BIZOMAT MAKEOS · Power Transmission
Universal-Joint Drive (Single or Double Cardan: Speed, Torque, Inertia)
How much does the output speed of this Cardan shaft fluctuate, is a double-joint arrangement phased correctly, and what peak torque do the joints see?
Kinematic and torque check of a single or double Cardan (Hooke’s) joint drive: the output angle traced through a full turn for each joint, speed ratio extremes and fluctuation at the output and at the intermediate shaft (for a single joint, the limits match the universal joint tool), whether a double joint cancels the fluctuation (equal angles and yokes in phase), peak angular accelerations and the inertia torques they cause, and the peak joint torque against your rating.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Input speed | rpm | Speed of the input shaft. |
| Input torque | N·m | Torque on the input shaft. |
| Arrangement | choice | One joint, or two joints with an intermediate shaft. |
| Joint 1 angle | ° | Angle between the input and the next shaft at joint 1. |
| Joint 2 angle | ° | Angle at joint 2 (double arrangement). |
| Yokes on the intermediate shaft | choice | Whether the yokes on the two ends of the intermediate shaft lie in the same plane. |
| Inertia of the driven side | kg·m² | Inertia of the driven machine at the output shaft. |
| Inertia of the intermediate shaft | kg·m² | Inertia of the intermediate shaft (double arrangement). |
| Largest joint angle allowed | ° | Largest joint angle you accept for the speed and life (your value from the joint maker). |
| Joint torque rating | N·m | Torque rating of the joint for the speed and angle (from the maker). |
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: Input speed
- What it is
- The steady rotational speed of the input shaft driving the first joint.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Angular acceleration and inertia torque rise with the square of speed; the percentage fluctuation does not change.
- Get it right
- Use the highest operating speed; acceleration and inertia torque grow quickly with speed.
What this means: Input torque
- What it is
- The torque delivered into the input shaft. The joint torque peaks above it when the output runs at its slowest point.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The peak joint torque rises in direct proportion.
- Get it right
- Use the driving torque at the joint, including any gearbox ratio before it.
What this means: Arrangement
- What it is
- Whether the drive has a single Cardan joint, or two joints with an intermediate shaft between them that can cancel the speed fluctuation.
- Units and format
- Choose one of 2 options from the list: Double joint (intermediate shaft); Single joint.
- Example
- The form opens with “Double joint (intermediate shaft)” selected as a worked example. Choose the option that matches your case.
- Get it right
- With a single joint, the second joint angle, the phasing and the intermediate inertia are ignored.
What this means: Joint 1 angle
- What it is
- The angle between the input shaft and the next shaft at the first joint, measured between the shaft axes.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger angle increases the speed fluctuation and the peak joint torque.
- Get it right
- Measure the true angle between axes in three dimensions, not just its projection on one view.
What this means: Joint 2 angle
- What it is
- The angle between the intermediate shaft and the output shaft at the second joint, in a double arrangement.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Ignored for a single joint. Equal angles with in-phase yokes give constant output speed.
What this means: Yokes on the intermediate shaft
- What it is
- How the yokes at the two ends of the intermediate shaft are lined up: in the same plane, or turned 90° to each other.
- Units and format
- Choose one of 2 options from the list: In phase (same plane); 90° out of phase.
- Example
- The form opens with “In phase (same plane)” selected as a worked example. Choose the option that matches your case.
- Get it right
- In-phase yokes cancel the fluctuation when the joint angles are equal; out-of-phase yokes add to it. Ignored for a single joint.
What this means: Inertia of the driven side
- What it is
- The mass moment of inertia of everything turned by the output shaft, about its axis. It gives the inertia torque from the output speed fluctuation.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0 kg·m² to 100000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The output inertia torque rises in direct proportion.
- Get it right
- It is added to the peak joint torque only for a single joint; in a double arrangement the output inertia torque is reported but not added.
What this means: Inertia of the intermediate shaft
- What it is
- The mass moment of inertia of the intermediate shaft and its yokes about its own axis, which speeds up and slows down twice per turn.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0 kg·m² to 100000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.01 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The intermediate inertia torque, added to the peak joint torque, rises in direct proportion.
- Get it right
- Used only in the double arrangement. Include both yokes and any slip spline.
What this means: Largest joint angle allowed
- What it is
- The largest joint working angle you accept for the speed and life, compared with each joint angle.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 45°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the joint maker for your operating speed.
What this means: Joint torque rating
- What it is
- The torque the joint is rated to carry at the speed and angle of this drive, compared with the peak joint torque.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the maker’s rating for your speed, angle and life, not the static breaking torque.
Method and formulas
- Joint 1: φ = atan2(sin θ, cos θ cos β₁); ratio dφ ÷ dθ swings between cos β and 1 ÷ cos β (as the universal joint tool).
- Joint 2: in phase ψ = atan2(sin φ cos β₂, cos φ) (cancels joint 1 when β₂ = β₁); out of phase ψ = atan2(sin φ, cos φ cos β₂) (adds to it).
- Angular acceleration α = ω₁² d²ψ ÷ dθ², found point by point; inertia torque = J α.
- Peak joint torque = T₁ × the largest speed ratio’s reciprocal + the intermediate-shaft inertia torque.
- Example: at 15° the output swings 0% and the intermediate shaft 6.935%; the peak joint torque is 111.14 N·m.
Limitations
- Rigid shafts and joints; torsional resonance of the shaft is not checked.
- Friction and joint bearing loads are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a Cardan drive shaft layout
- Confirm a double joint runs at constant velocity
- Find the torque peaks from joint angle and inertia
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Speed limits and fluctuation at the output and intermediate shafts
- Phasing check for constant velocity
- Inertia torques and peak joint torque
Interpreting the result
- Equal angles with in-phase yokes give a constant output speed; any angle difference brings fluctuation back.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2445–2446. Topic reference; no source tables or recommended settings are reproduced.
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Open the Universal-Joint Drive (Single or Double Cardan: Speed, Torque, Inertia) calculator