算30和60度时的速度和加速度。为了计算力，质量必须乘以加速度，并且还必须加上任何摩擦力或重力。

The following equation calculates the area of the piston.   This calculation needs to be once for each direction.
The cylinder area must meet two conditions.  The force must be high enough to move the mass at the desired velocity and acceleration.  The natural frequency should be about 4 times the frequency of acceleration.  The maximum area should be used to look into a table to find the next biggest cylinder size.
Area = max( ((v2^2*F1-V1^2*F2)/(v2^2-v1^2))/Ps, 16*PI^2*Hz^2*CylLen*mass/β)
The first part of the equation uses the velocity and force at two points during the motion to calculate the required area.  The supply pressure is also required.   Too many hydraulic designers try to minimize the area of the piston by increasing the supply pressure.   The second part of the equation calculate the area necessary to achieve a natural frequency four times greater than the frequency of acceleration.

This formula works if there aren't any obstructions to the motion.
It is easy to calculate the velocity and acceleration at two points in the motion profile.
For a sine wave calculate the velocity and acceleration at 30 and 60 degree.   To calculate the force the mass must be multiplied by the acceleration and any friction or load do to gravity must also be added.

蜻蜓

PEN 发表于 2018-4-27 00:00
气缸尺寸必须在蓄能器和阀门尺寸之前计算。

泵需要提供比平均需求更多的流量。

The cylinder size must be calculated before theaccumulator and valve size.

对，应该先计算，这个油缸面积后面帖子再说。

So is 160 bar the operational pressure or the no flowpressure?

我初步选的是定量泵，是系统压力，这个压力我也可以提高到210bar，当做一个方便说明问题的压力即可。

您这里讲解是恒压变量泵，系统可以选变量泵，也可以选用定量泵。

泵流量分别占比按峰值流量百分比是多少比较合理？（或者说：峰值流量*系数=泵流量，我想知道这个系数）

我理解，这个系数应该介于0.5-1之间，高频系统这个系数大，低频系统这个系数小。

问题：定量泵和变量泵这两个“流量系数”怎么定性选取，或者更准确的定量计算？

The cylinder size must be calculated before The accumulatorand valve size.

Yes, should calculate first, this oil cylinder area after thepost says.

So is 160 bar the operational pressure or the no flowpressure?

My initial selection is the quantitative pump, which is thesystem pressure. I can also increase the pressure to 210bar, as a convenientway to explain the problem.

You are talking about the constant pressure variable pump,the system can choose the variable pump, also can choose the fixed quantitypump.

How much is the percentage of pump flow per peak flow?

I understand:

Peak flow + overflow valve overflow = accumulator flow + pumpflow.

Pump flow = oil cylinder peak flow * "coefficienta"

I want to know how this coefficient is selected andcalculated.

I understand that the coefficient should be between 0.5 and1, the high frequency system has a large coefficient, and the low frequencysystem has a small coefficient.

consult: how do you determine the "flow coefficienta" of the pump and the variable pump, or the more accurate calculationmethod?

back2049

加速时间142ms的依据是什么？