Exercises: Joining, guiding, and supporting elements

Classify these joints as non-permanent (can be separated without destroying anything) or permanent, justifying one case: (a) bolt and nut, (b) rivet, (c) weld, (d) pin, (e) epoxy adhesive, and (f) wood screws.

In any properly made bolted joint, a washer appears under the nut or the bolt head. Explain what it is for and what would happen if the nut were tightened directly against a soft aluminium part.

Explain the difference between an axle and a transmission shaft, and give an example of each on a bicycle.

1. a) Define what an axle is and what a transmission shaft is, indicating whether or not they transmit torque.

1. b) Give an example of an axle and an example of a transmission shaft on a bicycle, and justify your choice in each case.

Explain the difference between a plain bearing (sliding support) and a rolling bearing (rolling support with balls or rollers), and explain why rolling produces much less friction and heating than sliding.

Topic challenge. Rivets join sheets permanently by deforming their own shank.

1. a) Explain what riveting consists of.

1. b) Name two applications where rivets are preferred over screws.

1. c) Give a reasoned advantage of rivets over screws in one of the applications you have named.

What will be assessed: that you describe the process well (placing the rivet in the holes of the sheets and deforming the end of the shank to form a second head), that the two applications are appropriate, and that the advantage is justified.

Explain what welding is and how it differs from other joining methods (rivets, screws, adhesives, etc.). Name one type of welding you know and a typical application.

Pins and keys are small parts used to join and immobilize other parts.

Imagine a cylindrical pin housed in a hole that goes through two parts at once (for example, a shaft and the hub of a wheel).

1. a) Explain what function that cylindrical pin performs in the joint between the two parts.

1. b) Give an example of the use of a pin in an everyday object or machine.

Topic challenge. Every machine with moving parts needs lubrication.

1. a) Explain what oil or grease does when it is placed between two surfaces that move relative to each other.

1. b) State which two problems appear in the machine if lubrication is missing.

You will be assessed on: explaining in your own words the role of the lubricant between the surfaces and relating each problem to the friction between the materials.

Choose and justify the most suitable type of joint for each case: (a) an engine sump cover, which must be opened at every service; (b) the sheet metal frame of an electrical cabinet, which will never be disassembled; (c) the melamine boards of flat-pack furniture; (d) the casing of a remote control, which must be opened to change the batteries.

The figure shows the cross-section of a bolted joint between two flat components, with an element marked with a question mark, as shown in the figure.

(a) Name the labelled parts of the joint. (b) Identify the part marked with the question mark and explain its function. (c) Explain why, when tightening the nut, the shank is subjected to tension while the two parts are compressed against each other.

State whether these statements are true or false, justifying each one: (a) a rolling bearing reduces friction because it replaces sliding with rolling; (b) a drive shaft does not transmit torque, it only supports parts; (c) welding is a non-permanent joint; (d) a spring washer (Grower washer) helps prevent the nut from loosening due to vibrations.

For each application, choose plain bearing or rolling bearing and justify it: (a) the bushing of a door hinge, which rotates very slowly and few times a day; (b) the wheels of a scooter, which rotate fast and must roll freely; (c) the crankshaft support of an engine, subjected to shocks and pressure-lubricated.

Between the engine and the gearbox of a car there is a clutch, not a rigid coupling. Explain what a clutch allows you to do (connect and disconnect the transmission progressively) and what would happen when starting off if the engine and wheels were rigidly connected.

A disc brake presses pads against a disc that rotates with the wheel. Explain how it stops the vehicle (friction), what the kinetic energy is converted into (heat), and why brakes wear down with use and lose effectiveness if they overheat.

The figure shows a pulley mounted on a drive shaft, with the part that prevents relative rotation marked with a question mark, as shown in the figure.

(a) Identify the part marked with the question mark (the one housed half in the shaft and half in the pulley hub) and explain what stress it transmits. (b) Explain what the set screw is also used for. (c) Reason why an interference fit (friction alone) would not be sufficient to transmit high torque.

A rolling bearing in an industrial fan starts making noise and heating up. Describe two symptoms of bearing wear (noise, play, temperature), explain their probable cause (lack of lubrication or end of service life), and what maintenance operation corresponds in each case.

Two flat steel plates of a structure subjected to an axial tensile force $F = 18\ \text{kN}$ need to be joined. Standard M10 class 8.8 steel bolts are available (shear stress area $A = 58\ \text{mm}^2$, allowable shear stress $\tau_{\text{adm}} = 120\ \text{MPa}$). The friction coefficient between the contact surfaces is $\mu = 0,35$.

(a) A technician suggests installing a single bolt tightly tightened with an axial pre-tension force of $25\ \text{kN}$, claiming that "the joint will hold solely by friction without the bolt undergoing shear." Demonstrate numerically whether or not relative slip occurs between the plates under the $18\ \text{kN}$ load.

(b) If the plates do slip and the load is fully borne by pure shear on the bolt shank, calculate the minimum number of M10 bolts required for the joint to work safely.

(c) Explain why replacing the single-lap joint with a double-cover-plate joint (double shear plane) doubles the shear load capacity of the bolt and eliminates the parasitic bending moment that tends to tear the bolt heads.

A demountable test bench made of dense beech wood undergoes continuous assembly and disassembly every quarter for transport to trade shows. The original prototype was assembled by screwing $\varnothing 8\ \text{mm}$ wood screws directly into pilot holes drilled into the legs, but after the third disassembly, the joints have become loose and will not tighten.

(a) Justify the mechanical failure mechanism of direct wood screws over successive tightening cycles, considering the shear strength of the wood fibers compared to the metal thread profile.

(b) Design and describe an alternative demountable joint system that maintains tightness over an indefinite number of cycles, choosing between through-bolts with embedded nuts (threaded metal inserts, ramp type) or external hexagonal nuts, justifying how stress is transferred to the wood.

(c) Each joint must withstand an axial tightening force of $2,4\ \text{kN}$. If the allowable compressive stress perpendicular to the wood grain is $\sigma_{\text{adm}} = 3,5\ \text{MPa}$, calculate the minimum outer diameter the bearing washer under the nut must have so as not to crush the wood (assuming the washer's central hole is $8,5\ \text{mm}$).

Two rotating machines are compared: the drive drum of a Ferris wheel (rotates at $2\ \text{rpm}$ under a combined radial load of $95\ \text{kN}$ outdoors) and the impeller of an industrial centrifugal fan ($3000\ \text{rpm}$ under a reduced radial load of $0,8\ \text{kN}$ in a clean environment).

(a) An operator states that "ball bearings are always better than plain bearings because they never have friction." Refute this statement technically: analyze what problem the balls will suffer in the Ferris wheel due to the small contact area (Hertzian contact stress) at low speed, and what destructive phenomenon (false brinelling) is caused by static vibrations.

(b) For the drum's plain friction bearing ($d = 120\ \text{mm}$, bushing length $L = 150\ \text{mm}$), calculate the mean contact surface pressure ($p = F / (d \cdot L)$ in $\text{MPa}$) and justify why at $2\ \text{rpm}$ it is impossible to maintain a hydrodynamic fluid lubrication film, requiring self-lubricating bronze-graphite bushings.

(c) Justify why, for the fan at $3000\ \text{rpm}$, a ball bearing is the technically ideal choice compared to a simple plain bearing, taking into account the heat dissipated by viscous friction and power losses.

The dry single-plate clutch of a vehicle has a friction lining with an outer diameter $D = 220\ \text{mm}$ and an inner diameter $d = 140\ \text{mm}$ (mean friction radius $R_m = (D + d) / 4 = 0,09\ \text{m}$), with a dynamic friction coefficient $\mu = 0,35$. The disc transmits torque through two active contact surfaces.

(a) The engine delivers a maximum torque of $210\ \text{N}\cdot\text{m}$. Determine the total axial force that the springs must exert on the pressure plate to transmit this torque with a safety factor against slipping $C_s = 1,4$.

(b) During a forced start manoeuvre on an incline, the clutch slips for $3,0\ \text{s}$. The engine rotates at a constant average speed of $2400\ \text{rpm}$ while the output shaft connected to the wheels rotates at $900\ \text{rpm}$, transmitting a constant torque of $180\ \text{N}\cdot\text{m}$. Calculate the average mechanical power dissipated as heat and the total thermal energy generated in the linings.

(c) If the steel pressure plate has a mass of $3,5\ \text{kg}$ and absorbs $70\ \%$ of the heat generated with virtually no dissipation to the environment during those $3$ seconds (specific heat $c_e = 460\ \text{J}/(\text{kg}\cdot{^\circ}\text{C})$), calculate its temperature increase and deduce what physical consequences overheating entails for the friction coefficient of the lining (fading).

For the load-bearing structure of a temporary pedestrian footbridge installed during construction works at a station, there is a debate between joining the standard rolled steel sections using on-site weld beads or using bolted joint plates with preloaded high-strength bolts.

(a) Refute the proposal to weld the structure on site by analyzing three critical drawbacks: microstructural degradation in the heat-affected zone (HAZ), the impossibility of reusing the sections after the footbridge is removed, and the technical difficulty of performing non-destructive testing (ultrasound/penetrant liquids) outdoors compared to bolt tightening control.

(b) Due to the constant passage of pedestrians and adjacent traffic, the structure experiences cyclic dynamic vibrations. Explain the microscopic mechanism by which vibrations induce the spontaneous loosening of a conventional nut, and select with justification two mechanical retention or preloading methods to prevent it.

(c) If the assemblers tighten the bolts manually without a torque wrench, analyze the two extreme consequences: the risk of fatigue in the shank due to insufficient preload, and the risk of plastic failure due to overtightening.

The figure shows the cross section of a deep groove ball bearing with one of its key components marked with a question mark.

(a) Identify the element marked by the question mark (?) and analyze the kinematics of two adjacent balls if this element were to break: deduce the relative direction of peripheral rotation of two balls when they come into direct contact with each other, and reason how this would affect friction and frictional wear.

(b) During the assembly of the bearing onto the shaft with an interference fit, a mechanic makes the mistake of striking the raceway of the outer ring with a hammer and a drift punch instead of striking the inner ring. Predict what deformations the raceways and balls will suffer (brinelling or plastic indentation) and what audible and dynamic consequences this will present when rotating.

(c) If the radial load on the shaft acts vertically downwards, reason why the eight balls do not work equally: describe the active load zone (load arc) and deduce why each ball experiences a continuous cycle of variable stresses that leads to surface fatigue (spalling).

The steel shaft of an aggregate conveyor belt has a length between supports $L = 2,5\ \text{m}$ and a diameter $d = 70\ \text{mm}$. It supports a drum at its center whose total resulting radial load is $F = 16\ \text{kN}$. During continuous operation in summer, the shaft temperature increases by $\Delta T = 45\ {^\circ}\text{C}$ (linear thermal expansion coefficient of steel $\alpha = 1,2 \cdot 10^{-5}\ {^\circ}\text{C}^{-1}$).

(a) Calculate the total change in length ($\Delta L$) that the shaft experiences due to thermal expansion. Predict and justify what destructive mechanical stresses would appear in the bearings if the installer had axially fixed the outer rings of both supports to their respective pedestals ("two fixed supports"), and explain how this is resolved using a fixed and floating/free support arrangement.

(b) Under the $16\ \text{kN}$ load, the deflection of the shaft causes bending that generates an angular misalignment of $\theta = 0,9^\circ$ at the end supports. Justify why a standard deep groove ball bearing will fail prematurely and select with justification which standardized alternative (self-aligning ball bearing or spherical roller bearing) absorbs this bending without inducing edge stresses.

(c) Calculate the radial reactions at each support (A and B) assuming the load is centered. If, due to a leveling defect, support A is $3\ \text{mm}$ above the theoretical plane of B, interpret what additional parasitic stresses are induced in the shaft and in the baseplate.

In the maintenance plan of an automatic machining center that integrates precision spindle bearings ($6000\ \text{rpm}$), cast iron linear prismatic guideways on which the bed slides, and a roller link chain that moves the tool changer, three consecutive failures occur:

1. The spindle heats up to more than $90\ {^\circ}\text{C}$ after being greased by an operator who filled the bearing chamber $100\ \%$ with thick grease.

2. The roller chain squeaks intensely and shows severe wear on the internal pins and bushings despite having a thick layer of grease on its outer face.

3. The prismatic guideways move with spasmodic jerks at low speed when the guideway lubricant is replaced with standard engine oil.

(a) Physically analyze the origin of the spindle overheating in case 1: distinguish between churning friction of the lubricant and rolling friction, and indicate the recommended fill percentage guideline for high-speed bearings.

(b) Justify why greasing the outside of the chain in case 2 was useless: reason what viscosity and capillary properties the oil must have to lubricate the interior of the link subjected to contact pressure.

(c) Explain the physical stick-slip phenomenon suffered by the guideways in case 3 and its impact on the geometric accuracy of the manufactured parts. Justify why temperature monitoring and vibration analysis (predictive maintenance) save costs compared to repairing after failure.

Topic Challenge. Have you ever wondered how a piece of furniture or appliance in your home withstands stress and facilitates motion? You are going to audit and optimize its mechanical system.

1. Real data collection: Choose a functional household mechanism (a swivel office chair, a bicycle, or heavy drawer slides). Identify and measure with a ruler or tape measure at least two joining elements (bolts/screws, rivets), one guiding element (rail, slide), and one support element (bearing, bushing). Record the typical supported mass using a bathroom scale (for example, $m = 68,5\text{ kg}$).

2. Calculation and modeling: Determine the main static force $F = m \cdot g$ (with $g = 9,8\text{ m/s}^2$) and model the simplified assembly in Tinkercad or FreeCAD, detailing how the joint, guide, and support are assembled.

3. Technical proposal: Write a short report (one page) in LibreOffice proposing a reasoned improvement (changing the type of support to reduce friction or replacing fasteners to make disassembly easier).

Assessment criteria:

• Correct identification and rigorous measurement of the joining, guiding, and supporting elements.

• Accuracy in calculating the force and clarity in the 3D modeling of the assembly.

• Technical feasibility and justification of the proposed improvement.