Cold-Working Processes

By cold working is meant the forming of the metal while at a low temperature (usually room temperature). In contrast to parts produced by hot working, cold-worked parts have a bright new finish, are more accurate, and require less machining.

Cold-finished bars and shafts are produced by rolling, drawing, turning, grinding, and polishing. Of these methods, by far the largest percentage of products are made by the cold-rolling and cold-drawing processes. Cold rolling is now used mostly for the

production of wide flats and sheets. Practically all cold-finished bars are made by cold drawing but even so are sometimes mistakenly called “cold-rolled bars.” In the drawing process, the hot-rolled bars are first cleaned of scale and then drawn by pulling them through a die that reduces the size about 1 32 to 1 16 in. This process does not remove material from the bar but reduces, or “draws” down, the size. Many different shapes of  hot-rolled bars may be used for cold drawing.

Cold rolling and cold drawing have the same effect upon the mechanical properties. The cold-working process does not change the grain size but merely distorts it. Cold working results in a large increase in yield strength, an increase in ultimate strength and hardness, and a decrease in ductility. In Fig. 2–12 the properties of a colddrawn bar are compared with those of a hot-rolled bar of the same material.

Heading is a cold-working process in which the metal is gathered, or upset. This operation is commonly used to make screw and rivet heads and is capable of producing a wide variety of shapes. Roll threading is the process of rolling threads by squeezing and rolling a blank between two serrated dies. Spinning is the operation of working sheet material around a rotating form into a circular shape. Stamping is the term used to

describe punch-press operations such as blanking, coining, forming, and shallow drawing.

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Shell Molding

The shell-molding process employs a heated metal pattern, usually made of cast iron,

aluminum, or brass, which is placed in a shell-molding machine containing a mixture

of dry sand and thermosetting resin. The hot pattern melts the plastic, which, together with the sand, forms a shell about 5 to 10 mm thick around the pattern. The shell is then baked at from 400 to 700°F for a short time while still on the pattern. It is then stripped from the pattern and placed in storage for use in casting.

In the next step the shells are assembled by clamping, bolting, or pasting; they are placed in a backup material, such as steel shot; and the molten metal is poured into the cavity. The thin shell permits the heat to be conducted away so that solidification takes place rapidly. As solidification takes place, the plastic bond is burned and the mold collapses.

The permeability of the backup material allows the gases to escape and the casting to air-cool. All this aids in obtaining a fine-grain, stress-free casting. Shell-mold castings feature a smooth surface, a draft that is quite small, and close tolerances. In general, the rules governing sand casting also apply to shell-mold casting.

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Sand Casting

Sand casting is a basic low-cost process, and it lends itself to economical production in large quantities with practically no limit to the size, shape, or complexity of the part produced.

In sand casting, the casting is made by pouring molten metal into sand molds. A

pattern, constructed of metal or wood, is used to form the cavity into which the molten metal is poured. Recesses or holes in the casting are produced by sand cores introduced into the mold. The designer should make an effort to visualize the pattern and casting in the mold. In this way the problems of core setting, pattern removal, draft, and solidification can be studied. Castings to be used as test bars of cast iron are cast separately and properties may vary.

Steel castings are the most difficult of all to produce, because steel has the highest melting temperature of all materials normally used for casting. This high temperature aggravates all casting problems.

The following rules will be found quite useful in the design of any sand casting:

1 All sections should be designed with a uniform thickness.

2 The casting should be designed so as to produce a gradual change from section to section where this is necessary.

3 Adjoining sections should be designed with generous fillets or radii.

4 A complicated part should be designed as two or more simple castings to be assembled by fasteners or by welding.

Steel, gray iron, brass, bronze, and aluminum are most often used in castings. The minimum wall thickness for any of these materials is about 5 mm, though with particular care, thinner sections can be obtained with some materials.

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Power Transmission Case Study Specifications

A case study incorporating the many facets of the design process for a power transmission speed reducer will be considered throughout this textbook. The problem will be introduced here with the definition and specification for the product to be designed.

Further details and component analysis will be presented in subsequent chapters.

Chapter 18 provides an overview of the entire process, focusing on the design sequence, the interaction between the component designs, and other details pertinent to transmission of power. It also contains a complete case study of the power transmission speed reducer introduced here.

Many industrial applications require machinery to be powered by engines or electric motors. The power source usually runs most efficiently at a narrow range of rotational speed. When the application requires power to be delivered at a slower speed than supplied by the motor, a speed reducer is introduced. The speed reducer should transmit the power from the motor to the application with as little energy loss as practical, while reducing the speed and consequently increasing the torque. For example, assume that a

company wishes to provide off-the-shelf speed reducers in various capacities and speed ratios to sell to a wide variety of target applications. The marketing team has determined a need for one of these speed reducers to satisfy the following customer requirements. 

Design Requirements

Power to be delivered: 20 hp

Input speed: 1750 rev/min

Output speed: 85 rev/min

Targeted for uniformly loaded applications, such as conveyor belts, blowers, and generators

Output shaft and input shaft in-line

Base mounted with 4 bolts

Continuous operation

6-year life, with 8 hours/day, 5 days/wk

Low maintenance

Competitive cost

Nominal operating conditions of industrialized locations

Input and output shafts standard size for typical couplings

In reality, the company would likely design for a whole range of speed ratios for each power capacity, obtainable by interchanging gear sizes within the same overall design. For simplicity, in this case study only one speed ratio will be considered.

Notice that the list of customer requirements includes some numerical specifics, but also includes some generalized requirements, e.g., low maintenance and competitive cost.

These general requirements give some guidance on what needs to be considered in the design process, but are difficult to achieve with any certainty. In order to pin down these nebulous requirements, it is best to further develop the customer requirements into a set of product specifications that are measurable. This task is usually achieved through the work of a team including engineering, marketing, management, and customers. Various tools may be used (see Footnote 1) to prioritize the requirements, determine suitable metrics to be achieved, and to establish target values for each metric. The goal of this process is to obtain a product specification that identifies precisely what the product must satisfy. The following product specifications provide an appropriate framework for this design task.

Design Specifications

Power to be delivered: 20 hp

Power efficiency: >95%

Steady state input speed: 1750 rev/min

Maximum input speed: 2400 rev/min

Steady-state output speed: 82–88 rev/min

Usually low shock levels, occasional moderate shock

Input and output shaft diameter tolerance: ±0.001 in

Output shaft and input shaft in-line: concentricity ±0.005 in, alignment

±0.001 rad

Maximum allowable loads on input shaft: axial, 50 lbf; transverse, 100 lbf

Maximum allowable loads on output shaft: axial, 50 lbf; transverse, 500 lbf

Base mounted with 4 bolts

Mounting orientation only with base on bottom

100% duty cycle

Maintenance schedule: lubrication check every 2000 hours; change of lubrication every 8000 hours of operation; gears and bearing life >12,000 hours; infinite shaft life; gears, bearings, and shafts replaceable

Access to check, drain, and refill lubrication without disassembly or opening of gasketed joints.

Manufacturing cost per unit: <$300 Production: 10,000 units per year Operating temperature range: −10◦ to 120◦F Sealed against water and dust from typical weather Noise: <85 dB from 1 meter 

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Calculations and Significant Figures

The discussion in this section applies to real numbers, not integers. The accuracy of a real number depends on the number of significant figures describing the number. Usually, but not always, three or four significant figures are necessary for engineering accuracy. Unless otherwise stated, no less than three significant figures should be used in your calculations.

The number of significant figures is usually inferred by the number of figures given

(except for leading zeros). For example, 706, 3.14, and 0.002 19 are assumed to be numbers with three significant figures. For trailing zeros, a little more clarification is necessary.

To display 706 to four significant figures insert a trailing zero and display either 706.0, 7.060 × 102, or 0.7060 × 103. Also, consider a number such as 91 600. Scientific notation should be used to clarify the accuracy. For three significant figures express the number as 91.6 × 103. For four significant figures express it as 91.60 × 103.

Computers and calculators display calculations to many significant figures. However, you should never report a number of significant figures of a calculation any greater than the smallest number of significant figures of the numbers used for the calculation. Of course, you should use the greatest accuracy possible when performing a calculation. For example, determine the circumference of a solid shaft with a diameter of d = 0.40 in. The

circumference is given by C = πd. Since d is given with two significant figures, C should be reported with only two significant figures. Now if we used only two significant figures for π our calculator would give C = 3.1 (0.40) = 1.24 in. This rounds off to two significant figures as C = 1.2 in. However, using π = 3.141 592 654 as programmed in the calculator, C = 3.141 592 654 (0.40) = 1.256 637 061 in. This rounds off to C = 1.3

in, which is 8.3 percent higher than the first calculation. Note, however, since d is given with two significant figures, it is implied that the range of d is 0.40 ± 0.005. This means that the calculation of C is only accurate to within ±0.005/0.40 = ±0.0125 = ±1.25%.

The calculation could also be one in a series of calculations, and rounding each calculation separately may lead to an accumulation of greater inaccuracy. Thus, it is considered good engineering practice to make all calculations to the greatest accuracy possible and report the results within the accuracy of the given input.

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Dimensions and Tolerances

The following terms are used generally in dimensioning:

• Nominal size.

The size we use in speaking of an element. For example, we may specify a 1 1/2 -in pipe or a 1/2 -in bolt. Either the theoretical size or the actual measured size may be quite different. The theoretical size of a 1 1/2 -in pipe is 1.900 in for the outside diameter. And the diameter of the 1/2 -in bolt, say, may actually measure 0.492 in.

• Limits.

The stated maximum and minimum dimensions.

• Tolerance.

The difference between the two limits.

• Bilateral tolerance.

The variation in both directions from the basic dimension. That

is, the basic size is between the two limits, for example, 1.005 ± 0.002 in. The two

parts of the tolerance need not be equal.

• Unilateral tolerance.

The basic dimension is taken as one of the limits, and variation is permitted in only one direction, for example,

• Clearance.

A general term that refers to the mating of cylindrical parts such as a bolt and a hole. The word clearance is used only when the internal member is smaller than the external member. The diametral clearance is the measured difference in the two diameters. The radial clearance is the difference in the two radii.

• Interference.

The opposite of clearance, for mating cylindrical parts in which the internal member is larger than the external member.

• Allowance.

The minimum stated clearance or the maximum stated interference for mating parts.

When several parts are assembled, the gap (or interference) depends on the dimensions and tolerances of the individual parts.

The previous example represented an absolute tolerance system. Statistically, gap

dimensions near the gap limits are rare events. Using a statistical tolerance system, the probability that the gap falls within a given limit is determined.10 This probability deals with the statistical distributions of the individual dimensions. For example, if the distributions of the dimensions in the previous example were normal and the tolerances, t, were given in terms of standard deviations of the dimension distribution, the standard deviation of the gap w¯ would be

However, this assumes a normal distribution for the individual dimensions, a rare occurrence. To find the distribution of w and/or the probability of observing values of w within certain limits requires a computer simulation in most cases. Monte Carlo computer simulations are used to determine the distribution of w by the following approach:

1 Generate an instance for each dimension in the problem by selecting the value of

each dimension based on its probability distribution.

2 Calculate w using the values of the dimensions obtained in step 1.

3 Repeat steps 1 and 2 N times to generate the distribution of w. As the number of

trials increases, the reliability of the distribution increases.

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Design Factor and Factor of Safety

A general approach to the allowable load versus loss-of-function load problem is the deterministic design factor method, and sometimes called the classical method of

design. The fundamental equation is Eq. (1–1) where nd is called the design factor. All loss-of-function modes must be analyzed, and the mode leading to the smallest design factor governs. After the design is completed, the actual design factor may change as a result of changes such as rounding up to a standard size for a cross section or using off-the-shelf components with higher ratings instead of employing what is calculated by using the design factor. The factor is then referred to as the factor of safety, n. The factor of safety has the same definition as the design factor, but it generally differs numerically.

Since stress may not vary linearly with load (see Sec. 3–19), using load as the loss-of-function parameter may not be acceptable. It is more common then to express the design factor in terms of a stress and a relevant strength. Thus Eq. (1–1) can be rewritten as

The stress and strength terms in Eq. (1–3) must be of the same type and units. Also, the stress and strength must apply to the same critical location in the part.

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Stress and Strength

The survival of many products depends on how the designer adjusts the maximum

stresses in a component to be less than the component’s strength at specific locations of interest. The designer must allow the maximum stress to be less than the strength by a sufficient margin so that despite the uncertainties, failure is rare.

In focusing on the stress-strength comparison at a critical (controlling) location, we often look for “strength in the geometry and condition of use.” Strengths are the

magnitudes of stresses at which something of interest occurs, such as the proportional

limit, 0.2 percent-offset yielding, or fracture. In many cases, such events represent the stress level at which loss of function occurs.

Strength is a property of a material or of a mechanical element. The strength of an element depends on the choice, the treatment, and the processing of the material.

Consider, for example, a shipment of springs. We can associate a strength with a specific spring. When this spring is incorporated into a machine, external forces are applied that result in load-induced stresses in the spring, the magnitudes of which depend on its geometry and are independent of the material and its  processing. If the spring is removed from the machine unharmed, the stress due to the external forces will return to zero. But the strength remains as one of the properties of the spring. Remember, then, that strength is an inherent property of a part, a property built into the part because of the use of a particular material and process.

Various metalworking and heat-treating processes, such as forging, rolling, and cold forming, cause variations in the strength from point to point throughout a part. The spring cited above is quite likely to have a strength on the outside of the coils different from its strength on the inside because the spring has been formed by a cold winding process, and the two sides may not have been deformed by the same amount.

Remember, too, therefore, that a strength value given for a part may apply to only a particular point or set of points on the part. In this book we shall use the capital letter S to denote strength, with appropriate subscripts to denote the type of strength. Thus, Ss is a shear strength, Sy a yield strength, and Su an ultimate strength.

In accordance with accepted engineering practice, we shall employ the Greek letters ó (sigma) and ô (tau) to designate normal and shear stresses, respectively. Again, various subscripts will indicate some special  characteristic. For example, ó1 is a principal stress, óy a stress component in the y direction, and ór a stress component in the radial direction.

Stress is a state property at a specific point within a body, which is a function of load, geometry, temperature, and manufacturing processing. In an elementary course in mechanics of materials, stress related to load and geometry is emphasized with some discussion of thermal stresses. However, stresses due to heat treatments, molding, assembly, etc. are also important and are sometimes neglected.

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Economic and Market Analysis

The net result or purpose of most engineering designs is to produce a product that generates a profit for the company. Obviously, each alternative design has to be evaluated against criteria such as sales features, potential market, cost of manufacturing, advertising, and so on. Large companies often conduct marketing surveys to obtain a measure of what the public will buy. These surveys may be conducted by telephone interviews with randomly selected people, or they may be personal interviews conducted with potential users of a product. Our society is based on economics and competition. Many good ideas never get into production because the manufacturing costs exceed what people will pay for the product. Market analysis involves applying principles of probability and statistics to determine if the response of a selected group of people represents the opinion of society as a whole. Even with a good marketing survey, manufacturers never know for certain if a new product will sell.

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Product Safety and Liability

The primary consideration for safety in product design is to assure that the use of the design does not cause injury to humans. Safety and product liability issues, however, can also extend beyond human injury to include property damage and environmental damage from the use of your design. Engineers must also consider the issues of safety in design because of liability arising from the use of an unsafe product. Liability refers to the manufacturer of a machine or product being liable, or financially responsible, for any injury or damage resulting from the use of an unsafe product.

The only way to assure that your design will not cause injury or loss is to design safety into the product. You can design a safe product in three ways. The first method is to design safety directly into the product. Ask yourself, "Is there any probability of injury during the normal use and during failure of your design?" For example, modern downhill ski bindings use a spring-loaded brake that brakes the ski automatically when the ski disengages from the skier's boot. Older ski bindings used an elastic cable attached to the skier's ankle, but this had a tendency to disconnect during a severe fall.

Inherent safety is impossible to design into some products, such as rotating machinery and vehicles. In such cases you use the second method of designing for safety: You include adequate protection for users of the product. Protection devices include safety shields placed around moving and rotating parts, crash protective structures used in vehicles, and "kill" switches that automatically turn a machine off (or on) if there is potential for human injury. For example, new lawnmowers generally include a protective shield covering the grass outlet and include a kill switch that turns the motor off when the operator releases the handle.

The third method used in considering safety is the use of warning labels describing inherent dangers in the product. Although this method does not implement safety in design, it is primarily used as a way to shift the responsibility to the consumer for having ignored the safety guidelines in using the product. In most cases, however, a warning label will not protect you from liability. Protective shields or other devices must be

included in the design.

A product liability suit may be the result of a personal injury due to the operation of a particular product. The manufacturer and designer of a device can be found liable to compensate a worker for losses incurred during the operation or use of their product.

During a product liability trial, the plaintiff attempts to show that the designer and manufacturer of a product are negligent in allowing the product to be put on the market. The plaintiff's attorney may bring charges of negligence against the designer.

To protect themselves in a product liability trial, engineers must use state-of-the-art design procedures during the design process. They must keep records of all calculations and methods used during the design process. Safety considerations must be included in the criteria for all design solutions. The designer must also foresee other ways people could use the product. If a person uses a shop vacuum to remove a gasoline spill, is the

designer responsible when the vacuum catches fire? The courts can decide that a design is poor if the engineer did not foresee improper use of the product. It is imperative that you evaluate all of your alternative solutions against safety considerations. Reject or modify any unsafe elements of your design at this stage in the design process.

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Ergonomics

Ergonomics is the human factor in engineering. It is the study of how people interact with machines. Most products have to work with people in some manner. People occupy a space in or around the design, and they may provide a source of power or control or act as a sensor for the design. For example, people sense if an automobile air-conditioning system is maintaining a comfortable temperature inside the car. These factors form the basis for human factors, or ergonomics, of a design.

A design solution can be considered successful if the design fits the people using it. The handle of a power tool must fit the hand of everybody using it. The tool must not be too heavy or cumbersome to be manipulated by all sizes of people using the tool. The geometric properties of people-their weight, height, reach, circumference, and so on-are called anthropometric data. The difficulty in designing for ergonomics is the abundance of anthropometric data. The military has collected and evaluated the distribution of human beings and published this information in military standard tables. A successful design needs to be evaluated and analyzed against the distribution of geometry of the people using it. The following Figure shows the geometry of typical adult males and females for the general population in millimeters. Since people come in different sizes and shapes, such data are used by design engineers to assure that their design fits the user.

A good design will be adjustable enough to fit 95 percent of the people who will use it.

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Functional analysis.

This part determines whether the given design solution will function the way it should. Functional analysis is fundamental to the evaluation and success of all designs. A design solution that does not function properly is a failure even if it meets all other criteria. Consider for example the invention of the ballpoint pen. This common instrument was first invented and manufactured during World War II. The ballpoint pen was supposed to solve the problems of refilling and messiness inherent to the fountain pen. Unfortunately, this new design had never been evaluated for functionality. The early pens depended on gravity for the ink to flow to the roller ball.

This meant that the pens only worked in a vertical upright position, and the ink flow was inconsistent: Sometimes it flowed too heavily, leaving smudgy blotches on the paper; other times the flow was too light and the markings were unreadable. The first ballpoint pens tended to leak around the ball, ruining people's clothes. An elastic ink developed in 1949, allowed the ink to flow over the ball through smooth capillary action. Not until the 1950s did the ballpoint pen finally become a practical writing instrument, thanks to proper ink and engineering. Economy, appearance, durability, and marketability of a design are unimportant if the product does not function properly.

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GATHER PERTINENT INFORMATION

Before you can go further in the design process, you need to collect all the information available that relates to the problem. Novice designers will quickly skip over this step and proceed to the generation of alternative solutions. You will find, however, that effortspent searching for information about your problem will pay big dividends later in the design process. Gathering pertinent information can reveal facts about the problem that result in a redefinition of the problem. You may discover mistakes and false starts made by other designers. Information gathering for most design problems begins with asking the following questions. If the problem addresses a need that is new, then there are no existing solutions to the problems, so obviously some of the questions would not be asked.

· Is the problem real and its statement accurate?

· Is there really a need for a new solution or has the problem already been solved?

· What are the existing solutions to the problem?

· What is wrong with the way the problem is currently being solved?

· What is right about the way the problem is currently being solved?

· What companies manufacture the existing solution to the problem?

· What are the economic factors governing the solution?

· How much will people pay for a solution to the problem?

· What other factors are important to the problem solution (such as safety,

aesthetics and environmental issues)?

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Develop a Problem Statement

The first step in the problem-solving process, therefore, is to formulate the problem in clear and unambiguous terms. Defining the problem is not the same as recognizing a need.

The problem definition statement results from first identifying a need. The engineer at the

airbag company responded to a need to reduce the number of airbag inflation failures. He

made a mistake, however, in not formulating a clear definition of the problem before generating a solution. Once a need has been established, engineers define that need in

terms of an engineering design problem statement. To reach a clear definition, they collect data, run experiments, and perform computations that allow that need to be expressed as part of an engineering problem-solving process.

Consider for example the statement "Design a better mousetrap." This statement is not an adequate problem definition for an engineering design problem. It expresses a vague dissatisfaction with existing mousetraps and therefore establishes a need. An engineer would take this statement of need and conduct further research to identify what was lacking in existing mousetrap designs. After further investigation the engineer may discover that existing mousetraps are inadequate because they don't provide protection from the deadly Hantavirus carried by mice. Therefore, a better mousetrap may be one that is sanitary and does not expose human beings to the Hantavirus. From this need, the problem definition is modified to read, "Design a mousetrap that allows for the sanitary disposal of the trapped mouse, minimizing human exposure to the Hantavirus."

The problem statement should specifically address the real need yet be broad enough not to preclude certain solutions. A broad definition of the problem allows you to look at a wide range of alternative solutions before you focus on a specific solution. The temptation at this point in the design process is to develop a  preconceived mental "picture" of the problem solution. For example, you could define the better mousetrap

problem as "Design a mousetrap that sprays the trapped mouse with disinfectant." This statement is clear and specific, but it is also too narrow. It excludes many potentially innovative solutions. If you focus on a specific picture or idea for solving the problem at this stage of the design process, you may never discover the truly innovative solutions to the problem. A problem statement should be concise and flexible enough to allow for

creative solutions.

Here is one possible problem definition statement for our better mousetrap problem:

A Better Mousetrap: Certain rodents such as the common mouse are carriers and transmitters of an often fatal virus, the Hantavirus. Conventional mousetraps expose people to this virus as they handle the trap and dispose of the mouse. Design a mousetrap that allows a person to trap and dispose of a mouse without being exposed to any bacterial or viral agents being carried on the mouse.

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