Electrical Machine Design

Chapter 7
Mechanical, Structural and Acoustic Design

Bachelors Program in Electrical Engineering
Electrical Machine Design   •   Bachelor

Mechanical, Structural and Acoustic Design

Introduction

Electrical-machine design is not complete when the magnetic circuit, windings, and thermal performance have been specified. The machine must also survive mechanical forces, rotate safely, remain sufficiently rigid, contain or exclude environmental contaminants, and operate with acceptable vibration and noise. Mechanical failure can occur even when electromagnetic and thermal calculations are satisfactory. Typical causes include excessive shaft stress, inadequate bearing life, rotor unbalance, resonance, fatigue, loose structural joints, poor tolerances, and unsuitable enclosure construction.

Mechanical design therefore links electromagnetic loading to structural integrity and user requirements. Electromagnetic torque produces shaft stress; radial magnetic forces excite the stator and frame; rotor speed produces centrifugal stress; temperature changes alter clearances; and enclosure geometry affects both ingress protection and acoustic radiation.

Learning Objectives

After studying this chapter, a student should be able to:

  1. Select and size shafts, bearings, rotors, frames, and enclosures.
  2. Evaluate torsional, bending, combined, and centrifugal stresses.
  3. Explain critical speed, rotor balancing, vibration, tolerances, and fatigue.
  4. Relate electromagnetic forces to mechanical deformation and acoustic noise.
  5. Select appropriate ingress-protection, shock, and environmental provisions.
  6. Apply a structured mechanical-design procedure to an electrical machine.

1. Mechanical Design Requirements

The design begins with a specification rather than with a single formula. Important requirements include rated power and speed, starting and fault torque, duty cycle, mounting arrangement, ambient temperature, altitude, humidity, dust, water, shock, vibration, expected service life, permissible noise, maintenance method, and applicable standards.

The principal mechanical loads are:

  • transmitted torque;
  • bending from belt pull, gears, couplings, and rotor weight;
  • axial thrust from helical gears, pumps, fans, or magnetic asymmetry;
  • centrifugal forces in rotating parts;
  • electromagnetic radial and tangential forces;
  • thermal expansion and shrink-fit forces;
  • transportation and operating shock;
  • cyclic loads causing fatigue.

A sound design uses a load case matrix. Rated operation, overload, starting, plugging or braking, short circuit, overspeed, transportation, and fault conditions should be considered separately. The most severe condition for shaft stress may not be the same as that for bearings, frame deformation, or acoustic noise.

2. Shafts and Rotor Assemblies

2.1 Torque and transmitted power

For a rotating shaft, mechanical power, torque, and angular speed are related by

P = Tω = 2πnT/60

where P is mechanical power in watts, T is torque in newton-metres, ω is angular speed in radians per second, and n is speed in revolutions per minute. Thus,

T = 9550PkW/n

when P_kW is in kilowatts and n is in revolutions per minute, giving T in newton-metres. This relation assumes steady power transmission and neglects transient acceleration energy.

For a solid circular shaft subjected only to elastic torsion, the maximum shear stress is

τmax = 16T/(πd3)

where d is shaft diameter. The corresponding angle of twist over length L is

θ = 32TL/(πGd4)

where G is the shear modulus. These equations apply to a uniform, solid, circular shaft under Saint-Venant torsion, away from stress concentrations and plastic deformation.

For a hollow shaft with outside diameter d_o and inside diameter d_i,

τmax = 16Tdo/[π(do4 − di4)]

A hollow shaft can provide lower mass for a specified torsional stiffness, but its local stability, keyways, press fits, and manufacturing cost must be assessed.

2.2 Bending and combined loading

A shaft carrying a rotor, pulley, or coupling is usually subjected to bending as well as torsion. For a solid circular shaft, the bending stress at the surface is

σb = 32M/(πd3)

where M is the bending moment in newton-metres. A preliminary equivalent-stress check using the von Mises criterion is

σvm = √(σb2 + 3τ2)

where σ_b is normal bending stress and τ is torsional shear stress. For a ductile steel shaft under static loading, a design requirement is commonly written as

σvm ≤ σy/Sy

where σ_y is yield strength and S_y is the chosen yield safety factor. Actual machine design must also include fatigue, keyway effects, surface finish, size effects, and stress concentration factors.

A practical shaft may include shoulders, threads, keyways, retaining-ring grooves, and bearing seats. These features interrupt the ideal stress field. Fillets should be as large as compatible with bearing and assembly requirements, and abrupt changes in diameter should be avoided.

2.3 Torsional stiffness and transient torque

A shaft that is strong enough may nevertheless be too flexible. Excessive twist can cause rotor-position errors, coupling misalignment, torsional oscillation, or control instability. The torsional stiffness of a uniform shaft is

kt = GJ/L

where J is the polar second moment of area. For a solid circular section, J = πd^4/32. Starting, plugging, short-circuit, and load-rejection torques may substantially exceed rated torque. The shaft must therefore be checked for both peak stress and repeated torque cycles.

2.4 Centrifugal stress in rotors

Rotating components experience radial inertia forces. A thin rotating ring of density ρ, mean radius r, and angular speed ω has an approximate hoop stress

σ_θ ≈ ρω2r2

This simplified relation assumes a thin, free ring with uniform density and negligible restraint. It is not a substitute for a complete rotor analysis when the rotor contains slots, retaining rings, shrink fits, discontinuities, or multiple materials.

For a rotor component at radius r, the centrifugal acceleration is

ac = ω2r

and the radial force on mass m is F_c = mω²r. Overspeed testing and analysis are especially important for high-speed machines. The mechanical design must account for material strength at operating temperature, residual stresses, interference fits, rotor anisotropy, and possible loss of retaining capability.

2.5 Rotor construction

Common rotor elements include the shaft, core, conductors or bars, end rings, retaining components, balancing provisions, and cooling features. The design should prevent relative movement under electromagnetic pulsation and centrifugal loading. Rotor laminations may be keyed, shrunk, clamped, or mounted with suitable interference. The selected method must not create excessive distortion or close the air gap.

Rotor distortion is dangerous because it can produce eccentricity, rubs, unequal magnetic pull, and rapidly increasing vibration. Thermal gradients are also important: a rotor that is concentric when cold may become eccentric at operating temperature.

3. Bearings and Bearing Supports

Bearings locate the rotor, transmit radial and axial loads, and control the air gap. Their selection depends on load magnitude and direction, speed, lubrication, temperature, contamination, required life, allowable noise, and maintenance practice.

Rolling-bearing basic rating life is commonly expressed as

L10 = (C/P)p

where L_10 is rating life in millions of revolutions, C is the basic dynamic load rating, P is equivalent dynamic bearing load, and p is 3 for ball bearings and 10/3 for roller bearings. The formula applies to conventional rolling-bearing rating-life conditions and is not a complete prediction of field life. Lubrication, contamination, mounting, electrical erosion, and vibration may dominate actual life.

In hours,

L10h = 106L10/(60n)

where n is speed in revolutions per minute. The equivalent dynamic load combines radial and axial loads according to the bearing manufacturer's method. For many bearings it has the form P = XF_r + YF_a, but X and Y depend on bearing type, internal geometry, and loading ratio; they must not be assumed universally.

One bearing arrangement is normally designated as locating or fixed, controlling axial position. The other is allowed to accommodate thermal expansion. Incorrect axial constraint can generate large thermal forces. Fits must be selected so that rings do not creep under load, while excessive interference is avoided because it reduces internal clearance and increases temperature.

Bearing supports should be sufficiently rigid to preserve alignment. Flexible end brackets, poor machining, or uneven foundation stiffness can produce bearing misalignment and vibration even when the bearing itself is correctly rated.

Worked Example 1: Preliminary bearing life

An induction motor operates at 1,500 r/min. A selected ball bearing has C = 28 kN and an equivalent dynamic load P = 4 kN. Estimate L_10 and L_10h.

For a ball bearing, p = 3:

L10 = (28/4)3 = 73 = 343 million revolutions

Therefore,

L10h = (106 × 343)/(60 × 1500) ≈ 3811 h

This is only a rating-life estimate. If the required design life is 20,000 h, the bearing or loading arrangement must be reconsidered. In practice, contamination, lubrication, electrical fluting, and duty variation would also be evaluated.

4. Critical Speed, Vibration, and Balancing

4.1 Critical speed

A rotor-support system has natural frequencies. When running speed approaches a lateral natural frequency, resonance may produce large vibration. For a simple single-degree-of-freedom rotor model,

ωn = √(k/m)

where k is lateral stiffness and m is modal mass. The corresponding critical speed in revolutions per minute is

nc = 60ωn/(2π)

This model is a useful introduction but real machines have distributed mass, flexible shafts, bearing stiffness, support flexibility, gyroscopic effects, and several modes. A rotor may therefore have multiple critical speeds.

The design objective is not simply to place a critical speed far from rated speed. Start-up and coast-down must also cross critical speeds safely if the machine is designed as a flexible rotor. The passage rate, damping, unbalance, and control system influence the response.

4.2 Unbalance and synchronous vibration

An eccentric mass m_e at eccentricity e creates a rotating force

Fu = me eω2

This force increases with the square of speed. Small eccentricity can therefore be important in high-speed machines. Sources include material variation, machining error, key-seating, rotor bow, uneven winding, and deposits on fans.

Balancing may be static, couple, or dynamic. Static balancing corrects a single-plane resultant unbalance. Couple balancing addresses opposing unbalance forces in separated planes. Long rotors generally require two-plane dynamic balancing. Balance quality should be specified using the applicable balancing standard and the intended operating speed, rather than by an informal statement such as “balance carefully.”

4.3 Vibration sources and diagnosis

Vibration frequency is a valuable diagnostic indicator:

Frequency characteristicCommon indication
1× rotational frequencyUnbalance, bent shaft, eccentricity
2× rotational frequencyMisalignment, mechanical looseness, bent shaft
Electrical frequency or twice electrical frequencyElectromagnetic force or core asymmetry
Bearing characteristic frequenciesRolling-element damage
Broad high-frequency contentLubrication or bearing distress
Subharmonics or unstable componentsRub, looseness, or nonlinear behavior

Diagnosis should combine vibration amplitude, phase, speed, temperature, acoustic data, and inspection. A single spectrum is rarely sufficient to identify the root cause.

5. Frames, End Shields, and Structural Integrity

The frame supports the stator, bearings, terminal box, enclosure, and mounting feet. It must maintain the air gap and transmit electromagnetic and external forces to the foundation. Important structural properties are stiffness, strength, damping, dimensional stability, corrosion resistance, manufacturability, and heat-transfer capability.

Cast iron provides good damping and robust manufacture but may be relatively heavy and brittle. Fabricated steel frames can be lighter and easier to modify but may require attention to weld distortion and fatigue at joints. Aluminium frames offer low mass and corrosion resistance, though their lower modulus and thermal expansion may influence stiffness and alignment.

Frame deformation can be evaluated using beam or plate methods for preliminary work and finite-element analysis for complex geometry. A structural model should include mounting constraints, bearing reactions, electromagnetic forces, fan forces, and thermal loads. Boundary conditions must represent the actual foundation; unrealistically fixed supports can produce misleadingly low deformation.

Mounting feet should be coplanar and sufficiently thick. Soft foot, uneven shims, and weak foundations create distortion after tightening. Dowels or accurately machined locating surfaces may be used where repeatable alignment is required.

6. Electromagnetic Forces and Mechanical Interaction

Electromagnetic forces act on conductors, teeth, poles, rotor bars, end windings, and the air-gap surfaces. Radial forces can deform the stator and excite frame modes. Tangential forces produce torque and torque ripple. Unbalanced magnetic pull may arise from eccentricity, unequal air gap, bearing displacement, rotor asymmetry, or winding faults.

The local magnetic pressure in an air gap is approximately

pm = B2/(2μ0)

where B is air-gap flux density in teslas and μ_0 is the permeability of free space, approximately 4π × 10⁻⁷ H/m. This expression assumes a locally uniform magnetic field in a nonmagnetic air gap and neglects tangential field effects and saturation complexity.

The total force requires integration of pressure over the relevant surface. Pulsating forces occur at harmonics related to slotting, winding distribution, supply frequency, and electromagnetic asymmetry. If one of these forcing frequencies coincides with a structural natural frequency, noise and vibration can increase sharply.

Mechanical and electromagnetic design must therefore be iterative. Changing slot number, air-gap length, frame stiffness, rotor geometry, or winding arrangement can alter both electrical performance and mechanical excitation.

7. Tolerances, Fits, and Air-Gap Control

Tolerances define acceptable manufacturing variation. They should be allocated according to function rather than made unnecessarily tight. Critical dimensions include shaft seats, bearing locations, rotor outside diameter, stator bore, end-shield alignment, mounting surfaces, and concentricity.

A tolerance stack-up determines the possible variation of a functional dimension. For a worst-case linear stack, maximum variation is obtained by adding individual absolute tolerances. Statistical root-sum-square methods may be appropriate when independent, approximately random variations are justified, but they must not be used to conceal systematic errors.

The air gap is particularly sensitive. Rotor eccentricity can result from shaft runout, bearing clearance, bearing-seat error, end-shield misalignment, stator-bore error, and thermal deformation. Excessive air-gap variation increases unbalanced magnetic pull and may lead to rotor contact. Insufficient clearance increases sensitivity to thermal growth and bearing movement.

Fits must be selected with reference to load direction, speed, temperature, assembly method, and bearing manufacturer data. Press fits should be checked for contact pressure and shaft stress; sliding fits should prevent unwanted creep. Keys, splines, and shoulders must also satisfy the relevant stress and assembly requirements.

8. Fatigue, Shock, and Reliability

Many machine components experience millions of load cycles. Fatigue may occur at shaft shoulders, keyways, weld toes, bolted joints, rotor retaining parts, and fan blades even when the maximum stress is below yield strength.

A basic stress-life approach uses an alternating stress amplitude σ_a and mean stress σ_m. One commonly used screening relation is the modified Goodman criterion:

σa/σe + σm/σu ≤ 1/Sf

where σ_e is corrected endurance strength, σ_u is ultimate tensile strength, and S_f is a fatigue safety factor. This is an approximate design criterion for ductile materials under appropriate loading; surface finish, size, notch sensitivity, temperature, reliability, and load type must be included when determining σ_e. For combined bending and torsion, equivalent alternating and mean stresses require a consistent failure theory.

Shock loads are often represented by an impact factor or by a measured acceleration-time history. Transportation shock, dropped equipment, seismic events, and sudden torque reversals may require transient finite-element analysis. Bolted joints should be designed so that clamping force is retained under vibration; locking methods should not replace correct preload.

Reliability is improved by eliminating stress raisers, controlling surface quality, using corrosion-resistant materials or coatings, validating assembly procedures, and performing overspeed, vibration, thermal, and endurance tests appropriate to the machine.

9. Enclosures and Ingress Protection

An enclosure protects personnel and internal components while controlling cooling, noise, and contamination. Selection depends on dust, water, corrosive agents, hazardous atmospheres, washdown, altitude, and ventilation requirements.

Ingress-protection classifications specify protection against solid objects and water under defined test conditions. The code should be selected according to the applicable standard and installation environment; an IP rating is not a general guarantee against every form of contamination, corrosion, or continuous immersion. Cable glands, shaft seals, drain holes, joints, terminal boxes, and access covers must provide a protection level consistent with the complete assembly.

An enclosed machine may use natural convection, external fans, internal fans with heat exchangers, or liquid cooling. Ventilation openings should not compromise protection against water or dust. Condensation control may require drains, space heaters, breathable membranes, or specified storage procedures.

The enclosure must withstand pressure, handling, vibration, and accidental impact. Sharp edges should be removed, guards should prevent contact with rotating parts, and maintenance access should be possible without creating unsafe exposure. Hazardous-area machines require additional construction, temperature, and certification provisions that cannot be inferred from a standard industrial enclosure.

10. Acoustic Design

Noise consists of airborne sound and structure-borne vibration. Important sources include cooling fans, bearings, electromagnetic forces, rotor unbalance, gear meshing, turbulence, and enclosure panels. Sound-pressure level depends on distance, room reflections, directivity, and measurement conditions; sound-power level is a more transferable property of the source.

Sound-pressure level is defined by

Lp = 20 log10(p/p0)

where p is the measured root-mean-square sound pressure and p_0 is the reference pressure, conventionally 20 μPa in air. Decibels are logarithmic: two equal, uncorrelated sources do not produce a level that is twice as large. Their combined level is approximately L + 3 dB, while doubling the pressure amplitude increases the level by approximately 6 dB.

Noise reduction methods include:

  • reducing electromagnetic force harmonics through suitable slot and winding design;
  • improving rotor balance and shaft alignment;
  • selecting low-noise bearings and correct lubrication;
  • using quieter fans and avoiding excessive tip speed;
  • increasing panel stiffness to move resonances away from excitation frequencies;
  • applying damping treatments where compatible with temperature and enclosure requirements;
  • using acoustic barriers or absorptive materials without obstructing cooling;
  • isolating structure-borne vibration with suitable mounts.

Acoustic treatment must not create unacceptable temperature rise or reduce ingress protection. Noise testing should specify operating point, speed, load, background level, microphone positions, and relevant standards.

11. Integrated Design Procedure

A practical design sequence is:

  1. Define power, speed, duty, environment, life, noise, and safety requirements.
  2. Identify all steady, transient, fault, thermal, electromagnetic, and installation loads.
  3. Establish shaft geometry, bearing arrangement, rotor construction, and frame concept.
  4. Calculate torque, bending, combined stress, deflection, centrifugal stress, and fatigue margins.
  5. Select bearings using load, speed, lubrication, life, and electrical considerations.
  6. Determine rotor natural frequencies and assess critical-speed passage.
  7. Allocate tolerances and analyze air-gap, alignment, and thermal-growth variation.
  8. Estimate electromagnetic force harmonics and compare them with structural modes.
  9. Select enclosure, cooling, seals, drains, and ingress protection.
  10. Assess acoustic sources and define a verification test plan.
  11. Validate with finite-element analysis, prototype testing, balancing, overspeed tests, vibration measurements, and thermal tests.
  12. Review manufacturing capability, inspection methods, maintenance, and regulatory compliance.

Computer-aided analysis is valuable but only when material properties, contacts, constraints, loads, and mesh quality are credible. Model correlation with test data is essential. Artificially rigid supports or omitted joints can make a simulation appear safer than the physical machine.

Applied Case: Illustrative Medium-Size Induction Motor

Background

Consider an illustrative 75 kW, 1,500 r/min induction motor for a pump installation. The machine operates continuously, uses rolling-element bearings, and is installed outdoors under a roof with occasional moisture and dust.

Problem

The initial design meets electromagnetic and thermal requirements, but field prototypes show elevated 1× vibration, a warm drive-end bearing, and a noise peak near a structural resonance.

Analysis

Rated torque is approximately

T = 9550 × 75/1500 = 477.5 N·m

The vibration spectrum shows a dominant 1× component, suggesting unbalance, eccentricity, or misalignment. Inspection finds that the rotor was balanced with a temporary key while the operating coupling used a different key arrangement. The effective unbalance therefore changed during assembly.

The drive-end bearing temperature is higher than predicted. Review shows that both bearings were axially constrained, so rotor thermal expansion generated an unintended axial load. The bearing arrangement is revised to use one locating bearing and one expansion-capable arrangement, subject to manufacturer approval.

A structural modal analysis identifies a frame mode close to an electromagnetic force harmonic. Increasing local frame stiffness and modifying a panel bead moves the mode away from the forcing frequency. The enclosure remains ventilated, and the modification does not reduce its environmental protection.

Outcome

After rebalancing in the complete rotor configuration, correcting the bearing axial arrangement, and stiffening the panel, vibration and bearing temperature decrease. The acoustic peak is also reduced. The final verification includes balance documentation, vibration measurements at specified load and speed, bearing-temperature monitoring, enclosure inspection, and review of assembly tolerances.

Learning Points

  1. Balance must represent the final rotor and key configuration.
  2. Bearing location must accommodate thermal expansion.
  3. Electromagnetic and structural modal analysis must be coordinated.
  4. Field symptoms should be interpreted using frequency, phase, temperature, and inspection evidence together.
  5. A design change is acceptable only when it preserves cooling, safety, manufacturability, and ingress protection.

Challenges, Limitations, and Contemporary Practice

Mechanical design models are limited by uncertain loads, material variability, manufacturing deviations, lubrication behavior, and installation conditions. Fatigue data may not represent actual surface finish or corrosive environments. Acoustic predictions are particularly sensitive to damping and boundary conditions. Consequently, design margins and validation testing remain necessary.

Modern practice increasingly uses coupled electromagnetic–structural finite-element models, digital monitoring, laser alignment, operational modal analysis, and condition-based maintenance. Artificial intelligence can assist with anomaly detection in vibration and temperature histories, but it should not replace engineering judgment or physical safety limits. Training data must represent normal operating variation, and alarm thresholds should be traceable and validated.

Ethically and professionally, the designer must not trade away guarding, overspeed protection, environmental suitability, or documented safety margins merely to reduce cost or mass. Applicable electrical, mechanical, acoustic, environmental, and hazardous-location standards must be identified for the jurisdiction and product category. Design records should state assumptions, inspection points, acceptance criteria, and limitations.

Chapter Summary

Mechanical, structural, and acoustic design ensures that an electrical machine can transmit power safely, maintain its air gap, withstand operating and fault loads, and satisfy environmental and noise requirements. Shaft design requires consideration of torsion, bending, combined stress, stiffness, fatigue, and stress concentration. Rotor design must address centrifugal stress, shrink fits, thermal distortion, overspeed, and balancing. Bearings are selected from radial and axial loads, speed, lubrication, contamination, and rating life, while the bearing arrangement must accommodate thermal expansion.

Critical speeds and unbalance determine vibration behavior. Frames, end shields, and foundations must provide adequate stiffness and alignment. Electromagnetic air-gap pressure can excite structural modes and generate noise, making electromagnetic and mechanical design an iterative process. Tolerances and fits control air-gap uniformity and bearing performance. Enclosures must balance ingress protection, cooling, serviceability, and safety. Acoustic design addresses fans, bearings, electromagnetic forces, structure-borne vibration, and enclosure radiation. Reliable practice combines analytical calculations, standards, manufacturing control, simulation, and experimental validation.

Key Terms

Shaft: Rotating member that transmits torque and supports rotating parts.

Torsional stress: Shear stress produced by applied torque.

Bending moment: Internal moment caused by transverse forces.

Centrifugal stress: Stress generated by rotation-induced inertia forces.

Bearing: Element that supports and locates a rotating shaft.

Dynamic load rating: Reference load used in rolling-bearing life calculations.

Critical speed: Rotational speed near a rotor-support natural frequency.

Unbalance: Unequal mass distribution producing rotating force.

Dynamic balancing: Correction of unbalance in magnitude and angular position, usually in two planes.

Air gap: Radial clearance between stator and rotor.

Unbalanced magnetic pull: Net radial electromagnetic force caused by asymmetry.

Tolerance: Permissible variation in a manufactured dimension.

Fit: Relationship between mating dimensions such as a shaft and bearing ring.

Fatigue: Failure mechanism caused by repeated or fluctuating stress.

Ingress protection: Classified resistance of an enclosure to solids and water.

Sound-pressure level: Logarithmic measure of acoustic pressure relative to a reference.

Natural frequency: Frequency at which a structure or rotor vibrates freely.

Modal analysis: Determination of natural frequencies and mode shapes.

Structure-borne noise: Noise transmitted through solid machine structures.

Overspeed: Operation or testing above the rated rotational speed.

Review Questions

Short Answer Questions

  1. State the relationship between power, torque, and speed for a rotating shaft.
  2. Why must one bearing arrangement generally accommodate thermal expansion?
  3. What is meant by rotor unbalance?
  4. Define critical speed.
  5. Name two factors that can compromise enclosure ingress protection.

Long Answer Questions

  1. Explain the mechanical design procedure for a rotating electrical machine, from load definition through validation.
  2. Discuss the combined torsional and bending design of a motor shaft, including stress concentration and fatigue.
  3. Explain how electromagnetic forces can produce structural vibration and acoustic noise.
  4. Compare the functions and design considerations of bearings, frames, end shields, and foundations.
  5. Discuss the trade-off between enclosure protection, cooling, maintenance access, and noise control.

Analytical / Application Questions

  1. A 45 kW motor runs at 1,500 r/min. Calculate its rated shaft torque and explain why starting torque may require a separate shaft-load case.
  2. A ball bearing has C = 20 kN and P = 5 kN and operates at 1,000 r/min. Estimate its L_10 life in hours using p = 3, then state why field life may differ.
  3. A rotor has an unbalance mass of 0.002 kg at an eccentricity of 0.25 mm and rotates at 3,000 r/min. Calculate the approximate rotating force using F_u = m_e eω² and explain how the force changes if speed doubles.

Multiple Choice Questions with Answers

Question 1

A 30 kW motor operates at 1,500 r/min. What is its approximate rated shaft torque?

A. 95.5 N·m

B. 191 N·m

C. 477.5 N·m

D. 9,550 N·m

Correct Answer: B. 191 N·m

Question 2

For a solid circular shaft under pure torsion, maximum shear stress varies inversely with which power of diameter?

A. d

B. d²

C. d³

D. d⁴

Correct Answer: C. d³

Question 3

For a conventional ball bearing, the exponent p in L_10 = (C/P)^p is:

A. 1

B. 2

C. 3

D. 10/3

Correct Answer: C. 3

Question 4

The rotating force caused by a fixed unbalance is proportional to:

A. ω

B. ω²

C. 1/ω

D. 1/ω²

Correct Answer: B. ω²

Question 5

A critical speed occurs when operating speed approaches a rotor-support:

A. thermal limit

B. natural frequency

C. bearing static load rating

D. sound reference pressure

Correct Answer: B. natural frequency

Question 6

Which bearing arrangement normally permits axial thermal expansion of the rotor?

A. The expansion-capable or floating arrangement

B. A fully locked arrangement at both ends

C. A bearing with zero internal clearance

D. A bearing removed from the shaft

Correct Answer: A. The expansion-capable or floating arrangement

Question 7

The approximate magnetic pressure in an air gap is given by:

A. B/μ₀

B. B²/(2μ₀)

C. 2μ₀B²

D. μ₀/B²

Correct Answer: B. B²/(2μ₀)

Question 8

A dominant vibration component at 1× rotational frequency is commonly associated with:

A. Rotor unbalance

B. Only electrical insulation failure

C. Reference sound pressure

D. Bearing dynamic rating alone

Correct Answer: A. Rotor unbalance

Question 9

An IP classification primarily describes enclosure protection against:

A. All possible corrosion mechanisms

B. Solids and water under specified tests

C. Shaft torsional fatigue

D. Electromagnetic torque ripple

Correct Answer: B. Solids and water under specified tests

Question 10

If two equal, uncorrelated sound sources operate together, their combined sound level is approximately:

A. 1 dB higher

B. 3 dB higher

C. 6 dB lower

D. Twice the numerical dB value

Correct Answer: B. 3 dB higher

Electrical Machine Design
Chapter 7 of 15