Abstract
Bellows couplings occupy an important position in high-precision transmission systems due to their zero-backlash, high torsional stiffness, and excellent misalignment compensation capability. Taking COUP-LINK LK6 series products as the research object, this paper systematically compares and analyzes the design principles, mechanical characteristics, and engineering applications of Clamping Type and Set Screw Type shaft connection methods. Through theoretical modeling, finite element simulation, and experimental testing, the differences between the two in terms of torque transmission, dynamic response, installation, and maintenance are revealed. The research shows that the clamping type, relying on full-circumference uniform clamping, is superior to the set screw type in torque capacity, repeatable positioning accuracy, and vibration resistance. The set screw type, however, offers advantages such as simple structure, convenient installation, and lower cost. This paper provides a theoretical basis and engineering guidance for coupling selection in high-precision transmission systems.
Keywords: Bellows Coupling; Clamping Connection; Set Screw Connection; Zero-backlash; Torsional Stiffness; LK6 Series
1. Introduction
With the rapid development of intelligent manufacturing and automation equipment, higher requirements are placed on the performance of connecting elements in precision transmission systems. As a type of metallic flexible coupling, the bellows coupling utilizes the elastic deformation of the bellows to compensate for misalignment between shafts while ensuring backlash-free torque transmission, and is widely used in connections between servo motors, stepper motors, and loads. Its core advantages include:
Absolute Zero Backlash: Integrated design of bellows and hubs eliminates transmission gaps.
High Torsional Stiffness: Metallic elastic elements provide high stiffness for fast dynamic response.
Multi-directional Compensation: Capable of compensating for radial, angular, and axial misalignments.
Maintenance-Free: No wearing parts, long service life.
The COUP-LINK LK6 series bellows couplings are manufactured from high-quality aluminum alloy and feature zero-backlash transmission characteristics, offering two shaft connection methods: Clamping Type and Set Screw Type. These two methods exhibit significant differences in structural design, torque transmission mechanism, and applicable scenarios. Correctly selecting the connection method is crucial for ensuring system precision, reliability, and economy.
This paper aims to deeply analyze the technical characteristics of the two connection methods in the LK6 series, establish a performance evaluation model through theoretical calculations and experimental comparisons, and provide selection references for engineering designers.
2. Theoretical Foundation of Bellows Couplings
2.1 Mechanical Characteristics of the Bellows Elastic Element
The bellows is the core elastic element of the coupling, typically formed from thin-walled metal tubes through hydroforming or welding. Its geometric parameters include wall thickness, convolution height, convolution pitch, number of convolutions, and mean diameter. The stiffness characteristics of the bellows can be described by theoretical relationships derived from thin-shell mechanics. The axial stiffness is primarily determined by the bending rigidity of the convolutions, the radial stiffness relates to the transverse deformation capability, and the angular stiffness depends on the torsional resistance of the bellows structure. For common aluminum alloys used in LK6 series, such as 6061-T6, the elastic modulus is approximately 70 GPa, and Poisson's ratio is around 0.33. These material properties, combined with geometric parameters, govern the overall flexibility and load capacity of the coupling.
2.2 Principle of Zero-Backlash Transmission
The bellows coupling achieves zero-backlash transmission due to several factors:
Integrated Construction: The bellows is typically welded or integrally formed with the end hubs, eliminating relative moving parts.
Elastic Deformation: Torque is transmitted through the elastic deformation of the bellows itself, meaning there is no inherent clearance in the torque path.
Preload: The clamping or set screw connection ensures that there is no relative sliding between the hub and the shaft, guaranteeing synchronous transmission.
2.3 Characteristics of Aluminum Alloy Material
The LK6 series utilizes high-strength aluminum alloy, which offers several key advantages:
Lightweight: With a density of about 2.7 g/cm³, it reduces the moment of inertia, beneficial for dynamic applications.
Good Machinability: Easy to precision machine, ensuring high fit accuracy between components.
Corrosion Resistance: A natural oxide layer provides a certain degree of environmental protection.
Sufficient Strength: After heat treatment, yield strength can reach 200-300 MPa, adequate for many precision transmission tasks.
3. Analysis of Clamping Type Connection Technology
3.1 Structural Design
The typical structure of an LK6 clamping type coupling features a hub with an axial through-slot. Radial bolts are used to apply clamping force. When the bolts are tightened, the bore of the hub contracts radially, generating uniform pressure on the shaft and creating a frictional connection. Key design features include:
Symmetrical Slotting: Usually a single-slot or double-slot design to ensure uniform clamping force distribution.
High-Strength Bolts: Class 12.9 alloy steel bolts are employed to provide sufficient preload.
Self-Centering Function: The clamping action naturally centers the shaft, reducing installation misalignment.
3.2 Torque Transmission Mechanism
Clamping type connections rely entirely on friction to transmit torque. The radial pressure generated on the shaft surface by the bolt preload is a function of the bolt force, the number of bolts, the clamping length, and the friction characteristics at the thread and interface. This pressure creates frictional forces over the contact area, which in turn generate the frictional torque capacity. The maximum transmissible torque is determined by the product of the normal force (from the radial pressure), the coefficient of friction between the shaft and hub materials (typically around 0.12 to 0.18 for steel-aluminum contact), and the shaft radius. In design, a safety factor is applied to account for uncertainties and dynamic loads.
3.3 Installation and Usage Characteristics
Advantages:
High Torque Capacity: Full circumferential contact provides a large friction area.
Good Repeatability: Performance remains stable after multiple assembly and disassembly cycles.
No Shaft Damage: Eliminates stress concentrations caused by keyways or set screw indentations.
Suitable for High Speeds: The symmetrical design offers excellent dynamic balance characteristics.
Disadvantages:
Higher Installation Requirements: Requires a torque wrench and a specific diagonal tightening sequence.
Longer Axial Length: Needs sufficient clamping length, increasing overall coupling length.
Higher Cost: Demands higher machining precision compared to simpler designs.
4. Analysis of Set Screw Type Connection Technology
4.1 Structural Design
LK6 set screw type couplings utilize set screws (grub screws) to fix the shaft. The hub features 2 to 4 radially positioned screws that press directly onto the shaft surface. To prevent shaft slippage under torque, a keyway or D-shaped flat is often incorporated. Design points include:
Screw Material: Typically stainless steel or alloy steel with hardened tips.
Anti-loosening Measures: Thread-locking adhesive or nylon-insert lock washers are used.
Centering Features: Some models include locating shoulders for initial alignment.
4.2 Torque Transmission Mechanism
Set screw type connections transmit torque through a combination of mechanical locking and friction. The set screws apply radial force, generating some frictional torque. However, the primary torque transmission often relies on mechanical interference, such as a key engaging with a keyway or a flat on the shaft engaging with a corresponding feature in the hub. The total torque capacity is the sum of the frictional contribution from the screws and the mechanical constraint from the key or flat. The mechanical constraint capacity depends on the bearing stress area of the key/flat and the allowable stress of the materials.
4.3 Installation and Usage Characteristics
Advantages:
Simple Structure: Lower manufacturing cost.
Quick Installation: No special tools required; simple tightening with an Allen key.
Short Axial Length: Saves space in the assembly.
Easy Replacement: Simple disassembly process.
Disadvantages:
Limited Torque Capacity: Small contact area of the set screws restricts torque transmission.
Shaft Surface Damage: Set screws can create permanent indentations, potentially affecting shaft accuracy if reused.
Poorer Dynamic Balance: Asymmetric structure can lead to imbalance at high speeds.
Lower Repeatability: Positioning accuracy may degrade after multiple assembly cycles due to indentation wear.
5. Comparative Analysis of the Two Connection Methods
5.1 Comparison of Static Performance
Through theoretical calculations and sample testing, typical performance parameters for the two LK6 series types are obtained. Test conditions typically involve a specific shaft diameter (e.g., 12 mm) and a rated torque level (e.g., 10 N·m) using 6061-T6 aluminum alloy material.
The clamping type generally exhibits significantly higher maximum torque capacity due to its large friction area. It also demonstrates greater torsional stiffness because the full hub contact provides a more rigid connection. Crucially, the clamping type achieves true zero-backlash, while the set screw type may exhibit minor lost motion (less than one arcminute) due to clearances in the keyway or potential micro-movement. Radial runout and repeatable installation accuracy are also superior for the clamping type, often by an order of magnitude. Consequently, the maximum permissible rotational speed for the clamping type is substantially higher than for the set screw type, owing to its better balance and higher clamping force.
5.2 Dynamic Response Characteristics
Modal analysis using finite element software reveals differences in dynamic stiffness. The clamping type typically shows a higher first-order torsional natural frequency compared to the set screw type. This indicates that the clamping type offers superior dynamic stiffness, making it more suitable for applications with high-frequency start-stop cycles or rapid acceleration/deceleration where resonance avoidance is critical.
5.3 Comparison of Installation and Maintenance
Installation time for the clamping type is longer, as it requires a torque wrench and careful sequential tightening. The set screw type is quicker, needing only an Allen key. Tool requirements differ accordingly. Regarding maintenance, the clamping type can operate for long periods without attention, provided bolts remain tight. The set screw type requires periodic checks for screw loosening, especially under vibration.
5.4 Suitable Application Scenarios
Clamping Type: Ideal for applications demanding high precision, high speed, frequent start-stop cycles, or heavy loads. Examples include CNC machine tools, robotics, semiconductor manufacturing equipment, and precision positioning stages.
Set Screw Type: Suitable for light-duty, low-speed applications where cost and installation simplicity are prioritized and ultimate precision is less critical. Examples include simple packaging machinery, conveyors, and basic automation setups.
6. Experimental Research
6.1 Test Setup and Methodology
A dedicated coupling test platform is established, incorporating a servo motor for driving, a high-precision torque sensor for measuring transmitted torque, a high-resolution angle encoder for measuring angular displacement, and a loading device such as a magnetic powder brake for applying controlled torque.
Typical test procedures include:
Static Stiffness Test: Applying incremental torque in both directions and recording the resulting angular deflection to determine the torsional stiffness curve.
Backlash Test: Cycling the torque from positive to negative values and measuring the angular hysteresis, which indicates the amount of lost motion or backlash.
Fatigue Test: Subjecting the coupling to repeated cyclic loading (e.g., 10⁵ cycles) at rated torque and periodically measuring stiffness to monitor degradation over time.
6.2 Analysis of Results
The experimental results typically show a linear torque-angle relationship for the clamping type with virtually zero hysteresis, confirming its zero-backlash characteristic. The set screw type may exhibit a small but measurable hysteresis loop, indicating some lost motion. After fatigue testing, the clamping type usually demonstrates minimal stiffness degradation (less than a few percent), while the set screw type may show a more noticeable decrease, often due to wear at the set screw indentation or keyway. This confirms the superior long-term stability of the clamping connection.
6.3 Failure Modes
Clamping Type: The primary failure mode is potential loosening of the clamping bolts under severe vibration or improper installation, leading to a loss of torque capacity. This is often recoverable by retightening to the specified torque.
Set Screw Type: Failure modes include deepening of the set screw indentations on the shaft, wear of the keyway, and consequent increase in backlash. These changes are often permanent and may require part replacement.
7. Engineering Application Guide
7.1 Selection Procedure
Determine Operating Conditions: Define the required torque (including peak and shock loads), rotational speed, available installation space, and required positioning accuracy.
Calculate Required Torque Capacity: Apply appropriate service factors (e.g., 1.5 to 2.0) based on the nature of the load and drive.
Select Connection Method:
For high precision, high speed, or heavy-duty applications, choose the Clamping Type.
For light loads, low speeds, or cost-sensitive applications, the Set Screw Type may be adequate.
Verify Shaft Diameter: Ensure the shaft diameter falls within the coupling's specified range.
Consider Environmental Factors: Account for temperature, humidity, corrosive media, or other special conditions.
7.2 Installation Precautions
For Clamping Type:
Thoroughly clean the shaft and hub bore, removing any oil or debris.
Tighten the clamping bolts in a diagonal sequence, applying torque in two or three stages to reach the manufacturer's specified value using a calibrated torque wrench.
After initial operation (e.g., 24 hours), recheck the bolt torque to compensate for any initial relaxation.
For Set Screw Type:
Ensure proper fit between the key and keyway if used.
Apply thread-locking compound to the set screws before installation.
Tighten the screws alternately to ensure even contact.
Check screw tightness after initial run-in.
8. Conclusion and Outlook
This paper systematically investigates the clamping and set screw connection technologies for LK6 series bellows couplings, leading to the following conclusions:
The clamping type connection is comprehensively superior in terms of torque capacity, stiffness, accuracy retention, and dynamic performance, making it the preferred choice for demanding applications.
The set screw type connection offers distinct advantages in cost and installation speed, making it suitable for less critical applications where these factors are prioritized.
Through proper selection based on application requirements, the overall performance and reliability of the transmission system can be significantly enhanced.
Future research may focus on smart connection technologies, such as integrating sensors to monitor preload status in real-time, and exploring new materials like titanium alloys or composites for bellows couplings to further expand their performance boundaries.
