Mechanical Transmissions

A mechanical transmission carries energy from a prime mover to a working member and changes speed, torque, direction, motion type, or shaft arrangement. It does not create power: increased torque is accompanied by lower speed and losses.

Power and transmission ratio

For rotary motion,

$$P=T\omega,\qquad \omega=\frac{2\pi n}{60},\qquad T=\frac{9550P}{n}.$$

The transmission ratio and output torque are

$$i=\frac{\omega_1}{\omega_2}=\frac{n_1}{n_2},\qquad T_2=T_1i\eta.$$

For a multistage drive, \(i_\Sigma=\prod i_j\) and \(\eta_\Sigma=\prod\eta_j\).

Principal types

• Gear drives provide an exact mean ratio and high load capacity. Cylindrical, bevel, worm, rack, and strain-wave arrangements belong to this group.
• Chain drives provide positive engagement over relatively large center distances.
• Belt drives are quiet and compliant; friction belts may slip, while toothed belts engage positively.
• Friction drives and variators transmit force by contact friction and can provide continuously variable ratios.
• Power screws convert rotary motion into linear motion and force.

Selection and verification

Choose a transmission from power, speed, required ratio, shaft arrangement, duty, accuracy, noise, environment, and maintenance. Check strength, contact pressure, wear, temperature, stiffness, vibration, lubrication, shaft reactions, and service life.

Speed, torque, and losses

At each stage the power flow should be traced explicitly. Bearing, seal, mesh, belt, chain, and lubricant losses reduce available output and generate heat. For stage \(j\), \(P_{j+1}=\eta_jP_j\); the torque must be recalculated from the local speed rather than copied from the input shaft.

Ratio allocation in multistage drives

The total ratio is distributed among stages to balance size, speed, torque, efficiency, lubrication, and standard component ranges. An extreme ratio in one stage can increase sliding, reduce contact ratio, enlarge wheels, or overload the high-torque stage. Shaft speed also influences bearing type, seal selection, and critical-speed margin.

Loads on shafts and bearings

Every transmission creates reactions in addition to useful tangential force. Gears produce radial and sometimes axial forces; belts require preload; chains add dynamic and sag forces; friction drives require clamping force; power screws impose axial thrust. These reactions must be transferred through shafts, bearings, housings, and foundations.

Accuracy and dynamics

Backlash, elastic compliance, pitch error, slip, polygonal action, and torsional vibration determine motion quality. High positioning accuracy may require preload or closed-loop control, while shock-loaded machinery benefits from compliance and damping. The chosen transmission should match the dynamic behavior of both motor and working machine.

Thermal and lubrication checks

Loss power is \(P_{loss}=P_{in}-P_{out}=P_{in}(1-\eta)\). Steady temperature is reached when generated heat equals heat rejected by the housing, lubricant, airflow, or cooler. Viscosity must be sufficient at operating temperature without causing excessive churning loss at start-up.

Design sequence

1. Establish the duty cycle, required output motion, and peak load.
2. Select the transmission type and overall ratio.
3. Allocate ratios and estimate stage efficiencies.
4. Calculate speeds, torques, and all force components.
5. Size the transmission elements and verify life and temperature.
6. Design shafts, bearings, housing, lubrication, adjustment, and guarding as one system.