Not all motion happens in a straight line. Yet a quick review of a few design books shows mostly linear axes and guideways. But what if a sensor has to negotiate a corner or sweep through an angle? Do you not bid on those jobs?

Of course not. That would be foolish because there are a few circular tracks and systems for accommodating circular pathways. But their sizing guidelines differ from the hardware that travels on linear guides.

Guidance systems, for one, commonly move devices, such as sensors, on tracks that are circular, semicircular, oval, and even S-shaped. These ring slide and track systems fall into two categories: Those in which a carriage runs on a ring segment or track, and those in which a ring rotates, held by several bearing assemblies (or similar arrangements in which the ring is stationary and the bearings and load rotate). A few components in these machines include precision-ground tracks that come in 90 and 180° segments, and 360° rings. Diameters range from about 90 mm to over a meter. Carriages that run on these tracks use concentric and adjustable eccentric bearings that are lubed for life. And small external devices lubricate wheel-track contact surfaces to increase their load capacity and life.

Estimating system life

Sizing guide systems with curves begins by filling in a load-life equation based on bearing size and relative spacing, along with load orientations, locations, and magnitudes. In a nutshell, determine the radial, axial, and three moment loads on each carriage. Then calculate a load factor for the carriage with the heaviest load, and use the nomogram found in Bishop Wisecarver literature to find the corresponding estimated life.

For this article, axial loads, L₁, are parallel to bearing shafts while radial loads, L₂, are perpendicular to bearing shafts. M_s, M, M_v represent roll, pitch, and yaw moments.

Several other factors affect load capacity and life expectancy of ring, segment, and track systems. These include the ring size, number and speed of carriages, whether or not the track is lubricated, and the magnitude and direction of loads. With regard to speed, for example, some ring, segment, and track systems are rated for up to 1.5m/s when lubricated but only 1m/s when not. Higher speeds may be tolerated at reduced loads. And as a rule, use lubricators whenever possible. They increase capacity and extend system life. In addition it is usual to run systems with less than the maximum allowable load to prolong the life.

Path length is another consideration. Lengths less than 0.2 m call for reducing carriage life proportional to path length. For example, reduce the life of a 0.08-m stroke system (calculated from the nomograph) by (0.08 m/0.2 m = 0.4) or 40%.

If using a bogie carriage that differs from a standard length, then M and M_v moment-load capacities will increase proportional to the increase in distance between bogie-swivel centers. Also, include centrifugal force when calculating L₂ and M_s. The force acts radially outward from the center of mass of the moving object, C. Its magnitude is found with

F = DV²/R

where F = centrifugal force (N); V = velocity of C (m/s); R = distance from C to ring axis (m); and D = mass of the carriage load (kg).

Load factor equation

Find the load factor, L_f with:

L_f = M/M_max + M_v/M_{v max} + M_s/M_{s max} + L₁/L_{1 max} + L₂/L_{2 max}

where L_f = load factor, L₁ = axial load (N); L₂ = radial load (N). Parmeters with the “max” subscript are read from a table in BWC company literature for the selected carriage or ring. The load factor from the equation is located on a nomogram in company literature (one nomogram for lubricated systems, another for unlubed) which translates into a carriage life in km.

Of course, should the life of the selected components not meet system requirements it will be necessary to select larger components.

Circular motion under control

Characterizing the polarization properties of optical systems helps improve their production yields. These optical devices include liquid-crystal displays and projection systems, fluorescence microscopy, and biomedical testers. Polarization properties are beyond the scope of this article, so suffice it to say that industry growth has increased the importance of high-speed polarization metrology equipment.

A manufacturer of optical devices, Axometrics Inc, Huntsville, Ala, (axometrics.com), sought to improve the accuracy of its measurements while increasing throughput. The company built a testing machine that positions LCD test samples between the company's AxoScan SpectroPolarimieter's transmitter and receiver, which travel along a semicircular path. The heads measure polarization. The machine is unusual because it has linear axes that must coordinate with the circular axes.

Axometrics' engineers selected a precision HepcoMotion PRT ring and track system from Bishop-Wisecarver because it has an internal gear that makes it easier to meet rotational requirements and tolerances. The circular track is precision ground with hardened V faces. Transmitter and receiver heads mount on carriages that travel along the two 180° half-circular axes.

The linear positioning device that carries LCDs uses three linear axes, one horizontal and two vertical. The X-axis spans 1,600 mm and the Y-Y' axes, 900 mm and it moves at 1,000 mm/sec with a repeatability of ±0.1 mm. The panels it carries can have up to 60-in. diagonals.

Transmitter and receiver heads remain on the same plane and must be aligned to within ±0.2 mm over 165.1 mm. The heads rotate 70° in either direction at 40°/sec. with minimum moves of 0.05°. The guide rings had to be in 180° sections, one for each head, to provide space between them for LCD panels.