Motion System Design

# Engineering circular systems

Lubrication, loads, direction, speed, and distance determine which guide component — specified in terms of size and number of bearing assemblies as well as ring size — is best for a given system load capacity and life. For longer life, systems should be designed for loads higher than those to be carried during normal operation.

For HepcoMotion's PRT Precision Ring and Track systems from Bishop-Wisecarver, we calculate system life in three steps:

2. Obtain the system load factor LF

3. Apply the load factor to the appropriate nomagram to determine system life.

Load components affecting a carriage traveling on curved track are different than for rings rotating around fixed bearings — so different load factor equations are required to determine system life.

### Carriage capacity and life on rings, curved track

When calculating life for a curved track system, loading on the system must be resolved into direct load components L1 (axial loads parallel to bearing shaft) and L2 (radial loads perpendicular to bearing shaft), and three moment load components: MS (roll), M (pitch), and MV (yaw). Centrifugal force affects L2 and MS, because it moves in a radial direction, a force spiraling away from the moving-object center of mass (COM).

COM force is calculated F = DV2/R, where V is COM velocity (in m/sec), R its distance from the ring axis (in m), and D its mass. F is in Newtons. Next, we obtain main load factor LF with respect to duty cycle:

where maximum load capacities are obtained from the system manufacturer. Then, the direct and moment loads of the track components and type of carriage must also be identified.

### Capacity and life for rotating ring systems

In applications where a ring rotates around fixed bearings, assemblies should be equally spaced around the ring. (Where bearing assemblies rotate with load, assemblies can be spaced unequally.) Loading must be resolved into the two direct-load components (axial loads parallel to the ring axis LA and radial loads perpendicular to it LR) and the roll moment load component M.

As with carriages on curved track, centrifugal force affects factors LR and M. Here, the main load factor LF is:

Assume we have one 360° ring with a 25-mm cross-section (and 351-mm diameter) that rotates along six RLJ-25 fixed bearing assemblies. Also assume that the ring rotates once per second, has five lubricators, and that:

• Rotating assembly (ring, platform, payload) is 8 kg • COM is 100 mm from the ring axis, and 150 mm above the ring Vs • Duty cycle is 36 hours per week. Axial, radial, and moment loads are then resolved:

Axial load: LA = 8 kg × 9.81 m/sec2(g) = 78.5 N

Center of mass speed: 1 rev/sec = 2 × š × 0.10 m × 1 = 0.63 m/sec

Radial load: LR = DV2/R = 8 kg ×(0.63 m/sec)2 ÷ 0.10 m = 31.8 N

Moment load: M = LR × h = 31.8 N × 0.15 m = 4.77 Nm

From Table 1: Mmax = (187 + 2 × 37) × Øc = 261 × (0.351 + 0.020) = 96.8 Nm

LAmax = 750 + 2 × 150 = 1,050 N

LRmax = 400 + 2 × 100 = 600 N.

To obtain linear life, a 0.177 life factor value (calculated with the above equation) is entered into a load/life nomogram (shown above) for lubricated systems. The factor 0.177 corresponds to 39,000 km on the nomagram, which predicts system life in kilometers traveled.

There are two common carriage types for ring or curved-track guide wheel systems. Properly specified, they can move bidirectionally. Fixed-center carriages are typical for track systems of common bend radii without S bends, ring slide tracks, and segment tracks. Bogie carriages accommodate S bends and varying radii and (because of wide bearing spacing) they improve stability. A bogie carriage swivels on a self-lubricating axial/radial bearing with adjustable preload, for traversing straight and curved track joints without the clearance seen in fixed-center carriages.

Fixed-center carriage geometry enables traversal from straight to curve track section, allowing each pair of bearings to follow slides independently. Where bearing assemblies traverse straight and curved track joints, there's a small amount of play — but it usually doesn't affect system operation.