BIZOMAT MAKEOS · Springs
Lid Counterbalance with Torsion Springs (Balance, Handle Force, Spring Stress)
Will these torsion springs counterbalance my hinged lid so it is easy to lift and stays open, and are the springs within stress when wound up?
Check of a hinged lid, hatch or guard balanced by torsion springs at the hinge: the lid’s weight torque as it opens, each spring’s rate from its wire, coil and turns (as the helical torsion spring tool), the spring torque from the wind-up at the closed position, the out-of-balance torque over the whole opening and the largest force at the handle, whether the lid stays open and shut, and the spring stress at full wind-up against your allowable.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Lid mass | kg | Mass of the lid. |
| Hinge to lid centre of gravity | mm | Distance from the hinge axis to the lid’s centre of gravity, with the lid closed and horizontal. |
| Opening angle | ° | Angle the lid opens to from horizontal. |
| Number of springs | Number of identical springs sharing the load. | |
| Each spring | ||
| Wire diameter | mm | Wire diameter of each spring. |
| Mean coil diameter | mm | Mean coil diameter. |
| Body turns | turns | Number of body turns. |
| Elastic modulus | GPa | Elastic modulus of the spring wire. |
| Wind-up at the closed position | ° | Angle the springs are wound up when the lid is closed (they unwind as it opens). |
| Allowable bending stress | MPa | Allowable bending stress of the spring wire. |
| Handle | ||
| Hinge to handle | mm | Distance from the hinge to the handle. |
| Largest handle force | N | Largest force you accept at the handle anywhere in the swing. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Lid mass
- What it is
- The mass of the hinged lid, cover or door that the springs must balance, including handles and fittings attached to it.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 100000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The lid’s torque about the hinge rises in proportion to its mass.
What this means: Hinge to lid centre of gravity
- What it is
- The horizontal distance from the hinge axis to the lid’s centre of gravity when the lid is closed and horizontal.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The lid’s torque about the hinge rises in proportion to this distance.
- Get it right
- Measure to the centre of gravity, not to the far edge of the lid; for a uniform flat lid it is half the depth from the hinge.
What this means: Opening angle
- What it is
- The angle the lid swings through from closed (horizontal) to fully open.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 5° to 180°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The tool scans the out-of-balance torque over this range to find the largest handle force.
What this means: Number of springs
- What it is
- The number of identical torsion springs sharing the load, such as one at each hinge.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Total spring torque rises in proportion to the number of springs.
Each spring
What this means: Wire diameter
- What it is
- The diameter of the wire each torsion spring is wound from.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Spring rate rises with the fourth power of wire diameter, so small changes matter.
- Get it right
- Wire diameter, not coil diameter.
What this means: Mean coil diameter
- What it is
- The mean coil diameter of each torsion spring: outside diameter minus one wire diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 32 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Spring rate is inversely proportional to the mean diameter.
- Get it right
- Use the mean diameter, not the outside diameter or the arbor diameter.
What this means: Body turns
- What it is
- The number of turns in the coiled body of each torsion spring, not counting the straight legs.
- Units and format
- Enter a number in turns: a number of turns. The form accepts 0.5 turns to 1000 turns. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 turns as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Spring rate is inversely proportional to the body turns.
- Get it right
- Count body turns only; leg length is not included in this rate formula.
What this means: Elastic modulus
- What it is
- The elastic (Young’s) modulus of the spring wire, used because a torsion spring’s wire works in bending, from the wire supplier’s data.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 207 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Spring rate rises in proportion to it.
- Get it right
- Use Young’s modulus E, not the shear modulus G used for compression springs; enter gigapascals.
What this means: Wind-up at the closed position
- What it is
- How far each spring is wound up beyond its free position when the lid is closed. The springs unwind as the lid opens.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 3600°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More wind-up raises the spring torque throughout the swing and the spring stress.
- Get it right
- Measure from the spring’s free (unloaded) leg position, not from the lid’s open position.
What this means: Allowable bending stress
- What it is
- The largest bending stress you accept in the spring wire, from the wire supplier, a spring standard or your design rules for the duty.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1300 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Handle
What this means: Hinge to handle
- What it is
- The distance from the hinge axis to the handle where a person lifts or closes the lid.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Handle force is the out-of-balance torque divided by this distance.
What this means: Largest handle force
- What it is
- The largest force you accept at the handle anywhere in the swing, from your ergonomic or workplace manual-handling requirements.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Spring rate k = E d⁴ ÷ (64 D N_b) per radian; stress = K_i 32 M ÷ π d³ with K_i = (4C² − C − 1) ÷ [4C (C − 1)] (as the helical torsion spring tool).
- Lid torque = m g r cos θ; spring torque = n k (θ₀ − θ) at opening angle θ.
- Out-of-balance torque scanned over the opening; handle force = largest out-of-balance ÷ handle distance.
- Example: each spring has 7,896.4 N·mm/rad; the worst handle force is 9.9979 N at 40°; spring stress 1,143.8 MPa.
Limitations
- Lid centre of gravity on the line through the hinge when closed; offsets change the torque curve.
- Friction in the hinge ignored; it helps hold positions.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Balance a machine guard or hatch
- Check handle force on a heavy lid
- Choose torsion springs for a hinge
Who it is for
- Machine designers
- Product designers
- Design engineers
What you get
- Spring rate and torque
- Out-of-balance torque and handle force
- Spring stress at full wind-up
Interpreting the result
- A linear spring cannot match the cosine weight curve exactly: balance near the middle of the swing to keep handle forces low at both ends.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 333–343. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Torsion springs and counterbalanced lids
What it covers: How helical torsion springs work and how to check one: bending stress, wind-up angle, legs and arbor clearance, and balancing a hinged hatch over its whole opening.
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Open the Lid Counterbalance with Torsion Springs (Balance, Handle Force, Spring Stress) calculator