UNIT 2 SYSTEM OF LIMITS, FITS, TOLERANCES AND GAUGING Introduction Definition of limits Need for limit system Tolerance Tolerance dimensions ( system of writing tolerance) Relationship between Tolerance Vs Cost Compound tolerance. Tolerance accumulation or tolerance build up Specifying tolerances in assembly Interchangeability Selective assembly Limits of size Indian standard (IS 919-1963) Condition for the success of any system of limits and fits. Concepts of Limits of size and Tolerance Some Definitions Definition of Fit Types of Fit and their Designation (IS 919-1963) Specific types of Fit Allowance Geometrical Tolerance Positional Tolerance Symbols and terms used in IS 919-1965 System of Fits Hole Basis System Staff Basis System Significance of Hole Basis System Tolerance Grade Numerical Problems 1
INTRODUCTION: In nature two extremely similar (identical) things are difficult to obtain. If at all we come across exactly similar things, it must be only by chance. Its holds good for production of component parts in engineering. Every process is combination of three elements namely, man, machine and material A change in any of these constitutes a change in the process. The above said three elements are subjected to inherent and characteristics variations. Example: 1.Drilling operation is to be performed on castings. 2.Shaft rotating in bearing. Thus we conclude that: 1. It is not possible to make any part precisely to a given dimension, due to variability of elements of production process. 2. Even if by chance the part made exactly to a given dimension, it is impossible to measure it accuracy enough to prove it. 3. If attempts are made to achieve perfect size the cost of production will increase tremendously. Therefore, the magnitude of permissible variation in dimension has to be allowed to account for the variability. ******syllabus starts from here****** Limits: Definition: The maximum and minimum permissible sizes within which the actual size of a component lies are called limits. Limits are fixed with reference to the basic size of that dimension. Upper limit (The high limit ) for that dimension is the largest size permitted and the low limit is the smallest size permitted for that dimension. Need for limit system: The correct and prolonged functioning of manufactured products depends upon its correct size relationship between various components of the assembly. This means that the parts must fit together in a certain way. Example: Valve Assembly Hence purpose of limit system is to establish the types of fits and recommend the dimensions of the mating parts Tolerance: Definition: Tolerance can be defined as the permissible variation in size or dimension of a part. Or Tolerance is the difference between the upper limit and lower limit of a part. The word Tolerance indicated that a worker is not expected to produce the part to the exact size, but a definite small size error is permitted. 2
Tolerance Tolerance Basic size Tolerance Tolerance Tolerance Zone: The difference between upper limit and the lower limit of a dimension represents the margin for variation in workmanship, and is called a Tolerance zone. Example: a of 25 mm basic size may be written as 25 + 0.02. Upper limit = 25 + 0.02 = 25.02 mm Lower limit = 25 0.02 = 24.98 mm Tolerance = upper limit lower limit = 25.02 24.98 = 0.04 mm NOTE: The tolerance is always a positive quantitative number. *** very very imp. System of writing Tolerance (Toleranced dimensions): There are two systems of writing tolerance: 1. Unilateral system 2. Bilateral system 1. Unilateral system: When the two limit dimensions are only above or only below the nominal size (basic size) then the tolerances are said to be Unilateral. +0.03 +0.01-0.00-0.01 Example: 25 +0.02, 25 +0.00, 25-0.01-0.02 etc, 25 Figure: unilateral system 2. Bilateral system: When the limit dimensions are given above and below the nominal size (basic size) then the tolerances are said to be bilateral. Example: 25 +0.02 +0.00 etc, 25 3
Basic size Tolerance Tolerance Figure: Bilateral Tolerance Unilateral tolerance is preferred over bilateral tolerances because the operator can machine to the upper limit of the (or lower limit of the ) still having the w tolerance left for machining before the parts are rejected. It is easy and simpler to determine deviations GO gauge end can be standardized as the s of different tolerance grades have the same lower limit and all the s have same upper limit. Relationship between Tolerance and Cost: The relationship between tolerance and cost of production is shown in figure. If the tolerance are made closer and closer, the cost of production goes on increasing, because to manufacture the component with closer tolerance. 4
Specifying tolerance in an assembly: The type of assembly or fit between the mating parts will be decided based on the functional requirements (i.e., clearance type of fit like in bearing and.) Accordingly tolerances on the and are decided using the following two methods: 1. complete interchangeability 2. Statistical approach. In complete interchangeability, no risk is taken even for a single non-confirming assembly. If the fit between and is clearance type as shown in figure, then for the complete interchangeability. Tolerance on = Tolerance on = Half of the maximum clearance half of the minimum clearance In Statistical approach: Statistical approach bases the permissible tolerance on the normal distribution curve. Considering that only 0.3% of the parts would lie outside ±3σ limits. This approach, obviously, allow wider tolerances and permits cheaper production methods especially in mass production. It was estimated that about 33% more tolerance may be permitted by statistical approach compared to complete interchangeability. Compound Tolerance: A compound tolerance one which is derived by considering the effect of tolerance on more than one dimension. For example: in figure the tolerance on dimension L are dependent on tolerances on D, H, and Ө. This compound tolerance on L is the combined effect of all the three tolerances. The dimension L will be maximum when the base dimension is D+a, θ+α and the vertical dimension is H-d. The dimension L will be minimum when the base dimension is D-b, θ-β and the vertical dimension is H+c. L +c -d H q +a -b D +a -b figure: Compound tolerance 5
Tolerance accumulation or Tolerance Build-up : If a part consists of several steps, each step having some tolerance over its length, then overall tolerance on complete length will be the sum of the tolerance on individual lengths as shown on figure. Interchangeability: Interchangeability occurs when one part in an assembly can be substituted for a similar part which has been made to the same drawing. Suppose there are 100 parts each with a, and 100 s which have to fit into any of the s. If they is interchangeability then any one of the 100 s should fit into any of the s and the required kind of fit can be obtained. Hence, for interchangeability of s and s, we need a system of limits and fit which gives standard values for the limits on the and, so that particular type of fit can be obtained. Interchangeability is possible only when certain standard are strictly followed. In Universal interchangeability the mating parts are drawn/manufactured from two different manufacturing sources. Universal interchangeability is desirable and which will be an international standard. In Local interchangeability the mating parts are manufactured from same manufacturing sources, in which local standard is followed. The required type is obtained in an assembly either by universal or local/full interchangeability or selective assembly..selective Assembly: In selective assembly, the parts are graded according to their size by automatic gauging. In which only matched grades are assembled. This technique is most suitable for where close fit (Interference fit) of two component assembles are required. It results in complete protection against non-confirming assemblies and reduces machining costs, since close tolerance can be maintained. Example: practical example of this system is the assembly of piston with cylinder bores. Let the bore size be mm & the clearance required for the assembly 0.12mm on the diameter. Let the tolerance on bore and the piston each = 0.04mm. Then, Dimension of bore diameter is 50 +0.02 mm. Dimension of piston is 49.88 +0.02 mm. By grading and making the bores and the piston they may be selectively assembled to give the clearance of 0.12 mm as given below. Cylinder bore 49.98, 50.00, 50.02 Piston 49.86, 49.88, 49.90 6
MML LML MML LML Selective assembly is often followed in aircraft, automobiles and other industries where the tolerance are very narrow and are not possible to manufacturer by an sophisticated machine at reasonable cost. Here close tolerances to be achieved without actually being produced. Limits of Size: In deciding the limits for a particular dimension it is necessary to consider following. 1. Functional requirements: the intended function that a component should perform 2. Interchangeability: replacements of the component in case of failure/ damage without difficulty 3. Economy in production time and cost. Thus degree of tolerance provided on the mating components calls for a compromise. Number of standards on limit and fit systems has been published to help the designer in selecting the uniform limits and fits. Indian standard (IS 919 1963): The Indian standard system of limits and fits comprises suitable combination of 18 grades of fundamental tolerances or grades of accuracy of manufacturer (IT0 to IT16), and 25 types of fundamental deviations represented by letter symbols for both s and s (capital letters A to ZC for s and lower case letters a to zc for s). In diameter steps up to 500mm. The 25 fundamental deviations of are represented BY A,B,C,D,E,F,G,H,JS,J,K,M,N,P,R,S,T,U,V,X,Y,Z,ZA,ZB,ZC Maximum and minimum Metal Limits (Or Maximum and Minimum Metal conditions): HOLE SHAFT Figure: MML & LML of Hole and Shaft If the tolerance for the is given as 25 +0.05, the upper limit will be 25.05 mm and the lower limit will be 24.94 mm. The is said to be have Maximum Metal Limit (MML) of 25.05mm, since at this limit the has maximum possible amount of metal. The limit of 24.95 will then be the minimum or Least metal Limit (LML) because at this the will have the least possible amount of metal. 7
Lower deviation Max dia Min dia Min dia Max dia Upper deviation BASICSIZE Lower deviation Tolerance for Tolerance for Upper deviation Similarly, for is designated as 30 +0.05 mm. The upper limit will be 30.05 mm and the lower limit will be 29.95 mm. Then, the maximum metal limit (MML) of will be equal to 29.95 mm, since at this lower limit the has the maximum possible amount of metal. While the minimum metal limit (LML) of will be equal to 30.05 mm. then, the upper limit of the has the minimum possible amount of metal. Some Definitions: (Terminologies used in Limits and Fits) Shaft: The term refers not only to the diameter of a circular but also to any external dimension of a component. Hole: The term not only refers to the diameter of the circular but also any internal dimension of a component. HOLE ZERO LINE SHAFT Figure: Shaft and Hole System When an assembly is made of two parts, one is known as male-surface and the other mating part as female (enveloping) surface. The male surface is called as and the female surface is called as. Basic Size or Nominal Size: It is the standard size of a part in relation to which all limits of variation are determined. the basic size is same for and. Actual size: actual size is the dimension as measured on manufacturing part. Zero line: it is straight line drawn horizontally to represent the basic size. In the graphical representation of limits and fits, all the deviations are shown with respect to the zero line (datum line). The positive deviations are shown above zero line and negative deviation are shown below zero line as shown in figure. 8
lower limit basic size upper limit lower deviation tolerance Deviation: deviation is the algebraic difference between the size (actual, maximum, etc) and the corresponding basic size. Upper deviation: it is the algebraic difference between the upper (maximum) limit of size and the corresponding basic size. It is positive quantity when the upper limit of size is greater than the basic size and negative quantity when the upper limit of the size less than the basic size as shown in figure. It is denoted by ES for and es for. Lower deviation: it is it is the algebraic difference between the lower (minimum) limit of size and the corresponding basic size. It is positive quantity when the lower limit of size is greater than the basic size and negative quantity when the lower limit of the size less than the basic size. It is denoted by EI for and ei for. Fundamental deviation: either the upper or lower deviation, which is the nearest one to the zero line for either a or a. It fixes the position of Tolerance zone in relation to the zero line. tolerance zone (fundamental deviation) zero line 9
upper limit fundamnental deviation lower limit tolerance zero line (upper deviation) tolerance zone From the figure sit is very clear that when the tolerance zone is above the zero line, then lower deviation is fundamental deviation. While, the tolerance zone is below zero line, then upper deviation is fundamental deviation. Basic : basic is the whose upper deviation is zero. Thus upper limit of the basic is the same as the basic size. It is denoted by letter h Basic : basic is the whose lower deviation is zero. Thus lower limit of the basic is the same as the basic size. It is denoted by letter H Size Tolerance: The relationship of deviation with tolerance is given by, For, IT = es ei (upper deviation lower deviation) For, IT = ES EI (upper deviation lower deviation) Definition of fits, types of fits and their Designation (Is 919 1963): Fit: fit may be defined as a degree of tightness or looseness between two mating parts to perform a definite function when they are assembled together. Accordingly, a fit may result either in a moveable joint or a fixed joint. For example: a running in a bearing can move in relation to it and thus forms a moveable joint, whereas, a pulley mounted on the forms a fixed joint. Types of fits (Classification of fits): On the basis of positive, zero and negative values of clearance, there are three types of fits: 1. Clearance fit 2. Interference fit 3. Transition fit. 10
clearence 1. Clearance fit: In this type of fit, the largest permitted diameter is smaller than the diameter of the smallest as shown in figure. So that the can rotate or slide through with different degree of freedom according to the purpose of mating part. In this type of fit is always smaller than. Zero line Figure: clearance fit 2. Interference fit: In this type of fit the minimum permissible diameter of the is larger than the maximum allowable diameter of the. Here the and members are intended to be attached permanently and used as a solid component. Example: bearing bushes, steel rings on a wooden bullock cart wheel etc., 11
+ve clearence Interference Zero line 3. Transition fit. Transition fit lies mid way between clearance and interference fit. In this type of fit, the diameter of the largest allowable is greater than that of the smallest, but the smallest is smaller than the largest, so that a small positive and negative clearance exists between the and as shown in figure. Example: Spigot in mating s, coupling rings. -ve clearance Zero line 12
Maximum clearance: it is the difference between the minimum size of and maximum size of. Minimum clearance: it is the difference between the maximum size of and minimum size of. Special types of fit: 1. Slide fit: this type of fit has very small clearance, the minimum clearance being zero. Sliding fits are employed when the mating parts required to moving slowly in relation to each other. It is clearance type of fit Example: tailstock spindle of lathe, feed movement of spindle quill in drilling. 2. Driving fit: in this fit, the is made slightly larger than the. Such that parts can be assembled by driving force. This is employed when the parts are to remain in a fixed position relative to each other. It is an interference type of fit. 3. Push fit or Snug fit: this type of fit represent a close fit which permits assembling of parts by hand. It provides a small clearance It is transition type of fit Example: change gears. 4. Force fit or pressed fit: force fit are employed when the mating parts are not required to be disassembled during their total service life. In which assembly is obtained only when high pressure is applied. It is interference type of fit. Example: forging machine. 5. Selective fit or tight fit: it provides less interference than force fit. Tight fits are employed for mating parts that may be replaced while overhauling of the machine. It is interference type of fit. Example: cylindrical grinding machine. 6. Shrinkage fit: it refers to maximum negative allowance. Considerable force is necessary for the assembly. The fitting of frame on the rim can also be obtained first by heating the frame and then rapidly cooling it in its position. It is interference type of fit. 7. Freeze fit: in freeze fit the (internal member) is contracted by cooling and assembled with the (external member). 13
When the assembled parts are exposed to the atmospheric temperature, the contracted (internal member) expands and thus fit into the (external member). It is interference type fit. Example: insertion of valve seat in engine cylinder heads. Allowance: It is the intentional difference between the lower limit of the and upper limit of the. The allowance may be positive or negative. The positive allowance is called clearance and negative allowance is called interference. Difference between tolerance and Allowance; Figure: allowance Tolerance 1. It is the difference between the upper limit and lower limit of a part 2. It is the permissible difference in dimension or size of a part. 3.it is absolute value without sign 4. Tolerance provided because operator is not possible to produce a part to exact size. Allowance 1.It is the intentional difference between lower limit of to upper limit of 2. It is the prescribed difference between the dimensions of two mating parts. 3. allowance may be +ve or ve 4. allowance provided on mating parts to provide desired type of fit. Geometrical Tolerance: It is necessary to specify and control the geometric features of a component, such as straightness, flatness, roughness etc., In addition to linear dimensions. Geometric tolerances are concerned with the accuracy of the relationship of one component to another, and it should be specified separately. Geometric tolerance may be defined as the maximum permissible overall variation of form, or position of form, or position of feature. Geometric characteristics and symbols: It is of two types 14
1. Single feature 2. Related feature. Positional Tolerance: If A particular is to be drilled in a plate. First axis of the will be defined and located. Some tolerance is allowed on this. Thus center of itself can occupy any position within a square at the center depending on the tolerance specified to locate center Then some tolerance has to be specified for manufacturing. Thus obtained will be having cumulative effect of two tolerances. This problem is obviated by specifying positional tolerances. In conventional method a positional tolerance is given by tolerance coordinates is as shown in figure. In case of illustrated, it will be seen that the tolerance zone for a center is square. If the tolerance coordinate are not equal then zone would be rectangle. Thus permissible error in position of center varies within the direction of error. But, in most of the cases, the designer wishes to restrict the amount by which the may vary from its true position irrespective of direction of error. The method of tolerancing as shown in figure a and figure b provides a circular tolerance zone for the center and consequently permits the same error in any direction. A careful study of figure shows how much tolerancing allows a large positional error for a which is not on maximum metal condition. 15