Machine design - sintesi

Difference between Butt Joints and Fillets

The difference between butt joints and fillets is that the aim of butt joints is to create a complete weld seam (cordolo di saldatura), while fillets are used to join two pieces of metal at an angle.

Defects in Welding

Metallurgical defects are almost always present in welding, and the aim is to keep them under a maximum length. These defects include:

• Cracks
• Tears
• Inclusions

Geometric defects in welding include:

• Excess of filler
• Too low penetration
• Not aligned parts

Non-Destructive Tests (NDT)

Non-destructive tests are used to inspect welds without causing damage to the material. Some common NDT methods include:

• Visual Inspection (VI)
• Dye/Liquid Penetrant Examination (PT): only for surface cracks, a liquid penetrates and another liquid or powder brings it out, highlighting the crack
• Magnetic Particle Testing (MP)
• Ultrasonic Testing (UT)
• Radiographic Testing (RT)

Standards

The UNI EN 1993 (Eurocodice 3) standard does not directly consider welding defects, but their effect is considered indirectly. To avoid high residual stresses, it is suggested to avoid excessively long welded joints and to apply the PWHT (post weld heat treatment) procedure. More precise methods can be used to detect defects, which can reduce the need for PWHT.

conservative.Since the stress state inside a welded joint is really complicated, the standard proposes, for the assessment of the welded joint strength, to reduce the multiaxial stress to a mono-axial one and to compare it with the material strength.

Regarding the stress perpendicular to the welding axis (tension or compression) and for the shear stresses, the longitudinal welding section has to be considered as the resistant section. Its length is equal to the welding length whilst its width is equal to the shortest thickness between the two sides linked in the butt weld, or it is the thickness of the full penetration element in case of a T joint.

Regarding the stress parallel to the welding axis (tension or compression) the resistant section is the one normal to the welding axis (it is the one made by the base material plus the filler). After I calculated the parallel and perpendicular stresses and the shear one, I can make the assessment. The standard provides 2 classes of welded joints assessment,

Depending on the level of accuracy which I used for controls of the seam:

• I CLASS: more strict controls on welding procedures, including electrode control, removal of welding defects, more stringent X-Ray test requirements, etc. This more accurate controls allow me to use higher allowable stresses.
• II CLASS: less strict control; a more conservative design is thus needed. We expect a lower admissible stress for the II class since many defects will not be detected.

Remember: when I do an assessment, I have to consider 2 approaches:

1. LIMIT STATE: semi-probabilistic approach in which different effects are combined in order to provide a more refined estimation of the maximum load acting on the structure (e.g. taking exceptional wind, an earthquake...); the requirement is just that the structure does not collapse.
2. ALLOWABLE STRESS: typical approach for stress analysis, where a synthetic stress parameter representing the ordinary load that the structure will undergo is compared with an allowable stress.

The requirement is that the structure does not present any failure or permanent deformation.

Assessment for BUTT WELDS

Calculate the equivalent von Mises stress and compare it to the maximum stress of the PLATE:

∑2 2} + −σσ ≤ σT MAX2}σ +3 τTσ ∑ = ∑σ √vm

If I am using I CLASS controls, the maximum stress is the ADMISSIBLE STRESS OF THE MATERIAL OF THE PLATES, not of the welding (the aim of the welding is to create a continuum).

plates=σσ MAX ADMISSIBLE

If I am using II CLASS controls, the maximum stress will be a fraction of the admissible stress of the plate since I will not be able to detect many defects.

plates=0,85∗σσ MAX ADMISSIBLE

Assessment for FILLET WELDS

In fillets, I have both the risk of defects inside and the certainty that there will be a discontinuity (assumable as a crack) in the non-welded region.

The standard does not require to calculate the stress.

concentration factor, but it takes into account the above intrinsically by considering an EMPIRICAL SAFETY DOMAIN (no actual physical explanation). Stresses are the ones acting on the section [l x a], with l=length of the fillet -2a (ends are not perfect usually) and a=throat of the fillet, as follows; the standard does not require an accurate calculation of the stresses, but their average value (force over plane area):

• normal stress perpendicular to the throat section: σ
• normal stress parallel to the weld axes: σ
• shear stress on the plane of the throat section and perpendicular to the weld axes: T
• shear stress on the plane of the throat section and parallel to the weld axis: τ

TN.B.: Fe360 has a higher admissible stress since it has higher ductility. N.B.2: according to the standard, I can use the throat section as it is rotated on the vertical or on the horizontal side in order to simplify the calculations. N.B.3: Inertia moment of

two separated welds (as the flanges) can be calculated as the sum of the INTRINSIC INERTIA MOMENT (usually neglectable) and the TRANSPORT INERTIA MOMENT

In the case of web and flanges, we can assume that the web welds are supposed to react the shear stress (that acts along their main direction), while the flanges' welds are supposed to react the bending moment (that acts along their main direction)

15/05/2020

GEARS

Gears are toothed, cylindrical wheels used to transmit and manipulate motion, power and torque from one rotating shaft to another.

Often gears are employed to produce a change in the speed of rotation, in torque or in direction of rotation of the driven gear relative to the driving gear. [usually they reduce the rotation speed and increase the torque]

In Italia gli ingranaggi sono molto conosciuti ed è una delle maggiori produttrici di ingranaggi; la lingua italiana è l'unica a fare la distinzione fra:

- Ruota dentata: ruota dotata alla sua periferia

utilizzando i seguenti tag html:

1. di una dentatura, interna od esterna.
2. Ingranaggio: complesso di due ruote dentate opportunamente costruite al fine di ingranare tra loro.
3. Gears are used from 5000 b.c.
4. Alternative to gears we can transmit power by friction, but we it deeply depends on the preload (that cannot be infinite)
5. SPUR GEARS: the smallest is usually called pinion, while the other one is called wheel.
6. HELICAL GEAR transmits smoother movement but requires more constraints with respect to spur ones.
7. We will only analyse spur gears.
8. INVOLUTE

The involute is constructed on the BASE CIRCLE (the one on which we built the teeth) and not the pitch circle.

The involute will be the profile of the teeth in order to create an always parallel contact between the teeth of the different gears, allowing for a very smooth contact.

In this way a centre distance variation is tolerable.

Moreover, the involute geometry is really easy to fabricate.

9. KINEMATIC AND FORCES

It is possible to describe the kinematic (reciprocal movement) of two gears by

approximating them to circles [PITCH CIRCLES or CERCHI PRIMITIVI]: these are imaginary circles that rotates one against the other with no slippage. The angular velocity of the pinion will be higher, while the linear velocity will be equal at the contact point.

ω d ω d1 1 2 2= =v 2 2+dd 1 2a= 2ω d1 2=i= ω d2 1

Is very important that the two wheels have the ratio Z/R in order to work properly: Z= number of teeth, R = pitch radius

p2 π R p=p=PITCH Z 2 Rp p=MODULUS=m= π ZR ω 2p 1 =TRASM . RATIO=τ= R ω 1p 2

FORCES

The transmitted force will be equal on each wheel, while the torque will depend on the diameter (pinion will transmit to its shaft a lower torque and a higher angular velocity, while both shafts will sustain the same force in opposite direction) To the shaft connected to the PINION (smaller gear) will be transmitted:

• Lower torque
• Higher angular velocity
• Same lateral forces (Fr and Ft)
• Same power

With respect to the counter-wheel shaft.

Typical

FAILURE of modern gears
Pitting is the main contribution to the noise.
Scuffing is a very peculiar pitting: when two gears rotate very fast and not lubricated enough, they heat a lot and instantaneously weld together and detach later, damaging the teeth.
FATIGUE OF METALS
Time varying stresses (NOT FORCES) can cause fatigue, which is the main cause for components failure. Stress variation on a single grain can be obtained by variation of loads or by rotation of the component.
Fatigue consists in the propagation of a crack due to cyclic loading, until the remaining resistant area of the structure is so low that it cannot resist anymore the applied load, so it fails (by STATIC FAILURE in BRITTLE MODE, with very low plastic deformation).
N.B.: fatigue is highly sensitive to notches.
FATIGUE FAILURE SURFACE: is mainly divided in 3 parts: initiation, a very smooth part with BEACH MARKS where the propagation has occurred and a very irregular surface, were the final static failure occurred.
The right approach fordesign is a crucial aspect in ensuring the safety and longevity of structures. It involves testing critical structures for both fatigue and static failure. However, it is important to use different prototypes for each test, as plasticization occurring during the static test could be beneficial for the fatigue behavior. One approach to fatigue design is the fail-safe approach. This design philosophy provides redundancy in the constraints and critical components of a structure, so that it can still function even if some parts fail. In the past, the safe-life approach was used, which assumed that each part of the structure should last for its entire lifetime. Another design philosophy adopted nowadays is the damage-tolerant approach. This approach focuses on building structures that can continue to function even with defects. Periodic checks for defects are set to ensure the ongoing safety of the structure. It is important to note that all materials are subjected to fatigue, with metals being the most sensitive. However, other materials such as polymers and composites are also susceptible to fatigue. In conclusion, fatigue design plays a crucial role in ensuring the safety and longevity of structures. By testing for both fatigue and static failure, using different prototypes, and adopting fail-safe and damage-tolerant approaches, structures can be designed to withstand the challenges of fatigue.e to the irreversible slippage of crystalline planes caused by shear stresses. This introduces a very small notch on the material surface due to the irreversible slippage of crystalline planes caused by shear stresses.