Leveraging the complementary strengths of orbitless and planetary drives

An orbitless drive is a novel, fixed-ratio, epicyclic drive that includes a second carrier in place of a ring gear. It has been shown to have superior efficiency to a planetary drive and is shown here to produce less vibration and noise at the expense of reduced torque capacity and ratio. A prototype 16mm orbitless drive is constructed and compared to an off-the-shelf planetary drive. Vibrations that occur at the planetary tooth engagement frequency are absent from the orbitless drive. A higher-quality, 32mm orbitless prototype is evaluated in a multi-stage environment in both a stand-alone and multi-stage configuration. It is shown that sound levels are reduced; sound quality is improved, and it is concluded that an orbitless primary stage may be mated with conventional technologies to minimize NVH levels in multi-stage gear drives.

1 Introduction

Parallel-axis and planetary drives are centuries-old technologies that form the foundation of the gearing industry. The orbitless drive [1, 2] is a newly patented gear technology [3, 4] that is co-axial and epicyclic, similar to a planetary drive, but lacks idler gears, similar to a parallel-axis drive. Orbitless planets circulate but do not rotate, resulting in reduced friction losses, as reported in [5, 6].

Although all three technologies may be configured in a variety of ways to achieve reduction, over-drive, low, high, positive and negative ratios, this paper only considers the most fundamental, low-ratio, configuration where the input and output are the pinion and bull-gear respectively (parallel-axis), or the sun and carrier respectively (epicyclic). Parallel-axis drives are the simplest and most common, with non-coaxial drive shafts that rotate in opposite directions. Planetary drives have higher-power density and coaxial drive shafts that rotate in a common direction. Orbitless drives may be configured for either coaxial or offset drive shafts that rotate in a common direction.

In Section 2, the relative strengths of planetary and orbitless drives [5, 6] are identified and SimulationX^TM [7] is used to demonstrate reduced orbitless planet vibration. It is proposed that a high-speed, low-noise orbitless primary stage may be mated with one or more compact, high-torque planetary downstream stages to minimize noise without sacrificing torque capacity or compactness. In Section 3, a prototype orbitless micro-drive is constructed and compared to an off-the-shelf planetary drive using sound measurements to corroborate the simulated results. In Section 4, a high quality Maxon Motor^TM [8] orbitless/planetary multi-stage drive is developed, and noise is recorded and analyzed to support the proposal made in Section 2. Finally, a summary and conclusion are presented in Section 5.

2 Relative Strengths

An orbitless gear-head resembles a planetary gear-head in that a high-speed (input) shaft drives a sun pinion that is surrounded by a collection of planet pinions that ride on an output carrier that drives a low-speed (output) shaft, as illustrated in Figure 1. Instead of an orbit (ring) gear, an orbitless gear-head includes a second reaction carrier that engages each planet on a second planet axis. Although the two planet axes must not coincide, they may otherwise reside anywhere on the planet. Orbitless planets do not rotate. They circulate the sun at a fixed orientation, so it is not necessary for either axis to intersect the planet center (see Figure 1, right).

In Figure 1, the coaxial version (left) has its drive carrier planet axes intersecting the center of each planet, which results in coaxial input (high-speed) and output (low-speed) shafts. The non-coaxial version (right) has symmetrically eccentric planet axes, which accommodate large planet bearings for greater durability. It has non-coaxial input and output shafts with a shaft distance that is equal to the distance between the planet’s central and drive axes.

The reduction ratio i, and pitch line velocity V_PL of a planetary and orbitless drive are derived in [1] and shown in Equations 1-4 where Z_S  and Z_P  are the teeth on the sun and planet, ω_S  is the angular velocity of the sun (high-speed shaft), ω_C  is the angular velocity of the carrier (low-speed shaft), and M is the tooth module.

Equations 2 and 4 are plotted against Z_S in Figure 2 with M=1, ω_S=1, and Z_S+Z_P=36. The assembly criteria are always satisfied when the number of planets N=3 and all drives have a similar outer diameter. In Figure 2, the corresponding reduction ratios and sketches of the associated drive topologies are superimposed for Z_S=[9 18 24], and the curve is re-plotted with ratio on the x-axis.

In Figure 2, the planetary curve has both a higher value and a steeper slope over the entire range of practical sun geometries. For geometrically similar drives, the orbitless pitch velocity is from 20% (Z_S=9) to 50% (Z_S=24) lower, and for functionally similar drives (i=3:1 to 4:1), the orbitless pitch velocity is about 50% lower throughout. These are sufficiently significant to indicate meaningful improvements in efficiency, NVH, and speed rating.

To compare performance characteristics, geometrically equivalent planetary and orbitless drives are simulated side-by-side in a common SimulationX Multi-Body System (MBS) environment. SimulationX Version 3.9.2 is used to develop a planetary drive model, which is then duplicated, the ring gear is erased, an offset bore is added to each planet, and an offset carrier is added and connected to the planets with rotary joints. In doing so, it is assured that all other parameters are identical between the two models.

The parameters are shown in Table 1 and the 2-model environment is shown in Figure 3. PA is the gear tooth pressure angle; physical units are absent for all parameters that are pure; two ratios are specified because uniform geometry results in a higher planetary drive ratio, and the outer diameter (OD) neglects housing thickness. From Equations 2 and 4, the orbitless pitch velocity is 22% lower for a common input speed.

To verify the implementation, an X-Y plot of radial-tangential planet force is plotted and compared against a Matlab^TM plot of the theoretical equivalent, which neglects load sharing error and centrifugal forces but includes separation forces resulting from a 20° pressure angle. In the Matlab plot, the tooth force is represented by the red vector with its tip at the origin and its tail tracing the red circle for carrier angles varying from 0 to 360°, and where Ft is its maximum amplitude. Similarly, the blue vector (Fd) represents the drive carrier pin force, and the green vector (Fr) represents the reaction carrier pin force. As shown in Figure 4, the two results are equivalent for the drive pin carrier force once the SimulationX model has reached steady-state (i.e., full torque).

Although SimulationX MBS Version 3.9.2 does not simulate gear tooth friction, a new “gearLosses” block (beta version) computes the friction of gear meshes associated with a rotary joint and applies an equivalent amount of friction to that joint.

The orbitless load consists of a 117 µNms/rad damper applied to its output joint. Since the ratio of the planetary drive is 2x as high, its load damper should be 4x larger, but to compensate for non-uniform tooth friction, it is 3.7x larger to keep the input speed, torque, and power as consistent as possible. The input shafts are accelerated to 7,000 RPM at which point approximately 8.5 W of power flows. The associated total system power loss and corresponding efficiency are plotted in Figure 5. As expected, the planetary drive has approximately twice the losses due to its higher pitch velocity and additional gear meshes.

Noise is not explicitly measured by SimulationX but may be estimated by planet vibration. In Figure 6, the planetary radial separation forces show cancellation of opposing sun and ring forces, with a high- frequency and DC component remaining. Orbitless separation forces are uni-directional and predominantly DC. The associated FFTs show a spike centered at the planetary toothing frequency but a consistently decaying orbitless frequency spectrum.

Phase differences between radially opposing separation forces induce vibrations that are transmitted into, and possibly amplified, by the planetary housing (see Figure 7). Orbitless separation forces are uni-directional, so the planets vibrate less and do not contact the housing, so sound transmission is impeded. The complementary advantages of orbitless and planetary configurations are summarized in Table 2.

The above properties motivate the use of an orbitless drive as a primary stage. The conceptual multi- stage drive shown in Figure 8 combines an orbitless primary stage with two planetary downstream stages. The low pitch and bearing velocities of the orbitless primary stage maximize speed rating where internal velocities are highest, and superior NVH properties combined with plastic planets minimize noise where most of it is generated. Compact, high-ratio, metal planetary downstream stages maximize output torque capacity and reduction ratio for long service life and a small footprint.

3 Single-Stage Orbitless Prototype

A single-stage orbitless prototype is constructed to validate the simulated planet vibrations shown in Figure 6. The prototype is co-axial with plastic planets that are supported on both sides by the central carrier and is mounted to a Maxon DCX16 motor, as shown in Figure 9. It is too small for planet bearings, so planet and carrier bores are given tolerance for a sliding fit, and polished shafts are used wherever possible. The 2-sided central carrier is male on the left and female on the right, and the offset carrier is male. The 2-sided central carrier provides stability to prevent planet yaw as described in [5, 6], and offset bores in the planets are contained entirely within the large male members to avoid weakening adjacent tooth roots. The toothed planet body has only a central bore to maximize wall thickness.

The technical specifications are shown in Table 3, many of which are chosen to satisfy the challenging manufacturing constraints, such as 3D-printing resolution, standard tooth modules, and minimum available bearing and shaft diameters, of a 16mm micro-gear-head.

The sun has a collar with a 2mm D-shaft given tolerance to slip fit onto the motor shaft. Roller bearings are used between the carriers, and the housing is constructed from 3D-printed plastic adapter plates, and aluminum tube stock is fixed on each side by 3 set-screws for easy disassembly. The multi-part housing is a source of gear misalignment, which increases sound volume.

A variety of 3D-printing technologies are used to construct the components, with multiple technologies used for the carriers and gears for the purpose of experimentation. Figure 10 shows a version using metal planets and plastic carriers. The prototype 2.77:1 orbitless gear-head is compared with a Maxon Low-Noise 3.9:1 GPX16 planetary drive, factory assembled with the same Maxon DCX16 motor. The prototype orbitless gear-head has a high-resolution metal sun and carriers, high-resolution plastic planets, and a light coating of WD40^TM for lubrication. Both gear-motors are connected by a flexible coupling to a DC motor with a load resistor across its terminals. Due to variations in reduction ratio, load resistor values are chosen so that equal power is delivered at 7,000 RPM (input). Both motors draw the same current and rotate at the same speed during the comparison.

Uncalibrated loaded and unloaded sound measurements are recorded with a microphone placed 5cm away from the front face of the gear head to minimize the sound contribution of the motor. FFTs of the recordings are shown in Figure 11. The maximum loaded and unloaded amplitudes are similar, in spite of the inferior manufacturing quality of the 3D-printed, hand-assembled, unlubricated orbitless prototype.

The commercial planetary drive produces frequency spikes near the tooth engagement frequency of 1.7 KHz, which amplifies under heavier loads. The orbitless drive has a flatter spectrum, regardless of load, with no distinct spikes (tooth engagement frequency = 1 KHz). It is assumed that a comparable manufacturing quality would result in reduced sound amplitude, improved sound quality (mellower tone), and minimal high-frequency gear whine.

4 Multi-Stage Orbitless Planetary Prototype

To evaluate its performance with a more comparable manufacturing quality and in a multi-stage environment, a prototype orbitless gear head is constructed by the Maxon Motor research and development department. It is interchangeable with a Maxon GPX32 planetary gear head so it may be used stand-alone or in series with an off-the-shelf GPX32.

All male joint members are machined into steel planets with ceramic offset shafts pressed in for added strength. Plain bearings are pressed into a 2-sided central and 1-sided offset carrier. The technical specifications are shown in Table 4 and photos of an assembled gear-motor, a disassembled gear head, and a close-up of a planet are shown in Figure 12.

Ball bearings are used between the carriers and housing, brass bushings are used to support the two smaller planet shafts on the central and offset carriers, and two different types of high-performance plastic plain bearing (V1 & V2) are used to support the large planet shaft on the central carrier. Each version is operated as a 1-stage and a 3-stage drive, where a 2-stage 16:1 GPX32 planetary gear head is mounted to the output for a combined reduction ratio of 32:1. Each gear head is mounted to a Maxon DCX32 motor and is spun at 6,000 RPM in a noise chamber with a microphone placed 10cm from the gear head. The resulting FFTs of the audible frequency range for 1-stage orbitless and 3-stage orbitless/planetary drives are shown in Figure 13.

In all cases, the spectrum is flat with no perceptible spikes (tooth engagement frequency = 900 Hz). There is no significant difference between V1, V2, single, or multi-stage drives. These results are consistent with predicted values and the presumption that the primary stage is the dominant sound source in a multi-stage drive.

5 Conclusion

In multi-stage drives, each sequential stage rotates slower and delivers more torque. The low pitch and bearing velocities, fewer gear engagements, and uni-directional separation forces of an orbitless drive result in high-speed ratings and low NVH levels at the expense of decreased ratio and load capacity, making it particularly viable as a primary stage.

A SimulationX MBS model demonstrates a vibration spike at the tooth engagement frequency for a planetary drive but not for an equivalent orbitless drive. A prototype single-stage 16mm orbitless gear  head demonstrates these predicted noise characteristics. A high quality 32mm orbitless primary stage is integrated with a 2-stage planetary to achieve a compact, high-ratio, high-torque, multi-stage drive that emits a low-noise volume with a flat-frequency spectrum across the entire audible range. 

Bibliography

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3. L. J. Stocco, 2014, Orbitless Gearbox, US Utility Patent, US 9,970,509 B2, May 2018.
4. L. J. Stocco, 2014, Hybrid Orbitless Gearbox, US Utility Patent, US 10,247,278 B2, April 2019.
5. L. Stocco, R. Gloeckner, “Smashing the Efficiency Barrier – A Practical Comparison of Planetary and Orbitless Gear-Heads”, Proceedings of 7th International Conference on Gears, Munich DE, Sept. 13-15, 2017.
6. L. Stocco, R. Gloeckner, “A New Standard of Epicyclic Efficiency – A Practical Comparison of Planetary and Orbitless Gear-Heads”, Forschung im Ingenieurwesen, Springer-Nature, Vol. 81, Iss. 2-3, pp. 153-161, Sept. 2017.
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8. https://www.maxonmotor.com

^{Printed with permission of the copyright holder, the American Gear Manufacturers Association, 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314. Statements presented in this paper are those of the authors and may not represent the position or opinion of the American Gear Manufacturers Association. (AGMA) This paper was presented October 2019 at the AGMA Fall Technical Meeting in Detroit, Michigan. 19FTM08}