From Creep to Control: Why Slip is a Feature, Not a Flaw
From Creep to Control: Why Slip is a Feature, Not a Flaw
Abstract
The Archimedes Drive offers a high-precision motion control solution by addressing micro-slip and creep challenges inherent to rolling contact systems. Unlike traditional gear systems with backlash, the Archimedes Drive achieves superior accuracy through real-time correction of minor velocity losses using integrated output sensors and a cascaded PID control strategy.
The drive operates efficiently in the linear traction region, provides over-torque protection, and maintains high torque efficiency, achieving overall performance exceeding 90% under full-speed and full-load conditions. Additionally, micro-slip helps distribute stress more evenly, enhancing the drive’s operational lifespan. This makes the Archimedes Drive an ideal choice for applications requiring exceptional precision and reliability, such as robotics, medical devices, and defence systems.
Introduction
The Archimedes Drive is a high-precision speed reducer system designed for applications requiring exceptional accuracy, repeatability, and efficiency. Unlike conventional gear systems, the Archimedes Drive utilizes smooth inner Flexrollers, instead of gear teeth, to transmit torque through rolling contact. This eliminates backlash and achieves high structural stiffness. This unique design allows the drive to maintain precise positioning without the need for complex compensation algorithms.
However, the use of rolling contacts introduces the phenomena of micro-slip and creep, which are inherent to systems relying on traction. Micro-slip refers to minor localized slips within the contact patch, while creep is the gradual deviation between input and output motion. Although micro-slip causes small velocity variations, it does not introduce the significant positioning errors seen in traditional backlash-prone systems.
Understanding micro-slip is essential, as it influences the drive’s accuracy, and efficiency. The Archimedes Drive leverages real-time correction mechanisms by integrated output sensors, and continuous contact patches.
We begin by examining micro-slip in the Archimedes Drive and its relationship to creep (A), contrasting it with backlash in conventional gear systems (B). Next, we explain how motion control strategies mitigate creep (C) and analyze the traction behavior of the drive concerning full-slip (D). Finally, we discuss additional considerations regarding creep’s impact on drive longevity, efficiency, and lubrication (E).
A ) Mechanism property of creep and micro-slip :
1 – Contact patch:
Figure 1: representation of a contact patch between two rollers
The contact patch refers to the actual physical region of interaction between two surfaces under load. Many imagine this contact patch as a line. In reality, there is no such thing as a perfect point or line contact between two surfaces. All contact involves deformation, leading to a finite contact area (the contact patch), forming a “lumpy” surface area rather than a point or perfect circle. While the physical contact area is a 3D surface with typically a of pressure distribution at the center, it is often represented as a 2D contact patch for ease of mathematical analysis.
Example:
Figure 2: visualization of a contact patch from 3D to 2D for mathematical ease
When a roller rests on a flat surface, like a cloth, the two objects deform under the applied load.
The ball typically forms a concave deformation on the surface it rests on (or vice versa), creating a small lumpy “bowl-like” or 3D contact region. This contact area has depth, width, and length. If you flatten this contact region, you get a circle.
2 – What is creep?
Figure 3: power transfer through 2 rollers where one is the driver and the other one is the driven
When two rollers work together to transfer power, they ideally roll without slipping, meaning their surfaces move in perfect harmony. However, in reality, a slight difference in speed often develops between the driver (the roller providing the force) and the driven roller (the one receiving the force). This tiny speed difference, usually less than 1% of the rolling speed, is known as “creep.” The amount of creep depends on the traction force, the more force the more reference and actual velocity deviate, “The larger the shear force, the greater the creep rate”. Chris Wright, Middlesex University
Note: By creep we mean the creep happening in the rolling contact surfaces, not the creep in material sciences.
3 – Micro-slip vs. Full-Slip
- Micro-slip: Micro-slip occurs within the contact patch between rollers during creep, where only specific areas experience microscopic sliding, while the remaining regions remain locked together without relative motion (stick). These localized, minor slips are caused by elastic deformations and friction within the contact patch of rolling components. Micro-slip is a natural phenomenon in rolling contact systems and is widely recognized in various applications, such as railways and traction-based mechanisms. Read more on creep here (creep whitepaper).
Figure 4: representation of the displacements in two rollers under a shear force
- Full-slip: In contrast, slip refers to a situation where the entire contact area between the rollers slides against each other, leading to a complete loss of traction.
Figure 5: Evolution of the slipping area when torque varies
4 – Relate to the Archimedes Drive
In the Archimedes Drive, micro-slip manifests as minor velocity losses. The magnitude of these losses is often expressed as the creep rate, calculated as follows:
When the traction rollers of the Archimedes Drive are stationary, they are extremely difficult to displace due to the high stiffness of the contact and the absence of backlash. However, as the rollers begin to move, the output develops a slight drift relative to the input. This drift causes the motion of one roller to deviate slightly from the ideal reference case.
Example: Velocity variation due to deformation of two wheels
Figure 6: variation of velocity between two wheels due to traction force
To visualize this phenomenon, imagine two wheels rolling on a flat surface, both subjected to the same downward pressure (normal load). When stationary, they are difficult to displace due to the absence of backlash and high contact stiffness. However, as they begin to roll, the wheels experience varying traction forces in the rolling direction, resulting in different behavior despite identical normal loads:
- Wheel A is pushed normally (without a motor), and rolls freely without additional traction forces. It delivers no traction (in the vertical direction). It experiences minimal micro-slip and covers the expected distance.
- while Wheel B is pushed by a motor and delivers a given amount of traction, which means it grips the surface more effectively (deformation at the contact point). It experiences more micro-slip, leading to a shorter travel distance.
We measure the distance realized after shaft of both wheels has rotated 1 revolution: Distance 1 > Distance 2: The higher deformation of Wheel B leads to increased creep at the contact points, reducing the effective motion achieved. This difference directly translates to velocity loss during operation.
B ) Micro-slip and backlash:
1 – Key Differences in Performance:
Micro-slip cannot be compared to backlash in traditional geared systems:
- Backlash is a static phenomenon occurring when the geared drive is stationary and the direction of the load changes, which introduces hysteresis and positional uncertainty. Hysteresis is caused by the mechanical play between gears when the driving torque reverses. The system does not immediately respond because the gears must first “take up the slack” (dead zone where no motion occurs). This results in positioning errors and non-linear motion. This requires complex compensation algorithms and slower operations to maintain precision.
- In a system with micro-slip (e.g., the Archimedes Drive), there is no mechanical clearance, and therefore no dead zone in motion. Micro-slip, which happens only during motion, may cause small fluctuations in velocity, but these are continuously corrected with sensor data on the output. This means that the system achieves higher repeatability and accuracy.
2 – Illustrating the Difference:
Figure 7: Comparison of backlash in geared systems and micro-slip in traction drives, highlighting their impact on positioning accuracy and correction mechanisms.
C ) Output Position Measurement
Figure 8: Cascaded position, velocity, and current control loops for precision motor control using the Archimedes Drive.
In the Archimedes Drive, due to the micro-slip phenomenon, the actual output position drifts away with respect to the value based on the motor shaft position. Making the traditional approach of using a single motor-mounted encoder insufficient for accurately controlling the output.
The drift, which happens only when the drive is in motion, is dependent on the amount of torque and increases for applications where the applied torque differs for the forward and backward motion (as the drift is not compensated by the drift in the other direction).
Instead, on top of having an input sensors our drive employs a second sensor located at the output that measures the actual position of the output shaft. These sensors ( input and output sensors) ensure that even the smallest deviations caused by slip are accounted for, maintaining unparalleled accuracy and reliability.
Note: Dual-encoder functionality is standard in modern servo drives and motor controllers for high-precision applications, so its use does not add costs in this market segment.
A hierarchical control strategy ensures accurate system operation:
– The current loop (fastest loop): regulates the voltage such that the correct amount of current/torque is supplied. (Current and torque are almost the same for motors).
– The velocity loop regulates the required torque, to meet the demanded velocity.
– The position loop (slowest loop) adjusts the demanded velocity, to regulate the position
D) Traction Behavior
1 – Traction curve
The traction curve is a critical tool for understanding how micro-slips translate into the overall behaviour of the system at the macroscopic level. By describing the relationship between transmitted traction force and creep, the traction curve provides insights into how rolling contacts behave under varying load.
𝜇: The maximum traction force per unit of normal force.
Figure 9: Traction curve illustrating the relationship between creep and normalized traction force, transitioning from linear behavior to non-linear transition and full sliding.
Linear Region
- The drive operates efficiently with high precision and minimal energy loss.
- Micro-slip dominates the linear region; they grow proportionally with traction.
Transition Region
- Slipping increases; the relationship between traction and creep becomes nonlinear. The region helps manage overload conditions.
- This signal approaching system limits, critical for overload management.
Full Sliding Region
- Traction force saturates at the friction coefficient (μ).
- The entire contact patch slips, and the drive enters full-slip (overtorque protection), dissipating energy safely when the load is over 𝜇 to prevent mechanical failure under excessive loads.
2 – Speed ratio behaviour
In a traditional gear-based system, the torque ratio, speed ratio, and gear ratio are inherently linked and remain fixed due to rigid mechanical engagement. However, in the Archimedes Drive, due to the creep phenomenon, this fixed relationship is altered:
- Torque ratio and gear ratio remain stable.
- Velocity losses occur due to creep, affecting the speed ratio.
- The speed ratio may experience slight velocity variations due to creep
- The torque ratio remains fixed because the drive still adheres to the fundamental principle of mechanical advantage.
It is crucial to emphasize that the Archimedes Drive is NOT a continuously variable transmission (CVT). Unlike a CVT, which actively changes its ratio based on input conditions, the Archimedes Drive has a designed, fixed ratio with only minimal deviations:
Figure 10: Relationship between output torque and speed ratio, showing linear operation, transition to non-linearity, and slip beyond the maximum slip torque
How the speed ratio evolves as a function of output torque:
1. Linear Region (Stable Speed Ratio): The drive operates efficiently with minimal velocity loss due to creep. This is the ideal operating range, where the drive maintains predictable performance.
2. Non-Linear Transition Region (Creep-Induced Variations): Due to creep effects, the speed ratio starts to increase gradually: the output velocity does not increase proportionally with the input velocity. The drive enters a non-linear region, where efficiency begins to drop, but it remains functional.
3. Maximum/Slip Torque Region (Severe Velocity Loss): At the maximum slip torque, the drive experiences substantial velocity losses due to full sliding.
E) Additional consideration
1 – Impact on Stress Distribution in motion
Micro-slip, plays a significant role in enhancing the longevity of the Archimedes Drive by altering the fatigue stress distribution within the drive’s internal components.
In traditional gear systems, cyclic motion or repetitive control tasks often lead to localized stress concentrations in specific regions. These regions experience repetitive peak stress, which accelerates fatigue and ultimately limits the system’s operational lifespan.
Figure 11: Three Dimensional Von Mises Stress distributions inside tooth of spur Gear, when the load acts at the tip of tooth. (Source: https://www.researchgate.net/publication/315796574
_Enhancement_of_Bending_Strength_of_Helical_Gears_
In contrast, the Archimedes Drive leverages micro-slip to distribute stress more evenly across its internal components. As the loaded raceway region drifts over time due to creep, the fatigue stress is spread over a larger area rather than being concentrated in a few critical regions effectively extending the drive’s .
2 – Efficiency of the Archimedes Drive
- How we define efficiency:
The creep affects the mechanical efficiency of the system. The efficiency of a mechanical system is defined as the ratio of output power to input power, where power is the product of torque and speed. This results in the following expression for efficiency:
This shows that very loosely speaking, efficiency is the product of a torque-efficiency, related to the ratio between the torque at output and input, and a speed-efficiency, related to the ratio of the output speed to the input speed.
Micro-slips influence efficiency in two primary ways:
- Speed Efficiency Loses: At each transmission stage, minor micro-slips lead to slight reductions in the output speed compared to the ideal kinematic ratio. This results in a speed efficiency that is slightly lower than 100% (a small percentage of rotational input speed is lost in micro-slip motion). This is atypical for most speed-reducer mechanisms.
- High torque ratio: On the other hand, the torque-efficiency of the Archimedes Drive is high compared to other high-ratio gear systems. Due to smooth rolling contacts, the friction losses are small and the ratio of the output torque to the input torque is high.
- Performance Results: Our tests have demonstrated efficiencies exceeding 90% under full-speed and full-load conditions in a high-ratio, single-stage drive.
3 – Impact of micro-slips on lubricants
The Archimedes Drive utilizes traction fluids, a type of non-Newtonian fluid that exhibits shear-thickening behavior under extreme pressure. When subjected to high contact pressure within the contact patch, the fluid’s viscosity increases significantly, causing it to behave like a solid within that localized area. This unique property enables efficient power transmission.
Usually, the selected lubricant influences the traction curve, but for the selected lubricants the overall shape/behavior of the curve remains the same.
Conclusion:
- Micro-slip and Creep: Micro-slip, a byproduct of rolling contact, introduces minor velocity losses but does not compromise positional accuracy.
- Output Feedback and Control: To address micro-slip (induced velocity losses), the Archimedes Drive integrates output encoders and a cascaded PID control strategy.
- Traction Behavior and Overtorque Protection: The traction curve reveals how the drive operates predictably in the linear region. And how under extreme loads, the drive transitions into full sliding, providing a unique overtorque protection feature.
- Efficiency: The loss of speed efficiency are compensated by the torque efficiency. Tests demonstrate performance exceeding 90% under full-speed and full-load conditions.
- Lubricants: The overall traction behavior remains consistent.
By addressing the velocity losses caused by creep with integrated output sensors and hierarchical control strategies, the drive maintains exceptional positional accuracy. This precision is further supported by its high stiffness and lack of backlash, which prevent errors typically found in traditional geared systems.
