Understanding Limits, Fits & Tolerances in Engineering Drawings

1. Chaptr -2 Limit, Fit, Tolerance

2. Co • C505.2 • Know the system of limits, fits, tolerances and correlate it with machine drawing.

3. Hole Shaft LIMITS, FITS & TOLERANCE • Terminology:- The terms related to limit system as per BIS are as below; • Size:- It is a number expressed in a particular unit in the measurement of length. • Basic Size:- It is the size based on which the dimensional deviations are given. Basic Size • Actual Size:- It is the size of the component by actual measurement after it is manufactured. It should lie between the two limits of size.

4. Limits of size:- These are the extreme permissible sizes within which the operator is expected to make the component. Maximum limit of size is the greater of the two limit size, whereas the Minimum limit of size is the smaller of the two limit of size. • Hole:- In the B.I.S. system of limits and fits, all internal features of a component including those which are not cylindrical are designated as ‘Hole’. Basic size Hole Shaft • Shaft:- In the B.I.S. system of limits and fits, all external features of a component including those which are not cylindrical are designated as ‘Shaft’.

5. Upper Deviation Lower Deviation • Tolerance:- It is the difference between maximum limit of size and the minimum limit of size. It is always positive and is expressed only as a number without a sign. Tolerance Hole Max.dia. Min.dia. Shaft • Zero line:- In graphical representation of the above terms, the zero line represents the basic size. This line is also called as the line of zero deviation.

6. Upper Deviation Lower Deviation Tolerance Tolerance Hole Max.dia. Min.dia. Max.dia. Min.dia. Shaft • Fundamental deviation:- There are 25 fundamental deviations in the B.I.S. system represented by letter, symbols (Capital letters for Holes and small letters for Shaft)

7. Upper Deviation Lower Deviation • Fundamental Tolerance:- This is also called as ‘grade of tolerance’. In the Indian Standard System, there are 18 grades represented by number symbols, both for hole and shaft denoted as IT01, IT0, IT1, IT2.....IT16. A high number Tolerance Max.dia. Hole Min.dia. Max.dia. Min.dia. Shaft

9. Hole Shaft • FIT:- It is the relationship that exists between two mating parts, a hole and shaft with respect to their dimensional difference before assembly. Three types of fit are given hereunder; • Clearance fit:- It is a fit which always provides clearance. Here the tolerance zone of the hole will be above the tolerance zone of the shaft. Maximum clearance is the difference between the maximum hole and minimum shaft. Minimum clearance is the difference between the minimum hole and maximum shaft. Clearance fit

10. Tolerance Zone of Shaft Tolerance Zone of Hole Shaft Hole • Interference fit:- It is a fit which always provides interference. Here the tolerance zone of the hole will be below the tolerance zone of the shaft. Maximum interference is the algebraic difference between the minimum hole and maximum shaft. Minimum interference is the algebraic difference between the maximum hole and minimum shaft.

11. Shaft Hole Hole Hole Shaft Shaft • Transition fit:- It is a fit which may sometimes provides clearance and sometimes interference. When this class of fit is represented graphically, the tolerance zone of the hole and shaft will overlap each other. Mass Production :- Mass production means production of a unit, component or part in large numbers.

12. Advantages:- 1.Time for the manufacture of components is reduced 2.The cost of pieces is reduced. 3. Spare parts can be quickly made available. Disadvantages:-1. Special purpose machines are necessary. 2.Jigs and Fixtures are needed. 3. Gauges are to be used instead of conventional precision instruments. 4. Initial expenditure will be very high.

13. Interchangeability:- When components are mass produced, unless they are interchangeable, the purpose of mass production is not fulfilled. By interchangeability, we mean that identical components, manufactured by different personnel under different environments, can be assembled and replaced without any further rectification during the assembly stage, without affecting the functioning of the component when assembled. • Hole Basis System:- Where the size of the hole is kept constant and the size of the shaft is varied to get the different class of fits, then it is known as the hole basis system.

14. MQAR Metrology, Quality Assurance & Reliability Text Books : Engg. Metrology by R.K.Jain Reference Books : 1.Statistical Quality Control by M. Mahajan, 2.Reliabity Engg. by L.Srinath . 1.Need of Inspection 2 . Standards of Measurement 3. Angle Measurement 4. Inspection of Screw-thread elements 5. S.Q.C. 6.Reliability Data Analysis TOPICS TO BE COVERED from greek “metron” (measure) and –logy. metrology is the science of measurements and that to measure is to compare with something (a unit) which is taken as the basis for comparison. (Measurement standard) includes all theoretical and practical aspects of measurement. Quality: a product’s fitness for use. the totality of features that bear on a product’s ability to satisfy a given need. the ability of a system or component to perform its required functions under stated conditions for a specified period of time. –Failure: the inability of an equipment to perform its required function –Reliability: the probability of no failure throughout a prescribed operating period. Metrology: Reliability This is the set of actions taken to develop primary standards of measurement for the base units and the derived units of the International System of Units (SI). Legal metrology Scientific metrology It is that part of metrology which treats units of measurement, methods of measurement and the measuring instrument, in relation to the statutory, technical and legal requirements. It assures security and appropriate accuracy of measurement. Industrial metrology The function of industrial metrology is mainly the proper calibration, control and maintenance of all measuring equipment used in production, inspection and testing. The purpose is to guarantee that the products will comply with quality standards. For convenience, a distinction is often made between the several fields of application of metrology Process of Measurement set of operations having the objective of determining a value of a quantity  Measurand: particular quantity subject to measurement  Reference/Standard of Measurement:  Comparator: Fixed Gauges / Measuring Instrument: Needs of Inspection To ensure that part and components are confirmed to required standards. To meet the need of Interchangeability of parts. To maintain good customer relationship by ensuring that No faulty product reaches the customer. The result of inspection are forwarded to the manufacturing department, thus helps in improving the quality. It helps to purchase good quality raw material, tool and equipment. It led to development of precision measuring instruments. High Quality Product performs its functions reliably performs its functions for a long time performs its functions conveniently Low Quality Product does not perform its function reliably fails or breaks after short time of use is difficult to use GOAL Continuous Quality Improvement (functionality, reliability, durability, …) Inspection (Measurement) What? When? How? Inspection specific to PRODUCTS Electronic parts (circuits, chips, etc.) Machine elements (engines, brakes, gears, etc.) Heat and thermodynamic components (engines, fuel injectors, etc.) Medical and Bio-related products (implants, dental devices, surgical parts, etc.) … Inspection specific to PROCESSES Chip removal processes (turning, milling, drilling, etc.) Chipless manufacturing (casting, molding, forging, etc.) Non-traditional methods (EDM, ECM, ultrasonics, etc.) … Inspection AFTER production costly production steps already complete high cost of rejection or rework difficult to test for all possible defects difficult to identify responsibility for defect Inspection DURING production defects found early, at each production step reduced cost of rejection or rework facilitates continuous process improvement Measurement of DIMENSIONS Linear measurements (length, thickness, etc.) Angular measurements (taper, angle, etc.) Measurement of surface texture (roughness, waviness, etc.) Measurement of geometric shape (roundness, flatness, squareness, etc.) Measurement of screw threads and gears Inspection for DIMENSIONAL ACCURACY post-process (traditional) in-process (modern trend) DIMENSIONAL TOLERANCES permissible variation in dimensions directly affects product quality and cost SOURCES OF ERRORS an error is defined as real (untrue, wrong, false, no go) value at the output of a measurement system minus ideal (true, good, right, go) value. Error = Ŧ(MV – TV) Classification of errors: 1.Absolute Error:- It is the algebraic difference between the result of measurement and the value of comparison. (a) True absolute error: algebraic difference between result of measurement and conventional true value. (b) Apparent absolute error: if a series of measurements are made, the difference between one of the measurement and the arithmetic mean. 1.Relative Error:- It is the ratio of absolute error and the value of comparision used for measurement. Relative error = (Absolute error/True value) TYPES OF ERRORS Static Error Reading Error Environmental Error Characteristic Error Dynamic Error Systematic Error Random Error Instrumental loading Error 1. Static Error: these result from the physical nature of the various components of the measuring system as the system responds to a fixed Measurand input. Due to intrinsic imperfections in the hardware and apparatus compared to the ideal instrument. (a) Reading Error: i. Parallax Error: Possibility of Error due to parallax (Read out). Use of mirror behind the read out or pointer virtually eliminates such type of error. ii. Interpolation Error: It can be tackled by increasing Optical resolution by using a magnifier or using digital read out devices. (a) Environmental Error: This error is due to the effect of surrounding temperature, pressure and humidity on measuring system. External influences also include Magnetic or electric fields, nuclear radiation, vibration or shock etc… these factors affects both measuring system and measurand. (b) Characteristic Error: The deviation of the output of the measuring system under constant environmental conditions from the theoretical predicted performance or from nominal performance specification. 2. Instrumental loading Error: This result from the change in measurand itself when it is being measured. It is thus the difference between the value of the measurand before and after the measurement system has measured. 1. Dynamic Error: (Related with time) This error caused by time variation in the measurand and results from the inability of a measuring system to respond faithfully to a time varying measurand. Usually dynamic response is limited by inertia, damping, friction or other physical constraints in the sensing, read out or display system. Systematic Errors Come from the measuring instruments. Something is wrong with the instrument or its data handling system, or instrument is wrongly used by the Experimenter. The errors in temperature measurements because of poor thermal contact between the thermometer and the substance. Errors in measurements of solar radiation astrees or buildings shade the radiometer. Random Errors Caused by unknown and unpredictable changes in the experiment. May occur in the measuring instruments or in the environmental conditions (humidity, temperature, etc.) The errors in voltage measurements because of an electronic noise in the circuit of electrical instrument. irregular changes in the heat loss rate from a solar collector due to the wind. A thermometer that always Reads 3ºcolder than the actual temperature A thermometer that gives random values within 3º either side of the actual temperature Systematic Errors Reproducible between measurements. In principle, they can be eliminated partially or completely.(Controllable error) Accuracy is often reduced by systematic errors, which are difficult to detect even for experienced researchers. We must define their size To estimate what confidence We have in our measured value. Random Errors Not reproducible, but fluctuate in magnitude and sign between measurements. We can only know the probable range over which a random error lies. Precision is limited by the random errors. It may usually be determined by repeating the measurements. They can be estimated so that the measured value can be adjusted to allow for them. Accuracy and Precision Precision is defined as the repeatability of the measuring instrument. It shows how close the measured values are to each other. The precision of a measurement is the size of the unit you use to make a measurement. Ex: 12 s and 12 day The number of decimal places in a measurement also affects precision. 10,10.1, 10.12, 10.1237….. Accuracy is how close a measured value is to the actual (true) value. The accuracy of a measurement is the difference between your measurement and the accepted correct answer. The bigger the difference, the less accurate your measurement. Mistake of 5 cm in measurement of 100 cm or 1000cm… Difference between Accuracy and Precision Low Accuracy High Precision High Accuracy Low Precision High Accuracy High Precision apply a systematic adjustment need to change the equipment or methodology used If the instrument measures in "1"s then any value between 6½ and 7½ is measured as "7" If the instrument measures in "2"s then any value between 7 and 9 is measured as "8" Degree of Accuracy Accuracy depends on the instrument you are measuring with. But as a general rule: The degree of accuracy is half a unit each side of the unit of measure Factors affecting Accuracy: 1. Standard: ambient influence, stability with time, elastic property, Position of use…… 2. Work piece: ambient influence, cleanliness, surface condition, Elasticity, support arrangement, defining datum. 3. Instrument: hysteresis, backlash, friction, zero drift, error in Amplification, calibration error etc….. 4. Personal: Improper training for handling instrument, skill, sense of Precision and accuracy, attitude…… 5. Environmental: temperature, vibration, lighting, pressure…. SENSITIVITY OF MEASUREMENT Smallest difference in a dimension that an instrument can distinguish or detect. It may be defined as the rate of displacement of the indicating device of an instrument, w.r.t the measured quantity. In other words, sensitivity of an instrument is the ratio of the scale spacing to the scale division value. For example, if on a dial indicator, the scale spacing is 1.0cm and the scale division value is 0.01cm, then sensitivity is 100. It is also called as amplification factor or gearing ratio. Environmental changes affect instruments in two main ways, known as zero drift and sensitivity drift. Zero drift describes the effect where the zero reading of an instrument is modified by a change in ambient conditions. Sensitivity drift (also known as scale factor drift) defines the amount by which an instrument's sensitivity of measurement varies as ambient conditions change. CALIBRATION Calibration is the set of operations that establish, under specified conditions, the relationship between the values of quantities indicated by a measuring instrument and the corresponding values realized by standards. Calibration is the process of establishing the relationship between a measuring device and the units of measure. This is done by comparing a device or the output of an instrument to a standard having known measurement characteristics. When the instrument is made to give a null indication corresponding to a null value of the quantity to be measured, the set of operation is called zero adjustment . Calibration can be called for: with a new instrument when a specified time period is elapsed when a specified usage (operating hours) has elapsed when an instrument has had a shock or vibration which potentially may have put it out of calibration whenever observations appear questionable Calibration Adjusting or setting of an instrument to obtain accurate readings within a reference standard. Readability Susceptibility of an instrument for having its indications converted to a meaningful number. Precision Degree of agreement in the measurements of the same quantity. Repeatability Ability to do the same thing over & over. Error between a number of successive Attempts to move a machine to the same position. Terminology Accuracy Degree of agreement of the measured dimension with its true magnitude. Sensitivity Smallest difference in a dimension that an instrument can distinguish or detect. Resolution Smallest dimension that can be read on an instrument. Reproducibility Degree of agreement in the individual results using the same method and the same test substance, but a different set of laboratory conditions. 1 75 2 35 3 50 4 85 5 95 6 92 7 45 8 56 9 86 10 71 Mean 69.0 1 74 2 73 3 72 4 64 5 65 6 66 7 69 8 68 9 70 10 69 Mean 69.0 Standard Deviation A measure of the spread of a probability distribution, random variable, or multiset of values. More formally, it is the root mean square deviation of values from their arithmetic mean. In practice, it is often assumed that the data are from an approximately Normally distributed population. According to this, confidence intervals are: σ: 68.26894921371% 4σ:99.99366575163% 2σ:95.44997361036% 5σ:99.99994266969% 3σ:99.73002039367% 6σ:99.99999980268% Interchangeability An interchangeable part is one which can be substituted for similar part manufactured to the same drawing. The required fit assembly can be obtained in Two ways. a)Universal or full interchangeability b)Selective assembly Full interchangeability means any component will mat with any other mating component without classifying Manufactured components into sub groups or Without carrying out minor alteration for mating Purpose. It requires precise machines or processes whose Process Capability is equal or less than the manufacturing Tolerances allowed for that part. So every component produced will be with in desired tolerances and capable of mating(Fitting) with any other mating components to give the required Fit. Process capability of a machine is defined as its ±3σ spread of dimensions of components produced by it. Advantages of Interchangeability 1.Assembly time is reduced considerably. 2.There is an increased output with reduced production cost. 3.It facilitates production of mating components at different places by different operator. 1.The replacement of worn out or defective parts and repair becomes very easy. 2.The cost of maintenance and shutdown period is also reduced to minimum. Selective Assembly: In selective assembly components produced are classified into groups according to their sizes by automatic gauging. This is done for both Holes and Shafts and then corresponding parts will be matched properly. It reduces chance of defective assembly and also the cost of assembly as parts may be produced in wider tolerances. Ex: Assembly of piston with cylinder bores. Bore size = 50 mm clearance required for assembly= 0.12 mm Tolerance in both bore and piston = 0.04 mm Dimension of bore diameter = 50 ±0.02 mm Dimension of piston = 49.88 ±0.02 mm By grading and marking the bores and pistons, they can be selectively assembled as follows… Cylinder Bore= 49.98mm 50 mm 50.02 mm Piston = 49.86mm 49.88 mm 49.90 mm Limits, Fits and Tolerances: 1.It is not possible to make any part precisely to a given dimension due to variability of elements of production processes. Man Machine Material 2. If by chance the part is exactly to a given dimension, it is impossible to measure it accurately enough to prove it. 3. If attempts are made to achieve perfect size, the cost of production will increase. For a given system of Limits and fits to be successful following conditions are to be satisfied:  It must be based on same standard so that every body alike and a given dimension has the same meaning at all places.  The range of sizes covered by the systems should be sufficient for most purposes.  Each basic size of hole and shaft must have a range of tolerance values for each of the different fits.  Both unilateral and bi lateral methods of tolerances and hole basis or shaft basis system should be acceptable.  The fundamental deviation required to give a particular fit must increase with the basic size. Size Designations  Shaft: It refers not only to the diameter of a circular shaft but Also to any external dimension of a component. (Male surface)  Hole: It refers not only to the diameter of a circular Hole but also to any internal dimension of a component. (Female surface)  Basic Size or Basic dimension: It is the theoretical size worked out by purely design consideration, from which limits of size are derived by the application of allowances and tolerances.  Actual Size: is the measured size of the finished part.  Zero line: It is the straight line drawn horizontally to represent the basic size. All the dimensions are shown w.r.t the Zero line. Some Definitions Limit: Due to inevitable inaccuracy of manufacturing methods, it is not possible to make a part precisely to a given dimension and may only be made to lie between to extremely permissible sizes called the limits for the actual size. Upper/Lower limit: Largest/Lowest size permitted Tolerance: The permissible variation in size or dimension of a part is called Tolerance. It is the difference between U.L and L.L of dimension. It is the amount by which the job is allowed to go away from accuracy, with out causing any functional trouble. Tolerance is always +ve. Unilateral Tolerance: In this, the dimension is allowed to vary only in one direction of Basic Size, either above or bellow it. Bilateral Tolerance: In this the dimension of part is allowed to vary in both the sides of the basic size. Deviation: It is the algebraic difference between the actual size and the corresponding basic size. Upper Deviation: It is the algebraic difference between the upper (Max) limit and the corresponding basic size. Denoted by “ES” for Hole and “es” for shaft. +ve when UL> Basic size & -ve when UL< Basic size. Lower Deviation: It is the algebraic difference between lower limit and corresponding Basic size. Denoted by “EI” for Hole and “ei” for shaft. +ve when LL> Basic size & -ve when LL< Basic size. So, Tolerance = IT For Shaft: IT = es – ei For Hole: IT = ES - EI Fundamental Deviation: (FD) It is one of the two deviations (Either UD or LD) which is conventionally choosen to define the position of tolerance Zone in relation to the zero line. It is one of the two deviations (Either UD or LD) which is Nearest to the zero line for either hole or shaft. When tolerance zone is above the zero line, LD is the FD. When tolerance zone is bellow the zero line UD is the FD. Maximum Metal Limit (MML): At this limit the part has maximum possible amount of metal. UL for Shaft and LL for Hole. Least Metal Limit (LML): At this limit the part has minimum possible amount of metal. LL for Shaft and UL of Hole. Basic Shaft (h) It is the shaft whose upper deviation is Zero. UL= basic size. Basic Hole (H) It is the hole whose lower deviation is Zero. LL= basic size Tolerance Zone: It is the zone bounded by two limits of size of a part. Tolerance grade (IT): It is the degree of accuracy manufacture and is designated by the letter IT followed by a number. There are 18 grades of tolerances – IT01, IT0, IT1 to IT16 Larger the number, greater will be the tolerance. IT01 to IT4 - For production of gauges, measuring instruments IT5 to IT 7 - For fits in precision engineering applications IT8 to IT11 – For General Engineering IT12 to IT14 – For Sheet metal working or press working IT12 to IT14 – For Sheet metal working or press working IT15 to IT16 – For processes like casting, general cutting work Standard Tolerance Unit (i) A unit, which is a function of Basic size and which is common To the formula defining the different grades of tolerances. It is denoted by letter “i” and expressed in Microns. It serves as a basis for determining the standard tolerance (IT) Of the system. (Micron) where, D (mm) is the geometric mean of the lower and upper diameters of a particular diameter step within which the chosen the diameter D lies. Clearance: This is the difference between the sizes of the Hole and shaft before assembly when this difference is positive. Maximum size of Hole-Minimum size of shaft=Max. clearance Minimum size of Hole-Maximum size of shaft=Min. Clearance. Size: A number expressing the numerical value of a length in a particular unit. Allowance: It is the prescribed difference between the dimension of two mating parts (Hole and Shaft) It is the intentional difference between lower limit of hole and Higher limit of shaft. Allowance= LLH-HLS It may be +ve or –ve. +ve allowance = clearance -ve allowance = Interference Tolerance Allowance • Permissible variation in dimension of a part. • Tolerance= UL – LL • It is provided to the dimension of a part. • It has Absolute value with out sign. • Prescribed difference between the dimension of two mating parts. • Allowance = LLH - ULS • Provided on the dimension of mating parts to obtain the desired type of fit. • It may be +ve. or –ve. “Go” limit and “NOGO” limit: “GO” limit refers to UL of shaft and LL of Hole. Thus it corresponds to MML. “NOGO” limit refers to the LL of a shaft and UL of a hole. Thus it corresponds to LML. Fits: It is the degree of tightness or looseness between two mating Parts to perform a definite function when they are assembled Together. A fit may result either in a movable joint or a fixed joint. Ex: Shaft in Bearing, Pulley on a Shaft. Classification Clearance fit a) Slide Fit b) Easy Slide fit c) Running fit d) Slack running fit e) Loose running fit Transition fit a) Push Fit b) Wringing fit Interference fit a) Force Fit b) Tight fit c) Shrink fit Clearance fit: In this type of fit Shaft is always smaller than the Hole i.e. UL of shaft is smaller than LL of Hole. Clearance fit exists when the shaft and the hole are at their MML. The Tolerance zone of hole will be above the shaft tolerance. Allowance is +ve. Ex: Shaft can rotate or slide in a bearing with different DOF according to purpose of mating part. a)Slide Fit: Tail stock spindle of Lathe b)Easy Slide fit: Spindle of lathe & dividing head, Pistons & Slide Valves, Spigots etc. c)Running fit: Gear Box Bearings, Shaft Pulleys d)Slack running fit: Arm Shaft of IC Engine, Shaft of CF Pump e)Loose running fit: Idle Pulley on their shaft (Quick Return Mechanism) Interference fit In this type of fit, LL of shaft is larger than UL of Hole. Thus, the shaft and holes are attached permanently and used as a solid Component. Elastic strains are developed during the process of assembly. Allowance is –ve. (Interference) Ex: Bearing bush, Small end in connecting rod, Gear in intermediate shafts in trucks. a)Force Fit: Gears on the shaft b)Tight fit: Stepped pulley on drive shaft of a conveyor, Cylindrical Grinding M/C. A)Shrink fit/ Heavy Force fit: Metallic rim on the wheels of a cart. Transition fit: It lies midway between the clearance and interference fit. In this, tolerance zone of hole and shaft overlap completely or in part. UL of hole > LL of shaft but LL of hole < UL of shaft. Ex: Spigot in Mating parts, Coupling rings etc. a)Push Fit: Change gears, Slip bushings b)Wringing fit: Parts which can be replaced with out difficulty during minor repairs. Hole Basis System: The size of hole is kept constant and shaft sizes are varied to Give various types of fits. In this, lower deviation of the hole is Zero i.e. LL = Basic size. Hole basis system is commonly used as it is convenient to make a hole of correct size due to availability of standard drills, Reamers, with less cost. Shaft Basis System: The size of the shaft is kept constant and sizes of hole are varied to get the required type of fit. In this, Upper Deviation of the shaft is zero i.e. UL= Basic size. This system is not suitable for mass production because it is Time consuming and costly to make a shaft of correct size. Recommendation for limits and fits for Engineering: For universal Interchangeability it is essential to follow a uniform standard Through out the world. Indian standards (IS) are in line with ISO recommendations. It consists of 25 Holes designated by capital letter 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 It consists of 25 shafts designated by small letter 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 Each of holes and shafts has a choice of 18 Grades of Tolerances Designated as: IT01, IT0, IT1, IT2, IT3, ……… IT15, IT16. IT01 – 0.3 + 0.008D IT0 – 0.5 + 0.012 D IT1 – 0.8 + 0.020D IT2 – 2.7i; IT3 - 3.7i; IT4 – 5i; IT5 – 7i; IT6 – 10 i; IT7 – 16i; IT8 – 25i; IT9 – 40i; IT10 – 64i; IT11 – 100i; IT12 –160i; IT13 – 250i; IT14 – 400i; IT15 – 640i; IT16 – 1000i. The value of IT for Hole and shaft Using the value of “i” as Where D=Geometric Mean Diameter of the lower and upper diameters of A Particular diameter step in which diameter lies in mm. The seven Tolerance grades IT01, IT0, IT1, IT2, IT3, IT4, IT5 covers diameter Sizes up to 500 mm and rest eleven grades i.e. IT06 – IT16 covers diameter Sizes up to 3150 mm. Fundamental Deviation are obtained from Empirical Formula (Table/Given in Question) for shaft and hole respectively up to 500 mm. FD for Hole A – H are same as that of Shaft a – h but opposite in direction. They provide clearance fit. FD for hole “H” and shaft “h” are Zero. Now IT = ES – EI (Hole) IT = es – ei (Shaft) Basic size followed by symbol Φ30 H7/h8 Hole with tolerance Grade IT7 = 16i Shaft with tolerance grade IT8 = 25i. If Hole basis system FD for hole = 0 FD for shaft can be found out from the table or given in the question. Example #1 Evaluate limits and fits for a pair of – Diameter 6 H7/g6. The size 6 mm lies in the diametral step of 3-6. Standard tolerance for hole H7 is 16i and shaft g6 is 10i. Fundamental deviation for g shaft is µ. Calculate the limits of sizes for φ 25 S8/h7 and identify the fit. The size 25 mm lies in the diametral step of 24-30. The fundamental deviation S8 hole – IT7 + 0.4D. For grade 8 and 7 the standard tolerance is 25i and 16i respectively. Calculate the limits of sizes for φ 60 H8/m6 and identify the fit. The size 60 mm lies in the diametral step of 50-80 mm. The fundamental deviation for m is IT7 – IT6. For grade 6 and 7 the multipliers are 10 and 16 respectively. Calculate the limits of sizes for φ 32 S7/h6 and identify the fit. The size 32 mm lies in the diametral step of 30-50 mm. The fundamental deviation S is IT7+0.4D. For grade 6 and 7 the multipliers are 10 and 16 respectively. GAUGES Gauges are scale less inspection tools at rigid design which are used to check the dimensions of manufactured parts. Measurement by gauges is Easy and rapid. So they are suitable in mass production. Instead of measuring actual dimension of each part which is time consuming and Costly, the conformance of part with tolerance specification can be checked by gauges. Measuring Instrument Gauges 1. They carry calibrated scales. 1. With out scales. They are general purpose instrument. They are made for a particular component. Measures actual dimension of part. Checks whether the dimensions of parts are with in the specified tolerance limit or not. Time consuming and not suitable for mass production. Easy and rapid, suitable for mass production. Skilled labour to handle. No need of skilled labour. Increased cost. Reduced cost. Adjustment is required. No adjustment PLAIN GAUGES Plain gauges are used to check plain, i.e. unthreaded holes and shafts. Classification: 1.According to Type (a)Standard Gauge: If a gauge is made as an exact copy of the mating part Of component to be checked, it is called standard gauge. A standard gauge can’t be used to check interference fit. It has limited application. (a)Limit Gauge: Two gauges are used to check each dimension of the Part i.e. upper and lower limit. These are “GO” and “NO-GO” gauges. GO gauges check MML and NO GO gauges check LML. These are widely used industries. A part is considered to be good if the GO gauge pass through the work and the NO GO gauge fails to pass under the action of its own weight. This Confirms the actual dimension of part with in the specified tolerances. If both the gauges fail, it indicates that hole is under size and shaft is Oversize. 1. According to Purpose: a) Workshop gauge b) Inspection gauge c) Reference or master gauge d) Purchase inspection gauge 2. According to the form of the tested surface: a) Plug gauges for checking holes b) Snap or Ring or Gap gauges for checking the shaft 3. According to their design: a) Single limit or double limit gauges b) Single ended or double ended gauges c) Fixed and adjustable gauges Difference between work shop gauge and Inspection gauge? Work shop gauge: 1.Used by the operator during manufacture of a part in shop. 2.Usually have limits with in those of components being inspected. 3.The tolerance is arranged to fall inside the work tolerance. 4.Some of the components which are in work tolerance limit may be rejected under these gauges. Inspection Gauge: 1.Used by inspector for the final inspection. 2.These gauges are made slightly larger tolerance than the work shop gauges. 3.The tolerance on inspection gauges is arranged to fall outside the work tolerance. 4.Some rejected parts may be accepted. IT of Inspection Gauge>Work tolerance>W/S Gauge Tolerance. Gauge Tolerance/ Gauge Maker’s Tolerance/ Manufacturing Tolerance: In actual practice Gauges can’t be manufactured to the exact size (Due to imperfection in the process). Some allowance must be provided to the gauge maker known as gauge tolerance. Gauge tolerance should be kept as small as possible but this will increase the cost of manufacturing the gauges. Gauge tolerance of limit gauges (GT)= 1/10th of Work Tolerance (WT) Or Work shop Gauges (GO, NOGO Gauges) (10%) Gauge tolerance for Inspection gauges (GT) = 5% of WT (GO, NOGO Gauges) Gauge tolerance for Master/Reference gauges (GT) = 10% of WT Wear Allowance: The measuring surfaces of GO gauges rub constantly against the surfaces of work piece during checking. This results in wearing of measuring surfaces of gauges. The size of GO plug gauges is reduced and that of Ring or Snap Gauges is increased. Wear allowance is provided to the gauges in the direction Opposite to that of the wear. WA is not provided for NOGO gauges as they are not Subjected to much wear compared to GO gauges. GO plug gauges => WA is added. GO snap or ring gauges => WA is subtracted. WA = 5% of WT or 10% of GT. WA may be avoided in clearance fit. WA is applied to W/S GO gauges not to Inspection GO gauges. Providing WA, the GO gauge will reject more number of acceptable parts as compared to gauge with only GT. WA is provided when WT>0.09 mm. Three basic size of Gauges: 1.Work shop gauge: GT is with in WT, some accepted parts are rejected, WA is given to W/S GO Gauge. 1.Inspection gauge: GT is out side the WT, some rejected parts are Accepted, As GO gauge for inspection is fairly slack, no WA is required. 1.General gauge:  To over come the draw back of w/s and inspection gauge, general gauge has been recommended.  Tolerance zone of GO gauge placed inside Work tolerance.  Tolerance zone of NOGO gauge placed outside work tolerance.  GO gauge of General gauge is taken same as W/S gauge.  NOGO gauge of General gauge is taken same as Inspection gauge. Taylor’s Principle of Gauge Design: It states that 1. “Go gauges should be designed to check the Maximum Metal Limit (MML) while the NO GO gauge should be designed to check the Least Metal Limit (LML).” GO plug gauge should correspond to LL of Hole. NOGO plug gauge should correspond to UL of Hole. GO snap gauge should correspond to UL of shaft. NOGO snap gauge should correspond to LL of shaft. The difference between the GO and NOGO plug gauge as well as the difference in size between GO and NOGO snap Gauge is approximately equal to the work tolerance. 2. “GO gauges should check all the related dimensions (Roundness, size, location, straightness etc). NOGO gauges should check only one element of the dimension at a time.” GO plug gauge should have a full circular section and full Length of the hole it has to check. It ensures that any lack Of straightness or roundness of the hole will prevent the entry Of full length GO gauge. The length of GO plug gauge should not be less than 1.5 times the diameter of the hole to be checked. Calculate the dimension of Plug and ring gauges to control the production of a part 50H7d8. Given: 50 mm lies in the step 30-50. For d shaft FD= - 16 D 0.44 µ. IT6=10i and above it tolerance magnitude is multiplied by 10 at each fifth step. Determine actual dimension to be provided for shaft and hole of 90 mm size for H8/e9 type of fit. Size 90 falls on Diameter steps of 80 and 100. FD for “e” type shaft is = - 11 D 0.41 µ. Also design “GO” and “NOGO” gauges. IT8=25i and IT9=40i. Calculate the limits of size for inspection gauges conforming to Taylor’s principle to check the rectangular hole . The limits of size for a 50 mm H8 hole are low limit 50.000 mm and high limit 50.039 mm. The limits of size for a 75 mm H8 hole are low limit 75 mm and high limit 75.046 mm. 50 mm diameter step lies 30 – 50. 75 mm diameter step lies 50 – 80. State Taylor’s Principle of Gauge Design of Limit gauges. Design the “Work shop” “Inspection” and “General” type of GO and NOGO gauges for checking the assembly Φ 30 (mm) H7/f8. Fundamental deviation for “f” shaft is = -5.5 D 0.41 µ. Diameter step for Φ 30 is 18 – 30 mm. Fundamental tolerance for IT7 and IT8 are 16i and 25i respectively. Also determine I. Type of fit II. Allowance for the above fit III. Other shafts giving the same type and same degree of fit IV. Equivalent fit in shaft based system Part A Tolerance of Part B Tolerance of B

15. Shaft Zero line Basic Shaft System • Shaft Basis System:- Where the size of the shaft is kept constant and the variations given to the hole to get the different class of fits, then it is known as the shaft basis system.

17. GAUGES • Gauges are scale less inspection tools at rigid design which are used to • check the dimensions of manufactured parts. Measurement by gauges is • Easy and rapid. So they are suitable in mass production. Instead of • measuring actual dimension of each part which is time consuming and • Costly, the conformance of part with tolerance specification can be • checked by gauges.

19. Types of Gauges Plain gauges are used to check plain, i.e. unthreaded holes and shafts. • Classification: • 1.According to Type • (a)Standard Gauge: If a gauge is made as an exact copy of the mating part • Of component to be checked, it is called standard gauge. • A standard gauge can’t be used to check interference fit. • It has limited application. • (a)Limit Gauge: Two gauges are used to check each dimension of the • Part i.e. upper and lower limit. These are “GO” and “NO-GO” gauges. • GO gauges check MML and NO GO gauges check LML. • These are widely used industries. • A part is considered to be good if the GO gauge pass through the work and • the NO GO gauge fails to pass under the action of its own weight. This • Confirms the actual dimension of part with in the specified tolerances. • If both the gauges fail, it indicates that hole is under size and shaft is • Oversize.

20. According to Purpose: a) Workshop gauge b) Inspection gauge c) Reference or master gauge d) Purchase inspection gauge 2. According to the form of the tested surface: a) Plug gauges for checking holes b) Snap or Ring or Gap gauges for checking the shaft 3. According to their design: a) Single limit or double limit gauges b) Single ended or double ended gauges c) Fixed and adjustable gauges

21. Taylor’s Principle of Gauge Design: • It states that • 1. “Go gauges should be designed to check the Maximum Metal Limit • (MML) while the NO GO gauge should be designed to check the Least Metal Limit (LML).” • GO plug gauge should correspond to LL of Hole. • NOGO plug gauge should correspond to UL of Hole. • GO snap gauge should correspond to UL of shaft. • NOGO snap gauge should correspond to LL of shaft. • The difference between the GO and NOGO plug gauge as well as the difference in size between GO and NOGO snap Gauge is approximately equal to the work tolerance. • 2. “GO gauges should check all the related dimensions (Roundness, size, location, straightness etc). • NOGO gauges should check only one element of the dimension at a time.”

23. Recommendation for limits and fits for Engineering: For universal Interchangeability it is essential to follow a uniform standard Through out the world. Indian standards (IS) are in line with ISO recommendations. It consists of 25 Holes designated by capital letter 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 It consists of 25 shafts designated by small letter Recommendation for limits and fits for Engineering: For universal Interchangeability it is essential to follow a uniform standard Through out the world. Indian standards (IS) are in line with ISO recommendations. It consists of 25 Holes designated by capital letter A, B, C, D, E, F, G, H, JS, J, K, M,N, P, R, S, T, U, V, X, Y, Z, ZA,, ZC It consists of 25 shafts designated by smal letter 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 Each of holes and shafts has a choice of 18 Grades of Tolerances Designated as: IT01, IT0, IT1, IT2, IT3, ……… IT15, IT16. IT01 – 0.3 + 0.008D IT0 – 0.5 + 0.012 D IT1 – 0.8 + 0.020D IT2 – 2.7i; IT3 - 3.7i; IT4 – 5i; IT5 – 7i; IT6 – 10 i; IT7 – 16i; IT8 – 25i; IT9 – 40i; IT10 – 64i; IT11 – 100i; IT12 –160i; IT13 – 250i; IT14 – 400i; IT15 – 640i; IT16 – 1000i. 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 Each of holes and shafts has a choice of 18 Grades of Tolerances Designated as: IT01, IT0, IT1, IT2, IT3, ……… IT15, IT16. IT01 – 0.3 + 0.008D IT0 – 0.5 + 0.012 D IT1 – 0.8 + 0.020D IT2 – 2.7i; IT3 - 3.7i; IT4 – 5i; IT5 – 7i; IT6 – 10 i; IT7 – 16i; IT8 – 25i; IT9 – 40i; IT10 – 64i; IT11 – 100i; IT12 –160i; IT13 – 250i; IT14 – 400i; IT15 – 640i; IT16 – 1000i.

24. Selective Assembly In selective assembly components produced are classified into groups according to their sizes by automatic gauging. This is done for both Holes and Shafts and then corresponding parts will be matched properly. It reduces chance of defective assembly and also the cost of assembly as parts may be produced in wider tolerances. • Ex: Assembly of piston with cylinder bores.