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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  • Mechanical Engineering
    McGraw−Hill Primis
    ISBN: 0−390−76487−6
    Text:
    Shigley’s Mechanical Engineering Design,
    Eighth Edition
    Budynas−Nisbett



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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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  • Mechanical Engineering
    McGraw−Hill Primis
    ISBN: 0−390−76487−6
    Text:
    Shigley’s Mechanical Engineering Design,
    Eighth Edition
    Budynas−Nisbett


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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.


    Mechanical Engineering
    McGraw−Hill Primis
    ISBN: 0−390−76487−6
    Text:
    Shigley’s Mechanical Engineering Design,
    Eighth Edition
    Budynas−Nisbett



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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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  • Mechanical Engineering
    McGraw−Hill Primis
    ISBN: 0−390−76487−6
    Text:
    Shigley’s Mechanical Engineering Design,
    Eighth Edition
    Budynas−Nisbett



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