Torsion Spring Design

A Practical Guide to Torsion Spring Design

Spring Calculator Instructions

Attention! Input results shown will be +/- 10% from middle value. Hint: The closer your min and max inputs are, the more accurate your results will be!

Attention! Input results shown will be +/- 10% from middle value. Hint: The closer your min and max inputs are, the more accurate your results will be!

Attention! Input results shown will be +/- 10% from middle value. Hint: The closer your min and max inputs are, the more accurate your results will be!

What’s a Torsion Spring?

A torsion spring is a specific type of helical spring that operates by twisting its ends along its axis to store and release rotational energy. Unlike compression or extension springs that work by compressing or extending along their axis, torsion springs exert torque or rotary force when twisted. They are designed to be twisted rather than compressed or stretched, and they offer resistance to rotational motion, making them ideal for applications where a rotational force is required.

Torsion springs come in various configurations and sizes, including:

  • Small Torsion Springs: Used in precision devices like hinges or small mechanisms.
  • Heavy-Duty Torsion Springs: Found in industrial equipment and heavy machinery.
  • Double Torsion Springs: Consist of one right-hand and one left-hand coil section connected together, providing balanced torque.
  • Extended Length Torsion Springs: Feature longer coils or legs for specific applications requiring additional reach or flexibility.

How Torsion Springs Work

Torsion springs operate on the principle of torsion, which involves twisting an object around its axis. When the spring's legs are rotated about its center, it stores mechanical energy in the form of torque. The amount of torque produced is directly proportional to the angle of twist applied, as long as the material remains within its elastic limit.

Here's a more detailed explanation:

  • Twisting Action: Applying force to the legs of the spring causes it to twist, increasing the stress within the coils.
  • Energy Storage: The twisted spring stores potential energy due to the deformation of its material.
  • Resistance to Twist: The spring exerts an equal and opposite torque, resisting the applied force and attempting to return to its original position.
  • Release of Energy: When the force is removed, the spring unwinds, releasing the stored energy and providing rotational force to move components back to their initial positions.

An important characteristic of torsion springs is that their inner and outer diameters change slightly during operation. Twisting the spring's leg in the direction of the wind will reduce its diameters, while twisting the legs in the opposite direction the diameters will increase. This behavior must be considered during the design to prevent the torsion spring binding on a shaft or rod or have interference with surrounding components.

Common Applications

Torsion springs are versatile and used in numerous applications across various industries. Some common uses include:

  • Door Hinges: Provide the self-closing mechanism in doors, gates, and lids, ensuring they return to their original positions after being opened. A torsion spring can also take a lot of weight off of heavy lids and hatches so the user doesn't lift excessive weight. 
  • Automotive Components: Used in vehicle suspension systems, hood mechanisms, and trunk lids.
  • Clamps and Clips: Act as gripping devices in hose clamps, paper clips, and binder clips. 
  • Mechanical Watches and Clocks: Regulate the movement of gears and hands through precise torque control.
  • Industrial Machinery: Control levers, switches, and actuators requiring rotational force.
  • Agricultural Equipment: Implemented in mechanisms like tillers and seeders for operational efficiency.

Understanding the specific application is crucial in selecting the appropriate torsion spring design, as different uses may require variations in torque, deflection, and material properties.

Key Parameters in Torsion Spring Design

Designing an effective torsion spring involves careful consideration of several key parameters. These parameters influence the spring's performance, durability, and suitability for the intended application.

Wire Diameter

Definition:

The wire diameter (d) is the thickness of the wire used to manufacture the spring.

Impact on Design: 

  • Strength and Stiffness: A thicker wire increases the spring's stiffness and torque capacity, allowing it to handle higher loads without deforming.
  • Flexibility: Thinner wire provides greater flexibility and allows for more angular deflection, but may reduce the torque force the spring can exert.
  • Stress Distribution: The wire diameter affects how stress is distributed throughout the spring, influencing its fatigue life and durability.

Considerations:

  • Manufacturing Limitations: Extremely thick or thin wires may present challenges during torsion spring manufacturing, affecting cost and feasibility.

Mean Diameter

Definition:

The mean diameter (MD) is the average diameter of the spring coil, calculated as the outer diameter (OD) minus one wire diameter (d).

Formula:

MD = OD − d

Impact on Design: 

  • Torque Capacity: A larger mean diameter generally reduces the spring's stiffness, decreasing the torque per degree of rotation, ironically this increases the amount of degrees the torsion spring can rotate (travel).
  • Stress Levels: The mean diameter influences the bending stress experienced by the wire during operation. A smaller mean diameter increases stress, potentially leading to premature failure.
  • Space Constraints: The mean diameter must be compatible with the available space in the application, considering any shafts or rods the spring may fit over.

Active Coils

Definition:

The number of active coils (N) refers to the coils that contribute to the spring's elasticity. In the case of torsion springs, all coils in the spring are active. You could say active coils or total coils in torsion springs and they would mean the same thing. 

Impact on Design: 

  • Angular Deflection: More coils allow for greater angular deflection, enabling the spring to twist further without exceeding material stress limits.
  • Torque per Degree: Increasing the number of coils reduces the torque provided per degree of rotation, as the load is distributed over more coils.
  • Body Length: Adding coils increases the spring's body length, which must be accommodated within the application's space constraints.


Considerations:

Active vs. Total Coils: In torsion springs active coils and total coils are the same thing. 

Definition: The spring index is the proportion of the mean diameter (MD) divided by the wire diameter (d) meaning how many wire diameters can go into the mean diameter. The spring index tells us how tightly wound the torsion spring is like in the case of a small index like 3,4,or 5 to 1 spring index which will give a higher torque. If you have a large index like 15 or 20 to 1 index, the torsion spring will be loosely wound and have a lower torque

Formula:

Spring Index = MD ÷ d​

Impact on Design:

  • Manufacturability: A spring index between 5 and 12 is generally considered optimal for manufacturing ease and performance. An index too low (<4) can make the spring difficult to manufacture and increase stress concentrations, leading to failure. An index too high (>25) can result in a spring that is too flexible and prone to buckling.
  • Stress Distribution: The spring index affects the distribution of stress within the coils. A low index increases stress, while a high index reduces it but may compromise stiffness.
  • Performance: The index influences the balance between torque capacity and angular deflection.

Considerations:

  • Adjustments: Modifying the wire diameter or mean diameter can help achieve an optimal spring index, improving performance and manufacturability.
  • Design Trade-offs: Changes to the spring index may impact other parameters, requiring a holistic approach to design optimization.

Leg Length and Configurations

Definition:

The legs of a torsion spring are the extensions of the coils that transmit force to the application.

Impact on Design: 

  • Force Transmission: The length and shape of the legs determine how the torque is applied to the components in the application. One can also induce more initial force by preloading the torsion spring a few degrees during installation. 
  • Mounting and Installation: Leg configurations must align with mounting points, ensuring proper installation and functionality.
  • Stress Concentrations: Complex bends or sharp angles in the legs can introduce stress concentrations, potentially leading to failure.

Common Leg Configurations:

  • Straight Legs: Simplest form, extending directly from the coils.
  • Radius <<bends on Legs: Provide attachment points for connecting to other components.
  • Offset Bends: Legs bent at specific angles to fit into confined spaces or meet design requirements.
  • Custom Shapes: Tailored to unique applications, potentially increasing manufacturing complexity.

Considerations:

  • Simplicity: Keeping leg designs simple reduces manufacturing costs and potential stress issues.
  • Functionality: The leg configuration must meet the functional requirements without compromising the spring's integrity.

Hand of the Spring

Definition:

The hand of the spring refers to the direction in which the coils are wound and determines the direction of torque when force is applied.

Types:

  • Left-Hand (L/H) Spring: Coils wind in a clockwise direction when viewed from the graphic below.
  • Right-Hand (R/H) Spring: Coils wind in a counter-clockwise direction when viewed from the graphic below.

Determining the Hand:

  1. Hold the spring with the coil facing you.
  2. Position the back leg (the leg further away) at the 12 o'clock position (top of the coil).
  3. Observe the direction the leg points:
    • If it points to the right, it's a right-hand spring.
    • If it points to the left, it's a left-hand spring.

Impact on Design:

  • Compatibility: The hand must match the application's rotational requirements to function correctly. In other words, always make sure the torsion spring rotates the correct way. Your torsion springs outer diameter should get smaller or tighten up when rotating the correct direction. If your torsion springs outer diameter gets bigger or starts to unwind, then you are rotating the torsion spring in the wrong direction, please stop and reverse direction. 
  • Interchangeability: Using the wrong hand can result in the torsion spring unwinding and taking a set by not returning to its original free position or not providing the desired torque.

Material Considerations

Selecting the appropriate material for your torsion spring is crucial for ensuring optimal performance, durability, and cost-effectiveness. The material affects the spring's mechanical properties, including strength, elasticity, corrosion resistance, and suitability for specific environmental conditions.

Common Materials and Their Properties

Music Wire (ASTM A228):

  • Characteristics: High tensile strength, excellent elasticity, and fatigue resistance. 
  • Applications: Suitable for static and dynamic applications at room temperature where corrosion is not a significant concern.
  • Limitations: Susceptible to corrosion; not ideal for humid or corrosive environments.

Stainless Steel (302 ASTM A313):

  • Characteristics: Good corrosion resistance, moderate strength, and suitable for higher temperature applications. 
  • Applications: Ideal for outdoor use, medical devices, and environments with exposure to moisture or mild chemicals.
  • Limitations: Slightly lower tensile strength compared to music wire; may be more expensive.

Chrome Silicon (ASTM A401):

  • Characteristics: High strength, good fatigue life, and better performance at elevated temperatures.
  • Applications: Used in automotive suspensions, heavy machinery, and applications requiring high stress tolerance.
  • Limitations: More expensive and may require additional heat treatment.

Phosphor Bronze (ASTM B159) and Beryllium Copper (ASTM B197):

  • Characteristics: Excellent electrical conductivity, corrosion resistance, and non-magnetic properties.
  • Applications: Electrical components, connectors, and environments where magnetic interference is a concern.
  • Limitations: Generally lower strength compared to steel alloys; more costly.

Modulus of Elasticity (E) and Modulus in Torsion (G)

These moduli are fundamental material properties that influence the spring's stiffness and stress characteristics.

  • Modulus of Elasticity (E): Reflects the material's stiffness under tensile or compressive loads.
  • Modulus in Torsion (G): Represents the material's stiffness under shear or torsional loads.

Typical Values (psi x 10^6):

  • Music Wire: E = 30, G = 11.5
  • Stainless Steel: E = 28, G = 10
  • Chrome Silicon: E = 30, G = 11.5
  • Phosphor Bronze: E = 15, G = 6.25

Environmental Considerations

  • Corrosion Resistance: Materials like stainless steel and phosphor bronze offer better resistance to corrosion, essential for outdoor or humid environments.
  • Temperature Tolerance: Chrome silicon maintains performance at higher temperatures, suitable for applications involving heat.
  • Electrical Conductivity: Phosphor bronze and beryllium copper are preferred for electrical applications due to their conductive properties.}

Cost Factors

  • Material Cost: Exotic materials or those with specialized properties tend to be more expensive.
  • Manufacturing Complexity: Some materials require specific manufacturing processes or heat treatments, affecting overall cost.

Considerations:

  • Balance Performance and Cost: Select a material that meets performance requirements without unnecessary expense.
  • Supplier Availability: Ensure the chosen material is readily available from suppliers to avoid delays.

Torsion Spring Formulas

Mathematical formulas are essential tools in torsion spring design, enabling engineers to predict performance characteristics like torque, stress, and deflection. Understanding these formulas allows for precise adjustments to meet specific application requirements.

Spring Rate Formula


The spring rate (k) defines the torque required per unit of angular displacement, typically expressed in inch-pounds per degree (in-lb/deg).

Formula:

Rt = Ed^4 / 10.8 DN S = 10.2 M / d^3 (correct for D/d)

Where:

  • Rt: Spring rate (in-lb/deg)
  • E: Modulus of Elasticity (psi)
  • d: Wire diameter (inches)
  • D: Mean diameter (inches)
  • N: Number of active coils

Impact on Design:

  • Torque Calculation: Knowing the spring rate allows you to calculate the torque at a given angular deflection.
  • Adjustments: Modifying parameters like wire diameter or number of coils can fine-tune the spring rate to desired levels.

Modulus of Elasticity and Torsion

These moduli vary based on the material and are critical in calculating the spring's behavior under load.

Modulus of Elasticity (E):

  • Represents the material's resistance to deformation under tensile stress.
  • Higher E values indicate stiffer materials.
  • Used in calculating the spring rate and stress.


Modulus in Torsion (G):

  • Reflects the material's resistance to torsional deformation.
  • Important for calculating angular deflection and shear stress.
  • Lower G values result in greater angular deflection for a given torque.

Use this Torsion Spring Force Chart to adjust your spring force accordingly

More Force

Less Force 
Smaller OD Larger OD
Less Coils More Coils
Thicker Wire Thinner Wire
More Travel Less Travel

Designing a Torsion Spring

Designing a torsion spring is a systematic process that requires careful consideration of application requirements, material properties, and mechanical principles. The following step-by-step guide provides a structured approach to creating an effective torsion spring design.

Step-by-Step Guide

  • 1. Define Application Requirements
    • Torque Needed (M): Determine the required torque to perform the intended function.
    • Angular Deflection (θ): Calculate the angle through which the spring must twist.
    • Environmental Conditions: Assess factors like temperature, corrosion, and exposure to chemicals.
  • 2. Determine Space Constraints
    • Inner Diameter (ID): Must accommodate any shafts or rods the spring fits over. On torsion springs always allow at least a 15% bigger inner diameter than the shaft or rod the torsion spring will go over. Why? Because when the torsion spring leg moves the inner diameter will shrink and you do not want the torsion spring to bind on the shaft. If the torsion spring binds on the rod or shaft the torsion spring will lose all its torque and fail to work. 
    • Outer Diameter (OD): Should not interfere with surrounding components or enclosures.
    • Body Length: Ensure the spring's length fits within the available space.
    • Leg Length and Orientation: Consider how the legs will connect to the application.
  • 3. Select Material
    • Performance Requirements: Choose a material that meets strength, flexibility, and environmental needs.
    • Cost Considerations: Balance performance with material and manufacturing costs.
  • 4. Calculate Key Dimensions
    • Mean Diameter (MD): MD = OD − d
    • Wire Diameter (d): Start with an estimated value based on torque and space constraints.
    • Spring Index: Spring Index = MD ÷ d​
      • Aim for a value between 5 and 12.
  • 5. Determine Number of Active Coils (N)
    • Angular Deflection Calculation:
      • Use the desired angular deflection and material properties to estimate N.
    • Balance:
      • Ensure the number of coils allows for required deflection without exceeding stress limits.
  • 6. Design Leg Configurations
    • Functionality: Legs must effectively transmit torque to the application.
    • Simplicity: Keep leg designs simple to reduce manufacturing complexity.
    • Angles and Bends: Specify precise angles and lengths to fit the application.
  • 7. Calculate Spring Rate (k)
    • Use the spring rate formula: Rt = Ed^4 / 10.8 DN S = 10.2 M / d^3​
    • Adjustments:
      • Modify d, D, or N to achieve the desired k.
  • 8. Prototype and Test
    • Build a sample: Create a prototype based on calculated dimensions.
    • Testing:
      • Install the actual application or a test setup.
      • Measure torque, deflection, and observe performance.
    • Iterate:
      • Adjust design parameters based on test results.

Practical Examples

To illustrate the design process, let's explore two practical examples: designing a torsion spring for a door hinge and a hose clamp.

Designing a Torsion Spring for a Small Light Door Hinge

Application Requirements:

  • Torque Needed (M): 0.11 inch-pounds (in-lb) to close the door.
  • Angular Deflection (θ): 90 degrees.
  • Space Constraints:
    • Inner Diameter (ID): Must fit over a 0.080-inch shaft.
    • Total Coils: 7.2 coils
    • Body Length: No more than 0.17 inches.
    • Material: Choose Stainless Steel 302 for corrosion resistance due to potential exposure to moisture.

Navigate to Spring Finder 5.0 and input the required dimensions:

From the suggested options, we choose part number PT020-131-7260-SST-LH-0250-N-IN given that it’s closer to the Torque we need.

Testing Your Torsion Spring

Testing is a critical phase in torsion spring design, ensuring that the spring performs as intended under real-world conditions. It helps identify potential issues related to torque, deflection, stress, and overall functionality before mass production or implementation.

Using Acxess Spring's Online Spring Force Tester

Acxess Spring provides an Online Spring Force Tester, a valuable tool for simulating and validating your torsion spring design.

Steps to Use the Tool:

  • Access the Tool:
    • From the product view page, navigate to the Online Spring Force Tester.
  • Set Testing Conditions:
    • Input the desired angular deflection (θ) in degrees.
  • Run the Simulation:
    • The tool calculates the expected torque.
  • Analyze Results:
    • Torque Output: Verify that the calculated torque meets or exceeds your application requirements.
    • Spring Rate (k): Confirm that the spring rate aligns with design expectations.
  • Iterate as Needed:
    • If results are not within acceptable ranges, adjust parameters:
      • Modify wire diameter, mean diameter, or number of coils.
      • Change material if necessary.
    • Re-run the simulation with updated parameters.

Benefits of Using the Online Spring Force Tester:

  • Cost-Efficiency: Reduces the need for physical prototypes, saving time and resources. 
  • Immediate Feedback: Provides quick insights into the performance of design variations.
  • Accuracy: Utilizes precise calculations based on material properties and mechanical principles.
  • Convenience: Accessible online, allowing for easy adjustments and comparisons.

Mastering Torsion Spring Design

Designing a torsion spring is a multifaceted process that requires a deep understanding of mechanical principles, material science, and practical application considerations. By thoroughly analyzing key parameters such as wire diameter, mean diameter, number of coils, spring index, and material properties, you can create a spring that meets specific performance requirements while ensuring durability and reliability.

Utilizing tools like Acxess Spring's Online Spring Force Tester enhances the design process by providing immediate feedback and allowing for iterative adjustments without the need for physical prototypes. This not only accelerates development but also improves the accuracy of your final design.

Key Takeaways:

  • Comprehensive Planning: Begin with a clear definition of application requirements and constraints.
  • Material Selection: Choose materials that balance performance, cost, and environmental suitability.
  • Mathematical Precision: Employ formulas to calculate torque, stress, and deflection accurately.
  • Optimal Design Parameters: Aim for a spring index within the ideal range and adjust parameters as needed.
  • Testing and Validation: Leverage simulation tools and real-world testing to validate designs before mass production.
  • Collaboration: Consider consulting with experienced spring engineers to refine designs and address complex challenges.

Whether you're working on a simple household gadget or a sophisticated piece of industrial equipment, the principles outlined in this guide provide a solid foundation for effective torsion spring design. By applying these concepts thoughtfully and diligently, you can enhance the performance and longevity of your applications, ultimately leading to greater success in your engineering endeavors.