RationalDMIS 2020 位置度計(jì)算方法

RationalDMIS 2020 對稱孔位置度檢測方法

位置度基礎(chǔ)知識(幾何公差) 2020

RationalDMIS 7.1 位置度評價(jià)2020

RationalDMIS 7.1位置度評價(jià)之參考組合類型

? ?位置度是GD＆T中所有符號中最有用和最復(fù)雜的符號之一。本頁上討論的兩種使用“位置”的方法將是RFS或與特征大小無關(guān)，并且在材料條件(最大材料條件或最小材料條件)下使用。但是，由于這是一個(gè)非常有用的符號，因此在接下來的幾個(gè)月中，我們將繼續(xù)為該漂亮的小符號的其他用途添加內(nèi)容和示例。

位置度是零件上的點(diǎn)，線，面等要素，相對其理想位置的準(zhǔn)確狀況。

摘要：

? 真實(shí)頭寸實(shí)際上只是在ASME標(biāo)準(zhǔn)中稱為頭寸。許多人稱該符號為“ True”位置，盡管這會有些不正確。位置公差是GD＆T符號和位置公差。真實(shí)位置是指由基本尺寸或代表標(biāo)稱值的其他方式定義的位置上的精確坐標(biāo)，換句話說，GD＆T“位置”公差是要素位置與其“真實(shí)位置”可以相差多遠(yuǎn)。盡管不正確，但我們?yōu)樵擁撁婕由狭藰?biāo)題，有時(shí)可能將符號稱為“真實(shí)位置”，因?yàn)檫@通常是人們在尋找指定公差時(shí)所參考的術(shù)語。但是，如果您想遵循ASME標(biāo)準(zhǔn)，則只需使用“位置”一詞

? ?位置定義為要素從其“真實(shí)”位置可以具有的總允許變化。

? ?根據(jù)呼出方式的不同，真實(shí)位置可能意味著不同的含義。可以與最大材料狀態(tài)(MMC)，最小材料狀態(tài)(LMC)，投影公差和切線平面一起使用。它可以應(yīng)用于任何尺寸特征(具有物理尺寸的特征，例如孔，槽，凸臺或凸舌)，并控制這些尺寸特征的中心元素。在這些示例中，我們將使用孔，因?yàn)檫@些是由真實(shí)位置控制的最常見的要素類型。

? 位置可以用于任何尺寸特征(但不能在使用輪廓的表面上使用)位置可能是GD＆T中使用最廣泛的符號。

(1)孔的真實(shí)中心位置(帶有2個(gè)基準(zhǔn)的RFS)

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

(3)要素的真實(shí)位置

? ?? 以軸，點(diǎn)或平面為單位的位置定義了要素與指定的確切真實(shí)位置之間可以有多少變化。公差是2維或3維公差帶，它圍繞要素必須位于的真實(shí)位置。通常，在指定真實(shí)位置時(shí)，將使用x和y坐標(biāo)作為基準(zhǔn)尺寸(沒有公差)來引用基準(zhǔn)。這意味著您將在一個(gè)確切的位置上找到位置，并且您的公差指定了距該位置的距離。通常使用兩個(gè)或三個(gè)基準(zhǔn)定位該位置，以精確定位參考位置。通常將真實(shí)位置稱為直徑，以表示圓形或圓柱形公差帶。??

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

? 與“最大實(shí)體條件”一起使用的位置成為非常有用的控件。具有大小特征的真實(shí)位置可以一次控制特征的位置，方向和大小。MMC的真實(shí)位置有助于創(chuàng)建功能規(guī)，該規(guī)可用于快速插入到零件中，以查看一切是否在規(guī)格范圍內(nèi)。雖然需要在其自身的控件上放置參考點(diǎn)位置的真實(shí)位置，但孔在MMC中的真實(shí)位置會設(shè)置孔的最小尺寸和位置，以保持功能控制。它通過允許向零件添加額外公差來實(shí)現(xiàn)。隨著零件距離MMC越來越近，約束也越來越嚴(yán)格，孔必須更靠近其位置。但是，如果孔稍大(但仍在規(guī)格范圍內(nèi))，則它可能會進(jìn)一步偏離其真實(shí)位置，并且仍然可以發(fā)揮適當(dāng)?shù)墓δ?例如螺栓穿過)

(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)位置度計(jì)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 ? (pin gauge)=Min ? of hole (MMC)-True Position Tolerance

(9)Gauging of an External Feature

For true position under MMC of a pin:

Gauge ? (hole gauge) = Max ? 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 ? -True position tolerance (bonus)

This example Pin ? = 9.9 – 0.2 = ? 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

為了了解我們對位置控制的容忍度，我們必須徹底了解我們的基準(zhǔn)。

現(xiàn)在，將重點(diǎn)放在基準(zhǔn)孔上。我們必須建立基準(zhǔn)軸[B]。右側(cè)的孔將相對于基準(zhǔn)軸[B]定位。我們在特征控制框中針對位置公差的基準(zhǔn)標(biāo)注告訴我們，基準(zhǔn)[B]必須垂直于基準(zhǔn)[A]。

? ?基準(zhǔn)孔不一定垂直于基準(zhǔn)[A]。基準(zhǔn)孔具有用于控制基準(zhǔn)孔方向的垂直度控件。垂直度控制表示存在一個(gè)直徑為0.1且與基準(zhǔn)點(diǎn)[A]完全垂直的公差圓柱體。基準(zhǔn)孔無關(guān)的實(shí)際配合包絡(luò)線的軸必須落入該公差圓柱體之內(nèi)。

? ?無關(guān)的實(shí)際配合包絡(luò)線的軸不能為基準(zhǔn)[B]，因?yàn)樵撦S不一定垂直于基準(zhǔn)[A]。基準(zhǔn)[B]是基準(zhǔn)孔的相關(guān)實(shí)際配合包絡(luò)的軸。相關(guān)的實(shí)際配合包絡(luò)是最大的完美圓柱體，該圓柱體完全垂直于基準(zhǔn)點(diǎn)[A]，并且仍然適合于基準(zhǔn)孔內(nèi)。

? ?建立基準(zhǔn)后，我們現(xiàn)在可以查看位置公差如何相對于基準(zhǔn)定位和定向孔。位置標(biāo)注的公差告訴我們存在一個(gè)直徑為0.2的公差帶圓柱體。該圓柱體與基準(zhǔn)點(diǎn)[A]完全垂直，并且該圓柱體的中心與基準(zhǔn)點(diǎn)[B]恰好為50。孔的無關(guān)實(shí)際配合包絡(luò)線的軸必須落入該公差圓柱體內(nèi)。

? 從下圖可以看出，對于不相關(guān)的實(shí)際配合包絡(luò)線落入此圓柱體的軸的要求，允許孔相對于理想位置向基準(zhǔn)點(diǎn)[B]移動0.1或從基準(zhǔn)點(diǎn)[B]移動0.1。該要求還允許孔相對于基準(zhǔn)點(diǎn)[A]傾斜，并且傾斜由保持在公差圓柱體內(nèi)的無關(guān)實(shí)際配合包絡(luò)的軸線限制。

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.

? ?為了使我們的圍欄柱做我們想要做的事，我們將使用“投影公差帶”修改器。投影公差帶修改器是特征控制框中圓圈中的字母P。投影公差帶修改器指定公差帶投影在零件上方。它不再位于零件內(nèi)部。它完全在零件上方。圓中的“投影公差帶”修改器之后的數(shù)字是我們要公差帶投影的零件上方的距離。在我們的情況下，我們的柱子將在地面上停留40公里。

? 因此，我們想將公差帶40投影到零件上方。現(xiàn)在，不相關(guān)的孔的實(shí)際配合包絡(luò)線的軸以及柱的軸必須保持在零件上方的該公差帶內(nèi)。這限制了允許的立柱傾斜。它將帖子頂部的移動限制在可接受的范圍內(nèi)。

? 下圖顯示了投影公差帶的經(jīng)典示例。在左側(cè)，公差圓柱體在零件內(nèi)部。螺栓將自身對準(zhǔn)螺紋孔中的螺紋。當(dāng)螺栓延伸通過蓋子時(shí)，其傾斜程度達(dá)到位置公差所允許的最大程度，因此螺栓和蓋子上的間隙孔側(cè)面之間會發(fā)生沖突。右側(cè)，公差區(qū)域從頂蓋的頂部凸出。底座蓋的頂部。孔的軸線(進(jìn)而是螺栓的軸線)在穿過蓋子上的間隙孔時(shí)保持在公差圓柱體內(nèi)，并且螺栓與蓋子上的間隙孔側(cè)面之間沒有沖突。

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.

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