MCE 419 Lecture 1 - Control Engineering PDF

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Control Engineering...

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Engineering Tolerance Engineering tolerance is the permissible limit or limits of variation in 1. a physical dimension, 2. a measured value or physical property of a material, manufactured object, system, or service, 3. in engineering and safety, a physical distance or space (tolerance), as in a truck (lorry), train or boat under a bridge as well as a train in a tunnel (see structure gauge and loading gauge). 4. in mechanical engineering the space between a bolt and a nut or a hole, etc. Example; for 0.500-0.506 inch the tolerance would be 0.006 inch. Tolerance can also be defined as the amount by which the job is allowed to deviate from accuracy and perfectness without causing any functional trouble, when assembled with its mating part and put into actual service. It has also been realized that exact size components are difficult to produce. Any attempt towards much closed dimensions of a product will increase cost of the production. The functional aspects of the component may be achieved even without going for its exact dimensions using limits, fit and tolerances. This reduces the unit cost of production and increases the rate of production. For example, a shaft of exact 10.00 mm diameter is difficult to produce by machining process. But if you provide tolerance, i.e. the amount of variation permitted in the size, and then such parts can be easily produced. A dimension 10 ± 0.05 means a shaft may be produced between 10.05 and 9.95. These two figures represent limit and the difference, (10.05 – 9.95) = 0.10 is called tolerance. Dimensions, properties, or conditions may vary within certain practical limits without significantly affecting equipment functionality or a process. Tolerances are specified to allow reasonable leeway for imperfections and inherent variability without compromising performance.

Considerations when setting tolerances A primary concern is to determine how wide the tolerances may be without affecting other factors or the outcome of a process. This can be by the use of scientific principles, engineering knowledge, and professional experience. Experimental investigation is very useful to investigate the effects of tolerances such as design of experiments, formal engineering evaluations, etc.

The process capability of systems, materials, and products needs to be compatible with the specified engineering tolerances. Process controls must be in place and an effective Quality management system, such as Total Quality Management, needs to keep actual production within the desired tolerances. A process capability index is used to indicate the relationship between tolerances and actual measured production. Mechanical component tolerance

Summary of basic size, fundamental deviation and IT grades compared to minimum and maximum sizes of the shaft and hole. Tolerances are assigned to parts for manufacturing purposes, as boundaries for acceptable build. No machine can hold dimensions precisely to the nominal value, so there must be acceptable degrees of variation. If a part is manufactured, but has dimensions that are out of tolerance, it is not a usable part according to the design intent. Tolerances can be applied to any dimension. The commonly used terms are:

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Basic size: the nominal diameter of the shaft (or bolt) and the hole. This is, in general, the same for both components.

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Limits: the extreme maximum and minimum sizes specified by a tolerance dimension. (a) Lower deviation: the difference between the minimum possible component size and the basic size (b) Upper deviation: the difference between the maximum possible component size and the basic size.

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Fundamental deviation: the minimum difference in size between a component and the basic size. This is identical to the upper deviation for shafts and the lower deviation for holes. If the fundamental deviation is greater than zero, the bolt will always be smaller than the basic size and the hole will always be wider. Fundamental deviation is a form of allowance, rather than tolerance. Allowance – An allowance is the intentional difference between the maximum material limits (minimum clearance or maximum interference) of mating parts.

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International Tolerance grade: this is a standardized measure of the maximum difference in size between the component and the basic size (see below).

For example, if a shaft with a nominal diameter of 10 mm is to have a sliding fit within a hole, the shaft might be specified with a tolerance range from 9.964 to 10 mm (i.e. a zero fundamental deviation, but a lower deviation of 0.036 mm) and the hole might be specified with a tolerance range from 10.04 mm to 10.076 mm (0.04 mm fundamental deviation and 0.076 mm upper deviation). In this case the size of the tolerance range for both the shaft and hole is chosen to be the same (0.036 mm), meaning that both components have the same International Tolerance grade.

Example A shaft of 25 mm basic size is given as 25 ± 0.02 mm. Find the tolerance.

Solution The maximum permissible size (upper limit) = 25.02 mm and the minimum permissible size (lower limit) = 24.98 mm

Then, Tolerance = Upper Limit – Lower Limit = 25.02 – 24.98 = 0.04 mm = 4 x 10– 5 m

There are two ways of writing tolerances (a) Unilateral tolerance (b) Bilateral tolerance.

Tolerance

Unilateral Tolerance In this system, the dimension of a part is allowed to vary only on one side of the basic size, i.e. tolerance lies wholly on one side of the basic size either above or below it.

Unilateral Tolerance

Examples of unilateral tolerance are:

Unilateral system is preferred in interchangeable manufacture, especially when precision fits are required, because

(a) it is easy and simple to determine deviations, (b) another advantage of this system is that Gauge ends can be standardized as the holes of different tolerance grades have the same lower limit and all the shafts have same upper limit, (c) this form of tolerance greatly assists the operator, when machining of mating parts. The operator machines to the upper limit of shaft (lower limit for hole) knowing full well that he still has some margin left for machining before the parts are rejected.

Bilateral Tolerance In this system, the dimension of the part is allowed to vary on both the sides of the basic size, i.e. the limits of tolerance lie on either side of the basic size, but may not be necessarily equally disposing about it

Bilateral Tolerance Examples of bilateral tolerance are:

This system is used in mass production when machine setting is done for the basic size.

Example 3.5 A 50 mm diameter shaft is made to rotate in the bush. The tolerances for both shaft and bush are 0.050 mm, determine the dimension of the shaft and bush to give a maximum clearance of 0.075 mm with the hole basis system.

Solution In the hole basis system, lower deviation of hole is zero, therefore low limit of hole = 50 mm. High limit of hole = Low limit + Tolerance = 50.00 + 0.050 = 50.050 mm = 50.050 x 10– 3 m

High limit of shaft = Low limit of hole – Allowance = 50.00 – 0.075 = 49.925 mm = 49.925 x 10– 3 m Low limit of the shaft = High limit – Tolerance = 49.925 – 0.050 = 49.875 mm = 49.875 x 10– 3 m The dimension of the system is shown below

Shaft with Bush Miscellaneous on Tolerance - Why is it needed: Nothing is perfect, hence, engineers have come up with a way to make

things close to perfect by specifying Tolerances. - Since variation from the drawing is inevitable an acceptable degree of variation must be specified. - Large variation may affect the functionality of the part - Small variation will affect the cost of the part because it requires precise manufacturing and requires inspection and the rejection of parts.

Importance of Tolerance (a) Assemblies: Parts will often not fit together if their dimensions do not fall within certain range of values. (b) Interchangeability: If a replacement part is used it must be a duplicate of the original part within certain limits of deviation.

- Cost generally increases with smaller tolerance - Small tolerances cause an exponential increase in cost - Parts with small tolerances often require special methods of manufacturing. - Parts with small tolerances often require greater inspection and call for the rejection of parts, requires greater quality inspection and greater cost. - Do not specify a smaller tolerance than is necessary.

Fits When two parts are to be assembled, the relation resulting from the difference between their sizes before assembly is called a fit. A fit may be defined as the degree of tightness and looseness between two relating parts. Fit refers to the mating of two mechanical components. Manufactured parts are very frequently required to mate with one another. They may be designed to slide freely against one another or they may be designed to bind together to form a single unit. The most common fit found in the machine shop is that of a shaft in a hole.

There are three general categories of fits: 1) Clearance fits for when it may be desirable for the shaft to rotate or slide freely within the hole; this is usually referred to as a "sliding fit."

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The parts are toleranced such that the largest shaft is smaller than the smallest hole.

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The allowance is positive and greater than zero.

In a clearance fit, the difference between the minimum size of the hole and the maximum size of the shaft is known as minimum clearance whereas the difference between the maximum size of the hole and minimum size of the shaft is called maximum clearance. The clearance fits may be slide fit, easy sliding fit, running fit, slack running fit and loose running fit.

Clearance fit can be sub-classified as follows: Loose Fit It is used between those mating parts where no precision is required. It provides minimum allowance and is used on loose pulleys, agricultural machineries etc. Running Fit For a running fit, the dimension of shaft should be smaller enough to maintain a film of oil for lubrication. It is used in bearing pair etc. An allowance 0.025 mm per 25 mm of diameter of bearing may be used. Fit and Tolerances Slide Fit or Medium Fit It is used on those mating parts where great precision is required. It provides medium allowance and is used in tool slides, slide valve, automobile parts, etc.

2) Interference fits for when it is desirable for the shaft to be securely held within the hole; this is usually referred to as interference fit. •

The maximum clearance is always negative.

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The parts must always be forced together.

In this type of fit, the size limits for the mating parts are so selected that interference between them always occur. It may be noted that in an interference fit, the tolerance zone of the hole is entirely below the tolerance zone of the shaft. In an interference fit, the difference between the maximum size of the hole and the minimum size of the shaft is known as minimum interference, whereas the difference between the minimum size of the hole and the maximum size of the shaft is called maximum interference. The interference fits may be shrink fit, heavy drive fit and light drive fit.

The interference fit can be sub-classified as follows:

Shrink Fit or Heavy Force Fit It refers to maximum negative allowance. In assembly of the hole and the shaft, the hole is expanded by heating and then rapidly cooled in its position. It is used in fitting of rims etc.

Medium Force Fit These fits have medium negative allowance. Considerable pressure is required to assemble the hole and the shaft. It is used in car wheels, armature of dynamos etc.

Tight Fit or Press Fit One part can be assembled into the other with a hand hammer or by light pressure. A slight negative allowance exists between two mating parts (more than wringing fit). It gives a semipermanent fit and is used on a keyed pulley and shaft, rocker arm, etc.

3) Transition fits for when it is desirable that the shaft to be held securely, yet not so securely that it cannot be disassembled, this is usually referred to as a Location or Transition fit. •

The parts are tolerance such that the allowance is negative and the maximum clearance is positive

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The parts may be loose or forced together

In this type of fit, the size limits for the mating parts are so selected that either a clearance or interference may occur depending upon the actual size of the mating parts. It may be noted that in a transition fit, the tolerance zones of hole and shaft overlap. The transition fits may be force fit, tight fit and push fit.

Transition fit can be sub-classified as follows:

Push Fit It refers to zero allowance and a light pressure (10 cating dowels, pins, etc.) is required in assembling the hole and the shaft. The moving parts show least vibration with this type of fit. It is also known as snug fit.

Force Fit or Shrink Fit A force fit is used when the two mating parts are to be rigidly fixed so that one cannot move without the other. It either requires high pressure to force the shaft into the hole or the hole to be expanded by heating. It is used in railway wheels, etc.

Wringing Fit A slight negative allowance exists between two mating parts in wringing fit. It requires pressure to force the shaft into the hole and gives a light assembly. It is used in fixing keys, pins, etc.

Within each category of fit there are several classes ranging from high precision and narrow tolerance (allowance) to lower precision and wider tolerance. The choice of fit is dictated first by the use and secondly by the manufacturability of the parts.

Systems of fit A fit system is the systems of standard allowance to suit specific range of basic size. There are two systems of fit for obtaining clearance, interference or transition fit. These are: (i) Hole basis system (ii) Shaft basis system

Hole basis system

Shaft Basis System

Hole Basis System In the hole basis system, the size of the hole is kept constant and shaft sizes are varied to obtain various types of fits.

In this system, lower deviation of hole is zero, i.e. the low limit of hole is same as basic size. The high limit of the hole and the two limits of size for the shaft are then varied to give desired type of fit.

The hole basis system is commonly used because it is more convenient to make correct holes of fixed sizes, since the standard drills, taps, reamers and branches etc. are available for producing holes and their sizes are not adjustable. On the other hand, size of the shaft produced by turning, grinding, etc. can be very easily varied.

Shaft Basis System In the shaft basis system, the size of the shaft is kept constant and different fits are obtained by varying the size of the hole. Shaft basis system is used when the ground bars or drawn bars are readily available. These bars do not require further machining and fits are obtained by varying the sizes of the hole.

In this system, the upper deviation (fundamental deviation) of shaft is zero, i.e. the high limit of the shaft is same as basic size and the various fits are obtained by varying the low limit of shaft and both the limits of the hole....