Friction Drives and Variators

Friction drives transmit power through tangential traction between pressed rolling bodies. A variator changes the effective contact radii to vary speed continuously.

Kinematics

Without slip, peripheral speeds are equal:

$$\omega_1r_1=\omega_2r_2,qquad i=\frac{\omega_1}{\omega_2}=\frac{r_2}{r_1}.$$

Elastic creep and microslip make the actual ratio differ slightly from the geometric value.

Traction capacity

The tangential force must satisfy

$$F_t\le\frac{\mu N}{n_s},$$

where \(N\) is normal force. Required clamping force therefore increases as the traction coefficient decreases. Contact pressure is checked with Hertz theory, and excessive slip is avoided to prevent scuffing and overheating.

Performance

Efficiency is reduced by creep, spin, bearing loss, and lubricant churning. Design must coordinate contact materials, surface finish, traction fluid, cooling, clamping control, ratio range, bearing reactions, and fatigue life. A variator needs sufficient normal force over the entire operating envelope—not only at nominal ratio.

Contact arrangements

Friction drives may use cylindrical, conical, spherical, toroidal, or disk contacts. Fixed-ratio drives keep the effective radii constant; variators move a roller or change the contact geometry. The usable ratio range is limited by contact size, pressure, spin, bearing loads, and control stability.

Creep, slip, and spin

Elastic deformation creates small differences in surface velocity across the contact, called creep. Gross slip begins when required tangential force exceeds available traction. In curved contacts, spin causes additional local sliding even when mean rolling speeds match. These effects generate loss and heat and alter the actual ratio.

Hertz contact

Normal force produces a concentrated elliptical or line contact. Maximum pressure and subsurface shear are evaluated with Hertz theory using local curvature and reduced elastic modulus. Increasing normal force raises torque capacity but also contact stress, rolling resistance, bearing reaction, and fatigue damage.

Clamping control

A constant excessive clamping force wastes energy and shortens life, whereas insufficient force allows destructive slip. Practical variators may regulate normal force approximately in proportion to transmitted torque. Transients, reversal, lubricant temperature, and the lowest expected traction coefficient require additional reserve.

Materials and traction fluids

Hardened steels provide fatigue strength and dimensional stability. Some drives use dry elastomeric or polymer surfaces; high-performance traction drives use special fluids whose effective shear strength rises under extreme pressure. Surface finish, cleanliness, and material compatibility are critical.

Efficiency and thermal behavior

Losses include creep, spin, bearing friction, seals, and lubricant churning. The thermal balance must keep contact materials and fluid within allowable temperature. Excess heat reduces viscosity and traction, which can trigger more slip and further heating.

Design sequence

1. Define power, ratio range, speed, duty, and required accuracy.
2. Select contact geometry, materials, and lubrication regime.
3. Calculate effective radii, surface speeds, and tangential force.
4. Determine clamping force with a traction reserve.
5. Check Hertz pressure, fatigue, shaft and bearing loads.
6. Verify slip, spin, efficiency, temperature, control, and wear.