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? Limits and Tolerances
? Dimensioning
The design of a machine includes many factors other than those of determining the loads and stresses and selecting the proper materials.Before construction or manufacture can begin, it is necessary to have complete assembly and detail drawings to convey all necessary information to the shop men. The designer frequently is called upon to check the drawings before they are sent to the shop. Much experience and familiarity with manufacturing processes are needed before one can become conversant with all phases of production drawings.
Drawings should be carefully checked to see that the dimensioning is done in a manner that will be most convenient and understandable to the production departments. It is obvious that a drawing should be made in such a way that it has one and only one interpretation.In particular, shop personnel should not be required to make trigonometric or other involved calculations before the production machines can be set up.
Dimensioning is an involved subject and long experience is required for its mastery.
Tolerances must be placed on the dimensions of a drawing to limit the permissible variations in size because it is impossible to manufacture a part exactly to a given dimension.
Although small tolerances give higher quality work and a better operating mechanism, the cost of manufacture increases rapidly as the tolerances are reduced, as indicated by the typical curve of Fig14.1. It is therefore important that the tolerances be specified at the largest values that the operating or functional considerations permit.
Tolerances may be either unilateral or bilateral. In unilateral dimensioning, one tolerance is zero, and all the variations are given by the other tolerance. In bilateral dimensioning, a mean dimension is used which extends to the midpoint of the tolerance zone with equal plus and minus variations extending each way from this dimension.
The development of production processes for large-volume manufacture at low cost has been largely dependent upon interchangeability of component parts. Thus the designer must determine both the proper tolerances for the individual parts, and the correct amount of clearance or interference to permit assembly with the mating parts. The manner of placing tolerances on drawings depends somewhat on the kind of product or type of manufacturing process. If the tolerance on a dimension is not specifically stated, the drawing should contain a blanket note which gives the value of the tolerance for such dimensions.However, some companies do not use blanket notes on the supposition that if each dimension is considered individually, wider tolerances than those called for in the note could probably be specified. In any event it is very important that a drawing be free from ambiguities and be subject only to a single interpretation.
Dimension and Tolerance
In dimensioning a drawing, the numbers placed in the dimension lines represent dimension that are only approximate and do not represent any degree of accuracy unless so stated by the designer.To specify a degree of accuracy, it is necessary to add tolerance figures to the dimension. Tolerance is the amount of variation permitted in the part or the total variation allowed in a given dimension. A shaft might have a nominal size of 2.5in.(63.5mm), but for practical reasons this figure could not be maintained in manufacturing without great cost. Hence, a certain tolerance would be added and, if a variation of±0.003in.(±0.08mm) could be permitted, the dimension would be stated 2.500±0.003(63.5±0.08mm).
Dimensions given close tolerances mean that the part must fit properly with some other part. Both must be given tolerances in keeping with the allowance desired, the manufacturing processes available, and the minimum cost of production and assembly that will maximize profit. Generally speaking, the cost of a part goes up as the tolerance is decreased. If a part has several or more surfaces to be machined, the cost can be excessive when little deviation is allowed from the nominal size.
Allowance, which is sometimes confused with tolerance, has an altogether different meaning. It is the minimum clearance space intended between mating parts and represents the condition of tightest permissible fit. If a shaft, size 1.498-0.003, is to fit a hole of size 1.500+0.003, the minimum size hole is 1.500 and the maximum size shaft is 1.498. Thus the allowance is 0.002 and the maximum clearance is 0.008 as based on the minimum shaft size and maximum hole dimension.
Tolerances may be either unilateral or bilateral. Unilateral tolerance means that any variation is made in only one direction from the nominal or basic dimension. Referring to the previous example, the hole is dimensioned 1.500+0.003, which represents a unilateral tolerance. If the dimensions were given as 1.500±0.003, the tolerance would be bilateral; that is, it would vary both over and under the nominal dimension. The unilateral system permits changing the tolerance while still retaining the same allowance or type of fit. With the bilateral system, this is not possible without also changing the nominal size dimension of one or both of the two mating parts. In mass production, where mating parts must be interchangeable, unilateral tolerances are customary. To have an interference or force fit between mating parts, the tolerances must be such as to create a zero or negative allowance.
Tolerances, Limits and Fits
The drawing must be a true and complete statement of the designer’s requirements expressed in such a way that the part is convenient to manufacture.Every dimension necessary to define the product must be stated once only and not repeated in different views. Dimensions relating to one particular feature, such as the position and size of a hole, should, where possible, appear on the same view.
There should be no more dimensions than are absolutely necessary, and no feature should be located by more than one dimension in any direction. It may be necessary occasionally to give an auxiliary dimension for reference, possibly for inspection. When this is so, the dimension should be enclosed in a bracket and marked for reference. Such dimensions are not governed by general tolerances.
Dimensions that affect the function of the part should always be specified and not left as the sum or difference of other dimensions. If this is not done, the total permissible variation on that dimension will form the sum or difference of the other dimensions and their tolerances, and this will result in these tolerances having to be made unnecessarily tight. The overall dimension should always appear.
All dimensions must be governed by the general tolerance on the drawing unless otherwise stated. Usually, such a tolerance will be governed by the magnitude of the dimension. Specific tolerances must always be stated on dimensions affecting function or interchangeability.
A system of tolerances is necessary to allow for the variations in accuracy that are bound to occur during manufacture, and still provide for interchangeability and correct function of the part.
A tolerance is the difference in a dimension in order to allow for unavoidable imperfections in workmanship. The tolerance range will depend on the accuracy of the manufacturing organisation, the machining process and the magnitude of the dimension.
The greater the tolerance range, the cheaper the manufacturing process. A bilateral tolerance is one where the tolerance range is disposed on both sides of the nominal dimension. A unilateral tolerance is one where the tolerance zone is on one side only of the nominal dimension, in which case the nominal dimension may form one of the limits.
Limits are the extreme dimensions of the tolerance zone. For example, nominal dimension
30mm tolerance +30.025+30.000 limits 30.02530.000
Fits depend on the relationship between the tolerance zones of two mating parts, and may be broadly classified into a clearance fit with positive allowance, a transition fit where the allowance may be either positive or negative (clearance or interference), an interference fit where the allowance is always negative.
Type of Limits and Fits
The ISO System of Limits and Fits, widely used in a number of leading metric countries, is considerably more complex than the ANSI system.
In this system, each part has a basic size. Each limit of size of a part, high and low, is defined by its deviation from the basic size, the magnitude and sign being obtained by subtracting the basic size from the limit in question. The difference between the two limits of size of a part is called the tolerance, an absolute amount without sign.
There are three classes of fits: 1) clearance fits, 2) transition fits (the assembly may have either clearance or interference), and 3) interference fits.
Either a shaft-basis system or a hole-basis system may be used. For any given basic size, a range of tolerances and deviations may be specified with respect to the line of zero deviation, called the zero line. The tolerance is a function of the basic size and is designated by a number symbol, called the grade—thus the tolerance grade.The position of the tolerance with respect to the zero line also a function of the basic size—is indicated by a letter symbol (or two letters), a capital letter for holes and a lowercase letter for shafts. Thus the specification for a hole and shaft having a basic size of 45 mm might be 45H8/g7.
Twenty standard grades of tolerances are provided, called IT01, IT0, IT1~18, providing numerical values for each nominal diameter, in arbitrary steps up to 500mm (for example 0~3, 3~6,6~10, ......, 400~500 mm).
The value of the tolerance unit, i, for grades 5~16 is i=0.453√－D +0.001D
Where i is in microns and D in millimeters.
Standard shaft and hole deviations similarly are provided by sets of formulas, however, for practical application, both tolerances and deviations are provided in three sets of rather complex tables. Additional tables give the values for basic sizes above 500 mm and for “Commonly Used Shafts and Holes” in two categories—“General Purpose” and “Fine Mechanisms and Horology”.
標(biāo)注尺寸
機(jī)械設(shè)計(jì)除了計(jì)算載荷和應(yīng)力、選擇合適的材料外，還包括許多其它因素。在建造或制造開(kāi)始前，完成裝配圖和零件圖以把必要信息傳達(dá)給車(chē)間工人是必須的。在送往車(chē)間前設(shè)計(jì)者常常被召集來(lái)檢查圖紙。而在精通生產(chǎn)圖紙的所有情況之前，需要有許多經(jīng)驗(yàn)并熟悉制造工藝。
圖紙必須仔細(xì)檢查其尺寸是否按生產(chǎn)部門(mén)最方便易懂的方式標(biāo)注。很明顯圖紙應(yīng)該只有唯一的解釋。 尺寸標(biāo)注是一項(xiàng)復(fù)雜的工作，要掌握它需要有豐富的經(jīng)驗(yàn)。尤其是不能要求車(chē)間工人在生產(chǎn)機(jī)械安排前進(jìn)行三角或其它復(fù)雜的計(jì)算。
由于要把零件加工到正好為給定尺寸是不可能的，因此圖紙的尺寸必須加上公差以限制其可允許的變化。
雖然較小公差能得到較高加工質(zhì)量和較好操作機(jī)構(gòu)，但隨著公差的減小制造成本會(huì)迅速增加，因此公差被定為從操作或功能考慮允許的最大值是重要的。
公差既可以是單向的也可以是雙向的。單向標(biāo)注有一公差為零，所有變化都由另一公差給定。而雙向標(biāo)注則采用一平均尺寸，它將公差帶中點(diǎn)從該尺寸雙向擴(kuò)展為相等的正負(fù)變化范圍。
大規(guī)模低成本制造生產(chǎn)工藝的發(fā)展很大程度取決于組成零件的互換性。因此設(shè)計(jì)者必須確定單個(gè)零件的合適公差以及配合零件裝配允許的正確間隙或過(guò)盈量。
在圖紙上標(biāo)注公差的方法相當(dāng)程度上依賴(lài)于產(chǎn)品的性質(zhì)或制造工藝的類(lèi)型。如果尺寸公差沒(méi)有特別注明，圖紙應(yīng)該包含一個(gè)給出這些尺寸公差值的普遍適用注釋。然而有些公司不采用普遍適用注釋?zhuān)俣總€(gè)尺寸是單獨(dú)被考慮的，可能會(huì)規(guī)定出比注釋中要求的更寬的公差。在任何情況下圖紙不模棱兩可并只服從于單一的解釋是十分重要的。
尺寸和公差
在圖紙標(biāo)注尺寸時(shí)，除非設(shè)計(jì)者有意標(biāo)明，注在尺寸線(xiàn)上的數(shù)字代表的尺寸僅僅是近似的，并不代表任何精度等級(jí)。為了詳細(xì)標(biāo)明精度等級(jí)，有必要在尺寸上增加公差數(shù)字。公差是零件允許的變動(dòng)量或給定尺寸允許的總變動(dòng)。
一根軸可能的名義尺寸為2.5in.(63.5mm)，但由于實(shí)際原因不用大成本是不能在制造中保持這個(gè)數(shù)字的，因此要增加確定的公差。如果允許有±0.003in.(±0.08mm)的變化，則此尺寸可表達(dá)為2.500±0.003(63.5±0.08mm)。
具有緊密公差的尺寸表示該零件必須恰當(dāng)?shù)嘏c某些其它零件配合。所采用的制造工藝和使利潤(rùn)最大化的最小生產(chǎn)及裝配成本都要求給定公差以保持所需允差。一般而言，零件的成本隨著公差的減小而上升。如果一個(gè)零件有若干或較多表面要機(jī)加工，且?guī)缀醪辉试S偏離名義尺寸，則成本會(huì)超過(guò)正常合理的界限。
允差，有時(shí)會(huì)跟公差混淆，但其具有完全不同的含義。它是配合零件之間最小的預(yù)期間隙空間，代表著允許的最緊配合條件。如果一根尺寸為1.498-0.003的軸與尺寸為1.500+0.003的孔配合，孔的最小尺寸為1.500而軸的最大尺寸為1.498。這樣允差就是0.002，而由最小軸尺寸和最大孔尺寸形成的最大間隙為0.008。
公差可以是單向的也可以是雙向的。單向公差意味著任何變動(dòng)都是只從名義或基本尺寸出發(fā)向一個(gè)方向變動(dòng)的。引用前例，孔的尺寸標(biāo)注為1.500+0.003，它表示了一個(gè)單向公差。
如果尺寸標(biāo)為1.500±0.003，就是雙向公差；即它可以在名義尺寸之上或之下變化。單向體系允許在依然保留相同允差或配合類(lèi)型的情況下改變公差。而雙向體系在不同時(shí)改變一個(gè)或兩個(gè)配合零件名義尺寸的情況下，這是不可能做到的。大規(guī)模生產(chǎn)中配合零件必須能互換，單向公差是經(jīng)常遇到的。為了使配合零件之間具有過(guò)盈或強(qiáng)制配合，公差必須產(chǎn)生零或負(fù)允差。
公差、極限和配合
圖紙必須按方便制造零件的方式將設(shè)計(jì)者的要求真實(shí)和完整地表達(dá)出來(lái)。
對(duì)每一描述產(chǎn)品所需的尺寸都只須標(biāo)注一次而不必在不同的視圖中重復(fù)。有關(guān)同一特性的尺寸，諸如孔的位置和大小，如果可能應(yīng)出現(xiàn)在同一視圖上
除絕對(duì)需要的尺寸外，不應(yīng)該有更多的尺寸；而在任意方向上，只能在一個(gè)尺寸上標(biāo)注特性要求。
偶爾也可能為了檢查而必須給出供參考的輔助尺寸。在這種情況下，尺寸應(yīng)該用括號(hào)括起來(lái)，以便參考。這樣的尺寸不受通用公差控制。
影響零件功能的尺寸總是應(yīng)該標(biāo)注的而不要留作其它尺寸的和或差。如果不是這樣，那尺寸允許的總的變化將形成其它尺寸及它們的公差的和或差，這會(huì)導(dǎo)致這些公差不得不定得過(guò)緊。總尺寸一般應(yīng)該標(biāo)注。除非另行說(shuō)明，所有尺寸都必須受圖上的通用公差控制。一般這樣的公差受到尺寸量值的控制。在影響功能或互換性的尺寸上必須標(biāo)注專(zhuān)門(mén)的公差。
為了允許在制造過(guò)程中必然會(huì)發(fā)生的精度變化，并提供零件的互換性和正確功能，一個(gè)公差系統(tǒng)是必需的。
公差是為了允許工藝上不可避免缺陷而存在的尺寸上的不同。公差范圍取決于制造機(jī)構(gòu)的精度、機(jī)加工過(guò)程和尺寸的量值。
公差范圍越大，則制造過(guò)程的成本就越低。雙向公差是在公稱(chēng)尺寸兩側(cè)都有公差帶的公差。單向公差是僅在公稱(chēng)尺寸一側(cè)有公差帶的公差，在這種情況下公稱(chēng)尺寸成了兩個(gè)極限中的一個(gè)。
極限是公差帶的極限尺寸。例如公稱(chēng)尺寸30毫米 公差 極限
配合取決于兩配合零件公差帶之間的關(guān)系，并且可以概括地分為具有正允差的間隙配合，允差可以是正或負(fù)的過(guò)渡配合和總是負(fù)允差的過(guò)盈配合。
極限和配合的類(lèi)型
在一些最主要采用公制的國(guó)家中廣泛使用的ISO的極限和配合系統(tǒng)，比ANSI的極限和配合系統(tǒng)要復(fù)雜得多。
在這個(gè)系統(tǒng)中，每個(gè)零件都有基本尺寸。零件尺寸的每一極限，不管大小，都通過(guò)對(duì)基本尺寸的偏差來(lái)定義；其量值和符號(hào)由正被討論的極限減去基本尺寸得到。零件尺寸的兩個(gè)極限之差稱(chēng)為公差，這是一個(gè)沒(méi)有符號(hào)的絕對(duì)量值。
存在三種配合：1)間隙配合，2)過(guò)渡配合(裝配后可以有間隙或過(guò)盈)，和3)過(guò)盈配合。
在一些最主要采用公制的國(guó)家中廣泛使用的ISO的極限和配合系統(tǒng)，比ANSI的極限和配合系統(tǒng)要復(fù)雜得多。
在這個(gè)系統(tǒng)中，每個(gè)零件都有基本尺寸。零件尺寸的每一極限，不管大小，都通過(guò)對(duì)基本尺寸的偏差來(lái)定義；其量值和符號(hào)由正被討論的極限減去基本尺寸得到。零件尺寸的兩個(gè)極限之差稱(chēng)為公差，這是一個(gè)沒(méi)有符號(hào)的絕對(duì)量值。
基軸制或基孔制均可采用。對(duì)任何給定的基本尺寸，公差范圍和偏差可以相對(duì)于被稱(chēng)為零線(xiàn)的零偏差線(xiàn)來(lái)確定。
公差是基本尺寸的函數(shù) 并通過(guò)一個(gè)被稱(chēng)為等級(jí)的數(shù)字符號(hào)標(biāo)明—即公差等級(jí)。公差相對(duì)于零線(xiàn)的位置同樣為基本尺寸的函數(shù)通過(guò)一個(gè)或兩個(gè)字母符號(hào)表達(dá)，大寫(xiě)字母表示孔而小寫(xiě)字母表示軸。這樣基本尺寸為45毫米的一個(gè)孔和軸配合規(guī)格可能是45H8/g7。
ISO規(guī)定了二十種標(biāo)準(zhǔn)的公差等級(jí)，稱(chēng)之為IT01，IT0，IT1~18，給在直至500毫米強(qiáng)行分段(例如0~3，3~6，6~10, ......, 400~500毫米)中的公稱(chēng)直徑提供具體數(shù)值。
對(duì)5～16級(jí)而言，公差單位i的值可用下式計(jì)算這里i的單位是微米，而D的單位是毫米。
標(biāo)準(zhǔn)的軸和孔偏差同樣都由若干公式提供；然而對(duì)實(shí)際應(yīng)用，公差和偏差都在三張相當(dāng)復(fù)雜的表格中規(guī)定了。
對(duì)基本尺寸大于500毫米和在“一般用途”和“精密機(jī)械和鐘表”兩個(gè)類(lèi)別中的“常用的軸和孔”而言，由附加的表格給出數(shù)值。