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RationalDMIS 2020 位置度计算方法

RationalDMIS 2020 对称孔位置度检测方法

位置度基础知识（几何公差） 2020

RationalDMIS 7.1 位置度评价2020

RationalDMIS 7.1位置度评价之参考组合类型

   位置度是GD＆T中所有符号中最有用和最复杂的符号之一。本页上讨论的两种使用“位置”的方法将是RFS或与特征大小无关，并且在材料条件（最大材料条件或最小材料条件）下使用。但是，由于这是一个非常有用的符号，因此在接下来的几个月中，我们将继续为该漂亮的小符号的其他用途添加内容和示例。

位置度是零件上的点，线，面等要素，相对其理想位置的准确状况。

摘要：

  真实头寸实际上只是在ASME标准中称为头寸。许多人称该符号为“ True”位置，尽管这会有些不正确。位置公差是GD＆T符号和位置公差。真实位置是指由基本尺寸或代表标称值的其他方式定义的位置上的精确坐标，换句话说，GD＆T“位置”公差是要素位置与其“真实位置”可以相差多远。尽管不正确，但我们为该页面加上了标题，有时可能将符号称为“真实位置”，因为这通常是人们在寻找指定公差时所参考的术语。但是，如果您想遵循ASME标准，则只需使用“位置”一词

   位置定义为要素从其“真实”位置可以具有的总允许变化。

   根据呼出方式的不同，真实位置可能意味着不同的含义。可以与最大材料状态（MMC），最小材料状态（LMC），投影公差和切线平面一起使用。它可以应用于任何尺寸特征（具有物理尺寸的特征，例如孔，槽，凸台或凸舌），并控制这些尺寸特征的中心元素。在这些示例中，我们将使用孔，因为这些是由真实位置控制的最常见的要素类型。

  位置可以用于任何尺寸特征（但不能在使用轮廓的表面上使用）位置可能是GD＆T中使用最广泛的符号。

（1）孔的真实中心位置（带有2个基准的RFS）

（2）Position of a hole under MMC (3 Datums) 

（3）要素的真实位置

     以轴，点或平面为单位的位置定义了要素与指定的确切真实位置之间可以有多少变化。公差是2维或3维公差带，它围绕要素必须位于的真实位置。通常，在指定真实位置时，将使用x和y坐标作为基准尺寸（没有公差）来引用基准。这意味着您将在一个确切的位置上找到位置，并且您的公差指定了距该位置的距离。通常使用两个或三个基准定位该位置，以精确定位参考位置。通常将真实位置称为直径，以表示圆形或圆柱形公差带。  

（4）True Position using material conditions (MMC/LMC)

  与“最大实体条件”一起使用的位置成为非常有用的控件。具有大小特征的真实位置可以一次控制特征的位置，方向和大小。MMC的真实位置有助于创建功能规，该规可用于快速插入到零件中，以查看一切是否在规格范围内。虽然需要在其自身的控件上放置参考点位置的真实位置，但孔在MMC中的真实位置会设置孔的最小尺寸和位置，以保持功能控制。它通过允许向零件添加额外公差来实现。随着零件距离MMC越来越近，约束也越来越严格，孔必须更靠近其位置。但是，如果孔稍大（但仍在规格范围内），则它可能会进一步偏离其真实位置，并且仍然可以发挥适当的功能（例如螺栓穿过）

（5）GD&T Tolerance Zone:

    True Position –Location of a feature

  A 2-dimensional cylindrical zone or, more commonly a 3-Dimensional cylinder, centered at the true position location referenced by the datums.

   The cylindrical tolerance zone would extend though the thickness of the part if this is a hole. For the 3-dimensional tolerance zone existing in a hole, the entire hole’s axis would need to be located within this cylinder.

（5）True Position using modifiers (MMC/LMC)

  The tolerance zone is the same as above except only applied in a 3D condition. A 3-Dimensional cylinder, centered at the true position location referenced by the datum surfaces. The cylindrical tolerance zone would extend though the thickness of the part if this is a through hole for the 3-dimensional tolerance zone similar to the RFS version. While this is the tolerance zone, the call-out now references the virtual condition of the entire part. This means that the hole’s position and size are controlled together as one. (see gauging section)

（6）位置度计算公式

     Gauging / Measurement:

    True Position –Location of a Feature

   True position of a feature is made by first determining the current referenced point and then comparing that to any datum surfaces to determine how far off this true center the feature is. It is simplified like a dimensional tolerance but can be applied to a diameter tolerance zone instead of simple X-Y coordinates. This is done on a CMM or other measurement devices.

This is a special case to deal with Circles where the centre point is True Position Calculation of Circles and Torus.

This is a special case to deal with Circles where the centre point is compared to the axis of the Nominal circle. This value can be interpreted as Coaxiality as defined in ISO 1101. The True Position is computed as twice the distance of the centre point of the Measured feature to the nominal axis. as an infinite line.

The True Position value represents the diameter of a cylinder, displayed in green below, around the nominal axis which contains the center point from the measured feature.

True Position Calculation of Points and Spheres 

The true position is calculated as twice the 3D distance between the measured and the nominal point. This True Position value represents a sphere around the Nominal Point which contains the Actual Point

The True Position value represents the diameter of a sphere, displayed in green below, around the nominal Point which would contain the Actual Point

This is a special case to d】eal with Circles w

True Position Calculation of Lines, Cylinders, Slots, and Cones 

When calculating the True Position of a Line-reduced feature, the end-points of the Measured feature axis are compared to the Nominal axis, as an infinite line. The end-points of the measured feature are determined by the captured measurement points. The True Position value is twice the largest distance from the endpoints to the nominal axis line

The True Position value represents the diameter of a cylinder, displayed in green below, around the nominal axis which contains the full axis line from the measured feature.

True Position Calculation of Slots.

  When calculating the True Position of slot features. both end centre points of the measured feature are used. Both are compared to the nominal axis, running the length of the slot and to theoretical axis through the nominal end points, which are perpendicular to the slot ' length' axis Two dimensions are calculated for each point. one to the ' lenath' axis (D1. D3) and another to the corresponding perpendicular axis (D2, D4):

The True Position value is twice the maximum value of the 2 calculations

here the cen

tre point is compared to the axis of the Nominal circle. This value can be interpreteThe True Position value represents the diameter of a cylinder, displayed in green below, around the nominal axis which contains the center point from the measured feature.d as Coaxiality as defined in ISO 1101. The True Position is computed as twice the distance of the centre point of the Measured feature to the nominal axis, as an infinite lin

（7）True Position Using material modifiers (MMC only)

   When a part is checked for true position under a feature of size specification, usually a functional gauge is used to ensure that the entire feature envelope is within specification. If you have a specification for Maximum Material Condition, the desired state is that a hole will not be too small, or a pin not too large. The following formulas are used to create a gauge for true position under MMC.*

（8）Gauging of an Internal Feature

For the true position under MMC of a hole:

Gauge Ø (pin gauge)=Min Ø of hole (MMC)-True Position Tolerance

（9）Gauging of an External Feature

For true position under MMC of a pin:

Gauge Ø (hole gauge) = Max Ø of pin (MMC) + True Position Tolerance

Locations of the gauge pins or holes are given on the drawing as basic dimensions. All gauge features should be located in the datum true positions, but sized according to the formulas above.

True Position –Location of Hole Example 1:

  Four holes are to be located on a block to ensure contact is always maintained and located within a specific position. The holes need to line up with the threaded connections in the mating part.

  With true position called out the holes do not need to be in exact positions as shown below, but their centers can vary by the amount specified by the tolerance. The basic dimensions (dimensions in the squares) are un-toleranced and describe the true location the hole would be in if it was perfect. In a 2D check of the upper right hole, the true location would be 40 mm from datum A and 40 mm from datum B. The holes center is calculated, usually by a CMM and compared to the true location. As long as the holes center is in the blue tolerance zone of 0.2 mm specified by the feature control frame, the part is in tolerance.

Note: in this case, the surface of the part is called out (Datum C). This means the entire hole must have its axis align with the datum. The tolerance zone would actually ensure that the location and the perpendicularity are within the specified tolerance. Since all the central points at any cross-section are controlled by true position, the parts axis (line between all central points) would be controlled for orientation.

The biggest thing to note about this design is that no matter what size hole you have, your true position would always have to be the same. This is ideal for when proper exact alignment is required for function of the part. It does, however, remove the possibility of using a functional gauge.

True Position – Hole size and location using MMC Example 2:

  Taking the same example, the true position can also be specified with a maximum material condition callout. This means you are now controlling the envelope of the entire hole feature, including the size of the hole throughout its entire depth.

With an MMC callout you now can use a functional gauge to measure this part, to determine that the size and geometric tolerancing are within spec at the same time.

Formula for a the functional gauge to measure the true position of all holes:

Individual Pin Diameters = Min hole Ø -True position tolerance (bonus)

This example Pin Ø = 9.9 – 0.2 = Ø 9.7

Location of pins: Same specifications

  This would be the go gauge that would measure for hole size, orientation, and position. The part would be pressed down onto the gauge and if it fits the part is in specification. Notice that datum A, B, and C are all included in the gauge to check the location of the hole. The desired function of the part is met by ensuring that the part touches all the datums and that the gauge pins are able to fully go through the holes.

   As long as the gauge can go into the part, it is in spec. This makes it very easy to accurately gauge the part right on a production line. The function of the part is confirmed because as long as the surface that the part is bolted to has the same tolerances, it will always fit.

Tolerance of Position RFS

为了了解我们对位置控制的容忍度，我们必须彻底了解我们的基准。

现在，将重点放在基准孔上。我们必须建立基准轴[B]。右侧的孔将相对于基准轴[B]定位。我们在特征控制框中针对位置公差的基准标注告诉我们，基准[B]必须垂直于基准[A]。

   基准孔不一定垂直于基准[A]。基准孔具有用于控制基准孔方向的垂直度控件。垂直度控制表示存在一个直径为0.1且与基准点[A]完全垂直的公差圆柱体。基准孔无关的实际配合包络线的轴必须落入该公差圆柱体之内。

   无关的实际配合包络线的轴不能为基准[B]，因为该轴不一定垂直于基准[A]。基准[B]是基准孔的相关实际配合包络的轴。相关的实际配合包络是最大的完美圆柱体，该圆柱体完全垂直于基准点[A]，并且仍然适合于基准孔内。

   建立基准后，我们现在可以查看位置公差如何相对于基准定位和定向孔。位置标注的公差告诉我们存在一个直径为0.2的公差带圆柱体。该圆柱体与基准点[A]完全垂直，并且该圆柱体的中心与基准点[B]恰好为50。孔的无关实际配合包络线的轴必须落入该公差圆柱体内。

  从下图可以看出，对于不相关的实际配合包络线落入此圆柱体的轴的要求，允许孔相对于理想位置向基准点[B]移动0.1或从基准点[B]移动0.1。该要求还允许孔相对于基准点[A]倾斜，并且倾斜由保持在公差圆柱体内的无关实际配合包络的轴线限制。

Projected Tolerance Zone

  The fact that tolerance of position allows some tilting should not be ignored.  Recall that the purpose of these holes is to plant fence posts in them for our fence that will keep the dog in the yard.  See the figure below that includes the fence posts. The fence will be okay with the fence post on the right being out of position to the extent allowed by the tolerance of position.  However, the tilting has a geometric effect.  This geometric effect will allow the top of the fence post to move much more than is acceptable.

   为了使我们的围栏柱做我们想要做的事，我们将使用“投影公差带”修改器。投影公差带修改器是特征控制框中圆圈中的字母P。投影公差带修改器指定公差带投影在零件上方。它不再位于零件内部。它完全在零件上方。圆中的“投影公差带”修改器之后的数字是我们要公差带投影的零件上方的距离。在我们的情况下，我们的柱子将在地面上停留40公里。

  因此，我们想将公差带40投影到零件上方。现在，不相关的孔的实际配合包络线的轴以及柱的轴必须保持在零件上方的该公差带内。这限制了允许的立柱倾斜。它将帖子顶部的移动限制在可接受的范围内。

  下图显示了投影公差带的经典示例。在左侧，公差圆柱体在零件内部。螺栓将自身对准螺纹孔中的螺纹。当螺栓延伸通过盖子时，其倾斜程度达到位置公差所允许的最大程度，因此螺栓和盖子上的间隙孔侧面之间会发生冲突。右侧，公差区域从顶盖的顶部凸出。底座盖的顶部。孔的轴线（进而是螺栓的轴线）在穿过盖子上的间隙孔时保持在公差圆柱体内，并且螺栓与盖子上的间隙孔侧面之间没有冲突。

附注：GD&T for beginners: MMC & bonus tolerance, explained in 3D

Figure 1. Geometric Dimensioning and Tolerancing: 2D versus 3D.

 Geometric Dimensioning and Tolerancing concepts are often difficult to grasp at first;  beginners can have quite a difficult time understanding the basic principles. One of the reasons for this difficulty is the visualization problem of 3D concepts in 2D documentation.

Maximum Material Condition (MMC) and Least Material Condition (LMC): Simple Definitions

   MMC is the condition of a feature which contains the maximum amount 

of material, that is, the smallest hole or largest pin, within the stated limits of size. LMC is the condition in which there is the least amount of material, the largest hole or smallest pin, within the stated limits of size.

Figure 2. MMC and LMC concepts for a pin

In our example in the animated Figure 2, we can observe that the MMC of the pin is 25 mm, while the LMC is 15 mm.

Why Use the MMC Concept?

MMC defines the worst case condition of a part that will still guarantee, because it is still within the prescribed tolerances, the assembly between pin(s) and hole(s). When a hole is at its smallest (MMC) and a pin is at its largest condition (also MMC), we can be sure that we will still be able to assemble that part. Thus, MMC is widely used in cases where clearance fits are common.

Bonus Tolerance Concept

Figure 3. Bonus tolerance explained: As the size of the pin departs from MMC toward LMC, a bonus tolerance is added equal to the amount of that departure. Bonus tolerance equals the difference between the actual feature size and the MMC of the feature. In this case, Bonus Tolerance = MMC-LMC=25-15=10.

Clearance for assembly increases if the actual sizes of the mating features are less than their MMC. If the pin is finished at less than its MMC and closer to its LMC limits, the clearance gained can be used as a bonus tolerance for form or position. In our example (Figure 3):

Example 1:  Pin diameter at Maximum Material Condition

Pin diameter at MMC= 25

Bonus Tolerance = 0

Position tolerance at MMC = 5

The concept of MMC and bonus tolerance becomes much clearer if visualized in 3D.

In this first video, the center axis of the cylinder representing the pin at MMC displaces around the position tolerance zone, which is defined as a cylinder with a diameter of 5mm.

Example 2: Pin diameter at Least Material Condition

Pin diameter at LMC= 15

Bonus Tolerance = Pin diameter at MMC – Pin diameter at LMC = 25 – 15 = 10

Position tolerance at LMC = 5 (Tolerance at MMC) + 10 (Bonus Tolerance) = 15

We see that when it has reached the LMC, the pin can have a larger position tolerance zone.

In the second video, the center axis of the cylinder representing the pin at LMC displaces around the position tolerance zone, which is defined as a cylinder with a diameter of 15mm. Take note that this time the allowed tolerance zone is much bigger at LMC, since we have a large bonus tolerance.

Example 3: Pin diameter somewhere in the middle

What would happen if the pin had a diameter somewhere between the LMC and MMC?

Pin diameter = 20

Bonus Tolerance = Pin diameter at MMC – Pin diameter = 25 – 20 = 5

Position tolerance = 5 (Tolerance at MMC) + 5 (Bonus Tolerance) = 10

In the third video, the center axis of the cylinder representing the pin at an arbitrary dimension displaces around the position tolerance zone, which is defined as a cylinder with a diameter of 10mm. (In our example, the pin diameter is at Nominal, however this doesn’t necessarily have to be the case.)

Datum feature shift relative to a pattern of holes

Now let's talk about datum feature shift relative to a pattern of holes. 

In the figure below, the outside holes are a pattern located relative to the center hole.  Datum [C] is referenced MMB, so datum feature shift is allowed.

We see below how the part fits on a gage.  The gage has a surface that represents datum [A] and another surface to represent datum [B].  There are three pins, each at the virtual condition size of their respective holes.

If the part has planar contact with [A] and line contact with [B] and at the same time slides over all of the pins, then it has met the tolerance of position requirements.

Now let's look at some extreme conditions.  Cross section A-A shows how the holes interact with the pins.  In this figure, the holes are at their LMC sizes and they are exactly perpendicular to datum [A].  This is the condition in which the holes can have their maximum allowable location error.  Note that in the figure, the hole on the left is shifted as far as it can be to the left.  The datum feature is shifted as far as it can shift to the right.  So the center of the hole on the left is as far as it can legally be from the center of the datum feature.

To calculate the total distance that the hole on the left can be from the datum hole, take the basic 20 and add the radial position tolerance plus the radial bonus tolerance.  Then add the radial datum feature shift.  Remember that datum feature shift is the difference between the max hole and the gage.  So it's 10.1-9.4=0.7.  Divide by two for radial and we have 0.35. 

Our total allowable center distance then between datum [B] and the center of the hole on the left is 20.55.  If we were to measure the distance between these centers on a CMM and find them to be 20.55 or less, we would say that the hole on the left is within spec.

But what about the hole on the right?  The datum feature is already shifted to the right.  So in our calculations we must subtract the shift instead of adding it.  The maximum we can have then between datum [B] and the hole on the right is 19.85.

What if we were to insist that the hole on the right should be able to add the shift just like the hole on the left?  The part would not fit on the gage.

The caution here is that the datum feature can only shift in one direction relative to a pattern.  If the shift increases the distance to one hole, it my decrease the distance to another hole.  We need to keep this in mind when using a CMM to gage the holes.  In this simple case, it's not too difficult to keep track of which is which.

What if we were to insist that the hole on the right should be able to add the shift just like the hole on the left?  The part would not fit on the gage.

The caution here is that the datum feature can only shift in one direction relative to a pattern.  If the shift increases the distance to one hole, it my decrease the distance to another hole.  We need to keep this in mind when using a CMM to gage the holes.  In this simple case, it's not too difficult to keep track of which is which.

This is where I fall back on what I often tell a CMM operator.  You are just going to need to use a fixed gage.  Of course, you may not have that option.  So then you need to befriend a CAD operator.

Probe your points like you normally would.  You will probably take 3 points to establish plane [A], two points to establish [B], and three points at each of the holes.

Give all of these coordinates to a CAD operator, and ask them to create a CAD model of your part as measured.

Ask them to also create a CAD model of the gage.

 Then ask them in CAD to determine whether or not the part as measured fits on the gage.  If the part fits, then it satisfies the tolerance of position requirements.  If not, it's a bad part.

来源：RationalDMIS测量技术