FREQUENCY ANALYSIS OF THE ROTATING SHAFT USING SOLIDWORKS SIMULATION

AIM

To perform the frequency analysis on the rotating shaft using solidworks simulation.

OBJECTIVE OF THE ANALYSIS

To find out the frequency and the resultant amplitude at different modes of vibration in the system.In this analysis i have performed two tests for two different materials for the shaft.The materials are selected based upon its properties for a basic selection of the rotating shafts.

The bearing fixture is provided at both the ends of the shaft.The fixture provided is at the stepped face of the rotating shaft.

The 5 modal shapes are analysed for critical frequency and resonant frequency is evaluated.

VIBRATION:

Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem (\"shaking, brandishing\"). The oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road.

Vibration can be desirable: for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker.

In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshing of gear teeth. Careful designs usually minimize unwanted vibrations.

TYPES OF VIBRATION:

Free vibration occurs when a mechanical system is set in motion with an initial input and allowed to vibrate freely. Examples of this type of vibration are pulling a child back on a swing and letting it go, or hitting a tuning fork and letting it ring. The mechanical system vibrates at one or more of its natural frequencies and damps down to motionlessness.

Forced vibration is when a time-varying disturbance (load, displacement or velocity) is applied to a mechanical system. The disturbance can be a periodic and steady-state input, a transient input, or a random input. The periodic input can be a harmonic or a non-harmonic disturbance. Examples of these types of vibration include a washing machine shaking due to an imbalance, transportation vibration caused by an engine or uneven road, or the vibration of a building during an earthquake. For linear systems, the frequency of the steady-state vibration response resulting from the application of a periodic, harmonic input is equal to the frequency of the applied force or motion, with the response magnitude being dependent on the actual mechanical system.

Damped vibration: When the energy of a vibrating system is gradually dissipated by friction and other resistances, the vibrations are said to be damped. The vibrations gradually reduce or change in frequency or intensity or cease and the system rests in its equilibrium position. An example of this type of vibration is the vehicular suspension dampened by the shock absorber.

FREQUENCY:

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency.

FREQUENCY FORMULA:

The formula for frequency is: f (frequency) = 1 / T (period). f = c / λ = wave speed c (m/s) / wavelength λ (m). The formula for time is: T (period) = 1 / f (frequency). λ = c / f = wave speed c (m/s) / frequency f (Hz).

OSCILLATION:

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.

Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.

RESONANCE:

Resonance describes the phenomena of amplification that occurs when the frequency of a periodically applied force is in harmonic proportion to a natural frequency of the system on which it acts. When an oscillating force is applied at the resonant frequency of another system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies. ^[3]

Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system.^[3] Small periodic forces that are near the intrinsic resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy.

Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR) and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency (e.g., musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies (e.g., filters)

NATURAL FREQUENCY:

Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving or damping force.^[1]

The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all parts of the system move sinusoidally with that same frequency).

If the oscillating system is driven by an external force at the frequency at which the amplitude of its motion is greatest (close to a natural frequency of the system), this frequency is called resonant frequency.

Free vibrations of an elastic body are called natural vibrations and occur at a frequency called the natural frequency. Natural vibrations are different from forced vibrations which happen at frequency of applied force (forced frequency). If forced frequency is equal to the natural frequency, the amplitude of vibration increases many fold. This phenomenon is known as resonance.^[2]

In a mass-spring system, with mass m and spring stiffness k, the natural frequency can be calculated as:

{\\displaystyle \\omega _{0}={\\sqrt {\\frac {k}{m}}}}

In electrical circuits, s₁ is a natural frequency of variable x if the zero-input response of x includes the term {\\displaystyle K_{1}e^{-s_{1}t}}, where {\\displaystyle K_{1}\\neq 0} is a constant dependent on initial state of the circuit, network topology, and element values.^[3] In a network, s_k is a natural frequency of the network if it is a natural frequency of some voltage or current in the network.^[4] Natural frequencies depend only on network topology and element values but not the input.^[5] It can be shown that the set of natural frequencies in a network can be obtained by calculating the poles of all impedance and admittance functions of the network.^[6] All poles of the network transfer function are also natural frequencies of the corresponding response variable; however there may exist some natural frequencies that are not a pole of the network function. These frequencies happen at some special initial states.^[7]

In LC and RLC circuits, the natural frequency of a circuit can be calculated as:^[8]

{\\displaystyle \\omega _{0}={\\frac {1}{\\sqrt {LC}}}}

NVH ANALYSIS:

Noise, vibration, and harshness (NVH), also known as noise and vibration (N&V), is the study and modification of the noise and vibration characteristics of vehicles, particularly cars and trucks. While noise and vibration can be readily measured, harshness is a subjective quality, and is measured either via \"jury\" evaluations, or with analytical tools that can provide results reflecting human subjective impressions. These latter tools belong to the field known as \"psychoacoustics.\"

Interior NVH deals with noise and vibration experienced by the occupants of the cabin, while exterior NVH is largely concerned with the noise radiated by the vehicle, and includes drive-by noise testing.

NVH is mostly engineering, but often objective measurements fail to predict or correlate well with the subjective impression on human observers. For example, although the ear\'s response at moderate noise levels is approximated by A-weighting, two different noises with the same A-weighted level are not necessarily equally disturbing. The field of psychoacoustics is partly concerned with this correlation.

In some cases the NVH engineer is asked to change the sound quality, by adding or subtracting particular harmonics, rather than making the vehicle quieter.

ROTATING SHAFT:

rotating shaft - a revolving rod that transmits power or motion. shaft. camshaft - has cams attached to it. crankshaft - a rotating shaft driven by (or driving) a crank. driveshaft - a rotating shaft that transmits power from the engine to the point of application.

CAD MODEL:

CASE (1):

• MATERIAL USED:
• NITRIDING STEEL
• GRADE: 34CrAlNi7-10
• NUMBER:1.8550

EN 1.8550 steel is an alloy steel formulated for primary forming into wrought products. Cited properties are appropriate for the quenched and tempered condition. 1.8550 is the EN numeric designation for this material. 34CrAlNi7-10 is the EN chemical designation.

It has a moderately low melting temperature among EN wrought alloy steels. In addition, it has a moderately high electrical conductivity and a moderately low thermal conductivity.

The graph bars on the material properties cards below compare EN 1.8550 steel to: EN wrought alloy steels (top), all iron alloys (middle), and the entire database (bottom). A full bar means this is the highest value in the relevant set. A half-full bar means it\'s 50% of the highest, and so on.

Mechanical Properties

Brinell Hardness

300

Elastic (Young\'s, Tensile) Modulus

190 GPa27 x 10⁶ psi

Elongation at Break

11 %

Fatigue Strength

470 MPa68 x 10³ psi

Impact Strength: V-Notched Charpy

34 J25 ft-lb

Poisson\'s Ratio

0.29

Shear Modulus

73 GPa11 x 10⁶ psi

Shear Strength

600 MPa87 x 10³ psi

Tensile Strength: Ultimate (UTS)

1000 MPa150 x 10³ psi

Tensile Strength: Yield (Proof)

760 MPa110 x 10³ psi

Thermal Properties

Latent Heat of Fusion

250 J/g

Maximum Temperature: Mechanical

440 °C820 °F

Melting Completion (Liquidus)

1450 °C2640 °F

Melting Onset (Solidus)

1410 °C2570 °F

Specific Heat Capacity

480 J/kg-K0.11 BTU/lb-°F

Thermal Conductivity

40 W/m-K23 BTU/h-ft-°F

Thermal Expansion

13 µm/m-K

Electrical Properties

Electrical Conductivity: Equal Volume

7.6 % IACS

Electrical Conductivity: Equal Weight (Specific)

8.8 % IACS

Otherwise Unclassified Properties

Base Metal Price

3.4 % relative

Density

7.8 g/cm³490 lb/ft³

Embodied Carbon

1.7 kg CO₂/kg material

Embodied Energy

23 MJ/kg9.8 x 10³ BTU/lb

Embodied Water

67 L/kg8.0 gal/lb

MATERIAL SELECTION CRITERIA:

This material is selected for first case because of its high hardness and can withstand corrosion with high tensile strength.

MODE SHAPES RESULTS FOR CASE (1):

CASE (2):

• MATERIAL USED:
• CHROMIUM STAINLESS STEEL

They do, however, exhibit lower corrosion resistance due to chromium depletion of the oxide film. They exhibit good strength and oxidation resistance up to 750°C, although their creep strength above 600°C is poor.

MATERIAL SELECTION CRITERIA:

This material is selected to increase resistance to oxidation and highly corrosive resistance.

MODE SHAPES RESULTS FOR CASE (2):

WHIRLING OF SHAFTS:

Whirling speed is also called as Critical speed of a shaft. It is defined as the speed at which a rotating shaft will tend to vibrate violently in the transverse direction if the shaft rotates in horizontal direction. In other words, the whirling or critical speed is the speed at which resonance occurs.

EXAMPLE FOR VIBRATION ANALYSIS:

PLOTS FOR BOTH THE CASES:

RESONANT FREQUENCY FOR CASE(1):

RESONANT FREQUENCY FOR CASE(2):

RESULTS:

• FOR CASE 1 THE MODE SHAPE 2 HAS VALUE OF 1.211 WHICH IS SIMILAR TO THE CASE 2.

• THE MAXIMUM BENDING OCCURS DUE TO THE WHIRLING OF THE SHAFT.

• THE RESONANT FREQUENCY VALUES FOR BOTH THE MATERIAL CASES IS QUITE SIMILAR WITH ONE ANOTHER.

• THE FREQUENCY AND TIME PERIOD IS ALSO SIMILAR.

REFERENCES: